Contents

Acknowledgments

Foreword

Notes

Introduction

Notes

References

1 The Fregean Perspective and Concomitant Expectations One Brings to Wittgenstein

Notes

References

2 How a Language Game Becomes Extended

Notes

References

3 Kinds of Expression

Notes

References

4 “Function” in Language Games and in Sentential Contexts

Notes

References

5 The Sound of a Sentence I: Singing from the Score

Notes

References

6 Projection: No Mere Mapping but a Creative Activity

Notes

References

7 The Sound of a Sentence II: Surface Grammar

Note

References

8 Complexity

Notes

References

9 An Integration of Wittgenstein and Frege?

Notes

References

10 Dummett’s Doubts and Frege’s Concept of “Sense”

Notes

References

11 Wittgenstein on “Communicating Something”

Notes

References

12 “Grammatical Sense” and “Syntactic Metaphor”: A Wittgensteinian Solution

Notes

References

13 A “Theory of Meaning” – In What Sense?

Notes

References

Index

This edition first published 2014

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Library of Congress Cataloging-in-Publication Data

Schneider, Hans Julius.

Wittgenstein’s later theory of meaning : imagination and calculation / Hans Julius Schneider; Translated from the German by Timothy Doyle and Daniel Smyth.

pages cm

Enlarged and completely revised version of one of the chapters of author’s Phantasie und Kalkül, 1992.

Includes bibliographical references and index.

ISBN 978-1-118-64230-6 (cloth)

1. Wittgenstein, Ludwig (Ludwig Josef Johann), 1889–1951. 2. Language and languages–Philosophy. I. Title.

B3376.W564S2785 2014

192–dc23

2013012714

A catalogue record for this book is available from the British Library.

Cover design by Richard Boxall Design Associates

Acknowledgments

I would like to thank a number of people for their help in making this publication possible: James Conant was the first to suggest that it would be desirable to supply a complete translation of my original, much larger book Phantasie und Kalkül (Suhrkamp, 1992). But it turned out to be extremely difficult to find a publisher who would be willing to read 560 German pages, let alone to eventually finance their translation.

Later, Robert Brandom proposed to publish in English the systematic core of the book, that is, the chapter on Wittgenstein and the paragraphs surrounding it, using the opportunity to situate the argument in the current philosophical debate. This idea seemed much easier to realize, so a translation had to be furnished. Here I have to thank two people, my student Timothy Doyle who, although he was still working on his dissertation at the time, did (if I may say so) the rough carpentry work, and Daniel Smyth, who is responsible for the (to my mind) perfect final outcome.

I am especially grateful to Charles Taylor for supplying the preface for this book and for a number of encouraging conversations. I would also like to mention the moral support I have received for the project from Joachim Schulte, and from Edith Baller of Suhrkamp. Last but not least I am thankful for the excellent cooperation with Jeff Dean and Lindsay Bourgeois of Wiley Blackwell. And a special “thank you” goes to Fiona Screen for her extraordinarily thoughtful editing.

Foreword

By Charles Taylor

This book gets to grips with a central problem in Post-Fregean philosophy; it in fact offers a treatment of linguistic structure in the framework set up by the later Wittgenstein. And since the post-Fregean is one of the dominant strands in Anglophone analytic philosophy today, the issue has great importance for analytic philosophies of language.

Gottlob Frege, the great 19th-century German philosopher of mathematics, was channeled into the Anglophone world partly by Bertrand Russell around the beginning of the last century. Russell had emancipated himself from his early period under the sway of the English Hegelians, and had reverted to an epistemlogical view based on the great 17th-century empiricists, the so-called “way of ideas,” soon to be re-baptized “sense data.”

Another route through which Frege’s work entered the English-speaking world was via the Vienna positivists, who gathered in the early century around Ernst Mach. These, too, combined Frege with a basically Humean epistemology. Originally, this movement had little to do with the English-speaking world, but the rise of Nazi-ism forced some of its best minds to emigrate, mostly to the United States.

Their temper was rationalist, tough-minded, suspicious of “metaphysics.” Their idea of properly valid discourse was the discourse of science, augmented by truths about observable objects of common experience. So the work of Frege enters the English-speaking world partly as a resource for a streamlined, rationalist, highly systematized view of language. His contribution to this was considerable: not only did he clarify the basic structure of the proposition as concept and object, but he also greatly enlarged the scope of logical connection through his invention of the logic of quantification.

One of the sites of this streamlined logical systematization was in the theories of linguistic competence, such as in the work of Michael Dummett and Donald Davidson. One of the widely noticed phenomena of our language competence from Humboldt to Chomsky was our ability to put finite resources to “infinite ends.” With a large, but not unlimited stock of words, we are able to create and/or understand an indefinite number of new sentences. Davidson proposes that we understand this competence as the mastery of a theory in which we can derive the truth conditions of declarative sentences from a combination of axioms attributing meaning to referring expressions and predicate terms.

Another terrain of systematization was the tracing of deductive relations between propositions with different ontological commitments. The resources of Fregean logic, including truth-functionality and quantification, make it possible to organize a host of possible sayables as derivations from more basic assertions. In this way, the products of our depictive power can be organized, one might say “regimented,” in relation to more basic depictions. This defined what Robert Brandom refers to as the classical program of semantic analysis. He sees this concern as lying at the heart of analytical philosophy: “I think of analytic philosophy as having at its center a concern with semantic relations between what I will call ‘vocabularies’. Its characteristic form of question is whether, and in what way, one can make sense of the meanings expressed by one kind of locution in terms of the meanings expressed by another kind of locution.”[1]

This opened a large field for the anti-metaphysical drive of 20th-century positivists and others who felt themselves to be the heirs of classical empiricism. Brandom described what he calls “the classical project of philosophical analysis as having the task of exhibiting what is expressed semantically by one vocabulary (one sort of meaning) as the logical elaboration of what is expressed by another.”[2]

Now traditionally, these projects were driven by metaphysical (sometimes expressed as anti-metaphysical) suspicion. Certain supposed realities were illusory or fraudulent, those postulated by religions for instance; or goods or values, like those of ethics or aesthetics, that claimed an ontological grounding (as against those which were seen as subjectively projected). But sometimes the suspect entities were condemned as merely superfluous posits, without warrant in reality, such as the self (Hume), or natural necessity (again Hume), or “society” and other such terms for collectivities (methodological individualists).

Brandom describes the two most widespread such projects of reduction, empiricism and naturalism:

What is distinctive of empiricism and naturalism, considered abstractly, is that they each see some one vocabulary (or vocabulary-kind) as uniquely privileged with respect to all other vocabularies. Empiricism takes its favored vocabulary (whether it be phenomenal, secondary-quality, or observational) to be epistemologically privileged relative to all the rest. In what I think of as its most sophisticated forms, the privilege is understood more fundamentally to be semantic, and only derivatively and consequentially epistemological. Naturalism takes its favored vocabulary (whether it be that of fundamental physics, the special sciences, or just descriptive) to be ontologically privileged relative to all the rest. In both cases, what motivates and gives weight and significance to the question of whether, to what extent, and how a given target vocabulary can be logically or algorithmically elaborated from the favored base vocabulary is the philosophical argument for epistemologically, semantically, or ontologically privileging the base vocabulary. These are arguments to the effect that everything that can be known, or thought, every fact, must in principle be expressible in the base vocabulary in question. It is in this sense (epistemological, semantic, or ontological) a universal vocabulary. What it cannot express is fatally defective: unknowable, unintelligible, or unreal. One clear thing to mean by “metaphysics” is the making of claims of this sort about the universal expressive power of some vocabulary.[3]

The stigmatized entities could be shown to deserve exclusion, either by being shown to be unintelligible in relation to the base vocabulary (the objects mentioned in meaningless “metaphysical” statements), or else by our showing that everything useful which could be said in statements mentioning them could be said perfectly adequately in the terms of the base vocabulary (all statements about society translated into statements about individuals, all statements mentioning material objects translated into statements about sense data, and so on). These putative objects could thus be eliminated without loss.

But sometimes the object of relating base to target was the positive one of saving some suspect entities which might otherwise be relegated to outer darkness. Thus Hume’s suspicion of natural necessity, something beyond the mere correlation he wanted to reduce it to, could be answered by showing that we can make perfect sense of it. This is a “saving” derivation that Kant claimed to accomplish; and Brandom does something analogous.[4]

The goal of this kind of regimentation was a language of minimal commitment, which would be able to capture all valid knowledge, including especially that gained by empirical science. In this way, 20th-century post-Fregean philosophy shows its debt to the pre-Fregean early modern theories of language, developed by Hobbes, Locke, and others. These had as their first concern a language which could be an adequate and clear medium for expounding valid scientific knowledge and avoiding illusion and imposture. The first requirement of such a language was clear definitions, and the second, equally important, was that one stick to these definitions once introduced. We can see here the important effects which stemmed from the contingent fact that Frege entered the Anglophone world alongside a reversion in this world to a pre-Kantian epistemology.

But Frege’s work wasn’t totally abandoned in the hands of philosophers with these epistemological concerns. It was wrenched into a quite new orbit by Ludwig Wittgenstein. Admittedly, his early work, the Tractatus, shared much of the outlook of Bertrand Russell’s Frege-reception. And it became an inspiration for the Vienna Circle. But Wittgenstein later turned against this, and leveled the most decisive criticisms against any attempt to see language through the prism of the forms of tight logical systematization described above, either in a deductive theory of the language capacity, or in a regimentation of modes of depiction.

For the later Wittgenstein, a given utterance could only be understood in the context of the language game in which it figured; and our language included an indefinite number of such games, themselves only comprehensible within our overall form of life. The goal of reducing them all to a single model, or mode of depicting the world, was a chimera.

As a general thesis, this seems to me unanswerable. There are utterances in contexts so far removed from the standard concern of depicting an independent reality with maximum accuracy and freedom from illusion, that it approaches the absurd to try to understand them on the same model. The well-known example is that of someone saying through clenched teeth “I’m in pain,” an utterance which could be accompanied, but also replaced by, a groan.

But does that mean that any attempt to understand language as a system is mistaken? That we can only grasp the multiple language games, with their indigenous rules? Hans J. Schneider, while greatly admiring Wittgenstein, demurs. What we need is a view of language which avoids the total logical systematization of a deductive theory of meaning, or of Brandom’s regimentations, on one hand, but also sees the multiple links between different uses of language on the other.

We might think of some examples: we say: (1) “George has a car,” but also (2) “George has an idea.” The first implies that there is an object (the car), which can become the property of some human being, and which in fact belongs to George. If we construe the second sentence on this logic, it begins to sound queer. But let’s stretch a point: George got this idea from Pete, from whom he also bought the car. But then how about (3) “George has a headache”?

This is the kind of issue often posed by Wittgenstein. If one thinks that all information-bearing propositions must have the same logical form, then it begins to look as though (2) and (3) have “surface” forms which fail to match their real logical form, and one engages in the game widely followed among post-Fregean philosophers: find the real logical form of X.[5]

But if we follow Hans J. Schneider, we might see the steps from (1) to (2) to (3) as more akin to metaphorical or analogical extensions. Schneider speaks of a “syntactical metaphor.” Our language is full of such leaps, where faced with a situation for which we do not yet have an adequate expression, we borrow from a more familiar context, thus giving an old expression a new twist. This also happens on the level of syntax. But this doesn’t mean that our language has no systematicity; on the contrary, we are always drawing on long-acquired resources to say something new. It just means that this systematicity can’t be explained in terms of tight logico-deductive relations.

Now to speak of metaphor is to awaken the beast in the classical Hobbes-Locke theory. As Hobbes put it:

To conclude, the light of human minds is perspicuous words, but by exact definitions first snuffed, and purged from ambiguity; reason is the pace; increase of science the way; and the benefit of mankind the end. And on the contrary, metaphors and senseless and ambiguous words, are like ignes fatui; and reasoning upon them is wandering among innumerable absurdities; and their end, contention and sedition, or contempt.[6]

And of course, in a sense Hobbes was right: if your goal is a deductive logical system, metaphors utterly queer the pitch; they are to such a system what sand is to the internal combustion engine. And so if the aim of a Brandomian regimentation is to give us an adequate language of science, then we have indeed to stay away from all figures and tropes. But that doesn’t mean that human language, as it operates in nature, as it were, doesn’t rely essentially on such leaps. It is, in fact, as Schneider argues in this highly insightful book, an artful combination of systematicity (Kalkül) and imagination (Phantasie).

Notes

1 Brandom, Robert (2008) Between Saying and Doing: Towards an Analytic Pragmatism, Oxford: Oxford University Press, p. 1.

2 Brandom (2008), p. 31

3 Brandom (2008), p. 219.

4 Brandom (2008), Chapter 4.

5 Cf. Davidson, Donald (1980) The logical form of action sentences, in Davidson, Essays on Actions and Events, Oxford: Clarendon, pp. 105–22.

6 Hobbes, Thomas, Leviathan, Part I, Chapter 5.

Introduction

Analytic Philosophy may not be the most “up to date” branch of the field but it has certainly produced a number of insights and procedures nobody would seriously want to miss out on. Concerning many philosophical questions (e.g., what are numbers, what are mental states, virtues, gods) it is still good advice to look at the words and phrases we use in trying to state the respective problem in an intelligible way as a prerequisite for answering it. Although hardly anyone would claim that philosophers are concerned with “mere words,” in most cases they cannot do their work without also having an eye on language; indeed, in many cases it is not at all clear what it would mean to look at “the things themselves.”

Yet the philosophical treatment of language has slowed down in the last decades. One symptom of this is that Michael Dummett (1975, 1976, 1981), who had offered many most valuable suggestions for the shape of a theory of meaning, did not complete his project, and it seems that ideas developed in the later philosophy of Ludwig Wittgenstein played no small role in this retardation.[1] In the same context, philosophers like Richard Rorty (1980) and John McDowell (1998, 1998a, 2007) have explicitly pleaded (against Dummett) for a “modest” theory of meaning, that is, one that would exclude the issues most relevant to philosophy, especially those pertaining to epistemology. Such a “modest” approach (in contradistinction to a “full-blooded” one) would simply use the logical tools provided by Gottlob Frege (1972) and his followers without asking (as Frege himself unceasingly did) the relevant philosophical questions such as why we are calling certain structures “logical” and why we think they shed light on what we do in using a natural language or in thinking. This negligence corresponds to the fact that in the newly flourishing philosophy of mind semantic concepts like “representation” and “reference” are mostly taken for granted instead of being explained, so that here too we have a kind of “modesty” that shies away from what used to be the “real” philosophical questions. Judged by older ideals, this approach to the mind constitutes a vicious circle, not unlike John Locke’s (1975) talk of “ideas” in his explanation of language, which so many of his contemporaries had difficulties in understanding. Locke explained language with recourse to “ideas,” and when his contemporaries pressed him to explain what he meant by ideas his answer was: the meanings of words.

This book investigates the significance of Wittgenstein’s later philosophy of language for a theory of meaning. Did he indeed give compelling reasons that force us to give up on the development of a “full-blooded,” epistemologically interesting theory of meaning? Is the “quietism” attributed to him, the idea that philosophy in all respects leaves everything as it is, a systematic result of his understanding of the functioning of language?[2] Or is it a personal preference? Is it even a mistake to attribute such a view to him, a false generalization of statements that were meant to have a much more limited scope? The answer worked out in these pages takes sides against the first alternative: There is nothing in Wittgenstein that would compel us to resign ourselves to a “modest” theory of meaning. Our claim is, on the contrary, that there is a systematic network of insights to be found in his later philosophy that is of epistemological relevance and that no philosophical treatment of language should neglect, although this body of insights does not (and indeed cannot, as we will see) take the form of an axiomatic-deductive theory, as Dummett had once envisaged. We shall see in detail why this is the case and why it nevertheless provides no reason for us to content ourselves with a “modest” theory. So the proposed answer to the question: “Can there be a full-blooded theory of meaning?” will take the form “Yes, but… .” The advice is: Let us not throw out the baby with the bathwater, let us not give up on the project of a systematic theory of meaning, even if we have to accept that it will not take the form of an axiomatic system and will be “systematic” in a sense different from what we know from such systems. So the quietism attributed to Wittgenstein has to be qualified to do justice to his thoughts.

The central claims in what follows are, first, that we have to acknowledge that in Wittgenstein we find a diachronic perspective. What appears to be unsystematic in his approach loses much of this appearance as soon as we see that the network he unfolds is the result of ever more complex activities proceeding in time. To put it in Nietzschean terms: What Wittgenstein unfolds is a genealogy, or, more precisely, a number of such genealogies discussed (and partly invented) to make visible kinds of systematic relationships we find in natural language.[3]

The second point is that, in these unfolding linguistic activities, processes of projection play a central role. Such processes are only possible in time since they presuppose that certain means of expression are already in place which (in a second, additional step) are then used in an “unorthodox” way, as, most prominently, in the case of metaphor. If such an as yet unprecedented use results in successful communication, this success rests on the capacity for imagination – on the part of the speaker as well as the hearer. The most obvious case is that of a new use of a word, where the hearer has to guess what the speaker means by an utterance that (judged from the rules applied until that moment) would have to be classified as a “misuse” of language. We will see that such projective steps also play a role in the realm of syntax, which has led Eric Stenius (1960, p. 212ff.) to speak of “syntactical metaphors.”[4] Their presence is a central feature of natural language; their existence is the main circumstance that blocks the possibility of an axiomatic-deductive theory of meaning.

It may be grasped from these introductory gestures that the resulting picture can indeed appear to be “unsystematic” if the calculating side of language (which is not at all denied here) is taken to be its only philosophically relevant aspect. This calculating side is certainly highly important and Dummett is surely correct when he claims that without Frege we would not have the slightest idea of how to handle this side of language, that is, the fact that we somehow “infer” the meaning of a new sentence from the meanings of its constituents and the way in which they are composed. We do not learn the sentences of our language one by one. But the contribution of Wittgenstein’s later works will here be seen not as contradicting this calculating aspect, but as adding something to it, and as an important qualification as to what “inferring” can mean here. We are not only calculating in our linguistic activities (it is, for example, not enough to get the verb forms right) but constantly using our powers of imagination in attempting to grasp the sense of an utterance (not just its point in the particular given situation, which is undisputed, but its sense). That this is the case is a systematic insight into what we do when we use language; it pervades the whole of language, it is not just a poetic quirk, irrelevant for more “serious” uses. Therefore, to acknowledge and correctly assess the imaginative side of our language competence is a central feature in the picture we should have of ourselves as agents.

The argument of this book will proceed as follows: Chapter 1 will summarize Frege’s philosophy of language, read from a perspective that stresses some of his late insights in order to bring his ideas as close as possible to those of the later philosophy of Wittgenstein. It will also formulate expectations that someone impressed by Frege might bring to Wittgenstein. Chapters 2 through 5 will engage in a close reading of Wittgenstein’s texts. The goal is to find out whether we can discover there any compelling reasons for excluding the possibility of a systematic theory of meaning, as Dummett has claimed to. This involves finding an answer to the question of why Wittgenstein so repeatedly showed contempt for “grammar” in the traditional sense. What does he really have to say about “kinds of words” and “parts of speech”? Why does he constantly use the word “grammar” but not set himself the task of actually writing a “philosophical grammar,” a book such as Frege’s Conceptual Notation (1972) or Carnap’s The Logical Syntax of Language (1964)?

In chapters 6 through 9 we will be able to propose answers to these questions, centered around the concepts of “imagination” and “projection.” They explain the limitations of a treatment of language that overstates its calculating side, but at the same time are basic enough to be integrated into a general picture of our linguistic abilities and (in this non-axiomatic sense) into a “theory of meaning.”

In chapters 10 through 12 we will discuss both Wittgenstein’s struggle with his older models of linguistic complexity as well as the consequences of the ideas developed so far for the prospect of integrating Frege and Wittgenstein. In particular, Dummett’s worry that Wittgenstein’s rejection of a Fregean concept of “sense” would exclude the possibility of a theory of meaning is treated in detail, and a solution is offered. The final chapter then spells out the consequences for the project of a “theory of meaning.” It is argued that it should not be modest (it can be philosophically interesting and important; it can treat more than the calculating side of language) but it should by this time be no surprise that an account of a basic human capacity such as using language involves “soft” concepts like “imagination” and “projection” and can therefore be no axiomatic system.

Notes

1 When I visited Dummett in Oxford in 1980, he told me that he had planned to write a third part of “What is a Theory of Meaning” and publish the three texts as “A Theory of Meaning” (cf. Dummett 1975, 1976). But at this time he encountered unexpected difficulties, some of which I hope to overcome in these pages.

2 The subject of Wittgenstein’s “quietism” is taken up again in Chapter 13.

3 Wittgenstein (2009 § 415) says that he would be supplying “remarks on the natural history of human beings.” When he adds that these are “facts which no one has doubted” and remarks that he would be “finding and inventing intermediate links” (2009 § 122), it is clear that his genealogical project is not a scientific one.

4 Cf. below, pages 160 and 162.

References

Carnap, Rudolf (1964) The Logical Syntax of Language, London: Routledge and Kegan Paul.

Dummett, Michael (1975) What is a theory of meaning?, in Mind and Language (ed. S. Guttenplan), Oxford: Clarendon Press, pp. 97–138.

Dummett, Michael (1976) What is a theory of meaning? (II), in Truth and Meaning: Essays in Semantics (eds G. Evans and J. McDowell), Oxford: Clarendon Press, pp. 67–137.

Dummett, Michael (1981) Frege and Wittgenstein, in Perspectives on the Philosophy of Wittgenstein (ed. Irving Block), Oxford: Basil Blackwell, pp. 31–42.

Frege, Gottlob (1972) Conceptual Notation and Related Articles (ed. and trans. Terell Ward Bynum), Oxford: Clarendon.

Locke, John (1975) An Essay Concerning Human Understanding (ed. P.H. Nidditch), Oxford: Clarendon.

McDowell, John (1998) In defence of modesty, in Meaning, Knowledge, and Reality (ed. J. McDowell), Cambridge MA, Harvard University Press, pp. 87–107.

McDowell, John (1998a) Another plea for modesty, in Meaning, Knowledge, and Reality (ed. J. McDowell), Cambridge MA, Harvard University Press, pp.108–31.

McDowell, John (2007) Dummett on truth conditions and meaning, in The Philosophy of Michael Dummett (The Library of Living Philosophers, vol. XXXI) (eds Randalle E. Auxier and Lewis Edwin Hahn), Chicago: Open Court, pp. 351–366.

Rorty, Richard (1980) Philosophy and the Mirror of Nature, Oxford: Blackwell.

Stenius, Eric (1960) Wittgenstein’s Tractatus: A Critical Exposition of its Main Lines of Thought, Oxford: Blackwell.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

1

The Fregean Perspective and Concomitant Expectations One Brings to Wittgenstein

We know from the Tractatus (Wittgenstein 1999, p. 28) that Wittgenstein was a great admirer of the work of Gottlob Frege. In this chapter we will give an overview of those of Frege’s basic contributions to a theory of meaning that are most important for an understanding of Wittgenstein’s later thought (Frege 1972, 1979, 1984).

As a starting point we can take the older idea of an “analysis” of words and sentences. When we explain the meaning of the word “bachelor,” for example, by saying that it is applied to unmarried men, it has long been common to describe the relation between the words involved by saying that the meanings of “unmarried” and “man” are contained in the meaning of the word “bachelor.” The process of bringing this to light was accordingly described as “analysis”: hidden or implicit components of meaning, not visible by just looking at the sign, are brought to light, are made explicit, in something like the way in which water is analyzed into its invisible components hydrogen and oxygen.[1] The usefulness of such an analysis lies in the fact that ignorance of such “meaning components” can lead our thinking astray, and in the idea that (positively) explicit knowledge of such components is necessary for a clear understanding of the meaning of the expression in question. Accordingly, complex expressions are taken to have a clear meaning if they have been “analyzed,” that is, broken up into constituent expressions the meanings of which are less apt to be unclear or controversial.

Frege also applied something like this strategy to sentences. Here too an “analysis” can bring out “hidden” meaning-components, for example when a sentence like “lions show aggressive behavior against humans” is paraphrased as meaning “all lions show this behavior”; the “all” had been hidden and has now been brought to light.[2] In a slightly different case it is the semantic structure of the sentence that cannot be unambiguously read from the words alone. The sentence “the lions show aggressive behavior against humans” might be paraphrased as “our group of lions here at London Zoo…” or as “all lions… .” A sentence like “you may have cookies or fruit” can be supplemented by “but not both” or by “or both”; our normal ways of speaking often leave it open whether the “exclusive” or the “inclusive” meaning of “or” is intended.

These cases of ambiguity and implicitness need not worry the speaker of everyday language, but where maximal clarity and precision is required (as for proofs in the Philosophy of Mathematics) they do matter. And it was his work on the foundations of Mathematics that inspired Frege to develop what he called a “concept script.” He envisaged it as a “language” that would, on the one hand, be quite restricted in that it would contain only sentences that can be true or false. In other words, it would treat only contents that are “judgeable” – no commands, no questions, no expressions of feeling, etc. Frege was quite aware that it would be absurd to recommend such a symbol system to be used in everyday life. He himself remarks that such a proposal would be like recommending the use of a microscope in the performance of everyday tasks (Frege 1972, 104f.) But on the other hand (on the positive side) his “concept script” would avoid what must, in Frege’s field, be seen as two shortcomings of our “ordinary” or “natural” language. First, it would make explicit all aspects of meaning that, in ordinary communication, are understood only implicitly. Nothing, Frege declared, should (in his delicate special field of inquiry) be left to guesswork. And, secondly, it should avoid all ambiguity: one form of signs should express only one kind of meaning. To use the same example again, one should be able to see, to read it off from the sign, whether an inclusive or an exclusive “or” is intended by the speaker. So “nothing implicit!” and “nothing ambiguous!” are the two imperatives that rule the construction of his logical notation, his “concept script.”

Is the project of such a construction realistic? It seems that it only takes a quite simple consideration to justify an affirmative answer here. As the few examples given above show, every speaker of English is able to note (to “perceive,” to “see”) implicit aspects of meaning as well as cases of ambiguity when such features occur in an utterance. Normally she can comment on them, she can easily formulate paraphrases that make explicit what has not been said (but has very often been understood). And so too in the case of ambiguity: every standard speaker of a natural language can easily formulate paraphrases and comments, can use additional or alternative expressions when the need arises to resolve an ambiguity. But if such improvements are indeed easy to provide in any given case, there seems to be nothing that would preclude a systematic approach as envisaged by Frege. In other words, it should be possible to gain an overview of all the ways in which meaning elements can be combined in order to form expressions for a complex content, that is, to form a sentence that can be true or false. Accordingly, it should also be possible to develop a notation that would (firstly) exhibit all aspects of meaning (as far as they are relevant for truth), leaving nothing to guesswork, and would (secondly) do so in an unambiguous way, so that there would be no difference in meaning that would not be apparent in the signs themselves. The reason for this seems simple: since we can detect what (from the perspective of a mathematical logician) are shortcomings in the workings of our natural languages, and since we can avoid them in any given case by choosing a more appropriate mode of expression, it seems that we should also be able to systematically exclude these shortcomings in a notation especially constructed for limited scientific and philosophical purposes, clumsy and unappealing as such a notation may be for the purposes of everyday life.

What then, in Frege’s eyes, are the “elements of meaning” and how can they be combined in order to express truth or falsehood? He was quite careful to avoid a trap that one might fall into right at the beginning. When the possibility of a “combination” of signs into a sentence is what is at stake, we have to see to it that we do not end up with just a list of words instead of a sentence (Frege 1984b, p. 193). There is a difference between a complex expression with a unified sentential character on the one hand, and a succession of a number of utterances tied together only by their proximity in time (or on a piece of paper) on the other. A shopping list, for example, is like a “list of names”: it does not show the unity that is characteristic of a sentence. So we have to ask right from the beginning: what constitutes the unity of a complex sign, whereby is it distinguished from a mere succession of simple signs?[3]

Frege’s answer to this question is his doctrine of “unsaturated” expressions, which is inspired by his work in Mathematics. He says: “And it is natural to suppose that, for logic in general, combination into a whole always comes about by the saturation of something unsaturated.” (Frege 1984d, p. 390; orig. pagination 37) His analytic procedure consists in starting with a consideration of a whole “thought,” a content that can be affirmed or denied, and only then breaking it up into parts. These parts are (at the level of expressions) proper names on the one hand (“Paris,” “Caesar,” “my eldest brother”) and concept terms (“city,” “person,” “family member”) on the other. So an important part of his philosophy of language is his claim that not all meaningful expressions should be understood as names. This corresponds to the fact that in Mathematics we have not only “names of numbers” like “five” or “thirteen,” but also functional expressions like “plus” or “divided by.” In a symbol system containing only names, complex expressions could be nothing but lists of such names. So one important point in Frege is that he saw that concept terms are not names; like functional expressions in Mathematics they can play their role only in connection with names. Speaking figuratively, Frege says that they are “unsaturated”; their expression in his concept script therefore contains an empty space (marked by a letter like “x”: “x is green”) that indicates the place where a name must be inserted so that a complete expression results. Using another figure of speech Frege says that a name can “stand alone,” like a person, whereas different kinds of unsaturated expressions (concept terms or other functional expressions) can be added to such a name like one or more coats placed over a person’s shoulders. The coats, on the other hand, cannot “stand upright by themselves.” (Frege 1984c, p. 388; orig. pagination 157)

By distinguishing kinds of expressions in this way Frege is able to give an account of the unity of the sentence. This unity arises from the “cooperation” of words of different kinds, which have quite different functions (logical roles), namely (on the most basic level) those of “naming” and of “speaking of” (predicating). Relational terms like “x is the brother of y” he treats as predicates with more than one object term (name). The relationship between object and concept, which is at the basis of all expressions that can be true or false, Frege calls the “fundamental logical relation.” (Frege 1979b, p. 118) To understand the unity of the sentence, then, we have to understand the interplay of these two (and later some more) types of words.

This interplay constitutes the “logical structure” of the sentence in question, and it is clear that the meaning of “logical” here is defined in view of the kinds of content the expressions hold. Therefore we can also speak of semantic functions or roles, to avoid a formal reading of the adjective “logical.” In the process of working out and arguing for his “concept script,” Frege uses the word “logical” always in its content related, never its formal, sense. This comprises the “conceptual” level of language (following the old understanding that logic is the theory of concepts, judgments, and deductions) so that instead of “logical” (and the much later coined term “semantic”) we can also speak of Frege as treating “conceptual” problems. Accordingly, he has chosen the term “concept script” for his newly developed symbol system.

What he then adds to the names and concept expressions are the by now familiar truth functions (“and,” “or,” etc.) that combine sentences; like concept terms, expressions for truth functions are not names. And (original to him and most revolutionary) he adds the machinery of quantification. Here his doctrine of “unsaturated” expressions brings a great advantage: in analyzing a sentence like “the lion is man’s enemy,” Frege no longer looks for a “general object” like “the species of lions” (a “platonic form”) which is taken to be named so that something is predicated of it (like his medieval predecessors did), but rather treats both “lion” and “man’s enemy” as unsaturated predicate expressions. He therefore paraphrases the sentence as: whatever name of an object will be put into the place of “x” in the expression: if x is a lion then x is man’s enemy, the result will always be true. The quantifier for him is a “second order concept,” a concept expression speaking about concepts.

For our purposes, these few hints must suffice to give an idea of the sense in which Frege’s concept script can serve as an inspiration and model for an attempt to understand the semantics of natural language. It is a proposal concerning how the “semantically relevant structure” of expressions should be viewed; it shows what it means to classify words according to their functions in the sentence. Names name a particular entity; concept- and relation-expressions classify the entities, that is, they say that a certain predicate is true of them or that they stand in a certain relation. Logical connectives enable us to combine component sentences to form a complex sentence, the truth of which depends solely on the truth of its constituents. And quantifiers express “second order concepts” in that they speak about the results of substitutions in sentences containing a space left open for a name. Accordingly, in Frege’s concept script we are offered a general understanding of the sense in which we can “infer” the meaning of a new sentence from the meanings of the constituent words and from the (semantically relevant, i.e., “logical”) structure of the sentence. This “inferring” is a kind of “calculating”: when we know the meanings of the words and the meaning of the structure-building devices (think of “Paul loves Mary” as compared to “Mary loves Paul” or of “a and b” vs. “a or b”) we can “arrive at” the meaning of a sentence we have never heard before.

It is remarkable that in this concept script we find a rather limited number of kinds of expression that seem to be able to express a huge number of (or even “all”) true thoughts. We also find that on the lowest level of the realm of “thoughts” (i.e., where we are concerned with truth and stay at the level beneath truth-functional combination and quantification) there is just one single way of building complexes: all complex expressions on this lowest level say that an object falls under a concept (or that a plurality of objects stand in a relation).

We now have to take a second look at the method Frege uses to determine the “elements of meaning” and the ways in which these can be combined in order to form an expression that can be true or false. How does he find out what the hidden elements of meaning are, and how they combine to form complexes that we do understand, but that we cannot (in natural languages) simply read off from the design of the sign? We noted above that what we normally do (and what Frege is doing in his writings) when we have to resolve an ambiguity (or are in some other way confronted with the necessity to clarify what we had expressed) is to formulate comments and paraphrases, that is, we clarify language with the help of language. Now, it is very tempting to use the following picture when we want to understand how this is possible: since we cannot detect the relevant meaning-aspects as something exhibited by the “mere sign” (for example a certain imprint of letters in a book), we look for something behind the sign (the “meaning”) and so are led to presume that the logician has to look in the realm of meaning (or, using Frege’s technical term, “sense”) in order to find out the logically relevant structures. There seems to be a structured realm of content behind any given linguistic expression. Every competent speaker seems to “see” it; she can move freely in it, for example when she tries to find helpful paraphrases. Frege here speaks of a realm of “thoughts” (in an objective, non-psychological sense) and what he is aiming to achieve when developing his “concept script” is to follow the structure of the respective “thought” in the closest possible way. The “logical structure of language” would then be something behind or above language, something by which a philosopher of language is guided when she discusses the semantic structure of imperfect utterances formulated in a natural language. Later, Wittgenstein (2009, § 102) would express this guiding picture in the following words:

The strict and clear rules for the logical construction of a proposition appear to us as something in the background – hidden in the medium of understanding. I already see them (even though through a medium), for I do understand the sign, I mean something by it.

Frege indeed very often speaks this way. We cannot get into the problems such a view comes up against in any detail here; just note that in the end it turns out not to be convincing.[4] There is no reality “behind” or “above” language in the sense of a language-independent world of thought or an invisible mechanism of “meaning something” that is so construed out of elements that the combinatorial possibilities determine the permissible combinations of words. Furthermore, it turns out that, in the realm of sense, one cannot speak of wholes and their parts, to be mirrored by the wholes and parts of a concept script. The part/whole relationship holds, when it holds at all, only at the level of expressions. (Frege 1984a, p. 165; orig. pagination 35f.; cf. Frege 1979c) But we can also note here that such a theory of a logical world behind language was seen as dubious by the later Frege himself. Indeed he gives a hint (Frege 1984d, p. 393) that it is not to a language-independent realm behind the sign, but rather to the “use as a sign” (Frege here speaks like the later Wittgenstein; the German wording is “Gebrauchsweise als Zeichen, das einen Sinn ausdrücken soll”) that we must look in order to detect the logical role of any given expression.[5] So we find formulated by Frege an idea that is usually only attributed to the later Wittgenstein: it is the use of a sign, its function in the act of communication and its function in the sentence that determines its logical classification as a sign of a particular logical type.

When we now turn to the philosophy of the later Wittgenstein, we should note that both his methods and his goals differ markedly in important respects from those of Frege. Two such differences are of special importance for us. First, Wittgenstein does not restrict his remarks to those aspects of language that are relevant to truth and logical deduction (in Frege’s words, to language as an expression of a “judgeable content”). He has neither the language of science nor that of mathematics in mind as the privileged area to which his considerations apply, and it is not his goal to propose a “concept script” that would better serve scientific purposes than does our natural language. This often leads him to develop his arguments using “primitive” forms of language that he has created for the purpose of clarifying his thoughts. They are so constructed that an instance of using them often cannot be described as the passing of a judgment. So, for example, if (on a building site) the order “Slab!” is used to request an object, then it is meaningless to ask about the truth-value of this utterance. To express it positively: Wittgenstein has in mind right from the start uses of language that are neither statements of propositions nor parts of such statements. Second, in contrast to Frege’s method of breaking down or “analyzing” the necessarily complex expression of a judgeable content, Wittgenstein chooses simple expressions as his starting point, and only then proceeds to the fact which is essential to linguistic competency, namely that there are various ways of expanding these simple expressions through the introduction of other linguistic elements. In this sense his procedure in the later philosophy, insofar as it concerns the first steps toward the clarification of linguistic complexity, is “synthetic,” and not, like Frege’s method, analytic.[6]

We have seen that Frege was aware of the problem of how, when constructing complex expressions out of their components, to avoid coming up with a list of names rather than a sentence. This led him to his strategy of not building a sentence out of its component parts, but of getting at the parts by breaking up a whole. Wittgenstein, despite his own “synthetic” approach, did not encounter this problem, because he followed Frege’s late insight to its logical conclusion, namely that the sense of an expression consists in its use as a sign. One of the main intentions of the philosophy of language strand of the Philosophical Investigations (Wittgenstein 2009) is to reject the idea that the meaning of a linguistic expression always consists in it being assigned some entity, for example for the name “Fido,” the dog Fido (or a mental image or representation of it). If linguistic expressions are not always names for entities but are rather meaningful primarily in that they play a certain role (out of a number of very different possible roles) in the use of language, then the problem of having to show that complex linguistic expressions are something other than lists of names of the entities for which they allegedly stand does not arise. It is reckoned right from the start that there are many cases in which such entities simply do not exist.

But the question that is of special interest here, namely how, according to such a view, the unity of the sentence is to be understood, is not fully answered with such a very general reference to “the use” of an expression. True, thanks to his new approach to the problem Wittgenstein, unlike Frege, avoids the task of having to draw a boundary between a sentence and a list of names, but he too must be able to distinguish the unified speech act completed through the utterance of a complex sentence from a succession of independent linguistic acts. Such independent utterance acts, like items read aloud from a grocery list, stand in no other relationship than that of being “coincidental” neighbors in time or space. Switching the order of entries in a shopping list generally makes no difference, but for a sentence such a switch can make a very great difference, as can be seen, for example, in the sentences “Romeo loves Juliet” vs. “Juliet loves Romeo.” And this fact must also be adequately accounted for by a use-related understanding of the semantic side of language.

When one keeps both these differences in mind and recalls the systematic results of our discussion of Frege’s views, then from Wittgenstein’s work (given a rough familiarity with his later philosophy) one could expect an approach to the questions posed here along the following lines: by way of creating simple “language games” Wittgenstein can be expected firstly to show his readers how a word appearing individually is applied, that is, a word the use of which is closely interwoven with extra-linguistic actions but that, as far as their linguistic surroundings are concerned, can occur without any surrounding verbal text. One could then expect him, again in Fregean terms, to make a second step in which he would discuss ways of expanding these types of language games (i.e., those that use independent or “saturated” expressions) in order to make understandable the use of newly added “unsaturated” expressions of various categories (logical connectives, possibly predicate expressions, etc.). Frege had in this context made use of the following evocative image (Frege 1984c, p. 388; orig. pagination 157):

I compare that which needs completion to a wrapping, e.g., a coat, which cannot stand upright by itself; in order to do that, it must be wrapped round somebody. The man whom it is wrapped round may put on another wrapping, e.g., a cloak. The two wrappings unite to form a single wrapping.

So in the second step we would expect Wittgenstein to explain the use of such “dependent” words (i.e., words that cannot appear without a linguistic context). Words of this kind are necessarily related to other expressions that are already mastered, words that also occur in the situation of use under consideration, but are modified in their meaning by the newly added expressions. These expansions should make the possibility of semantic complexity intelligible to us: that is to say, the difference between a complex expression with a unified sentential character on the one hand, and a succession of various utterances tied together only by their proximity in time on the other. Such expectations about Wittgenstein’s later philosophy are confirmed in the following passage from the Blue Book (Wittgenstein 1958, p. 17 [my italics]):

I shall in the future again and again draw your attention to what I shall call language games. These are ways of using signs simpler than those in which we use the signs of our highly complicated everyday language… If we want to study the problems of truth and falsehood, of the agreement and disagreement of propositions with reality, of the nature of assertion, assumption, and question, we shall with great advantage look at primitive forms of language in which these forms of thinking appear without the confusing background of highly complicated processes of thought. When we look at such simple forms of language the mental mist which seems to enshroud our ordinary use of language disappears. We see activities, reactions which are clear-cut and transparent. On the other hand we recognize in these simple processes forms of language not separated by a break from our more complicated ones. We see that we can build up the more complicated forms from the primitive ones by gradually adding new forms.

The last, italicized statement is of particular importance to us: does Wittgenstein claim that we can obtain the complex forms of our language through a step-by-step expansion of simple “language games,” by adding new forms? And does he thereby explain what it means to speak of the “forms” of language(s) in the sense of their “content-structures”? Could we arrive in this way at an extended version of Frege’s “concept script,” the syntactic forms of which would explicitly and clearly reflect the respective content-relationships – or would we discover hindrances that stand in the way of such a project?

Notes

1 Frege (1979c, p. 253) here consciously uses a term taken from chemistry: “Zerfällung.” In an earlier formulation Frege (1979a, p. 17) uses the closely related expression “zerfallen lassen,” which has been translated as “splitting up”: “We…arrive at a concept by splitting up the content of possible judgements.” Cf. Picardi 1992.

2 I leave it open as to whether this reading of the original sentence is correct or not.

3 This question has received a new prominence in recent years; cf. Davidson 2005, Burge 2007, Jolley 2007, Gaskin 2008, Picardi 2009, Tolksdorf 2009.

4 For details see Schneider 1992, Chapter III, § 10.

5 “As a mere thing, of course, the group of letters ‘and’ is no more unsaturated than any other thing. It may be called unsaturated in respect of its employment as a symbol meant to express a sense… .” (Frege 1984d, p. 393; orig. pagination 39) Cf. below, pp. 51f.

6 On the concept of analysis, compare the critical remarks in Wittgenstein 2009, § 60ff, and § 90ff.

References

Burge, Tylor (2007) Review essay of: Davidson, Truth and Predication. The Journal of Philosophy, 104: 580–608.

Davidson, Donald (2005) Truth and Predication, Cambridge MA: Harvard University Press.

Frege, Gottlob (1972) Conceptual Notation and Related Articles (ed. and trans. Terell Ward Bynum), Oxford: Clarendon.

Frege, Gottlob (1979) Posthumous Writings (eds Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach, with the assistance of Gottfried Gabriel and Walburga Rödding), Oxford: Blackwell.

Frege, Gottlob (1979a) Boole’s logical calculus and the concept script, in Frege 1979, pp. 9–46.

Frege, Gottlob (1979b) Comments on sense and meaning, in Frege 1979, pp. 118–125.

Frege, Gottlob (1979c) [Notes for Ludwig Darmstaedter], in Frege 1979, pp. 253–257.

Frege, Gottlob (1984) Collected Papers on Mathematics, Logic, and Philosophy (ed. Brian McGuinness), Oxford: Blackwell.

Frege, Gottlob (1984a) Function and concept, in Frege 1984, pp. 137–156.

Frege, Gottlob (1984b) On sense and meaning, in Frege 1984, pp. 157–177.

Frege, Gottlob (1984c) On concept and object, in Frege 1984, pp. 182–194.

Frege, Gottlob (1984d) Thoughts, in Frege 1984, pp. 351–372.

Gaskin, Richard (2008) The Unity of the Proposition, Oxford: Oxford University Press.

Jolley, Kelly Dean (2007) The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations, Burlington: Ashgate Publishing Company.

Picardi, Eva (1992) The chemistry of concepts, in Language and Earth: Elective Affinities between the Emerging Sciences of Linguistics and Geology (eds Bernd Naumann, Frans Plank, and Gottfried Hofbauer), Amsterdam: John Benjamins, pp. 125–146.

Picardi, Eva (2009) Wittgenstein and Frege on proper names and the context principle, in Wittgenstein: Mind, Meaning, and Metaphilosophy (eds P. Frascolla, D. Marconi, and A. Voltolini), London: Palgrave MacMillan, pp. 166–187.

Schneider, Hans J. (1992) Phantasie und Kalkül, Über die Polarität von Handlung und Struktur in der Sprache, Frankfurt: Suhrkamp.

Tolksdorf, Stefan (2009) Die Vielfalt semantischer Komplexbildungsweisen. Deutsche Zeitschrift für Philosophie 57: 597–617.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1999) Tractatus Logico-Philosophicus (trans. C.K. Ogden, with an introduction by Bertrand Russell), Mineola, New York: Dover.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

2

How a Language Game Becomes Extended

Let us look at how Wittgenstein applies his method of creating simple language games to discuss fundamental questions in the Philosophical Investigations (Wittgenstein 2009) and its preliminary works. The Investigations as well as the Brown Book (Wittgenstein 1958) and its German version Eine philosophische Betrachtung (Wittgenstein 1970) give the impression right from the start that he is interested in “kinds of words,” that is, in their diverse semantic roles. Concerning traditional understandings of meaning, oriented as they are on an Augustinian picture of language, Wittgenstein objects that these tend to overlook the fact that words of different kinds have meaning in completely different ways. He explicitly addresses these differences among ways of being meaningful, and, in light of Frege’s distinction between “saturated” and “unsaturated” expressions, we expect him to also make clear how he understands the unity of the sentence, which must arise from the “cooperation” of words of different kinds.

The first language game in the Brown Book is well known from the Investigations: a builder orders his assistant to bring him the types of stones needed by calling out “block”, “pillar”, etc. It should be mentioned in passing that, as opposed to Frege, Wittgenstein here uses “concept terms” as examples of terms that can “stand upright by themselves” – he does not use proper names, as Frege had. We will return to this difference, but for now let us move on to examine how Wittgenstein understands the expansion of this language game, the process of “synthesis.” His example is the introduction of numerals.

How can a one-word sentence like “Slab!” be expanded into a complex sentence? We would speak of it as a “complex sentence” only if it met the following two conditions: (1) its utterance results in a speech act containing moveable component speech acts, but (2) the resulting complex speech act cannot be adequately characterized as a succession of independently performable one-word sentences, like reading a grocery list could.

Wittgenstein (1958, p. 79) first describes the result of his view of this expansion: the assistant knows the words from “one” to “ten” by rote; when he hears the order, “five slabs!” he acts as follows: “… he goes to where the slabs are kept, says the words from one to five, takes up a slab for each word, and carries them to the builder.” Following Wittgenstein, if we say that the meaning is what an explanation of the meaning explains, we encounter the question of how this result could be arrived at. We are informed that the rote memorization of the numerals, which is an important part of this expanded language, is attained “demonstratively”: on the one hand this is similar to learning the words “slab,” etc., but on the other it is somewhat different. Wittgenstein (1958, p. 79) characterizes the difference thus:

But now the same word, e.g., ‘three’, will be taught by pointing either to slabs, or to bricks, or to columns, etc. And on the other hand, different numerals will be taught by pointing to groups of stones of the same shape.

The description is not suggesting that the assistant makes the step from “slab” to “five slabs” by learning to express two-part sentences consisting of a counting word on the one hand and a category word such as “slab,” “column,” etc., on the other. Rather, one-word sentences of the form “five” seem to be spoken as piles of objects are pointed at. This contrasts with the later use of numerals by the builder, where apparently only two-part sentences occur; the utterance of a single counting word like “seven!” does not seem to belong to the language game.

Wittgenstein seems to think that numerals can be learned alone, demonstratively, without further linguistic context; he altogether ignores Frege’s (1953, 59e (§ 46)) preferred interpretation “that the content of a statement of number is an assertion about a concept,” which, for Wittgenstein, would mean, among other things, that numerals can only be learned and used in conjunction with other words (“conceptual expressions”, i.e., predicates). What he alone emphasizes is the fact that in the case of numerals their sequence is learned by rote. This peculiarity of learning doesn’t appear in learning the vocabulary of the first language game, which is to be expanded through the inclusion of the numerals, and shows that with the introduction of the counting words a wholly new instrument is brought into the language. The further intimation that demonstrative gestures work differently in the two types of cases is uninformative at this point, because the difference mentioned is not further explained.

Intuitively we can surely agree with Wittgenstein’s claim that the expansion of sentences of the type “Slab!” into those of the type “Five slabs!” introduces a new kind of word: it appears that the numerals play a wholly new role as compared to expressions like “slab.” But still we have to insist that it would have been more illuminating had Wittgenstein, in the interest of clarifying the process he described in the citation above as “gradually adding new forms,” given a more exact and thorough characterization of the particular character of the numerals that makes them into a new kind of word. Given our considerations of Frege, one such quality that is particularly noticeable is the fact that the counting words serve (in a way yet to be described in detail) to complete or to expand other words, namely those of the “slab” type. That Wittgenstein at this point held such an explanation to be unnecessary leaves a circumstance in the background that he also neglects later, as we shall see, namely the fact that the words of a sentence stand not only in characteristic relations to extra-linguistic actions (be it to that of teaching, or to that of application) in which they are embedded, but also and above all to one another.

The version in which the passages just considered appear in the Philosophical Investigations contains no detailed discussion of these aspects of language, though it does hint at such aspects. True, in these passages Wittgenstein considers two separate sets of circumstances. On the one hand there is that of the individual “ostensive teaching of words” (§ 6)[1] in “instruction in the language” (§ 7); here the teacher points to an object and directs the hearer’s attention to it. On the other hand there is the “practice of the use of language”; in this practice, as Wittgenstein explains, “one party calls out the words, the other acts on them” (§ 7). However, in this later version of the text he also emphasizes that the ostensive teaching of an isolated word (he is thinking of words of the type “slab”) by itself does not lead to an understanding of the word, that is, to an ability to act upon the word, in the sense of “the practice of the use of language.” This goal is only reached through ostensive teaching “together with a particular kind of instruction”; furthermore “with different instruction the same ostensive teaching of these words would have effected a quite different understanding.” (§ 6)

What does this mean for learning the numerals? Is there, in the sense of the aforementioned split, an “ostensive teaching” of individual words which is distinguishable from teaching an expansion of “the practice of the use of language”? In particular, do we find in ostensive teaching simple, non-compound utterances of the type “four!” (or, following the Investigations, in which letters function as numerals, of the type “d”)? Or is it a necessary part of an ostensive teaching of the numerals that a numerical statement makes, as Frege calls it, “an assertion about a concept”? Wittgenstein (§ 9) writes:

When a child learns this language, he has to learn the series of number-words a, b, c…by heart. And he has to learn their use. – Will this training include ostensive teaching of the words? – Well, people will, for example, point to slabs and count: “a, b, c slabs”.

Here, in contrast to his thinking in the Brown Book, Wittgenstein no longer appears to hold that the numerals, when they are used for counting,[2] appear alone when we are taught them. In the description just quoted the “ostensive teaching” and thus also the “gesture” have lost their importance; instead we find our attention drawn to the fact that the numerals are linked with other words, in conjunction with which they appear in the utterance of a complex sentence. One can read in these passages the proposition that numerals characteristically appear, even as they are being learned, as a complement or expansion of other linguistic expressions (here, of the type “slab”); this relatedness of the numerals to other expressions is not something that appears after they are mastered, as a matter of application. While Wittgenstein says in the aforementioned passages that ostensive teaching only leads to what we would call the understanding of a word in conjunction with a “certain practice,” the latter formulation implies that already in the process of teaching there is a relationship to be understood that the single word to be learned bears to other, previously mastered words. In the case of the numerals, this relationship has to be understood already on the level of “ostensive learning.” Successful ostensive learning here involves words of different kinds; the action of counting requires an understanding of what is being counted, slabs or slab segments, trees or groups of trees, etc.[3]

In the text that follows the above-cited passage, which states that the same ostensive teaching can, depending upon the training connected up with it, lead to very different understandings of a word, we find the following picture (§ 6):

“I set the brake up by connecting up rod and lever.” – Yes, given the whole of the rest of the mechanism. Only in conjunction with that is it a brake-lever, and separated from its support it is not even a lever; it may be anything, or nothing.

Applying this reasoning to the foregoing discussion of the numerals therefore means: what belongs to “the rest of the mechanism,” without which an expression such as “four” (or “d”) is not a numeral, is not only (as in the case of words of the type “slab”) an extra-linguistic context of actions (in this case the building of a house), but also a linguistic context. Orders of the type “slab,” “beam” etc., must already be mastered in order that they can be expanded by expressions of the kind including “four,” “five” etc. (including “d,” “e,” etc.). In the absence of a word of the type “slab,” the numeral is not even a word, “it may be anything, or nothing.” In Frege’s terminology we can say: in Wittgenstein’s thought it is characteristic of the numerals that they are “unsaturated.”[4]

It must be admitted that Frege’s unsaturatedness can only function as a standpoint from which to distinguish word types in Wittgenstein’s texts if we strongly accentuate rather non-descript formulations. In order to sketch a more exact and textually adequate picture of how Wittgenstein sees the process of “gradually adding new forms,” we now turn toward another expansion step, in which we can see how he handles the relationships that words of different types have to one another within a complex expression. We consider his introduction of proper names. This step is of special interest to us because, as opposed to the extension of an imperatively interpreted predicate utterance through a numeral, it brings us to Frege’s “logically fundamental relationship,” and therefore furthers a comparison between Wittgenstein’s thought and Frege’s.

Concerning the question of how a simple language game of the type with which Wittgenstein begins can be expanded to include proper names, the later German revision is in agreement with the opinion of the Brown Book. Wittgenstein writes in the German revision (Wittgenstein 1970, p. 120):

Let us introduce another tool into our language: certain objects, such as certain individual stones to be used in building, are given names (proper names), one points to a stone and says its name. If A calls out the name, B brings A the stone.[5]

Wittgenstein approaches the question of how a proper name is differentiated from a concept expression of the type “slab” learned earlier by asking about the differences between how words of each type are taught. On the negative side, he determines that it does not reside in ostensive gestures, nor in the way in which the words are spoken, nor even in an “inner process” in the speaker or hearer during the teaching and learning. Positively formulated, the difference in these ways of teaching is:

…the role of the ostensive gestures and verbal accompaniments in the teaching of the language and in the use made of them in the practice of communication with the language. (Wittgenstein 1970, p. 120)[6]

But does ostending play a role within the practice of communication? If it does at all, isn’t it a rather indirect role inasmuch as the practice of communication only partly rests on the fact that, in teaching words of the relevant kind, something is often pointed at? And in what exactly does the difference between concept terms and proper names consist with respect to “teaching” as well as with respect to “the practice of communicating”? Is the above description of the role of proper names at all distinguishable from the earlier description of the role of words of the type “slab”? Doesn’t the utterance of the words in both cases serve to order building materials?

Apparently with the intention of following up on the idea that there is a difference between the kinds of pointing gestures and their respective relations to the objects concerned, Wittgenstein asks himself whether it would be adequate to say that “in different cases one indicates different kinds of objects,” and he compares the difference in teaching processes with two cases of pointing to a white sheet of paper, in one case meaning its form and in the other meaning its color. Concerning the distinction between proper names and concept terms, one must ask: can a person at one time point at a slab and mean it as an exemplar of the species of slabs, and at another time point to it and mean it as a particular object, as an individual? Wittgenstein (1970, p. 120) explains the distinction between pointing to a form versus pointing to a color:

The difference, one might say, does not lie in the act of pointing, but rather in the circumstances surrounding that act in the practice of language, in what precedes and what follows it.[7]

What does this imply about the distinction between proper names and concept terms? What are the “circumstances” that surround the act of pointing? Does the linguistic surrounding belong to that which Wittgenstein has in mind? For example, is he committed to saying that a proper name always has to be followed by a concept term if a complete move in the language game is to be made? One could expect this from a Fregean standpoint when one reads Wittgenstein as holding proper names (not concept terms) to be “unsaturated,” and this view could be strengthened by looking at his thesis that naming is not a move in a language game but preparation for a description. But this contradicts what we quoted Wittgenstein as saying regarding the introduction of proper names. Is he then thinking solely of the extra-linguistic aspects of the circumstances surrounding proper names? Let us suppose, for example, that “Rosetta” is the name of a certain individual stone and that a successful action segment has taken place in which A orders this stone from B, receives it and builds with it. Does Wittgenstein mean to explain the distinction between proper names and concept words by stipulating that any successive order using the name “Rosetta” would contradict the rules of this language game? If it is so meant, how could one teach such a rule?

In the passage under consideration, Wittgenstein does not address these questions, but instead goes on to new ways of expanding his original language game. Therefore we now turn our attention to the relevant sections of the Philosophical Investigations. The formulation that he uses there to expand the builder language game to include proper names is as follows:

The word ‘signify’ is perhaps most straightforwardly applied when the name is actually a mark on the object signified. Suppose that the tools A uses in building bear certain marks. When A shows his assistant such a mark, the assistant brings the tool that has that mark on it.

In this way, and in more or less similar ways, a name signifies a thing, and is given to a thing. – When philosophizing, it will often prove useful to say to ourselves: naming something is rather like attaching a name tag to a thing. (§ 15)

It is noteworthy that Wittgenstein doesn’t make it at all clear here that he is thinking of proper names; the reader is first informed of this by the explicit comment in § 41. The reader cannot conclude this from the quoted passage because Wittgenstein also uses the expressions “signify,” “name,” and “naming” in conjunction with terms such as “slab.” Thus he says, for example, in § 7 regarding the first, unexpanded step of the builder language game, “the learner names the objects”; in § 13 in relation to a language without proper names one could hold that “every word in the language signifies something”; in § 28 Wittgenstein speaks not only of proper names, but also of “the name of a color, the name of a material”; and in § 37 he states that in the simplest form of the builder language game, which only has words of one type, one can see what “the relation between name and thing named” consists in. Even if one thinks that Wittgenstein is here taking up the naïve use of language with a detachment that only later becomes clear, the fact remains that he does not distinguish between “naming” and “speaking of” (predicating).

One could also understand § 15 so that the sense Wittgenstein has in mind for the word “to signify” allows us to say that both concept terms and proper names signify something. Of the word types considered up until that point only the numerals and words such as “there” would be excluded, because one cannot use them to order building stones or tools. In both of the allowable cases one can imagine that every object, whether it be a slab or an individual tool, is marked with a sign, with a “name tag.” This can be of the form of “slab,” or the form “Rosetta,” but what the difference would amount to in the language game is not explained in the quoted sections. Quite the contrary: in both cases the utterance of the words counts as the ordering of an object.

So far we are also lacking any indication of the possibility of combining proper names and concept words in a complex sentence that gives expression to what Frege called the “fundamental logical relationship.” In addition to the general question of how individually occurring proper names and concept terms differ with respect to the roles they play at the level of development in the language games Wittgenstein has discussed thus far (i.e., to what extent they function as different “instruments”), it is also unclear what their relationship to one another is. Do they have some characteristic relationship different from, for example, that which holds between numerals and concept terms? The only thing that comes readily to mind (and is alluded to in Wittgenstein’s text) is the traditional view, that proper names are distinguished from expressions of the “slab” type because proper names refer to only one individual object:

Now suppose that the tool with the name ‘N’ is broken. Not knowing this, A gives B the sign ‘N’. Has this sign a meaning now or not? – What is B to do when he is given it? We haven’t settled anything about this. One might ask: what will he do? Well, perhaps he will stand there at a loss, or show A the pieces. Here one might say: ‘N’ has become meaningless; and this expression would mean that the sign ‘N’ no longer had a use in our language-game (unless we gave it a new one). (§ 41)

How does this case differ from one in which the building stones known as “slabs” are broken or used up? Here, too, nothing has been settled, and one could decide (as Wittgenstein does in the course of the quoted passage) that the correct answer to such a request is to shake one’s head. Again, we find that the decisive characteristic of the “context” or “circumstances” that mark the difference between a language game in which a concept word is used and one in which a proper name is used is not clearly stated – a difference in pointing (analogous to the difference in “pointing to the form” and “pointing to the color”) will not be sufficient for the desired distinction if both kinds of pointing differ only in an accompanying mental process of “meaning something.” In this respect our expectations remain disappointed for now.

We want to close our discussion of the step by which a simple language game becomes expanded through the introduction of expressions of the category of proper names with a consideration of the above-mentioned passage from the Philosophical Investigations (§ 49), which at first glance appears to have something to say about the interplay of proper names and concept terms in the building of a sentence. Wittgenstein says in this passage that naming is not a move in a language game but rather a “preparation for describing.” Because he makes reference to Frege’s “context principle,” which states that a word only has meaning in a sentence, one might be tempted to read Wittgenstein as holding the view opposite to Frege’s, that is, that naming expressions (and proper names in particular) are “unsaturated” while concept terms, as seen in the builder language game, are such that they “stand upright by themselves.” The example that Wittgenstein uses will also occupy us in the discussion of his thoughts on semantic complexity, so it is worth examining it thoroughly.

The context of these considerations is as follows: Wittgenstein is discussing the notion that proper names really signify simples, and he sketches a language game in which this is actually the case. It serves to represent combinations of colored squares that are ordered like a chessboard. The words of the language are “R,” “G,” “W,” and “B” for the colors red, green, white, and black, respectively. A “sentence”[8] is a row of words that gives the order of a row of colored squares from left to right, and the rows are read from top to bottom. Wittgenstein now asks himself what it means to say that the elements, the individual color patches, can be named but not described, and he responds: “…it could mean, for instance, that when in a limiting case a complex consists of only one square, its description is simply the name of the colored square.” (§ 49) This statement shows that on such an account “description” is understood to be something that can only take place with complex expressions, that is, with the “sentences” of the language in question, while in the case where only a single word is uttered this action is to be called “naming.” What counts as “describing” and as “naming” depends here upon whether a complex or a simple expression is uttered; “describing” in this language can only be done with complex expressions.

Wittgenstein now contrasts this view with another, in which one can say of an individual sign of the type “R” that it is sometimes a word, at other times a sentence, and the difference lies in the situation in which the utterance occurs. If the utterance is in answer to a command to describe a complex of colored squares, then it is a “sentence” or a “description,” even if it consists of a single sign (a single “word”), as when the described “complex” consists of a single square. If on the other hand the use of the sign is taught ostensively, while the sign is being spoken, these utterances are neither “sentences” nor “descriptions” but one should say that the elements are being “named.” Wittgenstein (§ 49) continues:

… it would be strange to say here that an element can only be named! For naming and describing do not stand on the same level: naming is a preparation for describing. Naming is not yet a move in a language game – any more than putting a piece in its place on the board is a move in chess. One may say: with the mere naming of a thing, nothing has yet been done. Nor has it a name except in a game. This was what Frege meant too, when he said that a word had meaning only in the context of a sentence.

The difference that Wittgenstein is getting at here is again that between the “teaching of the language” (in which naming appears and is preparatory) and the “practice of the use of the language,” which is the very thing being prepared for. These different contexts of action, or “levels,” are wrongfully run together when one says that an element can only be named, because this expression makes it sound as though an attempt to follow a command to describe a single square must fail, which is obviously not the case: the description in this case has the quality of consisting of a single sign. Wittgenstein’s point is to get at the difference between preparatory actions (here: the teaching) and the practice itself, a point also made clear by the chess analogy: setting the pieces on the board prepares for the game, but is itself not a move in the game. Likewise “naming” is for Wittgenstein preparation for the “practice of the use of the language” and not itself a move in a language game. Without reference to the practice of the language game it does not even make sense to say that the named thing has a name.

So we see that Wittgenstein’s distinction between “naming” and “describing” does not apply to different roles that expressions in a sentence have, so that, for example, object-names name objects while concept words describe them. His thesis that naming is preparatory for describing does not mean that it is necessarily only a part of a speech act, because this thesis can also be applied to single word sentences without any content being lost. That naming is not a move in a language game does not stem from the fact that words of a category inappropriate to the task are used, for the whole consideration has nothing to do with different types of words. It also tells us nothing about the particular role of proper names over and against that of descriptive words (“concept terms”). To give an example of what this means, Wittgenstein does not say that in a sentence like “Peter swims” the naming of the person Peter is only a dependent part of a complete speech act, in that it is a preparatory step which does not in itself constitute a move in the language game. The characteristic of not being a move in a language game really has nothing to do with Frege’s notion of “unsaturatedness.” Therefore, in relation to the roles of concept words and proper names, the text is not expressing a reversal of Frege’s thesis. This means in particular that there are no competing conceptions here of the “fundamental logical relationship” which for Frege is the central case of logical complexity. For Frege the main thing is the dissimilarity between sentence components necessary for the expression of a judgment, the structure of the sentence. Wittgenstein’s considerations have nothing to do with this set of questions.

Notes

1 From here on, citations not further specified are from Part I of the Philosophical Investigations (Wittgenstein, 2009) and will refer as usual to the number of the entry.

2 He continues in this entry with numerals for groups of things whose number can be taken in at a glance.

3 Compare Frege, 1953, p. 59e (§46).

4 For Wittgenstein, however, this does not make them into concept terms; not even into “second order concepts.”

5 “Führen wir ein weiteres Werkzeug in unsere Sprache ein: Bestimmten Gegenständen, etwa einzelnen bestimmten Steinen, die beim Bau verwendet werden sollen, werden Namen (Eigennamen) gegeben, man zeigt auf den Stein und sagt seinen Namen. Ruft A den Namen aus, so bringt B den Stein, dem er beigelegt wurde.“ (Translation by TD)

6 “…der Gebrauch, der von diesem Zeigen und Aussprechen im Lehren der Sprache und in der Praxis der Verständigung mit ihr gemacht wird.“ (Translation by TD)

7 “Der Unterschied, könnte man sagen, liegt nicht einfach in dem, was beim Zeigen vor sich geht, sondern vielmehr in der Umgebung dieses Zeigens, in dem, was ihm vorhergeht, und in dem, was darauf folgt.” (Translation by TD). Compare (Wittgenstein, 2009, § 33): “Just as making a move in chess doesn’t consist only in pushing a piece from here to there on the board – nor yet in the thoughts and feelings that accompany the move: but in the circumstances that we call ‘playing a game of chess’, ‘solving a chess problem’, and the like.”

8 A “sentence” is distinguished from a simple list in this case only in that the order of the words plays a role for the expected non-linguistic activity. What makes word order relevant in this kind of case is surely not what makes it relevant in a natural language. Cf. Chapter 8.

References

Frege, Gottlob (1953) Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl / The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number (trans. J.L. Austin), 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1970) Eine Philosophische Betrachtung (ed. R. Rhees), (Wittgenstein, Schriften Bd. 5), Frankfurt: Suhrkamp.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

3

Kinds of Expression

So far we have seen in two examples, namely numerals and proper names, how Wittgenstein discusses the step-by-step expansion of a language game, which at first only allows the speaker to utter one-word sentences. Now we want to see how he explicitly addresses the possibility of distinguishing between word types, and not only in the form of presentation of examples. It was mentioned on page 21 that this theme was already addressed at the beginning of the Philosophical Investigations; in the first paragraph Wittgenstein critically states that in the Augustinian picture of language “Augustine does not mention any difference between kinds of word”; he only seems to think of nouns and of people’s names, and “of the remaining kinds of word as something that will take care of itself.” (§ 1) What does Wittgenstein himself have to say about the “difference between kinds of word”?

After introducing numerals in the Brown Book and emphasizing that they are learned in a wholly different way than are previously mastered words of the type “brick,” etc., he goes on to say (Wittgenstein 1958, p. 79):

And this shows us that by introducing numerals we have introduced an entirely different kind of instrument into our language. The difference of kind is much more obvious when we contemplate such a simple example than when we look at our ordinary language with innumerable kinds of words all looking more or less alike when they stand in the dictionary.

We can easily agree with this, even though Wittgenstein, as already mentioned, neglected to note that there is a specific aspect of the difference between the two word types, namely that numerals and words like “slab” go together in specific ways that are related to the activity of learning how to count: a predicate expression like “slab” is necessary to make clear what is being counted. Still, there is enough that becomes clear in his presentation concerning the peculiar character of the new words for it to appear justified to speak of the introduction of a whole new kind of instrument into the language. The numerals compliment or modify the concept terms and are therefore used differently from these terms. Surely this difference in kind would be clearer in a language that had only two types of word than in our own everyday language, which has “very many” word types available. In the quoted text Wittgenstein uses the word “innumerable” to express this multiplicity, and we will have to see if we have reason to agree with this: Are there more kinds of words than can possibly be counted, or are there just “very many”? When we first read the claim that natural language contains a plethora of word types we read it as meaning: there are very many of them. And we note that the language Wittgenstein has thus far considered has exactly two. When he adds that the differences between these word types are easier to recognize in his surveyable language games than in our developed language, this is intended to show that the consideration of such simple cases should help us to recognize the differences between word types in our own complex language. The further question of whether the many word types of natural languages reduce, logically speaking, to a very small number that can be handled by a system like Frege’s can only be answered after we know more precisely what Wittgenstein means by kinds of words.

This interpretation is confirmed a little later, when Wittgenstein (1958, p. 83) returns to the problem of word types and says that we can, without difficulty, see a similarity between the function of the words “one,” “two,” “three” … on the one hand and the words “slab,” “column,” “beam” on the other, and that the parts of speech are thus distinguished. It might appear, however, that Wittgenstein immediately retracts the statement in the passages that directly follow it. He speaks there of an “infinite variety of the functions of words in propositions,” and since it is the function that determines the word type, one could see this as supporting the thesis that there are an “innumerable” (in the sense of an “infinite”) number of word types. This thesis, however, contradicts both common grammatical ideas as well as our own attempts, inspired by Frege, to locate in Wittgenstein a comprehensive answer to the question of the ways natural languages have of using signs so that we can understand the interplay of various word types in forming a unified sentence (the “semantic structure” of sentences). This investigation would be ill served by the suggestion that there are an infinite number of types of words. Here we see already that Wittgenstein might be using the terms “kind of word” and “part of speech” in a quite unusual way.

What are we to make of the apparent contradiction? Are there clearly distinguishable functions that the words can fulfill, and therefore, with a finite number of words, also a finite number of clearly distinguishable word types? Or is there an inconceivably large diversity of functions, so that the term “parts of speech” loses its usual grammatical sense of having relatively sharp borders and meaning that we must now speak of “unsurveyably many word types”?

Wittgenstein develops his ideas as follows: he considers a language game in which the order of words in a sentence such as “slab, column, brick” reflects the order in which the building elements are to be brought, in a manner similar to the way in which the words in the aforementioned color-square language game showed the order of occurrence of the colored squares. He finds that the function served in this game by the order of the words can, in another language game, be fulfilled in a different way. There might even be special words to fulfill this function, for example, numerals, so that we would find in this game expressions of the type “second, column; first, slab; third, brick.” Wittgenstein (1958, p. 83) continues:

Reflections such as the preceding will show us the infinite variety of the functions of words in propositions, and it is curious to compare what we see in our examples with the simple and rigid rules which logicians give for the construction of propositions.

Wittgenstein’s considerations show us on a first appraisal the great diversity of functions that words can have in sentences of different language games. We can imagine a language in which the counting numbers have the function of showing the order of actions that are to be carried out; and from the perspective of another language in which this same function is fulfilled by the word order alone it can appear surprising and odd that there should be words for this task at all. When one considers these highly different and, from language to language, highly variable tasks that the words have to fulfill, then the simple and rigid rules that logicians give for the construction of expressions for “thoughts” appear to bear a strange relationship to these manifold tasks.

We will for the present set aside the question of whether the logicians have good reasons for limiting the broad range of categories of words of natural languages to those that serve their purposes. First we must see whether Wittgenstein’s thesis completely nullifies the concept of word types (“kinds of words”), which it indeed would if his claim regarding the inconceivability of surveying them all were correct. And this would be true regardless of how differentiated or how spartan one’s approach to the construction of a concept script or the description of a natural language might be.

If we go with the understanding of his text sketched in the previous paragraph, such a rejection of the concept of “kinds of words” need not be what Wittgenstein intends. The thesis that words can function in propositions in an infinite variety of ways stems from the view that there is an infinite number of possible (including invented) languages. The inconceivability spoken of here – of surveying all the many functions that words may have in sentences (“propositions”) – may be taken to follow from the inconceivability of surveying all possible languages. This is compatible with the thesis discussed above that in a sentence of the type “two slabs,” for example, which belongs to a particular language, there are two words from exactly two word types, and that we recognize them as clearly differentiated kinds of instruments.

The German revision of the text appears, however, to express something different and seems therefore closer to another interpretation of the English text in which it is not the difference between various languages that is emphasized, but rather the fact that one and the same language (as is seen in the comparison of the functions of words like “slab” and “two”) already contains within it highly different types of instruments, something the logicians appear to have missed. In the German revision (Wittgenstein 1970, p. 124) we find the sentence:

Such considerations give us an idea of the enormous diversity of means of our language; and it is interesting to compare what we find here with what the logicians have said about the construction of all sentences.[1]

Here our sights are set on just one language, so that we are no longer concerned with the possibility of developing diverse new languages without limit. On the other hand, because Wittgenstein no longer uses the word “infinite,” there isn’t necessarily a contradiction with the thesis that in view of similarities in usage we can clearly and without problem distinguish between word types with different functions. It should come as no surprise that one finds in the natural languages very many more word types than did “the logicians,” above all Frege, Russell, and the Wittgenstein of the Tractatus, particularly if one does not limit one’s interest in language to the expression of a “judgeable content.”

The feeling of an unavoidable contradiction to the thesis of the possibility of a clear identification of word types stems from the following sentence, which appears in the Brown Book in the same entry and directly following the passage quoted above (Wittgenstein 1958, p. 83):

If we group words together according to the similarity of their functions, thus distinguishing parts of speech, it is easy to see that many different ways of classification can be adopted.

Is there then no possibility of a clear classification of words based upon their functions? Is the function of a word not something that it has, but rather something we can see as this way or that?

Wittgenstein says here that when we group words and distinguish word types according to the similarity or dissimilarity of their function, we could classify them in many varied ways. This cannot, however, mean that in the builder language game we could classify, for example, the word “slab” with the numerals, or the word “five” with the concept terms, and still retain the apparent division into numerals and concept terms. Wittgenstein does not say that from any given point of view we could classify individual words quite differently, but that there are various points of view, various ways of classification imaginable.

The simple fact that words can be classified in different ways is uninteresting and misses Wittgenstein’s point, if one is thereby thinking of words in general and of classification as something which includes, for example, the order of their constituent letters in the alphabet, like in a dictionary. On the other hand, it is unclear whether the claim that there are still many possible ways of classifying holds when similarity of function is the point of view for classification. From this it would follow that the formulation “similarity of function” is not yet an adequate specification of a starting point for classification. This means that with reference to a specific and precisely described sentence of a language game such as “four slabs,” the question of which word types are present, as measured by the functions of the words, cannot have a definite answer.

On this reading, the alleged contradiction mentioned above does not necessarily appear: of course it is true (so Wittgenstein could argue) that with reference to similarities of word usage we can group together the words “one,” “two,” “three,” etc. as one type, and the words “slab,” “column,” “beam” as another. At the same time, this way of grouping words and thus distinguishing types (even when we stick to the rather inexact criterion of “similarity of function”) leads to only one of many possible classification systems. And to the reader who asks how the examples of these two apparently quite different kinds of “instruments” could be grouped differently, yet still in accordance with the “similarity of function” criterion, Wittgenstein (1958, p. 83) gives the following answer:

We could indeed easily imagine a reason for not classing the word ‘one’ together with ‘two’, ‘three’, etc., as follows: …Consider this variation of our language game 2). [That is the builder language game expanded through the introduction of counting words; author’s clarification] Instead of calling out, ‘One slab!’, ‘One cube!’, etc., A just calls ‘Slab!’, ‘Cube!’, etc., the use of the other numerals being as described in 2). Suppose that a man accustomed to this form…of communication was introduced to the use of the word “one” as described in 2). We can easily imagine that he would refuse to classify ‘one’ with the numerals ‘2’, ‘3’, etc.

So Wittgenstein imagines a language in which counting begins with “two.” Numbers will begin where there is a plurality of things, and if asking for the number of things is introduced into this language (“how many slabs?”), then in the case where only one slab is at hand the question cannot be answered but only rejected.

This well-defined language game, of which we would probably still say that it has just two types of words (“2,” “3,” etc., and “slab,” “column,” etc.), is the point of departure. Now Wittgenstein brings in a case in which a speaker of this language is made familiar with the use of the word “one” as was described in the first expansion of the original language game. His thesis is that we can easily imagine this speaker would “find it odd” (Wittgenstein 1970, p. 124),[2] would hesitate, to categorize the word “one” together with the group of numerals “two,” “three,” etc.

There is apparently no doubt that the new word does not belong to the group containing “slab,” “column,” etc.; the question is only whether it should belong with the numerals already in use or not, or whether in the negative case it belongs to its own, a third type of word perhaps related to the numerals. To answer this question about word type it appears that recourse to what Wittgenstein rather non-specifically calls “the use” is insufficient; from the point of usage one could say either that “one” is a move in a language game very similar to “three” or “seven,” or, thinking in the opposite direction, one could emphasize that it is a sign whose use indicates that no plurality (e.g., of slabs) is being ordered. It might matter that the worker in this second case will not get into a position to carry out a task involving counting, perhaps because she has not yet mastered the action of counting or because it is the domain of a privileged group of workers. The maxim that one must look toward the usage cannot, without further information, determine which consideration is the better fit.

Although Wittgenstein’s example is so chosen because it handles the question of how an existing language is to categorize a newly introduced word, the example and the passages following it clearly indicate that the question “are the words W1 and W2, measured by their functions, of the same word type or not?” can also apply to two words that already belong to a familiar language. Wittgenstein writes in the German revision of the Brown Book (the Philosophische Betrachtung; 1970, p. 124): “Are black and white colors? In some cases one counts them among the colors, in others one does not.” And more generally: “Words can be compared with chess pieces in many ways. Think of the different ways of classifying the chess pieces (for example into officers and pawns).”[3]

Here it is apparent that Wittgenstein understands “types” of words in such a way that “color words” constitutes a word type, such that it makes sense to ask whether “black” and “white” belong to this category. Traditional grammar sees here only one type of word, the adjective. But what is the exact usage that Wittgenstein wants to make of the expression “word type”? What is its relationship to its use in traditional grammar, and how do these ways of using “word type” relate to Frege’s ideas about distinguishing different “functions of signs”?

Wittgenstein’s comparison of words with chess figures raises the question of whether his notion of “different ways of classification” leads to groupings that stand in relation to one another as genus to species: the division of chess figures into officers and pawns, or, for example, knights and rooks, oriented on the functions of pieces in the game and not on, say, their size or the material of which they are made. The classification of a piece as an “officer” simply lumps together a list of various functions and thereby distinguishes them from the simple functions of the pawn. In reference to the linguistic example, we must ask ourselves if the traditional word types such as “adjective” apply to Wittgenstein’s word types such as “color words” in the same way the genus “officer” does to the lower species “knight,” “rook,” etc. Does Wittgenstein’s thesis – that from the standpoint of function one could classify words in many ways – only refer to various finer classifications?

Let us first look at what he says in the Investigations concerning the problem of distinguishing types of words. Here we find the same dual-aspect that we found in the preliminary work. On the one hand he highlights the apparent dissimilarities between different words that play quite different roles in the fictitious languages, and he points out that it is easy to come up with a limited number of word types. In relation to the question of what sense it makes to say that someone’s words stand for something, Wittgenstein writes:

Equally one may say that the signs ‘a’, ‘b’, etc. signify numbers: when, for example, this removes the misunderstanding that ‘a’, ‘b’, ‘c’, play the part actually played in the language by ‘block’, ‘slab’, ‘pillar’…

But making the descriptions of the uses of these words similar in this way cannot make the uses themselves any more like one another. For, as we see, they are absolutely unlike. (§ 10)

Here Wittgenstein is examining types of words and he orients himself on the roles the words can play as members of a certain type; he is not focusing solely on the individual words. These types are, “as we see,” very different; the differences between words and between the types to which they belong are apparently supposed to be perfectly obvious. This thesis is repeated later at the beginning of a passage in which Wittgenstein uses the expression “kinds of word”:

We could say: In language (8) we have different kinds of word. (German: ‘Wortarten’ [author’s clarification]) For the functions of the word ‘slab’ and the word ‘block’ are more alike than those of ‘slab’ and ‘d’. (§ 17)

Again, Wittgenstein makes “function” the central factor in deciding between kinds of word. On the other hand he continues:

But how we group words into kinds will depend on the aim of the classification, – and on our own inclination.

Think of the different points of view from which one can classify tools into kinds of tools. Or chess pieces into kinds of chess pieces. (§ 17)

This statement is quite short and provokes a number of questions: why is our intention to use the functions of words as the deciding factor in their classification not enough; why (as it had appeared earlier) does it not lead to obvious classifications, and what role does our “inclination” play here? Do the different standpoints according to which one can divide up tools and chess pieces, based solely on function, merely lead to ever finer classifications, or to classifications that overlap and therefore constitute no unique order? Think, for example, of distinguishing saws from drills on the one hand, but then distinguishing metalworking tools (including metal saws, metal drills, etc.) from woodworking tools (e.g., wood saws, wood drills, etc.) on the other. And what light do these comparisons shed on language? Is the ordering in language just as makeshift and open to choice as it appears to be for tools, or must one say that, as an element of a language, a word has a function that is neither a matter of inclination nor of an accidentally chosen point of view?

The thesis of “the enormous diversity of means of our language” (Wittgenstein 1970, p. 124; see footnote1 and above page 39) appears in the Investigations in the following form:

But how many kinds of sentence are there? Say assertion, question and command? – There are countless kinds; countless different kinds of use of all the things we call “signs”, “words”, “sentences”. (§ 23)[4]

There follows a list of examples of language games, in which among others we find giving orders, describing, reporting, acting in a play, as well as requesting, thanking, cursing, greeting, and praying. Wittgenstein concludes this passage with the words:

It is interesting to compare the diversity of the tools of language and of the ways they are used, the diversity of kinds of word and sentence, with what logicians have said about the structure of language. (This includes the author of the Tractatus Logico – Philosophicus.) (§ 23)

The obvious objection against this is that the thesis of an infinite number of kinds of “tools in language” only gains its plausibility because Wittgenstein enumerates a plurality that doesn’t affect word and sentence types in their usual grammatical or (with Frege (1984a, p. 393; orig. pagination 39)), when he speaks of the “employment as a symbol”[5]) logical sense, but instead as a multiplicity of ways of using sentences that relies on their relationship to extra-linguistic actions. What Wittgenstein states applies as well to single-word sentences, so that a difference in semantic role, a role that words fulfill through their relationships to other words in the sentence, cannot be what is meant. The impossibility of enumerating all the ways of applying a single-word sentence is no argument for the thesis that the word constituting the sentence belongs to an unsurveyable number of types of words. Against Wittgenstein’s inclination to handle “ways of application,” “kinds of sentences,” and “kinds of words” alike, as if a usage of a sentence constituted a “kind of sentence” and the use of a word a “kind of word,” we hold that these are two related but (in a developed language) quite distinct things. Indeed, we hold that the grammatical sense of “word type” (and the logical sense, which is at this stage indistinguishable from the grammatical) is very relevant to the questions Wittgenstein is handling. Positively, we can note that in the text surrounding the cited passages, Wittgenstein hints that the classification of words or sentences by their ways of usage on the one hand and by their belonging to different types on the other, is a result of two different standpoints on the classification of elements of language. At this we now take a closer look.

Notes

1 “Solche Überlegungen können uns die ungeheure Mannigfaltigkeit der Mittel unserer Sprache ahnen lassen; und es ist interessant, mit dem, was sich uns hier zeigt, zu vergleichen, was Logiker vom Bau aller Sätze gesagt haben.” (Translation by TD)

2 The German original has “befremdlich finden”.

3 “Sind Schwarz und Weiß Farben? In manchen Fällen rechnet man sie unter die Farben, in manchen nicht.” – “Wörter lassen sich in vielen Beziehungen mit Schachfiguren vergleichen. Denke an die verschiedenen Arten die Schachfiguren zu klassifizieren (zum Beispiel in Offiziere und Bauern).” (Translation by TD)

4 The German for “countless” here is “unzählige.”

5 Cf. above, p. 14, n. 5.

References

Frege, Gottlob (1984) Collected Papers on Mathematics, Logic, and Philosophy (ed. Brian McGuinness), Oxford: Blackwell.

Frege, Gottlob (1984a) Thoughts, in Frege 1984, pp. 351–372.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1970) Eine Philosophische Betrachtung (ed. R. Rhees), (Wittgenstein, Schriften Bd. 5), Frankfurt: Suhrkamp.

4

“Function” in Language Games and in Sentential Contexts

Let us examine the last text in greater detail: Wittgenstein asks himself how many types of sentence there are, and considers the traditional grammatical answer that there are assertions, questions, and imperatives. Against this he offers a view that goes beyond these grammatical divisions, one based on types of sentence application, which appears to allow as many finer distinctions as one will. From this perspective it is pertinent that an assertive sentence like “you strive for a great public effect with your essay” can, on the one hand, be used to begin a discussion (that could be continued with, for example, “yes, and I ask myself if your journal can serve this purpose”), but can also, on the other hand, be used as an offensive remark (in response to which the conversational partner could say something like “I reject the charge of vanity; with me it is all about the topic”). Wittgenstein is certainly correct in holding that it would be an insurmountable task to try to give a complete count of all the “kinds of application” of sentences in this sense.

It seems that the way in which traditional grammar speaks of “kinds of sentences” is not something that simply has to be corrected by applying Wittgenstein’s views on usage. The grammarian can fully agree that among the expressions that count as assertions one can distinguish between those used as conversation starters and those used as offensive remarks; she would also not dispute that a sentence such as “your shoe is untied” may be understood as an order to tie it. But the grammarian would certainly add that we are not looking at a grammatical distinction in these cases. If this is correct then we have two different, though probably not unrelated, stances on classification: Wittgenstein’s, on the one hand, and the grammarian’s on the other, which can exist alongside one another. It remains to be seen what specifically the grammatical distinction between sentence types consists in, and whether, as Frege thought, there is also a logical distinction that would allow us to speak of a “logical grammar.”

This shift in theme in Wittgenstein’s writing from a grammatical to a non-grammatical classification of linguistic expressions is easy to see in the case of sentences. Less apparent but just as worthy of investigation is the fact that as Wittgenstein moves from “kinds of sentence” to “kinds of application,” he also assimilates the theme of “word” into the theme of “sentence”: he speaks of the “…kinds of use of all the things we call ‘signs’, ‘words’, ‘sentences’” (§ 23). Is it legitimate to posit this parallel between applications of a sentence and applications of a word if one thinks beyond single-word sentences, in which the distinction collapses? When we spoke above of “types of sentence application,” we were thinking of the role the sentence plays as a complete move in a language game, embedded in a context of action (e.g., conversation starter, pejorative remark, etc.). Can one, in this parallel sense, speak of “types of word application” when a word is considered that is a constituent part of a sentence? While it was plausible to speak, in relation to sentences, of a differentiation between “kinds of application” and kinds of sentences in the grammatical sense (we still must clarify just what is the grammatical sense of “kind of sentence”), it is unclear what it would mean to speak of the “ways of application” of words. Must not “kinds of application” of words always be tied to the sentences in which they occur?

Consider this example: in a passage closely preceding the one cited on page 48 (PI 21), Wittgenstein discusses the possibility that the expression “five slabs” can be used not only as an order (as originally introduced) but also (in a second step) as a report. This new use of the complete expression “five slabs” will then differ from its original usage. This can (following John R. Searle, 1969, who uses Frege’s “judgment stroke” to indicate the “report”)[1] be graphically depicted by the distinction of “! five slabs” (order) and “ five slabs” (report). Because we cannot trust ourselves to have an overview of all possible uses, one can speak of a “countless” number of kinds of applications of sentences. But does it then make sense to ask if we also have a multiplicity of kinds of words before us: should we, for example, say that the words “five” and “slab” belong not to two clearly distinguishable word types, but rather that every modification in the use of a sentence (order, report, pejorative, etc.) constitutes a new word type for a word contained? Does the word “five” (as well as the word “slab”), since it can appear in sentences that can be used in an unsurveyable number of ways, belong to an unsurveyable number of word types? What would then be expressed by the term “kind of word” if not the fact that the word “five,” for example, is known by its speaker to occur sometimes in an order and sometimes in a question, so that it would be superfluous and misleading to say not only of the sentence but also of the word that it is used in two different ways?

Let us look again at the case of sentences: there it appeared plausible to speak of a multiplicity of kinds of use; what we still have to clarify is how the usual grammatical sense of speaking of “kinds of sentences” relates to Wittgenstein’s talk of “ways of application.” Pertinent to this question is a passage in which Wittgenstein (2009, § 22) speaks of the “Fregean assertion sign” (“”).[2] His thesis is that the position he ascribes to Frege (namely: that an assertion contains an “assumption,”[3] which is asserted) rests on a particular possibility of the English (and the German) language to rephrase such sentences. In English we can rewrite every statement in the form: “It is asserted that such and such is the case.” And now Wittgenstein asks:

We might very well also write every assertion in the form of a question followed by an affirmative expression; for instance, ‘Is it raining? Yes!’ Would this show that every assertion contained a question? (§ 22)

In this fictitious language game the assertion takes the form of a complex: a question coupled with a positive answer. This appears plausible when we imagine that the development of this language game (this family of language games) began with questions, and assertions found their way into the game only later. In a language game with such a history, a new way of speaking (i.e., making assertions) always arises by borrowing from already existent expressions; these in our case originally functioned as questions. When Wittgenstein now speaks in the cited passage of the “form of a question,” he can only mean the grammatical form, because the function of the complete “enlarged” utterance in the practice of the language, the way of application, is that of an assertion, not of a question. This assertion contains no question as an illocutionary partial-act, although the expression does contain a partial expression that, on account of its grammatical form (which hangs together with the history of development of the language game family under consideration), can be described as a question. We see that Wittgenstein did not draw the conclusion that simply because the complete sentence is an assertion it is therefore senseless to speak of a part of a sentence as a “question.” On the contrary, his use of the word shows that he was not immediately characterizing the type of application of the sentence, but rather the “grammatical form” of a component of the sentence.

It is in agreement with this that Wittgenstein writes of the “assertion sign” (“”):

Of course, one has the right to use an assertion sign in contrast with a question mark, for example, or if one wants to distinguish an assertion from a fiction or an assumption. (§ 22)

In reference to the language game just discussed this means that in addition to expressions of the form “Is it raining? Yes!” the speaker would also find it sensible to use expressions such as “Is it raining? Suppose it is.” Here the task of the expression “suppose it is” is to distinguish the supposition from the assertion marked by the word “Yes!” But Wittgenstein asks if this is sufficient reason to say that a question forms a hidden part of an assertion as well as of a supposition. In order to be able to discuss the discrepancy between the grammatical form of a question and its role in the practice of a language (assertion, supposition), as Wittgenstein does, it seems it must be possible to say that in the corresponding complete expression there is a component expression in the grammatical form of a question. But what does it mean to say the component has the grammatical form of a question, yet is not a question? The presupposition seems to be that in the language game the move of asking a question (here: Is it raining?) is a possible independent move. What enables us to speak of the “grammatical form” (apart from the kind of application) is the fact that the expression “is it raining?,” together with the further expressions “yes” and “suppose it is,” can be used to carry out two new speech acts, that of asserting, and that of expressing a supposition. These two complex actions, taken as wholes, have (in the practice of the language) taken on roles different from the role of a question; and the act of questioning is nowhere hidden as a component action in either of these two new actions. At the same time both of these new actions are carried out in Wittgenstein’s language game through the use of an expression that can serve independently to ask a question, and this is still indicated by the question mark.

Wittgenstein now brings to the fore the previously mentioned fact that despite the situation just described we cannot say that in the fictitious language game one makes an assertion by first raising a question and then giving an affirmative answer. Even though anyone who makes an assertion in this language game does so by using an expression that, if used independently would articulate a question, it would be incorrect to say that the speaker can only assert something if she first asks a question. Wittgenstein writes in connection with the last cited passage:

It is only a mistake if one thinks that the assertion consists of two actions, entertaining and asserting (assigning the truth-value, or something of the kind), and that in performing these actions we follow the propositional sign roughly as we sing from the musical score. (§ 22)[4]

Here is the reason why, in relation to the language game under consideration, it is sensible and necessary to speak not only of the kind of application, but also of the “grammatical category of the sentence.” This would be superfluous if the assertion were a connected “train” of independent acts, namely the act of questioning and the act of answering in the affirmative. In this case it would suffice for an account of asserting if one were to name the individual acts of which it then “consists,” and to characterize them by giving their “function in the practice of the language” – a function they could also fulfill in cases where they occur alone. The form of an expression (for example, the form indicating a question), even if it is a component expression, would in this case always show the role that the speech act will play, and a complex speech act would be nothing more than a succession of simple speech acts. This would be like “singing from the musical score” in the limited sense used by Wittgenstein, where the “singing” consists in nothing more than hitting all the right notes and ignoring the aspects that give it unity, expressed in such terms as “melody,” theme,” etc.[5]

In the case of speech, however, it doesn’t work that way. More often than not, we can use elements of a mastered language game to make a (from the perspective of the possibilities of its elements) new move, which includes the phonetic aspect of these elements without containing them as moves. In this vein, Wittgenstein writes:

The Fregean assertion sign marks the beginning of the sentence. So its function is like that of the full stop. It distinguishes the whole period from a clause within the period. If I hear someone say “it’s raining” but do not know whether I have heard the beginning and end of the period, then so far this sentence fails to convey anything to me. (§ 22)

We can elaborate Wittgenstein’s example as follows:

If, on entering a room in which a conversation is going on already I only hear “it is raining,” but don’t know whether this was, for example, merely part of a clause such as “I doubt whether it is raining,” then what I have heard “fails to convey anything to me.” Although the sentence fragment has the grammatical form of an assertion it would be incorrect to say the speaker thereby asserted something.

The sentence element “it is raining” fits into the whole sentence in such a way that its character as an assertion is only indirectly noticeable. What remains, and what must be correctly grasped for an understanding of the complex speech act, is the “grammatical form” of the assertion. This provides a starting point for answering the question of just what the distinction is between the grammatical classification of sentences and their classification by application. We still await a more detailed explanation of which linguistic processes make it possible to speak of the function of a sentence element, since this function cannot be characterized in any direct sense as a function “in the practice of speaking the language.”

Let us return to the question as it pertains to words. From what viewpoint can words be classified more specifically than simply according to their “role in the language game,” in a way closer to the traditional grammatical sense (or, as Frege intended, in a logical sense)? Are there, in Wittgenstein’s work, starting points for such a project, and how does he judge the concept of the “grammatical”– first in the sense of a logical grammar, oriented at the kinds of use one can make of an expression, but also in the sense of the grammar of a natural language? We will now consider a passage in which Wittgenstein speaks of “the function of a word in a sentence.” (We encountered such functions in our discussion of Frege’s views as a criterion for distinguishing between expressions for objects and for concepts.)

Wittgenstein begins with the question: “What does it mean to say that the ‘is’ in ‘The rose is red’ has a different meaning from the ‘is’ in ‘Two times two is four’?” (§ 558) He immediately rejects the suggestion that we actually have here two different words that merely sound alike, but which have different sets of rules: we have here only one word. Against this rejection one might ask: when do we want to say that we have before us a single word, and when shall we speak of two words? The view Wittgenstein rejects – that we should distinguish two words when different sets of rules apply – he counters thus: “And if I attend only to the grammatical rules, these do allow the use of the word ‘is’ in both kinds of context.” (§ 558)

This means that one can imagine a grammar whose rules treat the expression “is” as a single word, but which nonetheless manages to determine which utterances containing this word are correctly constructed and which are not. The appeal to “grammatical rules” that are unspecified beyond their sole task of deciding correctly from incorrectly constructed sentences doesn’t necessarily lead to a criterion that can help us decide between a case in which we have two words that sound alike and a case in which we have just one word with a plurality of applications.

After these negative comments on the suggestions of the interlocutor, Wittgenstein gives a positive answer to his question:

But the rule which shows that the word ‘is’ has different meanings in these sentences is the one allowing us to replace the word ‘is’ in the second sentence by the sign of equality, and forbidding this substitution in the first sentence. (§ 558)

This rule is apparently not only oriented toward the correctness of an expression whose construction it would describe: in this sense, it is not merely a grammatical rule. It, however, is what shows the difference in the meanings of the word “is” in the two occurrences mentioned. What, then, is this difference in meaning, of which we have here learned to recognize a symptom? The rule mentioned for substitution is apparently a result of differences in meaning, not the difference itself. If there were no sign of equality in the language, there would not be this particular difference in substitutivity, yet still the differences in meaning discussed (now being considered in a comparison of languages) would remain. In what, then, do they consist?

Wittgenstein discusses the following thought, in the formulation of which he uses the word “function,” a word that was used above to determine the way in which words are to be grouped into types:

One would like to speak of the function of a word in this sentence. As if the sentence were a mechanism in which the word had a particular function. But what does this function consist in? How does it come to light? For after all, nothing is hidden – we see the whole sentence! The function must come out in operating the calculus. (Meaning-bodies.) (§ 559)

Indeed, one would like to speak of the function of the word “is” in the sentence “the rose is red” and would want to say that it is different from the function of the word in the sentence “two times two is four.” But what is meant by the word “function”? One uses a picture of a mechanism, whose various parts have certain functional relationships to one another: a belt transfers the rotation of one wheel to another, etc. But where does the “function” of one word lie in relationship to another? How does the image of a mechanism translate to the sentence?

Wittgenstein first sets the negative constraint: nothing is hidden, we see the entire sentence. This thesis that there can be nothing covert is also expressed by the term in parentheses, “Meaning-bodies.” It refers to another version of the image of a mechanism, one that Wittgenstein used repeatedly and which is quite clearly formulated in the Remarks on the Philosophy of Psychology (Wittgenstein 1980, vol. 1, p. 10 (§ 42)). There he says, in reference to the idea that there are cases in which one could say something but not mean it, that this is based on the following comparison:

…words fit together in the sentence, i.e. senseless sequences of words may be written down; but the meaning of each word is an invisible body, and these meaning-bodies do not fit together.[6]

What Wittgenstein rejects is the idea of a state of affairs existing in a realm of meanings, analogous to a “mechanism” made of invisible components, such that we could speak of the elements fitting together, working together, and thus of a function that one has relative to the others and whereby they form a whole. In opposition to this he says: there is nothing hidden, there is nothing “behind” the sentence, no invisible realm of meanings[7]; we see the entire sentence. What, then, is fitting about the expression that a word has a certain function in the sentence in which it appears, and that the sentence being “well-formed” hinges upon this? Speaking positively, Wittgenstein says only: “The function must come out in operating the calculus.” We shall leave this statement alone for now, but will return to it when we discuss a passage that has more to say about what this word “calculus” is meant to bring to light.

Wittgenstein does not rest with the hints given so far, but instead investigates the question anew: why does he say that the word “is” is used with two different meanings, rather than state that its meaning is its (many-sided) use? As an answer, he considers:

One would like to say that these two kinds of use don’t yield a single meaning; the union under one head, effected by the same word, is an inessential coincidence. (§ 561)

Here we arrive again at the problem of types of words. Earlier, Wittgenstein had discussed whether different sounding words, such as “one,” “two,” etc., are by virtue of their function similar instruments of the language, so that, despite sounding different, they should be considered as belonging to one word type. It turned out that the investigation of the “function in a language game” is too unspecific, and that it couldn’t serve as a criterion for distinguishing parts of speech (in the grammatical or even in the logical sense, as opposed to the non-specific delineation “kinds of words”). In the case under consideration, Wittgenstein brings forth a single word-sound, which is, he says, by virtue of its function used in two entirely different ways. What, however, constitutes a “kind of use”? Why do we not want to speak here of a single, though multifaceted, use, as we did above when we noted that an assertion can be used to open a discussion as well as to insult someone? In what sense do we have two different functions in the case of the word “is,” so that the identical sound is seen as an accidental coincidence? Alluding to the picture of invisible meaning-bodies, Wittgenstein asks:

But how can I decide what is an essential, and what an inessential, coincidental, feature of the notation? Is there some reality lying behind the notation, to which the grammar conforms? (§ 562)

In the light of our considerations of Frege’s ideas in Chapter 1, we can answer the last question in the negative: there is no reality “behind” or “above” language in the sense of a language-independent world of thought or an invisible mechanism of “meaning something” so constructed out of elements that the combinatorial possibilities of its elements determine the permissible combinations of words. Hence, the structure required for a “concept script” cannot be read off from something pre-existent; we ourselves must take up a point of view that allows us to set up norms, compliance with which will lead (from this point of view) to an “appropriate” medium. On what do we orient ourselves when we distinguish (even with reference to natural languages) essential characteristics of the notation (essential qualities of the grammar of the language) from inessential ones, e.g., from notational coincidences? Do we not want to say that in the expression “ten slabs” the component expression “ten” appears essential while its appearance in “tenterhooks” is a “chance coincidence”?

To attempt to answer this Wittgenstein again uses the analogy of a chess game: if we think that the meaning of a chess piece is its role in the game, do we want to count as part of the role of the king its use to determine which player gets to play the white pieces? And he answers:

So I am inclined to distinguish between essential and inessential rules in a game too. The game, one would like to say, has not only rules but also a point. (§ 564)

The concept of a “role in the game,” of an unspecified “rule” that determines what counts as correct, appears to Wittgenstein in this context to be too unspecific. It belongs, in this wider sense, to the orthographic-phonetic “rules” of English that the beginning of the word “tenterhooks” is written and spoken just like the word “ten,” but surely this is no rule of grammar. What distinguishes the “mere rule” (or even the marking of a regularity) from a “rule with a point”? Wittgenstein continues with his answer: “What’s the point of using the same word? In the calculus we don’t make use of such sameness of sign! – Why the same chess piece for both purposes?” But he immediately raises an objection: “But what does it mean here to speak of “making use of the sameness of sign”? For isn’t it a single use, if we actually use the same word?” (§ 565)

Along with the expressions “role in the game” and “rule,” the expression “use” also falls under suspicion of being too vague to be of help in answering the questions just posed. After all, when we use the king to determine sides, this constitutes a use of the figure, but apparently not one that should belong to the determination of the meaning of the king in the game of chess.

Wittgenstein has already mentioned a qualification of the concept of “use”: he said that we make no use of the similarity in the calculus. And, in the next passage, we find a clarification of this, which is very important to our formulated questions:

And now it looks as if the use of the same word or the same piece had a purpose – if the sameness is not coincidental, inessential. And as if the purpose were that one should be able to recognize the piece and know how to play. – Are we talking about a physical or a logical possibility here? If the latter, then the sameness of the piece is part of the game. (§ 566)

His thesis is that the occurrence of two homonyms would not be a coincidental, inessential move, if their sounding alike had a purpose. For the chess example this means that using the king to determine which color a player has is insubstantial to the actual playing of the game. There is no recognition of the chosen piece elsewhere; a pawn would have served just as well. But when the sameness has a “use in the calculus” then the purpose of the use of the same word is that one recognizes it and knows how to play the language game. When this “ability” is meant as a logical possibility, the sameness belongs to the game; it is no coincidental, inessential move. Its mention belongs to the rules of the game; it affects an aspect of the “use,” the understanding of which is constitutive of the understanding of the game. Its mention, we allege, belongs to grammar.

With respect to the example discussed above, this means that, other than in the case of the partial (acoustic) similarity between “ten” and “tenterhooks,” the overlap between “one” and “twenty-one” does have a purpose. It is that one should recognize the word “one” in “twenty-one” and know “how the game is played.” That is, to know which roles such constructed numerals play in the language game: for example, whether “twenty-one” is the correct answer to the question “how much is three times seven?” And certainly this recognition and ability to play is not meant in the sense of a physical ability, such as the volume of an utterance or the legibility of an inscription, but rather in the sense of a logical possibility. To master the language game involving the expression “twenty-one” means, among other things, to know that this expression contains the familiar word “one,” as well as how the role of the complex expression hangs together with that of the component expression. In constructing the complex expression, we make use of the expression “one,” and in understanding the complex expression, we make use of the homophonic expressions “one” as found originally outside this complex, and as the last syllable of the complex expression.

So what is the “function” of a component expression in a complex expression, the function of a word in the sentence of which it is a component? Based on the preceding discussion, we can say that the function is the use that we make of an expression in the construction of a complex expression, and, in particular, how this use affects the way component expressions combine to form a unified whole. The function is the kind of contribution the word meaning makes to the sentence meaning. The word “is” functions differently in the sentence “the rose is red” from how it does in the sentence “two times two is four.” The speaker uses this word, on the one hand, with the words “the rose” and “red,” and, on the other, with the words “two times two” and “four,” to build a unity in different ways. Seen the other way around: understanding the word “is” in the sentence “the rose is red” is not a logical prerequisite for understanding the sentence “two times two is four,” and vice versa. We make no use of this (viewed systematically merely “coincidental”) sameness in sound “in the calculus,” by which we determine what we mean by a complex expression on the basis of our knowledge of the modifying roles of its component expressions.[8]

Wittgenstein’s discussion of the “function of a word in the sentence” concerns the same characteristic of language that occasions us to speak of the “grammatical form of the sentence”: the fact that we can rely on homophonics to illicit a recognition of the simple component expressions out of which we build complex ones. At the same time, in using the simple expressions this way (and this is what gives rise to the expression “function”), the component expressions do not each independently play their roles (the utterance of a complex expression is not like singing from the score). The action of uttering the complex does not contain the individual actions that could be assigned to each of the component expressions, according to the roles they play when they occur alone. The complex utterance is “more” than a mere succession of independent linguistic actions.

In another passage, Wittgenstein discusses this possibility of using an expression as a component of a complex expression, and the associated misunderstandings that must be avoided. There, he says:

One may have the feeling that in the sentence ‘I expect he is coming’ one is using the words ‘he is coming’ in a different sense from the one they have in the assertion ‘He is coming’. But if that were so, how could I say that my expectation had been fulfilled? If I wanted to explain the words ‘he’ and ‘is coming’, say by means of ostensive explanations, the same explanations of these words would go for both sentences. (§ 444)

The doubt that Wittgenstein now brings against this way of speaking shows that he is still wrestling with the picture that the complexity of a sentence must correspond to something complex “in the world,” as if the complexity were a “reproduction,” a “mapping” of a chain of events:

But now one might ask: what does his coming look like? – The door opens, someone walks in, and so on. – What does my expecting him to come look like? – I walk up and down the room, look at the clock now and then, and so on. – But the one sequence of events has not the slightest similarity to the other! So how can one use the same words in describing them? – But then perhaps I say, as I walk up and down: ‘I expect he’ll come in.’ – Now there is a similarity here. But of what kind?! (§ 444)

And his answer is: “It is in language that an expectation and its fulfillment make contact.” (§ 445) Here it is clearly stated that the individual words which make up the complex expressions are explained the same way: we have no coincidental sameness of sound, rather, in the sentence “I expect that he will come,” we make use of the homophony of the words “he,” “will,” and “come” with the words “he,” “will,” and “come” that we learned in other circumstances.

It would be wrong to say that the sentence “I expect he is coming” describes a situation which, because the sentence contains the component expression “he is coming,” must correspondingly contain a “component situation” that would be correctly described as “he is coming.” Here Wittgenstein does not stress the fact considered above (i.e., that the speech act expressed by “I expect that he is coming” does not contain as a part the assertive act “he is coming”) but rather looks at the “non-linguistic correlate” – the so-called “situation,” of which we are tempted to say that the sentence would “describe” or “map” it. He determines that, even in cases where one can say that a longer sentence is a description of a situation, it does not follow that a component sentence contained within it is a description of a “component situation.” In this sense, the possibility of building a complex sentence, while characteristic of natural languages, is very different from the complexity of the “color-square language” – the language game Wittgenstein develops in which the elements of a “sentence” correspond exactly with the elements of a surface of colored squares. That kind of complexity is akin to the case of the shopping list: even though the shopping list case is so primitive that not even the order of elements plays a role, the color-square language resembles it insofar as all its elements function on the same “descriptive” level. An arrangement of colors whose description contains the complex “RG” must contain at some location a complex of two neighboring squares in which the left is red and the right (or the first of the next row) is green. But natural languages and their ways of building complex expressions from simple expressions do not function in this manner; a situation describable as “I expect he will come” does not necessarily contain as a “component” a situation describable as “he will come.”

Wittgenstein had already given an indication of this problem in the Brown Book (Wittgenstein 1958, p. 78), where he speaks of the systematic character of language. There he asks under what circumstances would we say that someone means the utterance “bring me a brick!” as a sentence consisting of four words, and when would we say that it is meant as a one-word sentence, as in the simple order “brick!” He leans toward the answer that we would say the speaker means the first option when she uses it in contrast to other sentences of the language that contain (either partially or wholly) the same words; he gives “take these two bricks away!” as an example. Wittgenstein puts particular emphasis on the negative determination that the speaker need not have such contrasts in mind at the time of her utterance; it suffices that these contrasts exist in the “system” of the language that the speaker uses.[9]

One could take a narrow or “abstract” perspective and say that the speaker is committing the same action in her utterances, namely insofar as she utters the same word “brick.” But this apparently happens in such a way that the resulting complex action does not consist of a chronological succession of self-sufficient component speech acts (over and above their acoustic aspect). In both of the aforementioned sentences, the word “brick” is a word that one should “recognize” and not simply an accidentally homophonic element. But despite this “sameness of the word,” the second sentence does not contain the one-word sentence “brick,” which was originally learned as an independent imperative sentence.

How are we to understand the complex-building devices of our language, when neither the “language” for describing the arrangement of color squares just revisited nor the kind of complexity Wittgenstein discusses as “singing from the score” works as an analogy? How does the “contact” he mentions (e.g., between the expression of an expectation and an expression of its fulfillment) take place? A few paragraphs later, in a passage on the picture of “meaning-bodies” in which “using a sentence consists in imagining something for every word” (§ 449), we find a measure of positive information: “One fails to bear in mind the fact that one calculates, operates, with words, and in due course transforms them into this or that picture.” (§ 449) How do these kinds of activities work?

What we have recognized so far from the examples is of the following nature: we use the expression “he will come” in the construction of the complex expression “I expect he will come.” In one of the language games Wittgenstein creates, he uses the expression “is it raining?” in the construction of the complex expression “is it raining? Yes!” We use the expression “slab” in building the complex expression “five slabs.” We use the expression “slab,” first introduced as an order, to form the description (or “report”) “ slab” and distinguish it from the order “! slab.”

Are there not types of operations here, and doesn’t grammar have something to say about these “ways of calculating”? In what sense are they comparable to a calculus, and how exactly is “translating into a picture” to be understood? In Wittgenstein, we find remarkably few answers to these questions, although he himself poses them, as the passages discussed show. His reticence may be partly because he has no solution to offer, but he also has a systematic motivation in doing so, which is of great importance to our inquiry because it calls into question the connection of his thought with that of Frege, which until now had appeared straightforward. We now turn our attention to this motive.

Notes

1 Cf. below, pp. 123f.

2 German: “Behauptungszeichen.”

3 German: “Annahme.”

4 Here Anscombe’s translation (Wittgenstein 1953) is to be preferred. Regarding the “parts of a thought,” Frege, too, was of the opinion that component expressions did not stand for component actions. He said, for example, that utterances of a compound thought express a complexity of thoughts not of acts of assertion, “…for it is not acts of judgement that are to be conjoined.” (Frege 1984c, p. 391 (orig. pagination. 38)). He judged complex expressions of a concept script differently, however, insofar as they consist of an expression of a (possibly compound) thought and a component that expresses an assertion or denial of that thought. There he applied the part/whole metaphor as if component expressions corresponded to component actions: “So it is possible to express a thought without laying it down as true. The two things are so closely joined in an assertoric sentence that it is easy to overlook their separability. …We have already performed the first act when we form a propositional question.” (Frege 1984b, p. 355f. (orig. pagination 62)). What is bound up together appears to be two actions: that of expressing (or, as Frege says earlier, “grasping”) a thought (possibly complex), and the assertion of its truth. For the first action Frege uses the same word that Wittgenstein cited, “assumption” (“Annahme”) (Frege 1984a, p. 149 (orig. pagination 21f.)). Wittgenstein denies that such an analysis is possible independently of the medium under consideration.

5 This recalls the picture (Wittgenstein 2009, § 6) of “striking a note on the keyboard of the imagination.” One should remember, however, that Wittgenstein, despite the unmusical or “tone-deaf” character of the analogy, had a very close relationship to music (cf. Wittgenstein 1984) and often used analogies between music and language to describe the unity of the sentence. See also Chapter 8.

6 Cf. the depiction of this image in Waismann (1965, p. 235). Waismann says the idea that, “only when the words are combined in accordance with their meaning do they form significant sentences may be illuminated by the following simile: Let us imagine a number of bodies: cubes, prisms, pyramids, made of glass and thus invisible in space, except for the bases of the pyramids and one surface – say a square – of each prism, which are to be coloured and therefore visible. We shall then perceive only a number of coloured surfaces distributed in space. These surfaces cannot be arbitrarily joined together because the invisible objects of which they are parts prevent certain configurations. The laws according to which surfaces can be joined seem to be embodied in those invisible objects.”

7 Compare also the quotation above (p. 14) about logic as something one believes to see in the background.

8 These observations, entirely from a “synchronic” perspective, are later modified, cf. Chapter 6. When Wittgenstein uses the word “calculus” here he is not asserting that the determination of sentential meaning can be achieved schematically from the meanings of the sentence elements and their manners of conjunction or composition; the reasons he has for this view are discussed in the next chapters.

9 The “system” refers to the “particular game” within which the question of active or passive has application. Wittgenstein says: “Asking ‘Is this object composite?’ outside a particular game is like what a boy once did when he had to say whether the verbs in certain sentences were in the active or passive voice, and who racked his brains over the question whether the verb ‘to sleep’, for example, meant something active or passive.” (Wittgenstein 2009, § 47)

References

Frege, Gottlob (1984) Collected Papers on Mathematics, Logic, and Philosophy (ed. Brian McGuinness), Oxford: Blackwell.

Frege, Gottlob (1984a) Function and concept, in Frege 1984, pp. 137–156.

Frege, Gottlob (1984b) Thoughts, in Frege 1984, pp. 351–372.

Frege, Gottlob (1984c) Compound thoughts, in Frege 1984, pp. 390–406.

Searle, John R. (1969) Speech Acts: An Essay in the Philosophy of Language, Cambridge: Cambridge University Press.

Waismann, Friedrich (1965) The Principles of Linguistic Philosophy (ed. R. Harré), London: MacMillan.

Wittgenstein, Ludwig (1953) Philosophische Untersuchungen / Philosophical Investigations (trans. G.E.M. Anscombe), New York: MacMillan.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1980) Remarks on the Philosophy of Psychology, vol. 1 (eds G.E.M. Anscombe and G.H. von Wright, trans. G.E.M. Anscombe), Oxford: Blackwell.

Wittgenstein, Ludwig (1984) Culture and Value (ed. G.H. von Wright in collaboration with Heikki Nyman, trans. Peter Winch), Chicago: The University of Chicago Press.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

5

The Sound of a Sentence I

Singing from the Score

It is a striking fact, and one in need of explanation, that in the Philosophical Investigations Wittgenstein repeatedly speaks of grammar in a way that, in light of our considerations in Chapter 4, must strike one as a surprising and, prima facie, unjustified belittlement. If those considerations are correct, then what we have so far designated by the expressions “sentence form” and “function of a word in a sentence” are features essential to the understanding of semantic complexity. What happens when we understand how a speaker in the framework of the language game discussed in Chapter 4 utters “is it raining? Yes!” and thereby uses the interrogative and affirmative forms to carry out a new form of speech act, that of an assertion, whose special character consists in its unity? It is this unity that distinguishes the complex utterance from a mere chronological succession of individual speech acts, and we appear, in cases like this one at least, to have made clear in what sense the action of uttering a sentence as a move in a language game can and must be “more” than a chronological succession of utterances of individual speech acts associated with each of its words. Seen from a Fregean standpoint, we have made it clear how a sentence distinguishes itself from a mere list of names. Up until now, what has come into play regarding “grammatical” considerations seemed to coincide with what we called in Chapter 1 “conceptual” or “logical” discussions, which are prior to the combinatorial logic of truth-functional complexity. So there seems to be no reason to belittle this realm.

It appears pressing to investigate more precisely which sense is connected with phrases such as “function of an expression in a sentence,” “grammatical form,” and “type of word” (in the grammatical sense); the tentative sketch of the field of “the grammatical” should move to the foreground of our interest. Against this stands Wittgenstein’s devaluation of this grammatical side of language (and, as we will later see, a whole new use of the expression “grammar”). He asks, for example, how he (in the Tractatus) could have fallen prey to thinking that the sentence “this is how things are”[1] is representative of the general form of a proposition, and he answers: “It is first and foremost itself a sentence, an English sentence, for it has a subject and a predicate.” (§ 134) He goes on to explain his use of the expression “English sentence” by means of a surprising and irritating observation: what he has just said would illustrate “that one feature of our concept of a proposition is sounding like one.” Does this mean that Wittgenstein thinks the grammatical classification of expressions as “subject” and “predicate” is based only on sound? From the perspective discussed in Chapter 4 we would expect this classification to indicate something about the function of expressions in a sentence, that is, how component expressions form a complex whole. This would be much more than a statement about the sound of the respective sentence constituents, regardless of whether one subscribes to Frege’s idea that in natural languages grammatical rules are neither explicit nor unambiguous. The traditional expressions that characterize “semantic roles” then would be by no means perfect but would concern characteristics of sentences, which would definitely not be merely a matter of sound. Admittedly, Wittgenstein says of our concept of a sentence that its sound is only one of its characteristics; but a further clarification is surely necessary.

A few sections later Wittgenstein repeats his claim that it is the sound that guides us when we say which constituent expression of a sentence is its subject and which its predicate. He speaks from a slightly different perspective, yet his claim is quite clear. With a common form of school instruction in mind, he asks:

What about learning to determine the subject of a sentence by means of the question ‘Who or what…?’ – Here, surely, there is such a thing as the subject’s ‘fitting’ this question; for otherwise how should we find out what the subject was by means of the question? (§ 137)

Here, it is not exactly the relation between subject and predicate whose status – as “mere sound” or as substantial connection between constituent actions – is at issue. Instead, it is the relation of “fitness” that holds between the question (as a device for detecting the subject of the sentence) “who or what…?”, and the subject expression that is thus detected. Looking back to the language game discussed on page 50 (in which all assertions are made in form “is it raining? yes!”), the relevant question is: “what (i.e., what question) is being affirmed?” With this form of question one can determine which sentential component has the grammatical form of a question. We would, of course, say that the component expression “is it raining?” fits the question “what question is affirmed?”, because an understanding of the speech acts of questioning and answering affirmatively (and, in particular an understanding of the fact that questions are the kind of entities that can be answered affirmatively) is, in this language game, constitutive of the speech act of asserting. The question “what is being answered affirmatively?” is related to this substantial understanding of the type of complexity of the assertive speech act, and serves as a vehicle for determining the grammatical components.

The answer Wittgenstein himself gives to his question is the opposite of what we have just sketched. Against the proposed thesis that in order for us to determine the subject the subject must fit the question “who or what…?”, Wittgenstein answers:

We find it out much as we find out which letter of the alphabet comes after ‘K’ by saying the alphabet up to ‘K’ to ourselves. Now in what sense does ‘L’ fit this series of letters? (§ 137)

Wittgenstein is apparently contending that it is simply linguistic habit (more specifically: a habit in our ways of hearing) that gives us the impression that the question “who or what…?” fits the subject expression of the sentence. After all, there is no internal, no semantically relevant, connection between the letters “K” and “L”; the proper explanation of alphabetical order is historical: it is simply common to say the letters in this particular order. The order of utterance does not constitute a unity of meanings, as do the words of a sentence.

Transferring this thesis from the relation between the question “who or what” to the relationship between the subject and predicate, it would read as so: any concept of “sentence” that orients itself on the rules of English grammar, which demand that a sentence must consist of a subject and a predicate, is a concept oriented on sound. The grammatical rule that a sentence requires a subject and a predicate is not a content-related, “inner” requirement based upon certain connections between component expressions. It only requires a habitually familiar sound pattern, whose role as a standard, just like the order of the alphabet, is historically explicable if one can explain it at all. But if there is no semantic connection between sentential components, but only an acoustic habit, then the utterance of a complex sentence, like the recitation of the alphabet, is a succession of actions of the sort Wittgenstein characterized with the example of singing from the score. Our view that a sentence is a whole and is “more” than just the chronological succession of its elements, would be an illusion supported by nothing more than the familiarity of a certain sound, exactly parallel to our familiarity with the series of letters A, B, C…as opposed to the strangeness of the sound of the succession C, A, B… .

These logical conclusions show that the strong reading of the thesis developed here of a purely sound-oriented character of the grammar of a single language (in this case, English) cannot be entirely right, and might not even be what Wittgenstein intended, because he only spoke of the sound as one characteristic of our concept of a sentence. We therefore seek a twofold understanding of the grammatical: on the one hand it should grasp sentences as whole units (not aggregates of the “singing from the score” type); on the other hand it should help us better understand the motivation for Wittgenstein’s thesis that the grammatical concept of a sentence is oriented by (among other things) sound. Only in this way can we hope to do justice to these as yet obscure motivations when it comes to drawing a systematic picture.

In order to render this motive intelligible, we now turn to texts stemming from a slightly earlier time than the preparatory works for the Investigations discussed so far, namely, to Philosophical Remarks (Wittgenstein 1975) and Philosophical Grammar (Wittgenstein 1974). In these works Wittgenstein compares a sentence’s grammatical form, in particular the subject-predicate scheme, with the result of projecting figures from one plane (I) to a second plane (II). He notes that in such a projection one can proceed in more than one way. One possible way would be to decide first for a certain method of projection, say the right-angle (“orthogonal”) projection, and then to carry out this method for the projection of all the figures. Then, when someone is considering the results of the projections, she will be in a position to determine, based on the form of the figures on plane II, at least one aspect of the form of the figures in the initial plane I: in the simplest case a rectangle in I appears as a rectangle in II, a circle as circle, etc.

The situation is different, however, if the person controlling the projection had the intention from the start to make all the figures, whatever their forms on plane I, appear on plane II as circles (or some other single type of form). This could be done by changing the method of projection from case to case. Instead of having one method of projection and the corresponding varied forms we would have various methods of projection and, as a result, figures of a single form. In concluding these considerations Wittgenstein writes:

In order in this case to construe the circles in II as representations of the figures in I, I shall have to give the method of projection for each circle; the mere fact that a figure in I is represented as a circle in II by itself tells us nothing about the shape of the figure copied. That an image in II is a circle is just the established norm of our mapping. – Well, the same thing happens when we depict reality in our language in accordance with the subject-predicate form. The subject-predicate form serves as a projection of countless different logical forms. (Wittgenstein 1974, p. 205)

The last two sentences, which introduce the theme of grammatical form, echo the earlier ideas of the Philosophical Remarks, as this somewhat longer passage shows:

It is like this with reality if we map it onto subject-predicate propositions. The fact that we use subject-predicate propositions is only a matter of our notation. The subject-predicate form does not in itself amount to a logical form and is the way of expressing countless fundamentally different logical forms, like the circles on the second plane. (Wittgenstein 1975, p. 119)

If we consider these passages with the goal of discovering why Wittgenstein belittles grammar, why he dismisses it as a matter of “acoustics,” we could see his claim that the universality of the subject-predicate form actually hides important differences to be central. Wittgenstein locates these differences both in the realm of the “reality” represented, as well as (because of this?) in the realm of “logical form.” But questions remain regarding how these two categories are to be understood and how Wittgenstein takes them to be connected.[2] All that is clear thus far is that the so-called “traditional grammar” of natural languages fails to meet the twin demands of accurately representing reality and of reflecting logical form: it distorts by hiding or doing away with relevant distinctions. When Wittgenstein then says that the subject-predicate form does not in itself “amount to” a logical form, this is akin to saying (like Frege) that it is a task for logicians to make apparent the diversity of the various logical forms (or “forms of reality”), the differences between which have been lost due to the particular “projection methods” that our respective natural languages provide. They have been lost on account of a specific trait of our symbol system, namely that it replaces a variety on plane I with a single grammatical form (or a small number of them) on plane II. On this reading, Wittgenstein would, in the spirit of Frege, appeal for what he calls an “orthogonal projection,” in other words he would call for replacing the traditional subject-predicate grammar with the grammar of a “conceptual notation” (a Begriffsschrift) which follows logical form. This would account for his dismissal of the traditional grammar of natural languages.

Such an appeal would, however, only make sense if its author did not want to completely discredit “the grammatical.” Instead, he must help us to understand the difference between a language that correctly mirrors logical form and one that distorts it – for example, one in which relevant differences are left to guesswork and the forms are in this way reduced to only a few. Must we think of plane I of the projection model as a reality formed without language in order to be able to say what it means to represent it accurately (“orthogonally,” in a “logical language”)? Or is it sufficient for our purposes that we can specify characteristics that a language must have in order to accurately express logical form? And could such logical demands be formulated without recourse to an independently specifiable “structure of reality”? What would the “logical” forms, in this sense, be if they were not the result of mapping something given? On this interpretation, the thesis that the subject-predicate form does “not amount to” a logical form appears to make sense only if no fundamental obstacles stand in the way of realizing the defined goal (like an “orthogonal projection,” or some other distinction of a particular form as “logical”).

Even if one cannot speak of an independently existing “form of reality,” Wittgenstein must be able to explain two things. First, how are forms constituted in such a way that grammar is not merely a matter of acoustics? Second, how can it so constitute itself as to be in some intelligible sense either logically correct, adequate, so that the language exhibits the logical form, or logically false, inadequate, as in the case of the subject-predicate form which Wittgenstein labels as “not amounting to” a logical form? On this interpretation (in which we discount the possibility of being able to exhibit the logical form by reference to the “form of reality”), the model of the two planes is no longer fitting. But we must not stick Wittgenstein with the defense of a theory which the later Frege had already recognized to be questionable (and which he himself criticized many times over), that is, that a language-independent structure of the world is accessible to us directly and without distortion.[3]

Yet our tentative interpretation of the thesis that there is in each case a definite logical form that the subject-predicate form does in many cases not adequately capture faces a problem. It conflicts with the claim, also in the cited text, that there are “innumerable fundamentally different logical forms.” Any grammar, including a logical grammar, can only have a finite number of forms: how, then, can it accurately articulate the logical forms (however they are distinguished) if there is an infinite number of them?

The thesis that there is an infinite number of logical forms reminds one of Wittgenstein’s view that there are countless kinds of words, and, as we will see, the two claims hang together. In Chapter 3, the assertion that there are innumerable kinds of words led us to the conclusion that Wittgenstein could not mean the expression “kind of word” in the usual grammatical sense of “part of speech.” Correspondingly, we might expect that the word “form” in the expression “logical form” is not meant in the sense it is in the expression “grammatical form,” and this indeed could be the case, independently of whether we consider a natural-language grammar or a logical grammar. But if Wittgenstein’s concept of form indeed strays this far from the usual concept, then in his conception a logical and a traditional grammar would not oppose one another, and so neither would a logical and a grammatical form, as in Frege’s writings. It could not be Wittgenstein’s intention in such a situation to side with logic. Rather, the thesis of innumerable different logical forms challenges a concept of form that grammar and logic share, and Wittgenstein seeks to replace it with another concept of form.[4] We must suppose that he had reasons for handling the questions differently (insofar as he addresses them at all) where other philosophers (such as Frege and Russell) were led to make the step away from a traditional and toward a logical grammar.

So we find that (so far as Wittgenstein’s positive attitude is concerned) there are two different tendencies indicated by the previous two cited text passages: (1) talk of innumerable logical forms suggests that one must give up completely on the idea of “logical form” or else wholly rework it, while (2) the picture of the multiple possibilities of projection of thought suggests there is something “in reality” on which a logical grammar can orient itself. The second reading, however, is hardly plausible as an interpretation of the late philosophy of Wittgenstein, inasmuch as he always fought against the idea that there is something on which grammar can orient itself. The first reading, on the other hand, carries with it the problem of explaining how we can hold any conception of form that is fit to describe what, according to this picture, appears to be the result of the “projection”; what can “forms” possibly be, if there is an infinite number of them?

In order to understand what lies behind the contradiction brought to light here, and in order to correctly assess which side Wittgenstein takes, it is helpful to look at the wider context in which the discussion of the picture of a projection method takes place. In the pertinent passage of the Philosophical Remarks, Wittgenstein addresses doubts that he has concerning Russell’s suggestions for logical standardization, and he considers the sentence “I see a circle on a red background.” He notes that Russell would handle this sentence as an existential proposition (“there is something such that it is a circle and it is on a red background”) and that this existential proposition would be treated as a denial of a general proposition (“it is not the case that for all x it is false that x is both a circle and x is on a red background”). Now Wittgenstein wants to insist that the generality of his sample sentence consists in leaving open some possibilities (e.g., color and size of the circle), and he asks critically what this kind of generality has to do with a “totality of objects,” to which a speaker makes reference if she uses Russell’s form of expression. On the basis of this example Wittgenstein makes an appeal for distinguishing different kinds of generality; he confronts the undifferentiated logical norms of Russell’s language with the differentiation in possibilities of expression found in natural languages, and suggests that the reader take this as an argument that calls Russell’s standardization into question.

Wittgenstein’s next step is to consider a possible objection to this criticism. According to this objection, his differentiation requirements are unjust when applied to Russell’s standard form, because it is characteristic for natural languages (and probably for languages in general) to be able to express very different things using only a few forms. Thus English can “express everything by means of nouns, adjectives, and verbs.” This self-introduced objection he now counters with: “…we can only say that then it is at any rate necessary to distinguish between entirely different kinds of nouns etc…”. (Wittgenstein 1975, p. 118)

In reference to the example, this means that even if we were to choose Russell’s form of representation (because, despite its limited forms of expression, we find it powerful enough for our practical purposes) we must recognize that quite different kinds of generality get represented by one and the same Russellian form of expression. There are differences in meaning that are not reducible to differences in content between individual words, but which at the same time are not captured by the forms of a Russellian language (despite the fact that they are differences in “judgeable content,” not just differences in the intended illocutionary role, and therefore in principle do belong to the realm that Frege’s and Russell’s forms were meant to treat).

But why is it, in Wittgenstein’s opinion, “necessary” to distinguish, for example, different kinds of nouns; and by “distinguish” does he only mean that one should notice these differences and take them into account (e.g., in a piece of reasoning), or does he mean that one should make these “word types” recognizable by their outward form?

His primary goal is apparently to make us aware of the differences in possibilities of use of an expression or of a type of expression, differences of the kind he discusses in reference to Russell’s notation. As an example he gives the possibility of using a general expression either in reference to a totality or without such a reference. Supposing we achieved a consensus concerning the differences he points out, would Wittgenstein be prepared to simply differentiate between types of use of an expression, or is he calling for a change in grammar when he demands that one must distinguish “types of nouns,” etc.?

As grounds for the thesis that a differentiation is necessary, he first offers: “…since different grammatical rules hold for them. This is shown by the fact that it is not permissible to substitute them for one another.” Wittgenstein considers the permissibility of substitutions as a criterion of whether two words belong to the same “grammatical” (in his sense) “kind.” He shows this a few lines later with an example: one can indeed say “take a measuring stick and check whether that is a circle or an ellipse,” but not, “take a measuring stick and check whether that is a circle or a hat.” Consequently, there are different grammatical rules for the words “hat” and “ellipse” and “this shows that their being nouns is only an external characteristic and that we are in fact dealing with quite different parts of speech [German: ‘Wortgattungen’].” (Wittgenstein 1975, p. 118).

If we were willing to follow Wittgenstein’s understanding of the term “Wortgattungen” as it is expressed in this statement, then we must also say that the words “flower” and “rose” belong to different “kinds of word.” Because one can say: “look and see whether that is a tulip or a rose,” but not: “look and see whether that is a tulip or a flower.” And Wittgenstein (1975, p. 118) says generally: “The part of speech (‘Wortgattung’) is only determined by all the grammatical rules which hold for a word, and seen from this point of view our language contains countless different parts of speech (‘Wortarten’).”

There follows the comment that “to give a name” means something different each time, depending upon whether we are naming a body, its color, its form, etc., and then he brings the picture, discussed above, of a projection method, a picture that confronts the undifferentiated subject-predicate form of natural languages with the innumerable and fundamentally different “forms of logic.” Next Wittgenstein offers the thesis that Frege’s distinction between concept and object is nothing other than the distinction between predicate and subject. (Wittgenstein 1975, p. 119; cf. Wittgenstein 1974, p. 205) To this distinction, in turn, he does not want to grant any special status that it might be thought to have simply on account of its special, “logical” content. He writes: “When Frege and Russell talk of concept and object they really mean property and thing; and here I’m thinking in particular of a spatial body and its color.” (Wittgenstein 1974, p. 202) And a little later:

If a table is painted brown, then it’s easy to think of the wood as bearer of the property brown and you can imagine what remains the same when the color changes. (Wittgenstein 1974, p. 205)

According to this, the universality of the subject-predicate form (as well as the object-concept form) is just the result of a declaration that a particular form should serve as a standard, even though that form originally served to express a particular content (or a particular type of content), with the result that this standard form is now used for every or nearly every content. And thus we complete a circle back to the beginning of the passages discussed here: Wittgenstein’s thesis that the subject-predicate form does not amount to a logical form refers not only to the subject-predicate form of natural languages, but also to the standardization of the “logical grammar” of Frege and Russell. Neither “grammar” manifests in its form what Wittgenstein called the “logical form” of the expressions in question. He treats “logical form” in this peculiar sense as something that can be characterized by rules; and he refers to these rules in an equally unconventional way as “grammatical rules.” This is in keeping with his unusual use of the term “word types” (“Wortarten,” “Wortgattungen”).

As a first step toward clarifying the ambiguities we have turned up in the image of a method of projection, especially the ambiguity involved in Wittgenstein’s goal (does he intend to improve on Russell’s standardization, or revise the concept of logical form perhaps by reducing it to absurdity?), we can note that he did not attempt to bring a language-independent “reality” to bear as the standard by which to critique the undifferentiated character of grammatical-logical forms. Instead, he points to differences in the use of expressions. In marked contrast to the usual terminology, he calls all rules (which he assumes to be either explicit or at least recognizable, i.e., able to be made explicit) that concern such differences in use “grammatical” rules, and he stipulates that they belong to the characterization of what he calls “logical form.” So when he says that the schematics of “subject-predicate” and “concept-object” do not amount to a logical form, he does not mean to imply that substituting these schemata by a number of finer-grained ones would do the job. Rather they do not amount to a logical form because they do not express the differences that result from the rules governing their use. These differences remain invisible in the concept scripts of the types discussed. Therefore, as expressions of “logical forms” in Wittgenstein’s very special sense, what these concept scripts can do is quite limited; their forms are, in this sense, incomplete.

The type of differentiation that Wittgenstein has in mind here is made clearer in the passage discussed above from the appendix to Philosophical Grammar. There, it becomes clear that he is not proposing to refine Russell’s or Frege’s form of notation in order to remove the alleged incompleteness. The context here again is the relationship between the subject-predicate form and Frege’s distinction between object and concept, and the theme of the discussion is the question of what an object-name is. Wittgenstein (1974, p. 202) says that a name “N” can be given to a thing through an ostensive explanation, and this explanation can be grasped “…as a rule substituting the word ‘N’ for a gesture pointing to the object,… .” But that would mean, he argues further, we could substitute such a gesture for any typical use of the name. Yet this is obviously not true of our use of names. Wittgenstein (1974, p. 202f.) continues:

…if N goes out of the room and later a man comes into the room it makes sense to ask whether this man is N, whether he is the same man as the one who left the room earlier. And the sentence “N has come back into the room” only makes sense if I can decide the question. And its sense will vary with the criterion for this being the object that I earlier called ‘N’. Different kinds of criteria will make different rules hold for the sign ‘N’, will make it a ‘name’ in a different sense of the word. Thus the word ‘name’ and the corresponding word ‘object’ are each headings to countless different lists of rules.

Wittgenstein would say that characterizing an expression as belonging to the word-type “name” involves clinging to its external features just as characterizing it as a “noun” does. Here, as in the case cited above, he thinks that it is necessary to distinguish kinds (of names, of nouns), “since different grammatical rules hold for them.” Whereas in the case of nouns he takes a lack of inter-substitutability to indicate that different rules are at work, in the text just cited he works out more exactly what he is thinking of when he speaks of rules.

First there is the rule of replacement of an indicative gesture by an expression “N.” To understand the meaning of this expression means to have mastered a rule. However, since we also employ names in the absence of the named object, knowing the meaning of the expression “N” also involves knowing the criterion by which we judge whether a given object is N or not. Insofar as there are different types of criteria (Wittgenstein gives the example of criteria by which we determine which of two merging rivers is the same as the resulting river), there would be different types of rules holding for the different types of names. Recognition of these rules is part of what we call the recognition of various types of names: these are, for example, river names, personal names, etc. The ability in question does not just concern the knowledge of the meaning of one particular name, like “Thames.” And to the extent that different kinds of rules are concerned, we are dealing with different types of words.

We can easily see that this distinction between types of words goes far beyond the school grammar term “parts of speech.” But whether the classification of a word as a “name” therefore deserves to be labeled a “superficial feature” (as if it were just a matter of sound) must remain as of yet an open question. One might oppose this by urging that these classifications, regardless of how “coarse” and inexhaustive they may be for characterizing the role of a word in a speech act, could still be decisive for the role that a word (so classified) plays in a sentence relative to the other words in that sentence.

This discussion of names provides an important clue for resolving the ambiguity in the image of various possibilities of projection. When Wittgenstein says that we give solid spatial objects names whose application rests on specific criteria of identification, which may, however, break down in cases of interpenetration (e.g., when two rivers run together), and when he then (Wittgenstein 1975, p. 203) speaks of the possibility that “…I go on to introduce a totally new criterion of identity…”, he indicates an active step which is, moreover, freely chosen: different criteria can be set to determine which name a confluence of two rivers shall bear. The criterion can be, for example, as Wittgenstein suggests, the direction of flow, but we might dissent from this and make it the rate of flow. So the rules that constitute different kinds of names (personal names, river names, etc.) are not determined by “reality.” Here it makes no sense to say that the distinctions between various parts of speech (as traditionally classified, or in his more subtle way) are logical distinctions whose rules (in the sense of an orthogonal projection) take reality as their point of orientation. We cannot read off from the behavior of the rivers which grammatical rules for naming rivers should hold. And this is not the only place where it is difficult to give a criterion for how to determine what is the “conceptually required.” When we attempt to name rivers as we do people, and our familiar criteria of identification prove inapplicable, we must determine new criteria ourselves, by taking a new and groundbreaking projective step.

If this is an accurate portrayal of Wittgenstein’s vision at the time he drafted the appendix to Philosophical Grammar, and if we are justified in transferring his reflections on the differentiation of types of words to complex-building forms such as the subject-predicate form, then we could set aside as inadequate the interpretation of the picture of projection methods that we considered above. Wittgenstein’s statement that the subject-predicate form does not amount to a logical form cannot, then, be read as expressing the opinion that there can be a “logical grammar” which would accurately represent “reality” (or “thought”), in the sense of an orthogonal projection. The distortion, the assimilation that takes place in language through the ubiquitous use of, for example, the subject-predicate form, cannot be avoided (as in the case of the different figures all projected as circles) simply by accepting only “orthogonal projections.” In the case of the projected figures, we recognize the actual figures on plane I, and we have the choice to project them either true-to-form (differentiated) or de-formed (standardized). And it is precisely this choice that we apparently do not have in language. The “logical form” which concerns Wittgenstein appears, moreover, to be impossible to represent in any usual grammatical or logical sense. The examples already given suffice to show that the consequences of the “totality of rules,” which he claims we must respect, cannot be captured in such a way that they can be read off from the forms of expressions.

Notes

1 German: “Es verhält sich so und so.”

2 This seems to be in accordance with Frege’s assertion that the grammar of a natural language is not explicit, and its forms are therefore ambiguous.

3 Cf. Wittgenstein’s and Waismann’s remarks on “meaning-bodies” quoted in Chapter 4, pp. 55 and 64 (note 6).

4 This reflects his diverging use of “grammar” and his use of the calculus analogy in describing the workings of language; the “use in the calculus” is inclusive of non-programmed (non-schematic) steps. See Chapter 12.

References

Wittgenstein, Ludwig (1974) Philosophical Grammar (ed. Rush Rhees, trans. Anthony Kenny), Oxford: Blackwell.

Wittgenstein, Ludwig (1975) Philosophical Remarks (ed. Rush Rhees, trans. Raymond Hargreaves and Roger White), Oxford: Blackwell.

6

Projection

No Mere Mapping but a Creative Activity

In the light of the previous chapter, we must now look for a new understanding of the picture of a “projection”; and indeed the example of river names suggests a new way of speaking of projections that is completely different from the sense considered in Chapter 5. It is not that an independent and diversely formed pre-existent reality is projected onto the plane of language, in the course of which some differentiation is inevitably lost, so that the same few forms of speech always appear, regardless of the “content.” Rather an existent form of expression (e.g., the kind of words used at first only as proper names for persons) is used in a new context of application, for example, in creating maps of rivers, and is thus “projected” onto new kinds of objects. The starting point of a projection in this sense is not a pre-structured reality, waiting to be articulated in language. The uniformity of grammatical forms is not the result of a reduction of an independently existing diversity to a limited number of linguistic forms. Rather, the starting point of a projection is a pre-existing grammatical form, at first necessarily specific to a particular area of discourse, which is then carried into new areas of discourse in a free, spontaneous act of creative imagination. This act was unforeseen in the previously available ways of speaking (i.e., available rules) of the language, but its freedom is limited, of course, by internal or external constraints of the situation and by the need to be understood. The recognition of the “logical form” in Wittgenstein’s new and unusual sense consists, then, of two components: the recognition of the grammatical form in the traditional meaning of the term on the one hand (it mirrors the original and previously available means of discourse), and the recognition of the availability and special sense of the projection on the other. The direction of the projection has turned one hundred and eighty degrees: it no longer goes from “reality” to language (whose structure, on the orthogonal view, corresponds to the structure of the “reality”), but instead goes from the language (from a particular language game) to areas of “reality” to which we have not yet given voice in language.

This is the understanding toward which Wittgenstein was working in the course of the clarificatory process documented in the (by him) unpublished typescripts, and this is clearly indicated by a passage from the Brown Book. The fact that he already uses the word “metaphor” there speaks in favor of the view that the direction of projection is from familiar forms of speech (e.g., the possibility of introducing names of people) to new areas of application (naming of rivers by modifying identity criteria): an available form of expression is transferred onto a new kind of case. We see and solve a new problem in the light of and with the help of an old linguistic form.[1] Wittgenstein (1958, p. 117) writes:

There are…various reasons which incline us to look at the fact of something being possible, someone being able to do something, etc., as the fact that he or it is in a particular state. Roughly speaking, this comes to saying that ‘A is in the state of being able to do something’ is the form of representation we are most strongly tempted to adopt; or, as one could also put it, we are strongly inclined to use the metaphor of something being in a particular state for saying that something can behave in a particular way.

We articulate the fact that someone is able to do something, e.g., to speak German, not only with the help of the word “able” but by describing the person as being in a particular state: she is “in a position” or “ready” to speak German. We do not articulate these facts in this way in order to pick out some occurrent or hidden feature of the person; it is merely part of our form of representation. We transfer the expression “state” or “position” from a case in which we could describe what it indicates (e.g., the spatial relations that the parts of a machine have to one another, or the bodily position of a person who believes that a certain object is within her reach) to a case in which we, literally speaking, know nothing of a “state” or a “position.” When we say that someone is “in a position to speak German,” we are not referring to the position of certain parts of the person’s brain relative to one another, we are using an expression originally deployed in one context in a second, a new sense. By doing so, we are seeing and articulating that which we express in a particular way, in a particular image: we are seeing our experiences of the person’s successful actions in the image of a state of that person. Wittgenstein speaks here of a metaphor: an expression that ordinarily would express A (the spatial situation of material parts) is used to articulate B (an ability to do something). In the present case B can be spoken of in two ways: with the word “ability” and with the phrase “in a position to.”

More important for Wittgenstein’s train of thought are those cases in which B, in the language under consideration, cannot be articulated “literally” (in which case there would be a choice) but can only be articulated by means of an expression which in other contexts is known to articulate A. In these cases he does not want to say that one is using an expression in a metaphoric way, because the goal of this kind of “transference” cannot be attained in any other way except with the help of this newly applied expression (or possibly another expression that in this case is also used in a new way). Wittgenstein speaks here of a “secondary” instead of a “metaphoric” meaning,[2] and as a somewhat odd but very clear example he offers this:

Given the two concepts ‘fat’ and ‘lean’, would you be inclined to say that Wednesday was fat and Tuesday lean, or the other way round? (I am strongly inclined towards the former.) Now have ‘fat’ and ‘lean’ some different meaning here from their usual one? – They have a different use. – So ought I really to have used different words? Certainly not. – I want to use these words (with their familiar meanings) here. (Wittgenstein 2009, Part II, § 274)

What is important here is that Wittgenstein rejects the objection that he mentions, namely that in such a case one should simply use other words. This would only be justified if the other words gave the “real semantic relationships,” which is clearly not possible in cases of “secondary meaning,” where no other modes of expression are in use. The transference in these cases carries nothing extraneous, that is, no embellishments.[3]

This is clearly expressed in the following sentences, which deal with a possibility of articulation, and which is not as odd as the classification of days of the week as “fat” and “lean”:

But how about an expression like this: ‘When you said that, I understood it in my heart’? In saying which, one points at one’s heart. And doesn’t one mean this gesture? Of course one means it. Or is one aware of using a mere picture? Certainly not. – It is not a picture that we choose, not a simile, yet it is a graphic expression. (Wittgenstein 2009, Part II, § 26)

A simile in the sense of a chosen image is a comparison: it serves, for example, as an illustration, as embellishment, or some other secondary purpose. In a comparison, both objects to be compared can be independently characterized, and the comparison says something about their similarity or dissimilarity. For a projection through which a secondary meaning is constituted, it is instead typical that it creates for the first time a possible articulation: the “figurative expression” is used to open up an area of discourse that otherwise, without the projective step, would not be available. Wittgenstein expresses this succinctly in the following passage:

Suppose we always expressed the fact that a man had an intention by saying “He as it were said to himself ‘I will…’” – That is the picture. And now I want to know: how does one employ the expression ‘as it were to say something to oneself’? For it doesn’t mean: to say something to oneself. (§ 658)

The question concerning the “logical form” of the expression “to, as it were, say something to oneself” is not answered by giving an expression that, by abstaining from an image, correctly mirrors the “real,” pre-established semantic relationship, in the sense of an “orthogonal projection.” It is difficult to imagine what it could mean here to determine (by criteria other than those of the correct projection of the relationships at hand) what would be a logical or conceptually “appropriate” form. Instead, what was known as “logical form” in the preliminary work cited above is provided by making plausible the transference step; and this happens when it is said or demonstrated how the figurative expression is used.

It is only consistent that Wittgenstein concludes that a “form of representation” cannot be wrong, although we are sometimes inclined to draw the wrong conclusions from it – for example, when we take it as a starting point for asking wrong-headed questions. Wittgenstein imagines that someone might take offense at the partial expression “I am having” in the expression “I now have such-and-such a visual image,” because, apart from the thing being imagined, there is nothing there that could correspond to this “having.” He writes:

You mean: the words ‘I have’ are like ‘Attention please!’ You’re inclined to say it should really have been expressed differently. Perhaps simply by making a sign with one’s hand and then giving a description.

And then he counters this with:

When as in this case, one disapproves of the expressions of ordinary language (which, after all, do their duty), we have got a picture in our heads which conflicts with the picture of our ordinary way of speaking. At the same time, we’re tempted to say that our way of speaking does not describe the facts as they really are. As if, for example, the proposition ‘he has pains’ could be false in some other way than by that man’s not having pains. As if the form of expression were saying something false, even when the proposition faute de mieux asserted something true. (§ 402)

Someone who raises Wittgenstein’s fictitious objection against the form of expression “I am having such and such an image” and who holds that one should express it another way has, as Wittgenstein says, another competing picture in mind. Such a person would probably say that to have an image or a pain is not like having gold teeth; an image is not like a thing that one can touch, it is more like a passing immaterial painting, so that it would be more fitting to signal its presence by a hand gesture or an expression like “I say!” followed by a description of the event.

Now Wittgenstein would not deny that the sense in which we have images and pains is different from the sense in which we have gold teeth. Rather, he counters such an objection by drawing our attention to the fact that expressions of the type “I have a toothache” perform their office: to understand them involves understanding this difference, that is, it involves understanding the accompanying projective step. And here again it does not seem very promising to search for an expression that not only “performs its office” but also provides a better conceptual fit in some straightforward sense. Thus, it is a mistake to attack a form of expression as if it were a proposition. Viewed the other way around, this means that the alternative picture proposed (i.e., that having an image is akin to seeing a painting in passing) equally does not have (as a picture) the character of a proposition, the truth of which can or must be defended against the truth of the picture of “having” a toothache. Wittgenstein states clearly:

The one party attacks the normal form of expression as if they were attacking an assertion; the others defend it, as if they were stating facts recognized by every reasonable human being. (§ 402)

Sometimes Wittgenstein himself turns against certain pictures, and one may be tempted to conclude that he holds them to be incorrect as forms of representation. In connection with the question of whether, in remembering, an inner process takes place he says:

The impression that we wanted to deny something arises from our setting our face against the picture of an ‘inner process’. What we deny is that the picture of an inner process gives us the correct idea of the use of the word ‘remember’. Indeed, we’re saying that this picture, with its ramifications, stands in the way of our seeing the use of the word as it is. (§ 305)

Indeed, Wittgenstein does turn against a picture here; but only insofar as we are inclined to draw a false conclusion from it – namely, that we are here making linguistic reference to “inner processes,” just as we would make reference to outer processes, with the only difference being that the inner processes have been less well researched than the outer ones. We would thereby deceive ourselves over the application of expressions such as “to remember” and “the mental process of remembering” in cases when they are unencumbered by philosophical and scientific speculation: both say the same thing, but the one form expresses it by picturing it as a process which (particularly when we practice philosophy or psychology and are not being careful) sends us off on a vain search for the peculiar, enigmatic and elusive nature of this “inner process.” This error of judgment is supported by the thought that words always refer to objects (which they either name or classify), and that the only thing in need of clarification are the particular qualities of the less easily accessible objects. Wittgenstein suggests instead:

The paradox disappears only if we make a radical break with the idea that language always functions in one way, always serves the same purpose: to convey thoughts – which may be about houses, pains, good and evil, or whatever. (§ 304)

On the one hand, Wittgenstein does not want to deny “that there is a mental process” (§ 306), yet on the other he appears to be denying exactly that, in claiming that the expression “mental process” does not refer to something in the same way as does the expression “bodily process” (e.g., the healing of a wound). This paradox disappears only if we refrain from concluding that, since the language game uses the picture of an inner process, there must be a “yet uncomprehended process in the yet unexplored medium” (§ 308), of which we only know at this point that it is a “process.” This is a false conclusion Wittgenstein says we can avoid if we keep in mind how we apply talk of inner processes:

Why ever should I deny that there is a mental process? It is only that ‘There has just taken place in me the mental process of remembering…’ means nothing more than ‘I have just remembered…’. To deny the mental process would mean to deny the remembering; to deny that anyone ever remembers anything. (§ 306)

When one wants to achieve a better understanding here one must ask questions about the use of a form of expression, not questions about a fundamental, “real” structure of thought (that would be made visible through an “orthogonal projection”), nor questions about unexplored facts concerning the peculiar nature of an unapproachable realm of objects. In reference to the expression “to have an opinion,” Wittgenstein writes:

Other questions that go deeper are: What, in particular cases, do we regard as criteria for someone’s being of such-and-such an opinion? When do we say that he reached this opinion at that time? When that he has altered his opinion? And so on. The picture that the answers to these questions give us shows us what gets treated grammatically as a state here. (§ 573)

This passage again shows the constitutive character of projection. For we cannot answer Wittgenstein’s last question – what it is that grammar treats as a state – with a sentence of the form “in reality what we are talking about is a…, but English grammar treats it as a state.” The type of representation cannot be replaced by a “correct” representation, an “orthogonal projection.” If a way of speaking requires explanation, this explanation can only consist of an explication of its usage. We might bring in another language game as a point of comparison – either one thought to be equivalent, or one that appears to us foreign or even fictitious – but not even doing this could lay claim to reveal the “true relations in the realm of thought” in a language-independent sense. Wittgenstein expressly states in another passage: “Regard the language-game as the primary thing. And regard the feelings, and so forth, as a way of looking at, interpreting, the language-game.” (§ 656)

This means: the entities (feelings, etc.) as such are first constituted by the language game; as entities they are “grammatical fictions” (§ 307). This does not, however, license the claim that there aren’t “really” any feelings, for the language game has a “point” (§ 564), an “importance”[4] for those who can play it; it is not a “mere game” and in this sense it gains legitimacy beyond itself as a “merely linguistic” activity. Because he does not deny these (from his standpoint self-evident) facts, Wittgenstein uses them to ward off the accusation that he is a nominalist.[5] But the only way to find what concerns us in the activities of the language game, which create these grammatical fictions, is to look at the context, with an eye to the needs, requirements, and motivations that enable those activities to succeed. It is in this sense that Wittgenstein claims that the language game (and this is always the unity of linguistic and extra-linguistic actions) is “the primary thing.”

If we want to learn a new application of an old form of expression – that is, to understand a projection of the type exemplified by the transition from “he said to himself” to “he said, as it were, to himself” – we must bring our imagination to bear. In a previously cited passage[6] from the Investigations, in which he is arguing against the idea that a meaningful use of a sentence consists in every word standing for something, Wittgenstein writes: “One fails to bear in mind the fact that one calculates, operates, with words, and in due course transforms them into this or that picture.” (§ 449)

Here “calculating” (think of the transition discussed above from “! five slabs” to “ five slabs”[7]) is mentioned in the same breath as the transition of an existing form of expression into a new, sometimes figurative, application (“he said to himself” – “he said, as it were, to himself”). Although, as we have seen, he sometimes neglects the first type of transition, both types are in Wittgenstein’s view typical in natural languages. A transition of the second type we recognize as a “projection” whose particular character consists in its being linguistic – an operation working with words which, in many cases, also involves a transition to a picture – and Wittgenstein draws upon this dual character as typical of the imagination. In “Remarks on Frazer’s Golden Bough” (Wittgenstein 1993, p. 131) he says:

If one holds it as self-evident that people delight in their imagination, one should bear in mind that this imagination is not like a painted portrait or plastic model, but a complicated pattern made up of heterogeneous elements: words and pictures. One will then no longer place operating with written and phonetic symbols in opposition to operating with ‘mental images’ of events.

Following the conception Wittgenstein expresses here, the ability to imagine is not a capacity to be led by an inner realm of uncontrolled waves of images prior to the ability to think; it is rather quite close to language, bound together with the ability to use words, and is therefore also an ability to act. Interpreted in the light of the passage just cited (§ 449), we can tentatively say that the “operations” of the imagination encompass a spectrum which includes, at one extreme, transitions so simple as to be scarcely noticeable as such (like calculations) and which we tend to see as nothing more than mere rule following. We imagine the rules to be like a track that has already been laid down and which stretches into the limitless future from the moment those rules are first learned. Here, we can once more use the oft-discussed example of the transition from “! five slabs” to the form “ five slabs” or to “! five slabs there.” For it appears that the type, the “rule” of this transition has already been understood on the basis of examples, and now the speaker is simply using the learned pattern in new but “similar” cases.[8] These steps have a certain similarity to the operations in a calculus: they can be portrayed schematically.

At the other end of the spectrum, we have projective steps such as that from “he said to himself” to “he said, as it were, to himself,” or that from “I understood” to “in my heart I understood.” Here our starting point is an initial expression, which may itself display the sort of complexity whose point must be understood through projection steps. The new projective step then moves freely, and cannot be gleaned from antecedently familiar examples. Moreover, this projective step must not only be created by the speaker but also reconstructed by the hearer. Such a projective step is not of a schematic nature. The considerations Wittgenstein discusses here indicate that the imagination (projection) is intertwined with calculation and that this should be considered a characteristic feature of natural languages: agreement about the success of the ongoing shared activities demands at every step the ability to project, to transfer – it demands creative imagination. Furthermore, such agreement then enables the construction of complex linguistic and non-linguistic activities, whose patterns can be applied schematically in new cases; new structures are built according to rules (“calculation”). If these rules are to hand and mastered they invite transformations, projections, “misusages”; – that is, they invite new, schematically unfathomable moves. These can in turn be differentiated, that is, expressed in new forms, which then allow new schematic steps, and so forth.

Assume that the picture of natural languages sketched by Wittgenstein is accurate. The typical reason for the “undifferentiated nature” of grammar (in the traditional sense) is then to be seen in the fact that forms of expression are constantly being used in novel ways in the evolution of languages, ways that point beyond those that have gone before. The constitutive case, one in which the new application cannot be replaced by a “literal” formulation already in existence, is not only characteristic for natural languages but is also, quantitatively speaking, the dominant and in this sense the “normal” case. But might one not see in this (despite Wittgenstein’s protestations to the contrary) an inadequacy of natural languages? Shouldn’t it be possible to rectify this through the construction of a concept script? Natural language might be left unchanged, but should it not be possible that a new medium, a concept script (to be developed following Frege’s ideas and expanding them) would be free of this imperfection? The inadequacy, one might be inclined to say, consists in using one form for many and diverse areas of application, and to rectify this one might demand that every new kind of application of a form of expression display its uniqueness through an external modification of “form.” Wouldn’t the realization of this demand represent a continuation of Wittgenstein’s thought (in that we are concerned to consider the diversity of possibilities of expressions) in the spirit of Frege (who wanted to make language explicit and unambiguous)?

But here an objection might be raised. Speakers (and hearers) of natural languages appear to benefit from understanding the analogy between the uses of a single expression (or form of expression) in a variety of different cases. Yet pursuing the suggested project would result in a language where all such analogousness would be eliminated. Would this be a loss or a benefit for communication? It can look like a benefit, since if one were to create a new word or a new grammatical construction for every newly realized possibility of articulation (won in natural languages by steps of projection), one would thereby capture the respective specific character that a plurality of undifferentiated “misuses” would leave unarticulated. But, on the other hand, the result of such a step would be a horrendous increase in expressions, the magnitude of which might endanger the very purpose of language, just as John Locke (1975, III, § I ff.) surmised would happen if every individual thing should be given its own name, shared by no other thing.

Whatever the chances are for such a project, Wittgenstein, at any rate, does not suggest to Russell a new notation for his type of generality. He also refrained from introducing variables of a new type for river names, for example. It was not his concern in his later work to attempt to reform or to regiment language, but rather to understand the actual workings of natural languages. Considerations up until this point have shown that the whole of what Wittgenstein misleadingly calls “logical form,” and later simply “grammar,” cannot be, in the case of “living” natural languages (i.e., barring any synchronically “frozen” state of a language), represented in grammatical forms, either in a traditional form or in a logical one. Rather, what he calls “grammar” can only be made explicit through grammatical forms together with a wealth of additional illustrative comments referring to usage.

This “grammar,” in Wittgenstein’s deviant sense (that is, the interplay of form and the always changing and growing modes of application, of imagination and calculation), is not hidden, and he can therefore say:

Philosophy just puts everything before us, and neither explains nor deduces anything. – Since everything lies open to view, there is nothing to explain. For whatever may be hidden is of no interest to us. (§ 126)

The only thing lacking is, in Wittgenstein’s opinion, an overview of the workings of our language. This overview can, he claims, be gained if we become aware of something by putting together a relevant collection of examples, examples of a feature that lies open to plain view, and is in a practical sense quite familiar to us. Theoretically, an insight into the workings of our language is all too often denied us because it is blocked by traditional pictures and prejudices. That is why philosophy plays such a decisive, critical role in its apparently quite conservative “mere description”: because it must point out how to distinguish those cases in which language “works properly” from those in which it leads us astray by “going on holiday” (§ 38). This sometimes overlooked critical impulse of Wittgenstein’s is expressed clearly when he writes (Wittgenstein 2005, p. 302e (§ 87)), for example:

If I rectify a philosophical mistake and say that this is the way it has always been conceived, but this is not the way it is, I must always point out an analogy according to which one had been thinking, but which one did not recognize as an analogy.

Notes

1 Compare the very useful definition from Soskice (1985, p. 15); “Metaphor is that figure of speech whereby we speak about one thing in terms which are seen to be suggestive of another.”

2 Wittgenstein, 2009, part II, §§ 276f.; compare the suggestion in Schulte (1989).

3 Compare also the guiding exposition in Goodman (1976), Chapter 2.

4 Wittgenstein Ms. 129, p. 193. Citation after Baker and Hacker (1980), p. 586.

5 Wittgenstein Ms. 129, p. 193.

6 Cf. above, p. 63.

7 Cf. above, p. 49.

8 That even this seemingly certain case is, in fact, no more certain than any other repeated success is one of the points of Wittgenstein’s discussion of rule-following. The same point can be expressed in the current context in the thesis that even the most tested application of a rule always requires imaginative steps.

References

Baker, G.P. and P.M.S. Hacker (1980) Wittgenstein: Understanding and Meaning: An Analytical Commentary on the Philosophical Investigations, vol. 1, Oxford: Basil Blackwell.

Goodman, Nelson (1976) Languages of Art: An Approach to a Theory of Symbols, Indianapolis IN: Hackett.

Locke, John (1975) An Essay Concerning Human Understanding (ed. P.H. Nidditch), Oxford: Clarendon.

Schulte, Joachim (1989) Wittgenstein’s notion of secondary meaning and Davidson’s account of metaphor – a comparison, in The Mind of Donald Davidson (Grazer Philos. Studien Bd. 36) (eds J. Brandl and W.L. Gombocz), Amsterdam: Rodopi, pp. 141–148.

Soskice, Janet Martin (1985) Metaphor and Religious Language, Oxford: Clarendon.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1993) Bemerkungen über Frazers Golden Bough / Remarks on Frazer’s Golden Bough, in Philosophical Occasions 1912–1951 (ed. James Klagge and Alfred Nordmann), Indianapolis IN: Hackett, pp. 118–155.

Wittgenstein, Ludwig (2005) The Big Typescript: TS 213, German-English Scholar’s Edition (ed. and trans. C. Grant Luckhardt and Maximilian A.E. Aue), Oxford: Blackwell.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

7

The Sound of a Sentence II

Surface Grammar

We can now take a second look at the question of how to understand Wittgenstein’s thesis, presented in Chapter 6, of grammar being a matter of sound. He repeats it in the Investigations in the following form:

In the use of words, one might distinguish ‘surface grammar’ from ‘depth grammar’. What immediately impresses itself upon us about the use of a word is the way it is used in the sentence structure, the part of its use – one might say – that can be taken in by the ear. – And now compare the depth grammar, say of the verb ‘to mean’, with what its surface grammar would lead us to presume. No wonder one finds it difficult to know one’s way about. (§ 664)

Wittgenstein distinguishes here two areas of what he calls the “use” of a word. First, there is the application of a word in the construction of a sentence, which he calls the “surface grammar.” Second, there is a usage that goes beyond the merely verbal part of language games, the rules governing which he terms “depth grammar.” These latter rules constitute what the preliminary work for the Investigations still referred to as “logical form.”

He indicates what the “surface grammar” of the word “to mean” would lead us to suspect by using a series of questions: If I appropriately say “I remember having meant him” (e.g., as I was waving with my hand), this form of expression suggests that I remember an action, a process, or a state, so that questions as to the beginning or the course of the event would make sense (§ 661). We fall into thinking that this is a report of an action, process, or state, because “to mean” is a verb, and, accordingly, its role in a sentence, as far as we “take it in by ear,” structurally is the same as the role of the verb “to wash” in the sentence “I remember having washed him.” We can now say: The verbal expression is a “form of representation” in the sense discussed above, and when we miss the transferring character – the projection that is involved in this particular use of the verbal form – then we are led into error by the “picture” of an action.

In the case of washing someone we can indeed ask: when did this action begin, how did it run, etc., which is senseless in the case of meaning someone. This senselessness remains invisible if we only consider the use of the word “to mean” in sentence construction, that is, its quality as a verb, and hence merely its ability to enter into certain syntactic connections. It only appears when we pay attention to the application of a complex expression such as “I meant him” in an activity, in a language game. We are considering that aspect of usage that Wittgenstein calls “depth grammar” when we consider this use of the expression in the relevant activities, that is, when we consider not only a speaker’s knowledge of the rules of (school) grammar, but the knowledge of the application of the expression which a speaker must also have in order for us to say that she knows the meaning of the expression “to mean.” Whoever sees this correctly understands the step of “projection” and recognizes how the “form of the expression” contributes to tempt us to see what an articulation is about in a certain way (in our case, to see it as an action). In seeing this, one is able to avoid wrong-headed questions – that is, the sort of questions we tend to ask when we are led astray by the form of representation, for example, when we inquire as to the true nature of the inner process or activity apparently indicated by the word “to mean.”

Now what is the relation between this “depth grammar,” which Wittgenstein often refers to simply as “grammar,” and the field of knowledge that we usually call grammar? In particular, what is its relation to what is commonly called “syntax”? How should we evaluate Wittgenstein’s characterization of traditional grammar as something one can “take in by the ear”? Are we reading him accurately when we say that, according to his view, the parts of a sentence belong together as do the letters of the alphabet (in their conventional order that is independent of any systematic relations), so that sentence structure would be only a matter of familiarity? Is there no “inner” connection of the parts of the sentence? Should we hold that the utterance of a sentence consisting of many words must be described as a sequence of isolated acts, like the singing of a random sequence of tones from a given score?

If the difference between “surface grammar” and “depth grammar” really rests on a projective step, whereby an old form (e.g., “he said to himself,” “he has gold teeth,” “he washed him”) is used for a new purpose (‘he said, as it were, to himself,” “he has a toothache,” “he meant him”), then, in all such cases, there must be an old form that is transferred or projected. Even when it is used in many different ways, the hearer must recognize it as a form that is familiar to her. She must recognize that the difference between the sentences “the child washed the cat” and “the cat washed the child” is something other than the difference between the series of letters “A, B, C” and “A, C, B.” Traditional grammar can describe the form that produces the similarity in sound between “I meant him” and “I washed him”; it speaks of subject and predicate, of an accusative object, etc. When, as in most cases, we are not dealing with idioms (i.e., expressions that do not demand an understanding of their structure) the speaker must recognize these grammatical forms and understand their functions. Our understanding of the “primary” usage of “he said to himself” is incorporated into our understanding of the secondary usage, and this is indicated by the phrase “as it were.”

An understanding of grammatical form in the traditional sense (an understanding which indeed involves sound, but at the same time is not just a recognition of a sound pattern[1]) is an understanding of the function of the words in the sentence, that is, the ways in which and the means by which they build a complex whole, whose content (which in paradigmatic cases the speaker could name if asked) is understood. An understanding of this “function in the sentence” is a necessary but often insufficient condition for an understanding of the linguistic act (the “move in a language game”) executed by uttering the sentence. Recognizing this “functioning of the constituents in the context of a sentence” is a prerequisite for following the projective step, and therefore for a proper understanding of the speech act. Wittgenstein (2009, Part II, § 276) expresses this in speaking of “primary” and “secondary” meanings. He says, “Here one might speak of a ‘primary’ and ‘secondary’ meaning of a word. Only someone for whom the word has the former meaning uses it in the latter.” But he tends to neglect the fact that there is also a parallel phenomenon connected with modes of sentence formation, which concerns semantic structure.

What appeared to us earlier as disregard for the grammatical, as disdain for the area of usage concerned with sentence construction, can indeed now be understood on the one hand as a warning: a similarity in the grammatical functions of two words in various sentences (of the same grammatical sentence form) should not lead one to conclude that there is a similarity in the “states of affairs” allegedly “described,” or that there is a similarity in the “function in the language game” directly attributable to the words. “The baker’s bread,” “the baker’s arm,” “the baker’s pain,” and “the baker’s death” – all these expressions sound alike, the possessive form and even the possessive component expression are shared, but that does not mean that the sense of “belonging” is the same in the case of the bread, the arm, the pain, and the death. There is no grammar-independent sense in which this is so. As a warning against this sort of misunderstanding, one might exaggerate and say that whoever adheres merely to the level of grammatical similarities is stuck at the level of sound.

On the other hand, the word “sound” and Wittgenstein’s analogy to the alphabet should not be taken to mean that our familiarity with the forms of grammar is simply a matter of habituation to a certain order of elements, an order that is freely interchangeable and which has no “inner” aspect. A pie apple is no apple pie and a fleet sailboat is no sailboat fleet. To spell out Wittgenstein’s analogy a little, he must mean that, just as we are accustomed to saying the alphabet aloud in a certain way, so too are we familiar with the forms of expression of our language, for example with the subject-predicate form. We first became familiar with these forms in the course of originally learning how to use them – that is, in learning certain ways of forming linguistic complexes at the level of content. Since then, we have used them as starting points for countless new projections in the most diverse areas of discourse – so much so that, in most (if not all) cases, their projective character is no longer apparent to us. These grammatical forms have separated themselves so far from their various concrete meanings that we perceive them as having a “quasi-formal” character, inasmuch as they range over many quite different kinds of content. The “feeling” that subject and predicate fit together does not rest on a constant fit between, say, object and quality in a language-independent sense, nor on a match between “meaning-bodies.” It does indeed rest upon our familiarity with the medium of our language, but this is a familiarity with complex-building forms, not a mere habituation to an order of sounds in a succession of isolated, context-independent elements. It is a familiarity with the sense of “primary” ways of conjoining words, as well as with the functions of countless projections of the most various kinds, all of which bestow sense and open up new ground.

Note

1 R. Carnap (1964, p. 1f.) expressed the idea that the constitutive “rules of form” of natural languages are “formal” in the sense that they do not make reference to the meanings of signs. In this sense he says “…that the word-series ‘Pirots karulize elatically’ is a sentence, provided only that “Pirots” is known to be a substantive (in the plural), “karulize” a verb (in the third person plural), and “elatically” an adverb.” (p. 2). But we should see here that in judging it to be a sentence no reference is made to what the imaginary words stand for, but that it is an understanding of the meanings of the grammatical signs they bear by which the hearer identifies their classifications as “noun,” “verb,” etc. So these signs do have a meaning for the speaker of a natural language. The traditional way of speaking of “grammatical forms” does not refer to forms aside from any and all content. The recognition of forms in this sense is always bound up with knowledge of paradigmatic examples of members of each class of form. This is not to deny that it is possible, after the construction of an appropriate type of “language,” to consider it in a “purely formal” way, as Frege has shown. This means: we only grasp a sequence of sounds “by ear” as a sentence if we understand the content of the “appropriate rules” and classifications of forms that Carnap speaks of here.

References

Carnap, Rudolf (1964) The Logical Syntax of Language, London: Routledge & Kegan Paul.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

8

Complexity

In Chapter 7, we went some way toward explaining what motivates Wittgenstein’s disregard for grammar in its traditional sense – namely, his desire to guard against overestimating how well grammatical structures (or, as his criticisms of Russell’s conception of generality show, also logical structures) express content. In particular, he warns against the mistake of concluding that similar grammatical forms rest upon similar ways of building up content. We now want to look at some of Wittgenstein’s statements, which directly concern the problem of linguistic complexity.

First, note that, though Wittgenstein does go so far as to call attention to that area of use that “can be taken in by the ear,” he does not treat it at any length (at least, not in comparison to the complimentary area of “depth grammar,” which encompasses the “use in the practice of a language”). Still less does he directly address questions relating to German or English grammar; he most often looks at grammar when it concerns language games that he himself has created. This is what one would expect: we are interested here in a systematic philosophical treatment of grammatical matters – a treatment that is not concerned with putting together a text for teaching a particular language, but rather with showing us in exemplary fashion the construction of grammatical structures, and the possibility of complex linguistic units, among other things. We are interested in a discussion of invented language games of the kind envisaged by Wittgenstein only insofar as they shed light on our language. And they can only do so if such largely fictitious language games are not really separated, as Wittgenstein says, by a break from our language.[1] In particular, this means that the games have structure – i.e. are complex – as our language is. A concept of language oriented on Wittgenstein’s views that does not include this quality of complexity cannot claim to be an adequate presentation of our language.

From our dealings with Wittgenstein so far, we can glean two negative insights concerning the complexity of content in language. Summarized as claims they are: (1) there is no special realm of sense between “reality” and language, which would be the domain of grammar (or logical grammar); and (2) employing a complex sentence is a complex action in a different sense of complexity than is the action of “singing from the score.” We discussed the first thesis in talking about Wittgenstein’s critical use of the picture of “meaning-bodies” in conjunction with the discussion of the function of an expression in a sentence. There is no realm of invisible “bodies” either accompanying or above the sentence, entities whose fit or lack of fit determines if the sentence to which they belong makes sense or not. This corresponds to an insight already expressed by the late Frege, namely, that in the realm of sense, one does not speak of wholes and their parts, and that talk of sense, seen clearly, is really talk about the use of an expression as a sign. As we mentioned in Chapter 1, the part/whole relationship holds, when it holds at all, only at the level of expressions.

But Frege came to this view rather late and with some hesitation, whereas Wittgenstein is adamant in his refusal to accept an independent realm of thoughts as intermediaries between “world” and language. Wittgenstein expressly criticizes the “tendency to assume a pure intermediary between the propositional sign and the facts.” But if there are no such “pure intermediaries” one cannot “try to purify, to sublimate, the sign itself” (§ 94), if by that one means they should accurately reflect some intermediate entity. In his earlier work, Philosophical Grammar, Wittgenstein (1974, p. 108 (V, § 66)) had already asked rhetorically:

Is it, as it were, a contamination of the sense that we express it in a particular language which has accidental features, and not as it were bodiless and pure?

Against this he says: “Thought can only be something common-or-garden and ordinary.” This refers us to the propositional sign in its “impure” form, partly determined by coincidence, and also refers us to the ways in which we make use of these circumstantially specified propositional signs in our actual utterances. What Wittgenstein says in the Investigations concerning the activity of derivation he could also have said about making a judgment. There he wrote that he was inclined to see every special case of derivation as a sort of “dressing up” of something with a kind of clothing:

…which had to be stripped from it if we wanted to see the essence of deriving. So we stripped off those particular coverings; but then deriving itself disappeared. – In order to find the real artichoke, we divested it of its leaves. (§ 164)

Again we are referred to real discourse in its particular form, in its special medium, and not to something “behind” this form, that gets “covered” or “dressed up” by it, or which is “realized” by it. If this answer is right, it also addresses the question of complexity; for this too must be understood as the complexity of circumstantially specified signs, without recourse to a “pure intermediary entity.” And these signs must not be seen as mere acoustic forms or graphic figures, but as bearers of meaningful linguistic actions.

The second negative insight to note is that the expression of a complex sentence is not an expression of a row of separate, isolated actions, like the consideration and then the assertion of a thought. Correspondingly, the hearing or reading of a sentence does not consist of a row of inner actions of meanings or thoughts that the hearer or reader executes by following the propositional signs as one might follow a musical score. Although the propositional sign “I do not think he is coming,” as a graphic figure contains within it the sign “he is coming,” the speech act, the move in a language game performed by uttering “I do not think he is coming” does not contain within it the move that would be made by uttering “he is coming.” One who states “I do not think he is coming” is not performing two actions, one of which would be the stating of “he is coming.” (§ 447) Complexity at the level of moves in a language game is therefore not to be grasped aggregately as the complexity of a “sum” of isolated partial-moves, held together by nothing more than their chronological succession.

In the Brown Book Wittgenstein (1958) had tried to clarify the concept of a complex sign with examples in which the connection of the elements of an utterance had an aggregate character. A sentence appears there as a succession of single speech acts that can be performed individually, so that reading a sentence appears both in its phonetic aspect and at the level of a “move in a language game” as a kind of “singing from the score.” He describes a language game in which person A gives to person B signs consisting of dots and dashes. B follows these figures as signs for dance steps: when given a dash she takes a step, and when given a dot she gives a little jump. Wittgenstein (1958, p. 99) calls the sign that corresponds to a complex dance figure, a series of movements, a “sentence,” and a single dot or dash, a “word.” In what sense is a “sentence” of this language game complex? What distinguishes it from any random string of signs (“words”)? Can this same game (and this also holds for the color-square language game in the Investigations) be described in such a way that it doesn’t even contain sentences, and therefore altogether lacks complexity, in the sense we are interested in?

This language game can indeed be conceived as the analogue of singing from the score (the kind of “non-musical” version resulting from monotonous exercise, as previously mentioned): every simple sign from person A corresponds to an action by person B; B follows the signs step by step. Both the giving of the signs and the actions following from them are aggregate: the whole is nothing more than a succession of its parts and every component sign corresponds to a component action.

The only circumstance that challenges this reading is the fact that the dots and dashes typically appear in relationships that both the person giving the signs and the person dancing perceive as constituting unities. What Wittgenstein means by a sign is always (or at least often) complex. This conjoining of individual “components” into a single complex sign cannot, however, be based solely on the fact that a longer period of time elapses between some signs than between others. The reason for speaking of sign components in such a way that only a plurality can form a sign must rather lie in the fact that what person B performs is grasped as a unified whole (or as a succession of such wholes), which is why the whole is called a dance figure or a dance. Our conception of a dance figure is therefore originally a conception of a whole, and only in the light of its preconceived unity is one justified (with regard to a sign for such a whole) in speaking of its components as elements of one sign (for the dance figure) instead of as a succession of individual signs whose number is simply the amount of dots and dashes that appear. What exactly makes a succession of dance steps into a dance figure (or what makes a succession of tones into a musical phrase – a question which also engaged Wittgenstein) is a question he leaves unanswered, and it is doubtful whether it is easier to answer than the question of what makes a succession of words a sentence.

Wittgenstein then asks what it means to say that person B follows the signs, lets herself be guided by the elements in carrying out her steps. His conclusion is that the view that being guided consists in B being able to follow the signs correctly is grounded in a picture of a mechanism built in a certain way. He then explains the type of mechanism underlying our talk of “being able to follow the sign correctly” and uses this opportunity to make a comment on the difference between complex signs (sentences) and simple signs (words).

A typical mechanism that illustrates what we mean by the phrase “to be led by the signs” is the player piano or pianola: here the “actions” of the hammers are guided by the pattern of holes in the paper roll. Wittgenstein (1958, p. 118) then writes:

…we might call patterns of such perforations complex signs or sentences, opposing their function in a pianola to the function which similar devices have in mechanisms of a different type, e.g., the combination of notches and teeth which form a key bit. The bolt of a lock is caused to slide by this particular combination, but we should not say that the movement of the bolt was guided by the way in which we combined teeth and notches, i.e., we should not say that the bolt moved according to the pattern of the key bit.

With regard to a criterion for distinguishing complex from simple signs, Wittgenstein asks whether a complex sign can be said to have a complex action corresponding to it, or whether, as the case of the key bit is supposed to make clear, one can distinguish parts of a sign even though there are no corresponding elementary “actions” (movements) to be made out. In this case, there is nothing on the level of actions that corresponds to the fact that the complex sign has parts.

What Wittgenstein is aiming at here is the distinction between parts of a complex sign that are signs in their own right and other kinds of parts that, although they can in some way be distinguished within the sign (e.g., the horizontal stroke of the letter “T”), are not themselves signs. Signs that consist of parts in this second sense, but not in the first sense, do not count as complex for Wittgenstein. For him words are just such non-complex signs; they consist of parts (individual sounds, or letters), but not of elements on the level of ‘moves in a language game.’[2] An utterance of “slab” can lead to the act of bringing a slab, but this does not consist in elemental actions as the word (in its written form) consists of the letters “s,” “l,” “a,” and “b.” Wittgenstein (1958, p. 119) writes:

We could say that the notches and teeth forming a key bit are not comparable to the words making up a sentence but to the letters making up a word, and that the pattern of the key bit in this sense did not correspond to a complex sign, to a sentence, but to a word.

Even if the demarcation between component signs and mere parts of signs appears plausible, Wittgenstein’s comparison has still not satisfactorily answered the question as to what constitutes the unity of a complex sign, whereby it is distinguished from a succession of simple signs. What are the criteria for a succession of elemental signs building a “pattern,” a “sentence,” a complex sign – the graphic form on the paper roll of the player piano, the pauses between the tones, or the judgment of the listener who distinguishes between musical phrases? What directs such a judgment? Wittgenstein makes clear that one should not speak of a complex sign if that sign does not contain components that are themselves signs; their presence is a necessary condition for the existence of a complex sign. But first (thinking of language), it is not the case that – as the example suggests – a component sign is only present when there is a corresponding component action (the striking of a note on the piano), and second, the condition is not sufficient, because it does not provide for a distinction between a succession of signs (recall the case of the grocery list) and a complex sign. The examples considered give no grounds for speaking of sentences instead of successions of words; the understanding of complexity is stuck at the level of “singing from the score.”

In the Investigations we find this tendency to focus on the very specialized and atypical case of aggregate actions only where Wittgenstein is discussing a counterexample to our language, the previously mentioned “color square language.” In another place we find a positive remark on the problem of complexity. There he discusses the question of when we would say that someone means an expression such as “bring me a slab” as one long word, and when as a complex sentence of four words – and it is clear that this question cannot be answered with recourse to a succession of actions corresponding to the succession of words. Wittgenstein suggests:

I think we’ll be inclined to say: we mean the sentence as one consisting of four words when we use it in contrast to other sentences such as ‘Hand me a slab,’ ‘Bring him a slab,’ ‘Bring two slabs,’ etc.; that is, in contrast with sentences containing the words of our command in other combinations. (§ 20)

The “other sentences” that Wittgenstein mentions (and therefore the connections the original sentence has to other possible linguistic utterances), here no longer concern the same actions in different order (as did the dance example from the Brown Book). Rather, altogether different actions are considered: whether the one or the other person is brought a slab is not a question of the order of component actions.

In the section following the quoted text, Wittgenstein further distances himself from his original model of complexity, in suggesting the possibility of using expressions containing exactly the same words as moves of completely different types; for example, as an order on the one hand and as a report on the other. The “report-” or assertion-sign “├,” grafted onto the order “slab” does not, for example, indicate an additional component action, one that is to be carried out along with bringing the slab. The complex sign does not owe its complexity to a “complex action”[3] that it could be supposed to command (or that would “be represented” by it). It is a complex sign because the speech act it expresses is complex in the following sense: it is complex insofar as someone who utters it makes use of the possibility of uttering “slab” as a move in the language game of requesting. She uses the additional sign “├” either in contrast with the bare sign “slab,” or to emphasize the difference between it and the sign for an order “!”. In both cases there is no corresponding succession of (inner or outer) actions that would be carried out according to the signs of the sentence. Such actions do not exist here. A report does not, for example, consist of the steps of first thinking to oneself (“just considering”) and then judging (“stating as true”).

Here we see the progress in handling the problem of complexity from the Brown Book to the Investigations. In reference to Wittgenstein’s earlier cited short formula (see page 61): it is “in language” that expectation and fulfillment meet, request and statement, question and answer – not in a succession of inner or outer actions running parallel to language. How exactly is this “meeting” to be understood? How is it that we build complexes by the step-by-step addition of new forms, in which we use a word “in contrast to others”? In short, how exactly do these form-related aspects interact with the “recognition” of ways that we “calculate with words”? (§ 449) Wittgenstein says very few general things about this; he limits himself to examples. But, as examples, they point beyond themselves.

The goal of achieving “a representation of pure thought,” of making visible the “real” semantic “depth structure” of a sentence (which can only be brought out through analysis, because it is hidden beneath the familiar surface level of sentences) with help of a schematically manipulable calculus of forms, appears distant at this point of Wittgenstein’s development. The question arises whether his exemplary discussions suffice to clarify the systematic connections between diverse forms of complexity in a natural language, as well as the process of their gradual construction, so as to render intelligible how we are in a position to correctly grasp the senses of an infinite number of new sentences. We find in the Investigations a discussion of the most varied ways of forming complexes, though not in the Fregean manner of a step-by-step systematic construction which guarantees that whoever understands this method and construction thereby gains an overview of the entire “Begriffsschrift.” In Wittgenstein, we find various forms and structures handled according to their content, but no “system” of the content side of language. What we find in Wittgenstein, therefore, appears unsuitable as material for a simple expansion of the “Begriffsschrift” as developed by Frege.

At the end of Chapter 1 we cited Wittgenstein’s intention, in the Brown Book, to show that the distance between his language games and our full-blown language can be bridged – that, by using examples, he could show the plausibility of developing our complex forms from simple ones. Did he accomplish this in the Investigations (to the extent that it is even possible), or did he give up on his intended goal? And if the latter is the case: on what grounds? Are these grounds (or the limitations inherent in the construction of an overarching “theory of meaning”) sufficiently clear and recognizable from our examination of his considerations, so that they only need to be explicitly assembled? In the Big Typescript Wittgenstein (2005, p. 156e (§ 46)) writes:

When I describe certain simple language-games, I don’t do this so I can use them to construct gradually the processes of a fully developed language – or of thinking – (Nicod, Russell), for this only results in injustices. – Rather, I present the games as games and allow them to shine their illuminating effects on particular problems.[4]

Just how far this “light” reaches, and to what extent it is possible to draw a systematic picture of a natural language while avoiding “injustices” (such as Russell’s preference for a single form of generality), will occupy us in the next chapter, where we examine the question of whether Frege’s and Wittgenstein’s attempts can be integrated.

Notes

1 Compare the citation on p. 17f., above.

2 This refers only to Wittgenstein’s primitive language games; the words of our language can be divided into parts such as root, prefix, etc.

3 Cf. Kambartel (1979), and (critical of it) Schneider (1983).

4 Jean George Pierre Nicod (1893–1924): a student of Russell’s, whose important work in logic contributed to probability theory and geometry.

References

Kambartel, Friedrich (1979) Überlegungen zum pragmatischen und argumentativen Fundament der Logik, in Konstruktionen versus Positionen: Beiträge zur Diskussion um die Konstruktive Wissenschaftstheorie (ed. K. Lorenz), vol. 1, Berlin: De Gruyter, pp. 216–228.

Schneider, Hans J. (1983) Komplexität als Eigenschaft von Handlungen und sprachlichen Ausdrücken, in Der Mensch und die Wissenschaften vom Menschen: Die Beiträge des XII. Deutschen Kongresses für Philosophie in Innsbruck vom 29. Sept. bis 3. Okt. 1981, vol. 2 (eds G. Frey and J. Zelger), Innsbruck: Solaris, pp. 1005–1011.

Wittgenstein, Ludwig (1958) Preliminary Studies for the “Philosophical Investigations,” generally known as “The Blue and Brown Books,” 2nd edition, Oxford: Blackwell.

Wittgenstein, Ludwig (1974) Philosophical Grammar (ed. Rush Rhees, trans. Anthony Kenny), Oxford: Blackwell.

Wittgenstein, Ludwig (2005) The Big Typescript: TS 213, German-English Scholar’s Edition (ed. and trans. C. Grant Luckhardt and Maximilian A.E. Aue), Oxford: Blackwell.

9

An Integration of Wittgenstein and Frege?

Our investigations in this book are aimed at the systematic goal of understanding the structured nature of natural language in terms of the content of those structures, that is, without reducing the structural aspect to its formal side. In light of the considerations addressed thus far this means that we are interested in linguistic structure to the extent that it can be understood in relation to linguistic activity. In order to arrive at an adequate, non-formal concept of structure, we oriented ourselves on Frege’s thought as the most plausible starting point. This is in agreement with the efforts of such contemporaries as Donald Davidson (1980, 1984, 2005) and Michael Dummett (1975, 1976), as they (each in his own way) attempt to sketch the contours of a “theory of meaning” for natural languages.

The views of Wittgenstein discussed in the previous chapters, and, in particular, his provocative thesis that Frege’s object-concept scheme (which Frege himself called the “fundamental logical relationship”) is actually nothing more than the form of expression for a particular relationship of content (“the table and its color”),[1] now appear to threaten the role envisioned for the “Begriffsschrift” in our understanding of the meaning side of a natural language. Wittgenstein appears to imply that we cannot expect Frege’s “fundamental logical relationship” to shed any light upon any essential quality of natural language. It seems rather to have been touted as the very standard of representation on merely external grounds stemming from Frege’s mathematical interests.

The idea of developing the characterization of an expression’s “logical form” within a natural language into a theory of meaning still plays a decisive role in modern discussions about this subject, even in contexts where Wittgenstein’s later work is recognized. The dispute as to the exact nature of this “logical form” continues even today with reference to Frege’s logic (be it in the form of a pragmatic version of it, as in Speech Act theory, or as a further development toward more powerful logical systems). The enduring prominence of Frege’s fundamental thought makes it difficult not to approach Wittgenstein’s theses about “logical form” with skepticism. If an exacting examination of these theses showed them to be untenable, then we could more safely rely on Frege for the sought-after understanding of linguistic structures in terms of content. In that case, it would be a reasonable project (given the undoubted worth of Wittgenstein’s other insights which do not pertain to the role of logic) to attempt an integration of his ideas with Frege’s. We would have to ask whether Frege’s understanding of the structure of a concept script (or of an appropriate further development of this understanding) could be applied to natural language after all, and if so, whether it is possible to combine this understanding with Wittgenstein’s observations about the active (the “language game”) side of natural language.

Behind such an integration-project lies the impression that Frege had important, perhaps irreplaceable, insights into an area about which Wittgenstein had conspicuously little to say, but which is at the same time an unavoidable topic for any philosophy of language: linguistic structure. However, Frege (1972, p. 104f.) focused his considerations on an artificial medium that is as different from natural language, he himself said, as a microscope is from the eye. Another obstacle to integration lies in the fact that he tended to determine the correctness of this new medium’s structure by way of comparison with an extra-linguistic realm of “sense” or “thought” prior to any linguistic activity. This is clearly a hindrance for the integration project. On the other hand, Frege did take some hesitating steps toward an understanding of meaning according to which the sense of an expression is nothing but its “employment as a symbol.” In this, his views approach those of Wittgenstein, and this is reason to examine whether the aforementioned peculiarities of Frege’s work represent insurmountable difficulties for a marriage of both philosophies. It cannot be denied, however, that a Fregean theory of meaning for natural language must pay heed to Wittgenstein’s observations about the “activity-side” of natural language and about the nature of certain of its workings. Otherwise it would remain, to use his own image, a “microscope theory” that tells us little about the eye – which is, after all, the subject matter of our inquiry.

To make clear what is at stake here, it is useful to note that there are great similarities in Wittgenstein’s and Frege’s starting points, but that both authors interpret them quite differently. Both observe that there is often a discrepancy between the grammatical and the content structure of sentences in natural languages. According to Frege, not all grammatical forms make the relations of content involved fully explicit (some leave it up to guesswork), and when a grammatical form does indicate a relation of content, it is not unambiguous: various relations of content can be expressed by the same grammatical form. Our ability to notice this is, for Frege, an indication of our access to a realm of “thought” lying “over” or “beyond” language, whose form does not coincide with that of natural language. We rely upon this grasp of thoughts and their apparently medium-independent “form” when we, for example, check the logical correctness of a conclusion formulated in a natural language. On this model, the aforementioned discrepancy first becomes apparent when we compare the expression in language with what was “meant”; if we had only the expression, so it seems, there could be no talk of a discrepancy between the expression and something else. Therefore, Frege can focus on the project of constructing a new medium of expression that mirrors this realm of thought accurately and completely. Since we recognize this realm, we ought to be able to give it expression, to represent it as it is. When we can avail ourselves of such a “correct” medium, we can translate the ambiguous and inexplicit expressions of natural language into sentences of this new and special mode of expression and so avoid these shortcomings. In addition, if it turns out that in understanding we have always been tacitly (“inexplicitly”) recognizing a structure that we now set out to make clear and “explicit,” then it is obvious that such a “concept script” should play a major role in our understanding of the meaning side of natural languages too. This applies particularly to the question of what relations of content exist between the component expressions of a complex sentence, as opposed to their “merely grammatical” relations.

Wittgenstein also sees these differences between the content side and the grammatical side of language and consequently the possibility of giving two differing accounts of how the parts of a sentence go together. But he interprets this discrepancy in a completely different way from Frege. The fact that we register a difference does not indicate to Wittgenstein that we have access to a realm of “thought” that stands over and against language, that shows the true content of what is meant, and that we compare with the gappy and ambiguous grammatical order. He does not consider language from the perspective of an imagined perfect structure – something Frege put forth as not only conceivable but as self-evident and necessary for us even to be able to notice what is “wrong” with grammar. Wittgenstein’s imagined starting point for his reconstructions is a necessarily particular way of forming a linguistic complex or a “form” which is to serve a particular, concrete purpose of communication and which is then used in a second (and a third, etc.) step to serve a new purpose. And, for Wittgenstein, it is this second step that creates the difference in content structure. On this conception the discrepancy arises when an old form is applied to serve a new function. Understanding this new function involves, on the one hand, appreciating its communicative success (grasping the new use of the old form), and, at the same time, seeing that this success does not rest on a quasi-mechanical continuation of its old function. Its application to a new case is not a matter of “objective correctness” in accordance with the same old “objective” category of complex formation. Rather, its success depends on the fact that one performs a “projection,” a transference of the old form into a new area of linguistic activity. One has to make use of the human capacity of imagination. This kind of bridging is most clearly exhibited in the case of metaphor, which involves understanding both an old and a new sense. The old form conveys the new sense without having to fit it to predetermined criteria.[2]

While Wittgenstein deemed such projective “leaps” indispensable for a hearer’s understanding of semantic complexity, Frege saw them as avoidable in an artificial language designed for discussing problems at the foundation of arithmetic (and, later, in scientific language in general). He not only held that a method for forming complexes, at least for the truth-functional expressions of the “Begriffsschrift,” always exhibits just one way of expressing the unity of content, but also held that, in the realm of “thoughts” – that is, where we are concerned with truth (and stay at the level beneath truth-functional combination and quantification) – there is just one single way of forming complexes. All complex expressions on this level say that an object falls under a concept (or that a plurality of objects stand in a relation). This austerity in forms did not, however, exclude a generosity concerning objects. He held the conviction that, from the perspective of logic, we have to deal with many quite different kinds of objects (e.g., locations, times, spaces, and value ranges); he also held that concepts can belong to different levels.

Wittgenstein abandons this ideal of uniformity. Because he holds the “realm of thoughts” to be a fiction, he has no need to find a single process of complex formation at work “behind” the diversity of the “surface” of language. As, for example, his discussion of the expression “d – slab – there!” (i.e., “put five slabs over there”)[3] shows, he accepts that there are many different ways that a second expression can combine with a first to form a unity which, if it plays the role of an assertion, can express a truth (“here are four slabs”). According to this view, any reduction to a single mode of combination requires a justification. From the perspective of the projection thesis discussed above, such a reduction is suspected of taking a specific complex-building device (oriented at first toward a particular content), and turning it into the only allowable “form of representation,” projecting it as a canonical form onto all possible contents. Viewed in this way, such a unifying process does not reflect something given, it does not reveal a deeper reality; instead it forces (in some contexts with good reason) a form upon us. According to Wittgenstein’s conception, Frege’s distinction between concept and object has no claim to special status so long as the object of investigation is the way that natural language functions, and not how, for some limited purposes, a medium could be constructed that, like a microscope, has a particular task to fulfill. Frege’s goal was indeed the development of a special and unique medium, not a theory of meaning for natural languages.

Wittgenstein holds that, within the scheme of “saying something about something,” a particular relation of content – such as the one exists between an expression for a particular table and an expression relating to its color – is made into a determinate “form of representation” which is then treated as obligatory for everything that can be said at the lowest level of Frege’s “Begriffsschrift.” Yet the generality of this particular device for forming complexes does not, in Wittgenstein’s opinion, register a discovery of what joins thought components “in reality,” independently of all questions of linguistic expression. The generality results instead from Frege’s decision to make a certain form of representation obligatory, in compliance with and in amplification of a certain tradition in logic. Wittgenstein (2009, § 132) does not deny that one can make such decisions – that such a mode of representation can be employed and may even be useful for some purposes, which he does not discuss in detail – but for his own philosophical purposes he apparently holds them to be useless.

We must keep these fundamentally different interpretations of the same phenomena in mind if we want to explore the possibility of combining Frege’s treatment of the structural aspects of the “Begriffsschrift” with Wittgenstein’s view of the activity of engaging in language games. There are many reasons to begin such a project with Frege’s thought, and only then attempt to integrate Wittgenstein’s views. An important rationale for this approach is found in Dummett (1978, cf. 1981). He is convinced that Frege’s thought offers the only viable way to an inclusive treatment of the meaning side of language, because only Frege’s approach gives us a chance of constructing a systematic theory of meaning. Dummett sees as a necessary condition for terming a theory of meaning “systematic” that it explains our ability to understand novel sentences. Without Frege’s outline, however, we would not have the slightest idea of how to attempt such a project: we would be forced into the absurd position of claiming that we learn the sentences of our language individually and as wholes. Stated more clearly, we would have no theory of meaning. What Dummett therefore sees as indispensable in Frege’s theory is the separation of a general and recursively characterized “content” or “sense” from what one can do or accomplish with the utterance of a sentence in a social context. Dummett holds that Wittgenstein denies the possibility of such a separation; and if Wittgenstein is correct it appears that, given our current state of knowledge, no systematic theory of meaning is possible. The problem of the separation of a level of “sense” must be solved before the integration project can be seriously undertaken. This will be our sole task in the next chapter.

There are also some more general considerations, which point toward beginning such an integration project with Frege rather than with Wittgenstein. Wittgenstein’s later philosophy has the reputation of being unsystematic and quite skeptical of theorizing; all the more reason to choose as a starting point an approach that is more ambitious and promises an inclusive systematization of the subject area, even if, for Frege himself, this subject area was not natural languages. One would have to test whether the essential parts of Frege’s system can withstand, where necessary, a partial alteration or re-interpretation (for example, a speech act theoretic interpretation of Frege’s distinction between object and concept), and whether the Wittgensteinian considerations we have discussed here can be interpreted as valuable additions. This could, for example, be the case if they affected only areas expressly excluded by Frege (non-truth-functional expressions; context-dependent expressions), or merely exceptional cases of marginal interest. Wittgenstein’s considerations could then be taken into account, without endangering the systematic and comprehensive character of the picture as painted by Frege. The parts that cannot be integrated would then be suspected of only affecting “superficial phenomena.”

The prospects for such an inclusive view – one that seeks to create a comprehensive picture based on Frege’s thought – do not, at first glance, appear to be so bad. Searle’s speech act theory (Searle 1969), developed after and with knowledge of Wittgenstein’s relevant later work,[4] can be read as an attempt to carry out just such an integration. Although on the one hand Searle’s views directly and repeatedly conflict with Wittgensteinian arguments, which have appeared so convincing in the last few chapters, on the other hand Searle’s views are backed up by the tradition of logic as well as strong speaker intuitions. Only after we have clearly determined what their intuitive appeal consists in can we begin to evaluate them critically.

The appropriateness of Searle’s theory for the integration project can be made to look plausible as follows. Suppose one sees the main difference between Frege and Wittgenstein to be that Frege consciously excludes many properties of natural languages in his single-minded focus on the area of truth and the language of science (the realm of possible “judgeable contents”), whereas Wittgenstein’s primary interest lies in the diversity of applications afforded by expressions of natural language that are not directly related to truth conditions. It is possible to see Frege’s orientation on the concept of truth as a completely thematic constraint, related to the scope of his investigations, and not to their systematic core. One could then seek to expand the limits that Frege draws (since what little interest he had in natural languages was limited to their divergences from the “Begriffsschrift”) through the inclusion of Wittgenstein’s insights into the non- (or only indirectly) truth-functional aspects of natural language. This angle appears to suggest that Searle’s treatment of the “propositional” side of language (in speech act theory terms: “referring” and “predicating”) can be seen as a pragmatic (i.e., action oriented) reinterpretation of Frege’s fundamental categories of “object” and “concept.” One might then think that Frege’s way of handling the content of expressions can be adapted, modified slightly, and complemented through consideration of usage. One would do justice to natural languages by including a discussion of the so-called “illocutionary roles” of expressions (question, order, promise, etc.), about which there is much to learn from Wittgenstein. Searle’s approach has the advantage of following through on Dummett’s call for a separation between the “content” and the “social” aspects of language. Searle treats content in Frege’s manner and complements his representation of content through the additional treatment of the action side of language. This addition appears partly as a complement to Frege’s concept script in the form of a further expression (the so-called “illocutionary force indicator,” which signals the role of the speech act), and partly as an interpretation of Frege’s fundamental categories, which remain essentially unchanged as forms of expression of speech acts (referring and predicating).[5]

In this way, Searle’s work can be read as an attempt to broaden the scope of a Fregean theory to include the use aspect of language, so that the theory in its entirety gives an impression of the possibilities of a Fregean integration project. Although his focus is on the use aspects of language and is obviously a reworking of Wittgenstein’s thought, Searle’s elective affinity with Frege appears unsurprising when one realizes that both he and Frege stand in the tradition of “formal” logic going back to Aristotle. This tradition is characterized by a representation of the activity of logical deduction in ordinary language through the introduction of special symbols, which allow one to analyze the logical steps without looking at their particular content. The arguments then appear as analyzable patterns of schematic operations on these newly introduced symbols.

In parallel fashion but widening the scope, Searle creates a notation for schematic expressions that he calls “standard forms” of types of speech acts, including those that are not primarily concerned with truth-values. He uses the expression “F (RP)” to represent the “standard form” of a speech act in which “F” marks the place of the “illocutionary force indicator,” e.g., the symbol “├” (for an assertion), “!” (for an order), “?” (for yes/no questions), etc. The letter “R” indicates the place for a referring expression (e.g., a proper name), the letter “P” for a predicating expression, so that “RP” corresponds to Frege’s “F(x).” According to Searle’s interpretation, the standard forms thus represented do not belong to any particular language but rather range over all individual languages, since they provide a notation for the categories of (component) speech acts which are severally necessary and jointly sufficient for the performance of the speech act in question, however it may be “realized” in a particular medium (a particular natural language) and however it may be “conventionally” regulated. Thus, Searle’s forms are based on linguistic activities (which appears to approach Wittgenstein’s thought about language games), yet they also seem to satisfy Frege’s logical demand that they remain independent of the “superficial appearances” of the particular grammars of natural languages.

It is characteristic of these standard forms that they consist of two component expressions; one (“RP”) for the “propositional content” of the represented expression, and one (“F”) for its “illocutionary role.” The component expression for the content expresses a “proposition,” a “judgeable content” in Frege’s sense of the term, while the component expression for the illocutionary role or “force” determines the use (as question, command, etc.) to which such a content is typically put. Because Searle’s understanding of the “propositional content” is in complete harmony with Frege’s distinction between object and concept, his forms can be seen as pragmatically interpreted “concept script” formulations of sentences of natural languages. Compared with Frege’s conscious restriction to truth, Searle’s formulations add a component expression that regulates their communicative use. The result of Frege’s efforts to give a “pure” representation of the structure of thought, of “judgeable contents” remains; in Searle, too, we have sentences before us in a standard form purportedly independent of the characteristics of any particular language, which can be used to express various contents. Yet these expressions are distinguished from the sentences of Frege’s “Begriffsschrift” mainly by having been complemented through the addition of a component that signals something about Wittgenstein’s favored aspect of use.

In light of the integrative efforts just discussed, such a project appears to be economical, because it makes use of Frege’s work and the logical tradition in its treatment of those “components” of expressions of natural languages that are used (in the standard form) for expressing propositional contents. Moreover, a treatment of semantic complexity that builds upon Frege by distinguishing between propositional and illocutionary aspects represents, according to Dummett’s criteria, perhaps the only apparent approach to a systematic theory of meaning. Dummett sees the deciding characteristic of a Fregean approach to be the distinction between the illocutionary role of an expression of a certain type and the sense of such an expression. Only when sense (or as Searle calls it, propositional content) is separated from use and is handled recursively, as Frege proposed, will we have an idea of what a systematic theory of meaning might look like. Dummett attributes to Wittgenstein a denial of such a level of sense, and claims that if Wittgenstein is correct then no systematic theory of meaning is forthcoming. If we want to explore the prospects for a systematic theory of meaning in Frege’s sense in a way that is at the same time compatible with Wittgenstein’s ideas, we must determine whether Wittgenstein really denies that there is a level of sense, whether the arguments to that effect are persuasive, and whether he develops something which can be a substitute for the role of Fregean sense in a “systematic” theory in some way that has as yet to be specified.

As suggestive and as promising as this idea appears at first, we must remind ourselves that we do find in Wittgenstein theses concerning truth-functional complex expressions which run directly counter to Frege’s thoughts. These theses must either be put to rest in the course of working out an integrative model, or it must be shown that they deal with superficial phenomena, special, or atypical cases. Then it would still make sense to speak of a “core area” of natural language for which a Fregean approach would work, and we could set aside special cases for later investigation. Here we should recall the two central statements with which Wittgenstein contradicts Frege. First is his thesis that there is no justification in the philosophy of language for isolating just one “fundamental relation” for the representation of all truth-relevant contents. Second is the thesis that it is typical of natural languages that one and the same kind of composition of expressions can have various meanings. With these points in mind, we will now turn to the fundamental problem that Dummett sees for the project of combining Frege’s and Wittgenstein’s conceptions of language.

Notes

1 See above, pp. 78f.

2 Cf. Ricoeur (1978, 1978a), and Goodman (1976), who says one could consider metaphor as a “calculated category-mistake” (p. 73).

3 Cf. Chapters 2 and 3.

4 Searle himself understands his speech act theory as a systematization of Wittgenstein’s thought; cf. his statements in the interview text from Magee. (1988, p. 342f.)

5 One finds uncritical acceptance of the traditionally characterized ‘“standard form” in, for example, Jürgen Habermas’s doctrine of ‘Universal Pragmatism’ (Habermas 1984/87, cf. Schneider 1982). From our perspective this is a shortcoming; on the other hand, we agree with the estimation of Wellmer (1989) that Habermas is “… hardly interested in the details of a logical-semantical construction of assertions…, which is central to the theories of the early Wittgenstein, of Dummett, and Davidson.” (p. 343)

References

Davidson, Donald (1980) Essays on Actions and Events, Oxford: Clarendon.

Davidson, Donald (1984) Inquiries into Truth and Interpretation, Oxford: Clarendon.

Davidson, Donald (2005) Truth and Predication, Cambridge MA: Harvard University Press.

Dummett, Michael (1975) What is a theory of meaning?, in Mind and Language (ed. S. Guttenplan), Oxford: Clarendon Press, pp. 97–138.

Dummett, Michael (1976) What is a theory of meaning? (II), in Truth and Meaning: Essays in Semantics (eds G. Evans and J. McDowell), Oxford: Clarendon, pp. 67–137.

Dummett, Michael (1978) Can Analytical Philosophy be systematic, and should it be?, in Dummett, Truth and other Enigmas, London: Duckworth, pp. 437–458.

Dummett, Michael (1981) Frege and Wittgenstein, in Perspectives on the Philosophy of Wittgenstein (ed. Irving Block), Oxford: Basil Blackwell, pp. 31–42.

Frege, Gottlob (1972) Conceptual Notation and Related Articles (ed. and trans. Terell Ward Bynum), Oxford: Clarendon.

Goodman, Nelson (1976) Languages of Art: An Approach to a Theory of Symbols, Indianapolis IN: Hackett Publishing Company.

Habermas, Jürgen (1984/87) The Theory of Communicative Action (2 vols.), Boston: Beacon Press.

Magee, B. (1988) The Great Philosophers: An Introduction to Western Philosophy, Oxford: Oxford University Press.

Ricoeur, Paul (1978) The Rule of Metaphor: Multi-disciplinary Studies of the Creation of Meaning in Language, London: Routledge.

Ricoeur, Paul (1978a) The metaphorical process as cognition, imagination, and feeling, in On Metaphor (ed. Sh. Sacks), Chicago: The University of Chicago Press, pp. 141–157.

Schneider, Hans J. (1982) Gibt es eine “Transzendental-‚ bzw. Universalpragmatik”? Zeitschrift für philosophische Forschung, 36: 208–226.

Searle, John R. (1969) Speech Acts: An Essay in the Philosophy of Language, Cambridge: Cambridge University Press.

Wellmer, Albrecht (1989) Was ist eine pragmatische Bedeutungstheorie? Variationen über den Satz ‚Wir verstehen einen Sprechakt, wenn wir wissen, was ihn akzeptabel macht, in Zwischenbetrachtungen: Im Prozess der Aufklärung (Jürgen Habermas zum 60. Geburtstag) (ed. A. Honneth et al.), Frankfurt: Suhrkamp, pp. 318–370.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

10

Dummett’s Doubts and Frege’s Concept of “Sense”

What does Michael Dummett demand of a “systematic” theory of meaning, and what understanding of Frege’s “level of sense” leads him to conclude that, if Wittgenstein is correct in denying that there is such a level, then no systematic theory of meaning is possible? On a first pass, we could make the negative point that, for Dummett, an understanding of the meaning side of language is not “systematic” if it must hold that a sentence is understood only because it (i.e., its application) has been previously learned as a whole. A systematic theory of meaning must minimally be able to explain our understanding of a sentence in terms of our understanding of its component words and the way in which the sentence is constructed out of them, so that we can understand novel sentences on the basis of this recognition. This means that the “systematic” character is constituted by underlying general rules or principles that allow us to work out the meaning of any given sentence from the meanings of its elements and the functions exhibited in its structure. The only alternative to such a systematic understanding of the meaning side of language is, Dummett believes, the assumption that we learn the sentences of our language individually and as wholes; the meaning of any sentence which was not learned in such a manner could at best be guessed at, but there is no way we could work it out on the basis of our knowledge of the meanings of its components and their mode of combination. This assumption appears quite absurd, so it ought to be possible to develop a “systematic” theory of meaning for natural languages (or more carefully: a systematic understanding of their meaning aspect).

On this first pass, we have spoken of “meaning” in an inexact, pre-philosophical sense. To reconstruct how Dummett arrives at Frege’s level of “sense” as crucial for a systematic understanding of complexity, we can begin with a hypothetical concrete situation and proceed step by step to rule out what is not meant by “meaning” when we speak of it as being systematically developed. It cannot mean the communicative significance of a particular concrete utterance of a sentence (of a token) with respect to a certain discourse partner, to a shared history, and to their actual situation. Such utterance meanings (Grice 1968) can vary quite radically; so, for example, an utterance of the sentence “you resemble N” can be a compliment, whereas another utterance of the same sentence can be an attempted insult, or the formulation of the suspicion of a hidden lineage, etc. Dummett (1979, p. 124) calls the meaning of an utterance, in this sense, its “point.” If we understand Wittgenstein’s suggestion that we look to the use of an expression in searching for its meaning as a recommendation that we look for the “point” of the expression, in this sense, then the level of meaning at issue is, indeed, fundamentally separated from the sort of meaning which can be construed on the basis of an understanding of the component parts and their mode of combination – for the “point” of an utterance cannot be determined from those alone.

Dummett puts a further constraint on the notion of “sense” when he (following Frege, not Searle) insists that one does not conflate the question of the normal illocutionary role of a sentence of a certain type with the question of the meaning of sentences of that type. Here, too, an important difference is lost if we take the term “meaning” in the expression “meaning is use” to refer to the normal illocutionary role of sentences of the type under consideration. The distinction that would be lost is that between the illocutionary role and the “sense” of an expression. Dummett’s reason for keeping them separate is his conviction that the only way to explain semantic complexity is in terms of this level of sense.

But what exactly argues against explaining complexity in terms of illocutionary role, and, accordingly, interpreting the maxim “meaning is use” as follows: the meaning of a sentence type is the illocutionary role associated with that type; and the meaning of a word (as a type) is how it contributes to making the sentence type in which it appears suitable for that particular illocutionary role? Dummett cites two facts that, in his view, argue against connecting the concept of meaning with the illocutionary role of complete sentences, and which necessitate the introduction of an additional level, the level of “sense”: the existence of logically complex sentences and the existence of affinities between the content as well as the syntax of sentences with different illocutionary roles.

Two sentences corresponding to the logical schemata “if A, then B” and “A or B” would both be, on account of their form (for example, because neither contains a question mark), assigned the illocutionary role of a statement. As far as is apparent merely from the form of the sentence and not from special contextual circumstances, whoever utters one of these sentences thereby makes a statement, the particular content of which is the meaning of the complex sentence. The meanings of these complex sentences can therefore be characterized through their use; illocutionary role and meaning are not separated here: the meaning of the sentence is, in each case, its use. For a systematic theory of meaning, however, the meaning of a complex sentence must be given by the meanings of its components and the way in which they are structured into a whole. If we equate meaning with illocutionary role, it must also be true that the meanings of the component sentences “A” and “B,” which are supposed to contribute something to the meaning of the complex whole, simply are their illocutionary roles, insofar as these correspond to their forms. But if one considers either one alone and tries to assign it a use in this sense, one would have to assign it the role of a statement, as this is the role signaled by its form. If we have no way of assigning a component sentence a meaning other than by the use indicated by its form as an isolated sentence, one must hold that the speech act of uttering either one of the complex sentences consists of making two statements – in other words, its component actions consist in stating “that A” and stating “that B.” These component actions are connected with one another in two different ways, not yet explained, that are indicated by the logical connectives. But it is not the case that uttering the two aforementioned complex sentences involves performing these two component actions: someone who states “if A, then B” has not also thereby stated “that A,” and whoever states “A or B” has not at the same time made the two statements “A” and “B.” This situation can also be described by saying that the use of the respective component sentence assigned by its form as a statement is suspended in most logically complex sentences; a logically complex statement is only a chain of two individual statements in the case of the connective “and.”

If the meaning of a complex sentence is to be systematically developed from the meanings of its components, we must not only assign meanings to the individual words (not represented in the propositional constants “A” and “B”), but also to the component sentences as components, that is, as relevant information for the process of forming the meaning of the complex. In the cases above, we saw that this meaning of the component sentences cannot be their use as statements. The meanings of the component sentences do not enter into the meaning of the complex sentence in such a way that a complex consisting of a plurality of statements is formed (as in the case of the logical connective “and”).[1] So what shall we do if we want to describe a component sentence’s contribution to the meaning of the entire sentence? One must be able to speak of its meaning in a way that abstracts from the illocutionary role that its sentential form indicates, and that it indeed plays when it appears alone (and when one abstracts from particular circumstances of its application, one thereby abstracts from the “point” of the respective utterance). It is this way of speaking of meaning that Dummett refers to when he uses the concept of “sense.”

This corresponds to the intuitive idea that one can “grasp” the meaning of a component sentence or even a sentence component in a certain sense (for instance of “A” in “A or B” or of “sweats” in “Hippocrates sweats”) without having heard the rest of the sentence, that is, without being able to identify the illocutionary role of the complex sentence. The component sentence (in Wittgenstein’s words) “fails to convey anything to me” (Wittgenstein 2009, § 22; cf. above, p. 53) yet one can nevertheless say that one has understood it. This understanding of the “content” or “sense” of an expression appears to detach itself from all considerations that concern the use of a sentence in the performance of a particular speech act. This intuitive notion of the meaning of a component sentence also corresponds with the fact that we say, in the two logically complex sentences “A and B” and “if A, then C,” that the component sentence “A,” assumed to be identical in both sentences, has the same meaning, although “A” in the first complex sentence is a component statement, while in the second sentence it is not insofar as the speaker here does not claim that A is the case. Without this assumption, the possibility of logically concluding “C” from the two sentences could not be made intelligible.

Dummett’s second argument for distinguishing and separating a level of sense from that of the “use” of a sentence (in the sense of its illocutionary role) involves referring to the fact that there are sentences with different illocutionary roles that nevertheless consist of the same words, and whose syntactic natures stand, as he carefully puts it (Dummett 1976, p. 73) in a systematic relationship.[2] Consider the sentence pair “I order you to feed the cat” and “I forbid you to feed the cat”; it appears to our naïve understanding of meaning that the phrase “to feed the cat” has a specific meaning and indeed the same one in both cases, although the illocutionary roles of these two sentences, considered as wholes, differ. This similarity is more than an acoustic harmony or one that affects only words; it also affects the ability of the words to form a complex content. The similarity does not, however, involve their sharing an illocutionary role (such a shared role does not exist here); according to Dummett this is the sharing of the “sense” of the complex component expressions (here: “to feed the cat”), which again seems to manifest its independence of the illocutionary role of the whole sentence.

What is this Fregean “sense” according to Dummett, which is less than the contextual communicative “point” of a complete concrete utterance but also less than the “use” of a sentence type in the sense of the illocutionary role assigned to it in its assumed normal usage? Dummett works this out in accordance with Frege’s suggestion (quoted in Chapter 1[3]) that to talk of the sense of an expression is to speak of its “employment as a symbol,” and also in agreement with Wittgenstein’s basic pragmatic outlook. He goes beyond Frege, however, in demanding that to specify the sense of an expression we do not have to point to an entity in some special ontological realm, but rather have to give a characterization of the linguistic ability that a speaker must have in order for us to ascribe to her a grasp of the sense. For Dummett, this is the ability to express a thought, and it consists, on the one hand, in the elemental ability to identify an object with the help of a name or an expression referring to a distinguishing characteristic (a “definite description”), and, on the other, in the ability to assign a concept to the object and to discern whether it fits or not, which is done through the use of an “unsaturated” expression. The linguistic expressions together express the thought that such and such an object falls under this concept, even when the thought is only hypothetically contemplated and not judged as true, either because its expression is only a component in a complex thought, or because it is a component in a complex expression that, as a whole, does not have the illocutionary role of a statement.

On this reading, the level of sense is always connected with the question of truth; here, talk of the “content” of a sentence is understood in such a way that, wherever one can speak of a content, one can always raise the question of whether a certain object falls under a certain concept. This question appears different from both the question of which illocutionary role the expressed content plays in specific sentence types, and the question of the “point” of a concrete, situated utterance of a sentence of a certain type. The complexity of the content of a sentence is, according to this view, always explained and understood using the same scheme. Also, the relationship between illocutionary roles and contents is assumed to be “systematic” in that a certain role-signal, say the question mark, always attaches to any content in the same fashion and leads to an illocutionary meaning of the respective sentence as a whole. When the construction of linguistic complexity is interpreted in this way, based on unified principles of combining content, it then appears plausible that a hearer can develop (or “derive,” in a wide sense) the sense of a novel sentence from the senses of its components and their mode of combination. To this development belongs in particular the correct grasp of the senses of the component thoughts, which are merely formulated, and considered, but not asserted. Because one can consider and formulate a thought without asserting it (e.g., if it expresses a state of affairs not yet existent), Dummett sees a need to speak of a level of content or “sense” on a pre-illocutionary level.

One can easily see, however, that this way of speaking of sense is not entirely free of the reflection of the illocutionary level, nor does it need to be. If one does not wish to postulate the possibility of expressing a thought in a process that is merely a sort of passive reflection and which does not involve sensible relations to other persons and other actions, it is plausible to imagine illocutionary roles at first connected up with every “move in a language game,” but which can be suspended under certain circumstances. This suspension is such that the linguistic action it constitutes (“entertaining a thought”) is itself a sensible move in an activity related to other persons and activities; it might, for example, ask a hearer to take a position. One who expresses content in this way would not assign to her utterance a particular illocutionary role, but insofar as the expression of a thought ought to be a sensible activity, there must be also in this case a “move in a language game,” a context that determines the specific character of the action and which differentiates the expression from a mere event (like the reflection of the sunset in the eyes of the speaker).

Dummett links the possibility of distinguishing such a level of sense from the levels of illocutionary role and of the “point” of an utterance to the possibility of speaking in a very general sense of a speech act of “assertion” – of an act of asserting the truth of an expressed “judgeable content.” This is plausible if one requires that, in the simplest case, the truth-functional content always refers to an object and then predicates something of it. “Grasping a thought” (and so “expressing a sense”) is not the same as asserting the truth of this thought, but it is very closely connected to it. From the point of view of a speech act theoretic interpretation of Frege’s logic, one must say that the acts of referring and of (assertively) predicating make intelligible what it means to merely grasp a thought. They alone enable us to speak of a level of sense that is neutral with respect to illocutionary force. Dummett’s thesis is then as follows: if it is not possible to speak in general of a language-wide sense of the expression of a content, and to clearly separate this act of expression from the question of what is then done with this content at the level of use (the levels of illocutionary role and “point”), then we have no idea how a systematic theory of meaning could be possible. Dummett finds in Wittgenstein’s writings a denial of this general conception of “expressing a content,” and reads this as a denial of the possibility of a systematic theory of meaning. Especially at places where Wittgenstein discusses the concept of “communicating something,” Dummett locates this crucial negative step.[4]

Notes

1 Cf. Wittgenstein’s discussion of a complex action as perceived under the model of “singing from the score” in Chapter 5.

2 This statement is more careful and more exact than Searle’s formulations, which involve no reference to the syntactical qualities of the chosen medium of expression but simply state that when two linguistic actions contain the same reference and the same predication they express the same proposition. (Searle 1969, p. 29). Cf. Schneider (1979).

3 p. 14.

4 The German words used by Wittgenstein in § 363 (which is crucial for Dummett) are the verb “jemandem etwas mitteilen” and the noun “Mitteilung.” Anscombe (Wittgenstein 1953, § 363) had translated these as “to tell” and “the language game of telling.”

References

Dummett, Michael (1976) What is a theory of meaning? (II), in Truth and Meaning: Essays in Semantics (ed. G. Evans and J. McDowell), Oxford: Clarendon, pp. 67–137.

Dummett, Michael (1979) What does the appeal to use do for the theory of meaning?, in Meaning and Use (ed. A. Margalit), Dordrecht: Reidel, pp. 123–135.

Grice, Paul (1968) Utterer’s meaning, sentence-meaning, and word-meaning. Foundations of Language, 4: 1–18.

Schneider, Hans J. (1979) Ist die Prädikation eine Sprechhandlung? Zum Zusammenhang zwischen pragmatischen und syntaktischen Funktionsbestimmungen, in Konstruktionen versus Positionen. Beiträge zur Diskussion um die Konstruktive Wissenschaftstheorie, vol. 2, (ed. K. Lorenz), Berlin: De Gruyter, pp. 23–36.

Searle, John R. (1969) Speech Acts. An Essay in the Philosophy of Language, Cambridge: Cambridge University Press.

Wittgenstein, Ludwig (1953) Philosophische Untersuchungen / Philosophical Investigations (trans. G.E.M. Anscombe), New York: MacMillan.

Wittgenstein, Ludwig (2009) Philosophical Investigations (the German text, with an English translation by G.E.M. Anscombe, P.M.S. Hacker, and Joachim Schulte), revised 4th edition by P.M.S. Hacker and Joachim Schulte, Chichester: Wiley-Blackwell.

11

Wittgenstein on “Communicating Something”

According to Dummett’s interpretation (Dummett 1981, 40f.), one finds Wittgenstein denying the existence of a general linguistic action of “communicating something” at many places in the Investigations.[1] Central for him is § 363, the context of which we will investigate briefly. Wittgenstein is examining the way in which we speak, for example, of a sensation of pain, in particular the idea suggested by the usual expressions of our language that such a sensation is something that one either “has” or does not “have.” (§ 351) Wittgenstein calls this idea a “picture,” and emphasizes that it would be a mistake to think that, by understanding an utterance using this picture, one knows what the relevant sentence “is about,” or that one knows, to use Frege’s term, the “object” that is allegedly spoken of, so that all that remains is for one to determine whether the affected person really has that which is spoken of or not – that is, whether the object falls under a certain concept (§ 352). It is not necessary for our purposes to investigate whether Wittgenstein’s construal is accurate to the entire realm of the “language of sensations and other mental objects”; this appears rather implausible. It suffices here to see whether there are cases in which we must accept his views.

He then looks at the phrase “to talk silently to oneself,” (§ 361) and emphasizes that we do not learn it by being told “what goes on here.” As in the case of feeling, there is no object, no process or activity to point to, no entity or recognizable object about which we speak. The inadequacy of the picture of “pointing to something” does not rest, according to Wittgenstein, on the fact that the person from whom we learned this way of speaking is unable to point to this (“his own, innermost”) object or process in a way that would make it visible for others. In Wittgenstein’s view, it is not the case that we can so much as give a correct ostensive definition of the expression to ourselves (§ 362). So when we understand the speaker teaching us the phrase correctly, this does not mean that we have understood that the word refers to a private process to which only the speaker has access. According to Wittgenstein it is misleading to describe such linguistic actions as cases of “speaking about something,” because the grammatical forms on which these descriptions rest are used in these cases as projections, in the sense that we worked out in Chapter 6.

When we begin a story with, for example, the words, “As I noticed that the saleswoman had given me too much change, I said to myself: ‘when she cashes up she will have to make it up out of her own pocket,’” then this report is not about an episode of “private speaking,” it is not information about an inner process, as for example a description of a dream.[2] An inner process or an inner experience is not really being spoken of here; it makes no sense to ask if it actually took place in these words, whether the reporter perhaps erred in some detail (did she, as she spoke to herself, actually use the word “pocket,” and not “wallet”?), etc. Instead the speaker explained to the hearer in a language game that points to the future, how she would like to have her actions understood and she does this by using the picture of “speaking to herself.” Instead of saying for example, “Asked for an explanation of my past actions, I now answer with the further question to my conversational partner, who should have paid for the damages,” she uses the picture of an “inner” monologue that has already taken place. She thereby expresses that she already understood herself at the time in question in the way she now indicates with her query, that is, with her way of continuing the interaction. But according to Wittgenstein, this “self-understanding” is not, despite its outward linguistic appearance, connected with any inner action, any hidden event, process, or object, “about” which the speaker speaks when she relates to us the way in which she understands herself at the time.

For such cases Wittgenstein’s argument is entirely plausible, and it is the same with many other expressions of feelings. Even with a sentence such as “I felt his answer to be an evasive maneuver” (or: to be unjust, to be harmful), the speaker does not refer to her feeling as an inner state or object, but rather interprets the situation, using a formulation in much the same way as we have just discussed. In everyday circumstances, we are in a position to use such modes of expression correctly. In Wittgenstein’s view, however, we err when (in philosophical contexts) we ignore the projective step and conclude from the meaningful applicability of the expression that we are speaking here of an “inner object of feeling” that should arouse our epistemological interest. We err in thinking that we speak of an “inner object” as we speak of the “inner object of a dream,” or that we speak of the inner action of “saying to oneself” as we speak of the outer action of “cutting one’s own hair.” If we ignore Frege’s terminology for a moment and orient ourselves on everyday language, it does not appear odd to say that such errors concern the “sense” or the “content” of the expressions considered. In particular they appear to concern the sense of sentence types, not merely the diversity of the realm of “points” of situated individual utterance-tokens of these sentences.

This is the context in which we encounter § 363; it is the most important passage for Dummett’s argument, and I therefore quote it in full:

“But when I imagine something, something goes on, doesn’t it?” Well, something goes on – and then I make a noise. What for? Presumably in order to communicate what went on. – But how, in general, does one communicate something? When does one say that something is being communicated? – What is the language-game of communicating something?

I’d like to say: you regard it much too much as a matter of course that one can communicate anything to anyone. That is to say: we are so much accustomed to communicating in speech, in conversation, that it looks to us as if the whole point of communicating lay in this: that someone else grasps the sense of my words – which is something mental – that he, as it were, takes it into his own mind. If he then does something further with it as well, that is no part of the immediate purpose of language.

One would like to say “It is through my communicating it that he comes to know that I am in pain; it produces this mental phenomenon; everything else is immaterial to the communicating.” As for what this remarkable phenomenon of knowledge is – that can be taken care of later. Mental processes just are strange. (It is as if one said: “The clock shows the time. What time is, is not yet settled. And as regards the point of telling the time – that doesn’t come in here.”)

The expression used at the beginning of this passage, “I imagine something” (like the phrases “to say to oneself” and “to feel something as to be…”), seems to suggest that it describes an action, an event, or a process (“…something goes on…”), and here too Wittgenstein holds this interpretation to be false. When one says to someone, “imagine that we are on the Canary Isles!” one does not thereby command her to perform some inner action. Furthermore, a report of something imagined is not a report that an inner event has taken place or that an inner action was performed. Wittgenstein denies that we use a sentence of the type “I imagined Niagara Falls as much larger” to refer to an object, to an “inner process” which we could, in principle, date and describe in detail, about the appearance of which we could make a report, and about which we could say that it falls under a certain concept.

According to the context described above, we can now propose the following understanding of the middle passage of § 363, which is so important for Dummett’s interpretation: Wittgenstein certainly does not want to deny that linguistic actions do include speech acts of communicating something or informing. But he wants to criticize the misguided idea that wherever a subject expression and a predicate expression occur in an assertoric connection, language always functions in one and the same way: namely, that a thought gets formulated (a content expressed) in the same kind of way whenever an object (designated by the subject expression) is said to fall under a concept (formulated by the predicate expression). If this were so, any remaining differences between two non-complex sentences in the grammatical mode of assertion would have to result from differences in the objects about which something is communicated, or differences in the contents of what is predicated of them. Any differences on the two levels distinct from that of sense would have to concern either the typical illocutionary role for such a form of expression or the particular “point” of the particular utterance in a particular situation.

When Wittgenstein now criticizes the seemingly obvious reading “…that it looks to us as if the whole point of communicating lay in this: that someone else grasps the sense of my words…,” Dummett interprets him to be saying that there is absolutely no aspect here that can be described as “grasping the sense.” If we interpret “grasping the sense” as “knowing which object is referred to and how it is characterized with help of a concept,” then this is indeed the case. However, if one reads the passage so as to emphasize the second word in the phrase – “the whole point” – and relates it to the next sentence, which contains the phrase, “…if he then does something further with it as well,” (where it means “sense of my words”) then one can read the passage in another way. Indeed, we must grasp the senses of the individual words (that is, we must understand some instances of their use), and we must relate them to one another in accordance with the intention of the speaker (we must understand some particular applications of the devices used to form linguistic complexes). But it would be a mistake if we understood this grasp of the senses of the words and the devices used in forming complexes in terms of their grammatical appearance alone, that is, as if it were merely a matter of (1) correctly understanding which language-independent entity is being talked about and (2) understanding what is being communicated or expressed about this object. So we conclude that our grammatical understanding does lead us far enough to enable us to say what the grammatical “subject of the sentence” is, and what (in the grammatical sense) is said or “predicated” of it. This grammatical understanding does not, however, lead us far enough to be able to say that we understand the thought expressed (that we understand what we have been told). In Wittgenstein’s view, sentences of the type, “I imagined Niagara Falls as much larger” do not serve to tell of a past inner process. They do not “bring it about” that the hearer now knows something about a process that she did not know before. Also, such knowledge is not conveyed as a first step for later use, neither on the level of illocutionary role nor on the level of the “point” of the utterance. In this sense, such sentences do not make the hearer aware that a specific object is subsumed under a certain concept, despite the fact that the linguistic form suggests this and that a parallel claim is true when we give a purely (surface-) grammatical meaning to the expressions “object” and “concept.”

This thought is complicated by the fact that Wittgenstein simultaneously tackles the question of whether one’s knowledge and grasp of sense are “mental phenomena,” as well as the question of what that term itself means. The only thing that is of interest for our purposes, however, is his intention to deny that there is always a separable act of pure expression of content (an act of “communicating something,” and, parallel to it, of pure grasping). Only if such acts were always the same would the following two questions be separable: (1) What communicative sense does the expression of a content have? (2) Which content is it about? Wittgenstein, however, emphasizes the possibility that a hearer may understand a sentence grammatically without having grasped an expressed thought, without having received a piece of information about something, without a something that has been communicated.

So Wittgenstein declares that it is a mistake in this case to separate the act of grasping the sense of an utterance (i.e., merely understanding its content) from a second act of “doing something further with it.” It is clear that he does not mean that he would understand this “doing something further” as pointing to an extra step that is performed only after the sense is fully grasped. This can, however, be read as a clue to how one might try to get at the “sense” of such an utterance (considered as “type,” not “token”) if one were to follow Wittgenstein’s view that it is a mistake to regard the meaning of such an utterance as “communicating something about a mental process.” We are directed toward, for example, what we earlier (see page 139) called the “articulation of a situational understanding.” In order to correctly grasp the sense of an uttered sentence, one must see what one can do with an utterance of, for example, the type “I imagined Niagara Falls as much larger.” In what language game could this sentence play a role?

If one has such a grasp of the entire expression (including a grasp of what one can do with it in a relevant language game), then one can ask in what way an understanding of its components and structure contributes to this understanding, and what role an understanding of the form “communicating something about something” plays even in the cases Wittgenstein discusses. This question regarding one’s understanding of the components formed the context in which Dummett claimed that we cannot do without a level of Fregean sense that is neutral with respect to illocutionary force. The controversial question was whether we should always look at what we can do with an expression as a second step in understanding, that is, a step that necessarily must be preceded by a pre-illocutionary step. Dummett is of the opinion that we should, and for him this first step consists in grasping the sense of the sentence, that is, in understanding the thought that is expressed (“communicated”). And it is just this possibility of separating sense from a wider perspective of use that Wittgenstein denies in the cases discussed.

Yet even Wittgenstein cannot doubt that understanding the words and their relationship to one another is a prerequisite for a proper understanding of a “move in a language game” (even if this alone is not sufficient for an understanding that can be described as “the correct understanding of a communicated content”). So we can (and must) ask whether Dummett is correct in holding that our only real alternatives here are either to endorse the story about Fregean “sense” or to abandon it in favor of a story about “use.” This “use” would encompass an undifferentiated, open realm that leans in the direction of “point” and goes no way toward solving the complexity problem. A third possibility might be to draw another line of separation that would accord with both Wittgenstein’s opposition to the static “communicating something” and Dummett’s argument for a level that (perhaps in some restricted form) plays the role of Frege’s “sense” with respect to the complexity problem.

The considerations raised in the preceding chapters about how to understand the concept of projection suggest the following interpretation. One might hold that, in the cases Wittgenstein is considering, a form of expression (“communicating something about something,” “saying what concept an object falls under,” “judging something about an object”) is projected onto an area of application where what is conveyed by its semantic structure cannot be taken literally. In such a case, the hearer must recognize the form of the expression being projected in order to execute the projective step from its old area of application to its new one. In terms of the simple example discussed in Chapter 6, this means that someone who correctly understands “he said, as it were, to himself” (and who did not coincidentally learn exactly this expression as a complete idiomatic phrase) must first be able to grasp the grammar of an expression such as “he said to himself, P…” and must not mistake it for an expression such as “he said about himself, P… .” At the same time, it is clear that the hearer has not thereby necessarily grasped what we commonly call the “sense” or “content” of the same expression, expanded by the phrase “as it were,” even if the words “as it were” are known to her in other contexts. It could be that, even in the case where she knows the meanings of all the words and grasps the semantic structure of the sentence correctly, the hearer still cannot give or even imagine a single example of a correct application of the sentence. Thus, she could not explain to anyone the sense of the expression and could not apply it herself. This establishes that in the common, everyday meaning of the word “sense” she does not know the sense of the expression in question; she has not understood.

But if this is what follows from Wittgenstein’s observations about the process of projection, we can now distinguish two levels of understanding in the problematic case he discusses. Hence, in addition to the alternatives Dummett offers (Frege’s sense or no systematic theory of meaning) we can open up a third possibility. On the first level of understanding, the hearer must know the individual words and correctly assess their grammatical relationships in the sentence. That means that she must know at least some way of using both the words as well as the grammatical forms. One can express this by saying that the hearer must correctly grasp the “senses of the words” and their semantic, their “sense-related” connections in a given sentence. This involves recognizing that, for example, the sentence “He meant it well” is grammatically constructed like the sentence “He said it well.” What is important here is knowing how (being practically able) to distinguish between subject, predicate, object, etc. This is the first level, which in many cases is the only one.

But there is a plethora of sentences for which an understanding on this first level is only a necessary but not sufficient condition for understanding the sentence in question – that is, for being able to give at least one context of its possible “application.” Therefore, we need to recognize a second level in order to see and explain how a “form of representation” can be transposed from one area of linguistic activity onto another, in such a way that the form of the expression alone does not clearly indicate what kind of application the sentence lends itself to. This claim relates to “types” of sentences, not to sentence “tokens”; it does not make the rather trivial point that, in concrete cases, where a certain utterance (token) is made in a context, the communicative, context-related “point” of the utterance cannot be read off the wording alone. That much is true of just about all sentences. Nor does it merely assert the inaccessibility of the illocutionary act from the word level. What is being claimed here is that the entire realm of possible applications of the sentence in question is inaccessible for those who do not understand the projective step. This means, in particular, that it is impossible in such a case to speak of the “communication of a content” (a case of “communicating something”), which a hearer would already have correctly identified in coming to a correct (“school-”) grammatical understanding of the sentence. One who does not recognize the projective step cannot even say that the sentence, on the basis of her grammatical understanding, expresses an identifiable thought.

This distinction between two levels (at least implied by Wittgenstein) does not coincide with the way in which Dummett draws a line between content and use. This can be seen from the fact that there are two ways in which one might have incomplete knowledge of the sense of a sentence (type). Suppose that someone does not know the expression “shortbread”; we could then say that her understanding of the sentence, “N had some shortbread for tea” is incomplete. She knows the rest of the words and their relationship to one another (and to the word unknown to her), and she would be right in this case to assume that the sentence with the expression unknown to her is used as in the sentence, “N had some cookies for tea.” That involves her ability to state correctly that the sentence can (but needn’t) be used to “communicate” something – as a way of communicating what someone had for tea. But it is different with the word “imagine.” Someone who does not know the word “imagine” gathers from the grammatical form of a sentence that the sense of the expression “imagine something green” is similar to that of “paint something green,” only that the verb indicates another activity, the identity of which she will understand with help of a dictionary. Here she commits the sort of error that Wittgenstein wants to draw attention to. She does not have a partial understanding of the kind of sense of “imagine something…,” which needs only to be fleshed out with the exact characteristics of the action in question. Instead, she has, if one does not unduly constrain or specialize the word “sense,” absolutely no idea what the sense of the complex expression is. Her lack of understanding does not refer to a secondary phenomenon – to the various ways of using an expression that need to be distinguished from its familiar sense – but rather refers to her inability to give any possible context of use at all.

Wittgenstein’s considerations do not concern the simple case in which a certain sentence suitable for communicating something can also be used in a secondary way, for example to express a command. The sentence “the light is still on” can serve, in an appropriate context, to order that the light be turned out. Here there actually is an illocutionary sense of assertion (the “communicating something”) that one can and indeed must understand first, before one takes the second step of seeking to correctly interpret the point of the particular utterance (why is she saying that to me?) by recognizing that the expression is being used (despite its outward form) in the illocutionary role of a request or command. Wittgenstein’s cases, however, are such that, despite a grammatical form suggestive of the illocutionary sense of assertion, there is no primary assertive reading of them, no “communicating something.” There simply is no statement to the effect that the entity named by the subject expression falls under a concept named by the predicate expression. In “he said, as it were, to himself,” the phrase “as it were” already signals that this is not a report of an inner dialogue. In “I feel his answer to be unjust,” it is not by recognizing the particular context that we understand that this is not a report of an inner process, while in another (“normal”) context it might be. In these sentences there is no primary illocutionary use that could be distinguished from a secondary use under special contextual conditions that would necessitate reinterpretation, as in a case of irony, for example. Hence there is also no level of a completely graspable sense or content that is neutral with respect to illocutionary force and only later undergoes a transformation in a secondary or special use. Consequently the border between sense and illocutionary role, or force, indeed blurs, as Dummett (1979, p. 127f.) says. For without knowing what type of linguistic action one can achieve by uttering such a sentence (what kind of “illocutionary” role it can play, in the widest sense), one cannot even speak of the sense of the sentence or, consequently, of the thought it expresses.

Dummett would like to claim that all sentential expressions, which meet certain syntactical criteria for assertions, require such a general, language-permeating level of sense, which is neutral with respect to any concrete speech act. In the cases Wittgenstein discusses, it is exactly this level of sense that goes missing when one focuses, as we have above, on an everyday understanding of the word “sense,” unmodified for the needs of a theory of meaning. So, for example, in everyday language one would not say that someone had understood the sense of an utterance of the type “I said to myself, when she cashes up she will have to make it up out of her own pocket” if one has merely correctly grasped the words and the construction, but is unaware that one does not (only) use this type of sentence as a report of a past conversation with oneself. Consequently, that which we call “sense” in everyday language is not something that can simply be read off from the senses of the words and the grammatical form of the sentence. Correctly grasping a projection in the relevant sense does not occur after the hearer has assigned a sense to the sentence in question. Rather, a correct understanding of the projective step is a necessary component of understanding the sense. Without an understanding of the projection there is no understanding of the linguistic action. One cannot say, “anyway, I understood what she said to me – which content she expressed – though I am still unclear why she said what she said when she did.” This distinguishes projection from another, previously mentioned step in understanding that leads, in cases such as an utterance of “the light is still on,” from an understanding of the grammatically signaled sense of a report or description to a grasp of the intended use of the utterance as a request or order.

Yet we emphasized above that an understanding of the words and a correct grasp of the grammatical structure of the utterance are prerequisites for executing the projective step. This lends support to the idea that we need to introduce an additional distinction within the “sense” of an utterance, corresponding to these two levels of understanding. Moving away from the everyday understanding, one could use Frege’s word “sense” to characterize this narrower area which concerns the grasp of grammatical construction (together with the senses of the individual words). In order to register this distinction terminologically, we might at this point introduce the term “grammatical sense,” and say that someone has understood an utterance on this level of “grammatical sense” when she understands the senses of its components and the way that they belong together grammatically in the sentence. This distinction allows us to speak of a (limited) understanding of sense (now: “grammatical sense”), even when the sentence in question is of the type Wittgenstein discusses. This enables us to say of someone that she understands the “grammatical sense” of a sentence, even though she can think of no context of application for it. With the introduction of this additional distinction we can now say that Wittgenstein did not deny a level of what we here call “grammatical sense.” What he rejects is the idea that the grammatical level is, at least for subject-predicate sentences, always interpretable in the illocutionary sense (that is, one that does not simply pertain to grammatical component acts) as a “communicating something about something” – as naming the object spoken of together with the statement that it falls under a certain concept. To deny this would mean to restrict oneself to the level of “surface grammar.”

Wittgenstein supports this thesis when he considers the process of projection, in which (as we have seen) a grammatical form from one context is projected onto a new context, in relation to which it has a non-literal character. If one now wishes to emphasize the retention of the grammatical form, one can describe it this way: in the case of a projective use of, say, the form “communicating something about something,” this form becomes a surface phenomenon, something that “can be taken in by the ear,” while the “depth grammar” that encompasses the type of new application (made possible by the projection) is not thereby recognized. Since such projections are manifold, it is understandable that one can lose sight of the meaning aspect of the form(s); the more diverse the possibilities of projection, the emptier (and in this sense: the more “formal”) the grammatical means appear to be.[3] It is interesting to note that in Noam Chomsky’s early reflections on “structural meaning” he does not discount a connection between syntactical structures and meaning relations such as “actor-activity.” But since he could not see this connection as a clear assignment of one meaning to one structure (and in that certainly was correct), he decided to exclude meaning from his treatment of syntax. (Chomsky 1957) We can now explain why he could not make such a one-to-one assignment work: it fails on account of the semantic diversity that arises through projections. When they are in use, we have the situation that one device for forming grammatical structures has a plurality of “structural meanings.”

There are contexts in which it is necessary to make statements on the level of this “surface form,” in the formulation of which one speaks of, for example, an “object of the sentence” or its “subject” – such as when giving grammatical explanations (in the traditional “surface” sense, not Wittgenstein’s use-oriented sense). A sentence “about” an earlier intention signals through its outer form that an object is subsumed under a concept. If one only sees this form, then one can describe how the relationship between the expression’s elements should be understood with words such as “he spoke of his earlier intention and said this and that about it.” Because a correct grasp of the unity formed by the elements of a sentence is always necessary for an understanding of complex expressions (except in idiomatic cases), this kind of description in its surface-grammar related sense is in no way false or superfluous. This corresponds to our intuition that in every complete declarative sentence “something is being spoken of.” That is correct in a way, if it is limited to “surface grammar.” But for a complete understanding of the sentence in question one must recognize the “depth grammar” in Wittgenstein’s sense. Even if the parts and their order are understood correctly, both grammatically and lexically, we must understand that the expression as a whole cannot be interpreted as if the speaker, in an illocutionary sense, first names an object (it might be thought of as difficult to access and therefore somewhat mysterious), and then “communicates” to us something about it or passes a judgment on it. Such an interpretation would leave the projective step, the “non-literal” character in the use of grammatical forms, overlooked or underemphasized; it would stay on the level of “grammatical sense.” Wittgenstein warns us again and again of the philosophical mistakes that result from neglecting this insight.

It is worth emphasizing once more that what we here call “grammatical sense” is in no way something “merely formal,” wholly lacking any semantic aspect. Therefore, it cannot be captured by a structural description based on sound alone. The hearer who correctly grasps the grammatical sense of an utterance must know at least one expression of the same form, and must also be familiar with a context of its application. The examples in the following chapter will make clear exactly what issues are involved here.

Notes

1 Dummett cites §§ 22f., 304, 317, and 363.

2 This does not, of course, rule out that in addition to such cases there are others in which one really “speaks to oneself.”

3 Cf. Carnap’s remarks about his made-up sentence about the “pirots,” quoted in Chapter 7, note 1.

References

Chomsky, Noam (1957) Syntactic Structures, Den Haag: Mouton.

Dummett, Michael (1979) What does the appeal to use do for the theory of meaning?, in Meaning and Use (ed. A. Margalit), Dordrecht: Reidel, pp. 123–135.

Dummett, Michael (1981) Frege and Wittgenstein, in Perspectives on the Philosophy of Wittgenstein (ed. Irving Block), Oxford: Basil Blackwell, pp. 31–42.

12

“Grammatical Sense” and “Syntactic Metaphor”

A Wittgensteinian Solution

If one accepts Wittgenstein’s diagnosis and the concept of “grammatical sense” introduced in Chapter 11, then the next step we need to take in clarifying the prerequisites for a systematic “theory of meaning” (in a strict or not so strict understanding) should be to examine whether the constrained conception of “grammatical sense” can achieve what Dummett takes to be the work of Fregean sense. We could then legitimately interpret a hearer’s ability to understand the meanings of novel sentences by considering the meanings of their components and the ways in which they are constructed in terms of the ability to correctly grasp the grammatical sense of a sentence. But this understanding of a new meaning is somewhat limited. In “understanding” the new sentence, the hearer has not necessarily correctly grasped the linguistic action – the “move in the language game” (i.e., the type of move, not some context-dependent particulars or the “point” of a concrete utterance). We must examine whether this explanation of the unlimited nature of linguistic competence (i.e., our ability to understand an unlimited number of new sentences) manages to avoid the difficulty that, because it ignores Fregean sense, one is committed to the absurd position that the sentences of a language are learned one at a time and as wholes, like idiomatic expressions. If this criticism that Dummett directs against Wittgenstein could be cleared away with help of our newly introduced concept of “grammatical sense,” it would appear unnecessary to assume a further (“Fregean”) level of sense at all. The concept of “grammatical sense” could explain semantic complexity without positing a “sense” on the illocutionary level of “communicating something.” In this way we could do justice to both Dummett and Wittgenstein and would at the same time achieve a new understanding of our competence to speak a natural language: it must include imagination; the ability to calculate is not enough.

In order to assess the aptness of the concept of “grammatical sense” for resolving Dummett’s problem, we will now offer a rudimentary sketch of a solution based on Wittgenstein’s very simple language games. This sketch will show what a systematic treatment of the meaning side of a language would look like (according to the understanding we have worked out in these pages) once one recognizes the facts of projection and gives up the requirement that forms for forming complexes must (first) always have just one meaning and (second) always lead the hearer to correctly grasp the “thought” expressed (‘communicated’) by the speaker. But we will not take the concept of a sense that is neutral with respect to illocutionary force to indicate a “pre-illocutionary” sense, as some of Dummett’s formulations suggest. For in that case, as we indicated on page 142, it would be difficult to avoid positing a certain kind of inner action: a pure “grasping of content.” Rather, we will view the “illocutionarily neutral” level as the result of suspending an illocutionary meaning, the original presence of which is unavoidable. We shall see whether our “grammatical” sense, despite these constraints, can play the role of Dummett’s Fregean sense in such a way as to answer his objections. So we start with a single method for forming complexes and examine how one can speak of “knowing the meaning of an expression” when the formation of the complex (by means of projection) no longer has an unambiguous content, and when the hearer is no longer reliably led to “the thought.” Later, we will look at Wittgenstein’s second central objection against a Fregean type of a “theory of meaning”: namely, that there is no reason for a philosophy of language to claim either the universality or the uniqueness of the object-concept scheme as the only possible basis for all assertive speech acts.

Using Wittgenstein’s methodology, we can imagine that elementary linguistic actions are learned as he describes in the beginning of the Investigations. This learning process proceeds incrementally until expressions are possible that realize the reference-predication scheme, which can later be projected onto new cases of application. We could follow Wittgenstein in creating a “natural history” of learning, according to which acts of uttering expressions like “slab,” “cube,” etc., originally have the sole illocutionary role of commanding, only later to undergo a transference whereby they come to serve the previously unknown role of reporting or asserting (§ 21). In the beginning, there is the builder language game in its simplest form, which contains only commands. “To know the meaning of a word” at this stage simply means having a practical mastery of the single socially established activity in which an utterance of the word plays a role: namely, giving and reacting on a command. Teaching meanings is, at this stage, a fairly straightforward affair, for it is related to a particular mode of interaction in which an utterance of the expression is a sensible component action in a more complex activity of fetching, building, etc. Every individual will learn the meaning of the word in one context of action (among many possible ones), and it may be that the members of the language community learn the meaning of the word in different contexts of action. To this extent, the meanings of the expressions of a language are always at first “concrete” for every speaker, and this means that, before any further differentiations are introduced into the language games, they are rooted in the illocutionary level in the widest sense, that is, they are located on the level of the “move in the game.”

Even at the level of single-word sentences in the sorts of language games Wittgenstein creates, “transferences” occur, and these, according to the terminology we proposed (p. 154, cf. pp. 40, 111) should be understood as changes in illocutionary role. Wittgenstein himself mentions the possibility of using an expression such as “slab,” which originally appeared as a command, as a “report.” We can further imagine that the expression could be used as a question – for example, as to whether a piece of material of a certain kind should be brought, etc. We are then able to say “in the abstract” that the word “beam” stands for beams precisely on account of the multiplicity of internally connected applications to which a phonetically unchanged single-word sentence can be put. The applications are internally connected insofar as, for example, the description “beam” can be made true if the command “beam” is correctly carried out. Thus, it is the diversity of contexts in which an expression of the same type makes sense, together with the internal relationship between these contexts, that allow us to say that (insofar as the various illocutionary acts sound alike) “the word beam” stands for the beams, regardless of whether it is being used as a question, command, or description. But does this characterization describe something that could also be seen as the determination of a “pure content”? Do we have here a naked articulation of sense?

According to the understanding just worked out, when we claim that someone understands the meaning of a word by saying, for example, that she knows that the word “slab” stands for slabs, we simply mean: she has mastered at least one context (normally more) in which the utterance of this word plays a role. Since the expression plays rather different (though internally related) roles in different contexts, one can abstract from the particular roles and say that the speaker knows “what the word stands for.” The wrong impression that such a form of expression encourages, however, is that there can be a simple relation of signifying, which we might represent by saying “‘P’ stands for Ps,” a relation which somehow exists independently of or even prior to any concrete language game. According to the interpretation given here, this is an illusion. Rather, the possibility of speaking of an “abstract” non-illocutionary level of sense arises by suspending the question of the illocutionary meaning of the relevant acts of utterance. The abstract level does not exist prior to the illocutionary meaning, nor does it make illocutionary meaning possible. This pertains to the beginning of language and to the question of whether illocutionary or pre-illocutionary sense is primary. What is primary in the relevant sense is the illocutionary meaning. But when one has mastered enough of a language to, for example, formulate definitions, then it is, of course, possible to introduce a new word into the language by means of an “abstract” definition that does not mention any illocutionary actions. It is possible to introduce a word into the language whose illocutionary meaning (in a case of use) is grasped with help of those parts of the language that are already mastered.

Imagine now that this language of one-word sentences with various illocutionary roles is widened enough to allow for “descriptions” such as “this slab” and that these descriptions combined with pointing gestures and a positive or negative copula (“is” or “is not”) serve to disambiguate assertions, as, for example, “this slab is (is not) usable.” In accordance with the Wittgensteinian considerations already cited, we can then imagine a further transference in which a complex expression of the form “this P is Q” changes its illocutionary role, and is no longer used as an assertion but as a question. Imagine further that the various roles are indicated graphically or phonetically in a way that corresponds to Searle’s notation of an “illocutionary force indicator,” and that the marking of an illocutionary role is obligatory – that is, an expression is not well formed if it does not contain a role-indicating mark. The language game thus created covers moves of the form “├ this slab is usable” (assertion) and “? this slab is usable” (question).

We can now ask: in what sense is it true to say that a speaker of this language develops the meanings of complex expressions from the meanings of component expressions, and what does it mean to attribute to her the knowledge of the meanings of the component expressions? Of particular interest to us is how one can speak of the “meaning” of component expressions apart from the illocutionary sense of an entire expression. This question applies to individual words as well as to complex component expressions, which do not in themselves indicate an illocutionary role but merely formulate a “content” such as “this P is Q.” (Since we made the inclusion of an illocutionary role indicator mandatory, such an expression would not be well formed, and would therefore not express an assertion).

If we look at the learning process, construed according to the considered model of a language game we have developed here, we can start to answer the first question concerning the “development” or derivation of sentence meaning out of the meanings of sentential components. The continued enrichment of simple language games through the introduction of new possibilities of expression is designed so that the newly created richer forms not only introduce new elements into the language (e.g., the expression “this”), but also utilize the linguistic possibilities of the lower competence levels, knowledge of which is prerequisite for the ability to understand each newly introduced step (“this slab”). The ability to immediately understand the transference from the command “! slab” to the description “├ slab” rests upon two things. First, it depends upon the pragmatic usefulness of the speech act of description, that is, on the possibility of immediately experiencing the new action as helpful. Second, such it depends upon anyone learning the new step having already mastered the game of commanding to which the expression “! slab” belongs. She has already developed the requisite ability to distinguish kinds of building material and is able to pronounce the words necessary to participate in the game. So learning new steps depends, in the sense described, on a prior mastery of old language games, not only because it introduces a new element, but because teaching the new step involves calling upon actions available from previously mastered games. Normally, these are not employed as illocutionary component acts but as component acts in the phonetic sense, whereby the sameness of sound indicates a relationship of content. In the pre-projective case, when the hearer encounters a new sentence, the several elements of which are familiar to her from other language games, her understanding of it (parallel to the learning process) consists in her ability to associate contexts of activities (i.e., of practical applications) with the original individual elements as well as with each additional “element” (i.e., word or structural element). In this way she can, by recursively applying the steps that she executed in learning, build a context in which the complex expression is a sensible act. This will only work for actions that she has explicitly learned, though she may have dealt with different kinds of objects during her own personal learning process (e.g., with the description of beams instead of slabs).

The answer to the second question now follows readily from these considerations. We asked what it means to attribute knowledge of the meaning of a component expression to a speaker when this knowledge cannot pertain to an illocutionary role, since component expressions of utterances (words, phrases) do not have such roles. Since our concern is the possibility or impossibility of separating the “sense” or “content” of an expression from its illocutionary role, we were particularly interested in the case where the component is an incomplete and “neutral” expression of the form “P is Q” (i.e., one which lacks an illocutionary force indicator). In light of the foregoing discussion, the answer is that, in attributing such knowledge, we state that the speaker or hearer has an understanding of at least one context of application for each component expression and each complex-forming device, in which context it would make sense to utter the respective expression. As applied to the restricted form of complexity we’ve been dealing with here, this means that the speaker can apply the component expression in question as part of a “move in a language game” – as part of an illocutionary act of her choice – by supplementing it freely with other suitable expressions (e.g., with illocutionary force indicators). The ability to understand component expressions which do not themselves play any illocutionary role is, therefore, the ability to complement them in such a way that the resulting whole is meaningful on the illocutionary level.

And these considerations lead to two further conclusions. First, it is not necessary to posit a shadowy pre-illocutionary “act” that consists in merely contemplating, imagining, grasping, or expressing a “pure” content. A “pure” grasp of the sense of an expression, an understanding that depends upon knowledge of no illocutionary use (alone or as a component expression), which is pictured as preceding and rendering possible all such applications, appears from this perspective to be an unnecessary and misleading fiction. It is as unnecessary here as it was in the aforementioned case of one-word sentences. On the understanding developed here, a speaker of a language must always know (some) concrete ways of applying individual words and devices for forming complexes. That is what her knowledge of the words and the ways of combining them consists in. The more modes of application there are (the more developed the language), the quicker their concrete character fades into the background – particularly when the linguistic competency becomes so great that it becomes possible to explain language through language.

In the very simple language games that we have considered so far, the process called (following Wittgenstein) “projection” has not yet come on the scene – that is, it has not yet happened that a mode of linguistic acting introduced in one context gets used in a second context, so different from the first that the very meaning of the act changes. In non-projective language games, knowledge of the words and the way they combine will always (provided the combination is grammatically permissible and has an illocutionary meaning) suffice for knowledge of the illocutionary sense of the utterance in question. This means that the hearer understands the move in the language game for the particular complex utterance she could produce. In our extremely simple language game an expression such as “├ this beam is usable” would be understood in its illocutionary sense by anyone who understood the expression “├ this slab is usable” and knew the word “beam,” even if the hearer had never encountered this particular configuration before. We discussed this above as the “development” or “derivation” of the sentence meaning out of the meanings of the components and their mode of combination, in such a way that there was nothing “left over”: it led to an understanding of the utterance as a complete act.

But precisely such a “derivation” of the meaning of a linguistic action as action ceases to be possible in cases where forms are projected. When it comes to multi-word sentences, the occurrence of a projection immediately opens up the possibility that someone may only understand the “grammatical sense” of the sentence and will be unable to say which action the speaker performed by uttering it, despite the fact that the sentence is well formed and does in fact bear illocutionary meaning. That is to say, projection can result in sentential expressions whose component words and semantic structure are understood by a particular speaker, in the sense explained above (i.e., the speaker is familiar with at least one application for each ‘component’); however, despite these two abilities the speaker might be unable to give even a single context in which the application of the expression as a whole would make sense. An understanding of the illocutionary force indicator does not here provide the required help.

Referring back now to the extremely simple language game that Wittgenstein created for the purpose of clarifying, and which we have already used, we can shed light on the process using the following example. Let us follow Wittgenstein in assuming that this language game is further developed, in the manner he describes, through the introduction of the numerals, “a,” “b,” “c”… . The numerals are used in counting pieces of building material as well as in expressions such as orders and assertions: “! c slabs” or “├ b cubes.” A very simple example of a projection in the sense discussed above would involve the introduction of expressions of the form “these slabs are c,” in which numerals are deployed in an unusual place in the sentence – a place where words such as “usable” normally stand. The semantic structure “x is/are P” must now be interpreted differently from before; an old form of expression is used to establish a new context of action, in which the results of counting activities are communicated (“…are c”) as if they were “characteristics of things.”

Although it is likely that the hearer first confronted with such an expression would successfully guess what is meant, it is clear that she cannot derive it in any strong sense from previous linguistic practice. In contrast to the case considered on page 159, where a prior ability is applied to a new object (from “this P is Q” to “this R is Q”), here a “leap” is required of the hearer, a guess at the meaning, whereby she gives free reign to her situational and language-related imagination. It may be that she does not succeed, that she does not guess the illocutionary sense of an expression that, by existing standards, is unallowable or wrongly constructed, despite the fact that she knows the meanings of its component expressions and the devices for forming such a complex. We may be inclined to say that she “understands the meaning” of the expression in a limited sense. According to the considerations above this is allowable: our second conclusion was that, just as we speak of “knowledge of the meaning of a component expression” as independent of the knowledge of an illocutionary role, we can also use our newly introduced term and say in this case that the hearer understands the “grammatical sense” of the expression, but does not understand its illocutionary role. She may be in a position to use each element and complex-forming device in making sensible moves in language games if she is allowed to isolate them from the rest of the expression and complement them as she will. Yet still she cannot be credited with understanding the utterance that is a result of a “projection.”

The possibility of linguistic projection, and the consequent possibility that one may only understand the grammatical sense of a complete sentence, is in general due to the fact that it is possible, even in a rudimentary complex language, to form sentences the sense of whose application is not determined by existent linguistic practices. Depending on the particular circumstances of the case, different responses are possible. It may be that the addressee of such an utterance reacts by shaking her head, by showing a lack of understanding, that is, by dismissing the utterance entirely: in the given context the linguistic action is, for her, senseless. But in some situations creative ways of handling these “rogue” sentences may be available which are not covered by current practices. New and sensible applications of sentences may be invented and guessed correctly, and may then themselves become established linguistic practices.

In order to see this more clearly in the case of projection, it is useful to remember that the transference steps discussed above are among these simple kinds of “misuse”[1] – the transference of an expression from one illocutionary role to another (e.g., from command to “report”). Our fictitious “natural history” can be represented in such a way that from the beginning there was an utterance whose “correct” extra-linguistic context was missing (for example: “slab” outside of the context of house building, i.e., outside the context of placing an order). This utterance might (in light of existing practices) have been regarded by a hearer as senseless. But the possible pragmatic worth of this prima facie senseless linguistic act might also have been so obvious that the discourse partner might easily see the point of such a “misuse.” In this way a former “misuse” becomes a new and regular use: that of describing or reporting.

The phenomenon of metaphor also belongs to this realm if one looks at its most fundamental form of use – not in a complex-forming device, but in deploying a “lexical” word in a way that does not correspond to established practices. In our simple language game one can think of the case of someone using the predicate “not-usable” (which has thus far been applied exclusively to building materials) in an act of commenting on the behavior of the person who called out the command. It is not difficult to imagine the moment of strangeness, the sudden understanding of the “point,” and the laughter that might follow such a “misused” expression. Even on the level of very simple language games, there are three different but related ways of fruitfully utilizing the possibility of creating new sentences, about which established linguistic practice says nothing definite: (1) Transference (application of an old expression in a new illocutionary sense, for example, “the light is still on” as a command); (2) projection, or “syntactic metaphor”[2] (the application of an old complex-building device in a new sense, for example, “these slabs are three”); and (3) metaphor in the traditional sense, which we now might refer to as “lexical metaphor.”

Let us once more address the question of whether this recognition of projection (syntactic metaphor) and of the other frequent cases of “positive misuse” in natural languages means that our understanding of the meaning side of language is overwhelmingly unsystematic. The answer, based on our above considerations, has to be no, in the following sense: we are not forced by this recognition to conclude that we learn the meanings of the sentences of our language individually and as wholes, one by one. We have to acknowledge that it is often the case that a hearer can work out only the “grammatical sense” of a sentence from the word meanings and the devices for forming complexes, but cannot, on this basis, get at its illocutionary sense. Thus, we have not achieved one of Dummett’s (1978, p. 450) stated aims, that of defining a unified concept of sense in such a way that

…once we know both the category to which a sentence belongs [i.e., the type of linguistic action in the sense of “question,” “order,” etc. – author’s clarification], and the sense which it carries, then we have an essential grasp of the significance of an utterance of the sentence.

This is precisely what is impossible when we only have the “grammatical sense”; the “significance” of the expression may remain inaccessible to the hearer. According to the considerations outlined above it is not the case that

…there is some uniform means of deriving all the other features of the use of any sentence from this one feature [i.e., from Fregean “sense” – author’s clarification] so that knowledge of that one feature of a sentence is the only specific piece of knowledge about it that we need to know its meaning. (Dummett 1976, p. 75)

Such a derivation in the strong sense can be seen to be impossible according to the arguments presented by Wittgenstein; there will always be gaps that we must close with our creative imagination. Despite this, sentences do have a “grammatical sense” that the hearer must indeed correctly grasp on the basis of sentence patterns known to her in order to understand the sentence’s type of complexity – and this clearly is not only a matter of sound. Recognizing this pattern (i.e., recognizing how the relevant linguistic means form a semantic unity out of the component expressions) involves schematic aspects that can be compared to “calculating.” One can think here of inflective word endings and of the connections they express, for example, that a particular adjective pertains to a particular noun. Because we learn this “calculating” as we learn a language, we do not have to learn each sentence individually and as a whole. Yet it does not always lead to a complete understanding of the sentence in question, and therefore the use of imagination is necessary above and beyond calculation. We have seen that this “use of imagination” involves procedures – it is not random or a matter of individual cases only. But at the same time, the steps to be taken in speaking and understanding a natural language are unlike the steps in a formal calculus. The procedures involved are very different from formal procedures. And this is one reason why Dummett’s project must fail.

Notes

1 With reference to using the expression “infrared light” for something invisible, Wittgenstein (1978, 33e) remarks: “There is a good reason for doing it, but we can also call it a misuse.” Concerning the positive role of such cases of “misuse” see also Schneider (1980).

2 Schneider (1990). The expression “syntactic metaphor” was originally introduced by Stenius (1960, p. 212ff.). He used it to characterize the logical status of meaningful expressions such as “red is not an object” (and Frege’s famous “the concept ‘horse’ is no concept”), whose meaning is unintelligible if one demands that meaning depend on the representational character of language alone. In general Stenius characterizes such sentences by saying: “Its sense does not have the form suggested by its logical syntax, but nevertheless this syntax seems to be the best syntax we can give it.” (p. 212) In light of our findings, this means the intended unity is not that which is signalled by the original use of the form, but we have no linguistic means by which to give the ‘correct’ form. Indeed, from the perspective developed here, it makes no sense to speak of ‘a correct form’. Our investigations can be read as a contribution to Stenius’s project of characterizing more exactly the non-representational aspects of language; they show, among other things, the ubiquity of the phenomena that, according to Stenius’s interpretation of the Tractatus, should merely be a special case. Cf. Jolley 2007.

References

Dummett, Michael (1976) What is a theory of meaning? (II), in Truth and Meaning: Essays in Semantics (eds G. Evans and J. McDowell), Oxford: Clarendon, pp. 67–137.

Dummett, Michael (1978) Can Analytical Philosophy be systematic, and should it be?, in Dummett, Truth and other Enigmas, London: Duckworth, pp. 437–458.

Jolley, Kelly Dean (2007) The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations, Burlington: Ashgate Publishing Company.

Schneider, Hans J. (1980) On language use and language structure. Kodikas/Code, 2: 77–85.

Schneider, Hans J. (1990) Syntactic metaphor: Frege, Wittgenstein, and the limits of a theory of meaning. Philosophical Investigations, 13: 137–153.

Stenius, Eric (1960) Wittgenstein’s Tractatus: A Critical Exposition of its Main Lines of Thought, Oxford: Blackwell.

Wittgenstein, Ludwig (1978) Bemerkungen über die Farben / Remarks on Colour (ed. G.E.M. Anscombe, trans. Linda L. McAlister and Margarete Schättle), Berkeley: University of California Press.

13

A “Theory of Meaning” – In What Sense?

In the previous chapters we have been engaged in a close reading of selected passages from Wittgenstein’s later work. We shall now explicitly assess the consequences which result from his reflections on the project of a “theory of meaning,” a subject we have thus far alluded to only in passing. In doing so, we enter into contested territory and encounter deeply opposed and passionately defended philosophical stances. It is therefore advisable to exercise extra care in considering what exactly the phrase “theory of meaning” can mean.

As a first step toward such clarification, we should, at this point, explicitly acknowledge that a naturalistic understanding of such a theory – that is, an understanding of such a theory as aspiring to give a scientific account of the emergence of meaningful (and especially linguistic) behavior out of forms of non-meaningful, non-intentional behavior or, alternatively, out of “representational processes” in the brain[1] – does not fall within the scope of topics Wittgenstein discusses. Consequently, it is not addressed in the present book. Now this does not, in itself, mean that the naturalistic question is uninteresting, or that we are presently in a position to formulate a priori grounds which guarantee that a convincing answer cannot be found. Whether or not this question can be answered will, of course, depend on our concept of naturalism, among other things. But this topic is simply foreign to Wittgenstein’s whole way of thinking and is therefore a subject about which the previous chapters have nothing to contribute. Stated positively, this means that when we speak in this chapter about the project of a “theory of meaning” we will remain within the philosophical domain, which here means the domain of clarifying an intentional activity by reflecting on it.

But does Wittgenstein’s thinking even allow for the possibility of philosophical “theories”? Would he not regard the very expression “philosophical theory” a contradiction in terms? We read, for example, in his Philosophical Investigations not only: “It was correct that our considerations must not be scientific ones” but also: “And we may not advance any kind of theory.” (§ 109) Has he not repeatedly stated that the task of philosophy is not to formulate and test hypotheses but rather to state what should be obvious, but what is in fact so close to our eyes that we are unable to see it? (§§ 89, 92).

These questions reveal the need for further distinctions among possible readings of the phrase “theory of meaning,” even after naturalistic readings are excluded. It is certainly correct to say that at no point in Wittgenstein’s extended and persistent efforts to clarify the many shades of a family of concepts connected with “meaning” is his procedure to postulate a realm of entities hidden from our view, to speculate about the relations they might have to one another, and to interpret on this basis what happens in the observable world of speech. In contrast to what he believes Gottlob Frege to have done in developing his ideas about Sinn and Bedeutung and in applying these ideas in a systematic way to proper names, predicate expressions, and sentences, Wittgenstein explicitly refuses to acknowledge a realm of meaning-entities (Bedeutungskörper) behind our linguistic utterances.[2] He is skeptical about a Fregean “third world” to which we should direct our attention when we want to discover the “logical form” of a given expression – a form taken by Frege to be hidden under its visible or audible surface. So if the phrase “theory of meaning” is supposed to have a sense, and if that sense is supposed to be compatible with the central tenets of Wittgenstein’s later reflections about the nature of philosophy, it cannot refer to the sort of “philosophical” theory that aims to explain something observable by recourse to something hidden. So far, then, we have two negative claims: (1) Wittgenstein’s later work is not concerned with developing a scientific theory about the emergence of meaning out of some state of affairs devoid of meaning; and (2) in his attempts to clarify what meaning is, Wittgenstein remains within the philosophical realm. For him this means that he is engaged in a reflection on our own activities, a reflection that we are able to pursue without any kind of (scientific or philosophical) “theory” about hidden entities “behind” language.

I would now like to add a third negative statement, namely that from (1) and (2) it does not follow that a philosopher of language must retreat to an attitude of “dismissive quietism.” Following Blackburn (1993) and Conant (1996),[3] this term is meant here to characterize the position that for a follower of Wittgenstein there are no relevant philosophical questions left to deal with and that if one adopts the attitude recommended by him one can be sure that no such problems will newly arise. Also, it does not follow that there are no philosophically relevant general claims that can be made about linguistic structure or that we must regard each problem in the philosophy of language as a singular phenomenon – like a particular occurrence of a mental disturbance in a particular patient, which, on account of the deep differences between different people’s developmental histories, it would be unreasonable to expect to recur in other circumstances. On the contrary, what our close reading of Wittgenstein has shown is that language itself does have a systematic side (in the narrower sense: it is like a calculus in certain respects – in containing kinds of words, for example) and that to understand and to spell out the (limited but existent) functioning of this systematic side of language requires some effort and is a prerequisite for understanding its other side, the side requiring imagination. If we want to call the results of such elucidatory efforts a “theory” (which Wittgenstein himself would have refused to do, to be sure), this would only mean an account of language that (among other things) makes it clear how the mentioned systematic aspects of language function as well as where their limits are, and why we have to expect that philosophical questions of the kind Wittgenstein is treating will continue to arise. The acknowledgment of the mentioned limits does not involve denying the existence of the systematic (or “calculus”) side, nor does it overestimate it by suggesting it comprehends something like a postulated “whole of linguistic meaning” – even if such a whole is understood in the strict and narrow sense of Frege’s Sinn, that is, as excluding the additional areas that Michael Dummett has called “force” and “point.”

To walk such a bipartisan line is not easy because, as we have seen, the interplay of “calculation” and “imagination” is very intricate indeed. It is therefore quite natural for one to fall into one of two traps: by overstating either the calculus side (as authors who take their orientation from Frege tend to do) or the side of imagination (a tendency found in some “quietists” who seem to deny that there are any systematic aspects to the semantics of natural languages). What our close readings of Wittgenstein have tried to show is that he provides an account that does justice to both these aspects, and (most importantly) that this account sheds light on the ways they interact. The ability to speak and understand a natural language is not the ability to operate a calculus; the description of this ability therefore cannot be a formulation of the rules of such a calculus – and for the same reason it cannot take the form of an axiomatic-deductive theory. But to say this is not to deny that we can distinguish parts of speech or that we can write grammar books for non-native speakers – books that make use of such distinctions in formulating rules as instruments to facilitate language learning. A proper grasp of grammatical categories and relations does play a role in one’s understanding of an utterance, and in this sense there is a formal side to language – even if an appreciation of this formal side frequently does not suffice for a speaker to so much as grasp the meaning of an utterance, as we have seen above. This important shortcoming has motivated us to introduce the technical term “grammatical sense.”[4]

So we must also recognize the other side. We have seen that, in order to acquire even the first steps of an extremely simple sign system (like the famous language game of the builders), it is necessary for one to have (in Robert Brandom’s terminology; Brandom 2008, pp. 91, 117) a “hermeneutic” understanding of the situation on the building site. The language learner has to grasp what is going on in the sort of social setting where a number of people are collectively engaged in a goal-oriented activity. When this language game (in the context of Wittgenstein’s fictitious tale) is later extended in such a way that the speakers can make use of structured utterances consisting of several words, the “calculus” aspect of language emerges and, with it, what Brandom calls an “algebraic” competence of the speaker: the language learner has to get the forms right. She has to see, for example, that “five slabs” has the same structure as (i.e., functions in a way analogous to) “seven columns,” and she must also appreciate the structural difference between “five slabs” and “green slabs.”

But even the ability to “get the forms right” is not the sort of competence that a speaker would have once she’d mastered a formal method that would enable her to grasp a fantasized totality (“the whole”) of what is linguistically meaningful. It is one of Wittgenstein’s most important contributions to have directed our attention to the fact that, in natural languages, grammatical forms are continually projected into ever new fields of activities. Consequently, analogies of the kind mentioned can become stretched to such a point that we may be inclined to say that the structural meanings themselves have changed. This change is comparable to the kind of change that takes place in the case of metaphor – confirming the aptness of Eric Stenius’s phrase “syntactic metaphor.”[5] To be able to grasp the meaning of such a projection, the hearer must once again possess a sort of hermeneutic understanding. She must understand how to make sense of a projection, despite the fact that it is, strictly speaking, a case of “misuse.” The meanings of such projections cannot be arrived at by calculation. Instead, projections open linguistic possibilities that lie beyond the scope of any rules that might have been stated up to that point. And this shows that the very idea of a “totality of meaning” is deeply misguided. To see that, and to see why it is misguided, is of great philosophical (and especially epistemological) importance.

We can therefore say that the results of the algebraic competence displayed in getting the forms right are used in later steps of making new projections, the meanings of which have then to be understood hermeneutically. And this third level of understanding cannot in turn be captured by algebraic means in a once-and-for-all fashion. Any structure that might be developed can (in a “living” language) itself be projected once again, thus once more opening up new possibilities. Therefore (and this is where the account given here seems to diverge from Brandom’s), the hermeneutic mode of understanding has a place not only at the base of language, but also at the highest levels of linguistic competence. It is this dialectical movement – from the hermeneutic or “imagination” side of language to its algebraic or “calculus” side, which then continues (on a higher level) to another “imaginative” step – that explains the discrepancies between grammatical and semantic structure: those discrepancies that so many philosophers and linguists have discussed and which have led Noam Chomsky (1957) to opt for a purely formal understanding of syntax. It is also this unavoidable difference between “surface” and “deep” structure that has led Wittgenstein (2005, 156e (§ 46)) to his claim that any fixation of a particular logical structure that would be taken (for example by philosophers like Russell or Carnap) as exhibiting a (or even “the only”) “fully developed language” would lead to “injustices”[6] in that it would promote one structure to a superior rank without a philosophical justification. The mentioned discrepancies might also be what led some contemporary authors to “dismissive quietism,” because they misread them as showing that there are no important generalities in natural languages at all. However, as we have seen in these pages, the kind of “explanation” (or “commentary,” “reminder”) practiced by Wittgenstein is possible, is not restricted to singular cases, and is philosophically helpful, although it does not involve any hypotheses about hidden entities, only a thorough reflection on our own complex activities and their internal relations.

Yet can such reflection be of epistemological relevance, as the founders of Analytic Philosophy claimed? Some commentators who sympathize with a “quietist” reading of Wittgenstein’s later works have pleaded that we give up this idea. Richard Rorty (1980), for example, has defended what he has called a “pure” philosophy of language, in the sense that it should steer clear of epistemology and treat only the workings of language (as philosophers like Gottlob Frege and Donald Davidson have done).[7] In a different but related way, other authors (notably John McDowell (1998, 1998a, 2007)), in a controversy with Michael Dummett (1987, 2007), have claimed that the most we can reasonably aspire to is a “modest,” not a “full-blooded,” understanding (or theory) of meaning. The term “modest” here is intended to mean the opposite of “full-blooded,” as per the term used by Dummett. According to Dummett’s usage, a full-blooded account of meaning is one that is of epistemological relevance, especially in that it avoids the attempt to explain linguistic meaning by recourse to psychological meaning in the realm of “thinking.” So a “modest” theory of meaning in Dummett’s sense is one which refuses to say what a speaker’s knowledge of the meaning of a word or phrase consists in, apart from saying that the speaker is in command of a related underlying “concept.” And what this in turn means is not explained in a modest theory, which for this reason cannot be of any help in normative epistemological discussions. Opposing this kind of modesty, Dummett has (rightly, I think) insisted that we need a more robust philosophical account here. A philosophical account of language should be epistemologically relevant, that is, it should help us in any particular case to distinguish meaningful statements from those that are not meaningful, that is, from utterances for which the speaker has not succeeded in making clear what sense these utterances are meant to have. In order to accomplish this distinction, we should be able to say what a speaker’s knowledge of the meaning of a word or phrase consists in, how this knowledge reveals itself. Dummett thinks that a legitimate account of the meaning side of language is not entitled to help itself to a semantic terminology from another field, like (scientific or “folk”) psychology. Talk of “concepts” in particular requires a philosophical clarification and cannot be taken for granted. If we were to stop short here we would be captured in a vicious circle of the kind we find in early Empiricism: language would be explained with recourse to “ideas,” and these in turn would be explained as meanings of linguistic expressions. As is well known, Wittgenstein opens his Philosophical Investigations with a criticism of this kind of recourse to “mental entities”; in his case it is St Augustine’s version of such a (as it were) “reduplication” theory of meaning.

If the very phrase “theory of meaning” is meant to imply a philosophical project that aspires to epistemological relevance by presuming to legislate over a purportedly surveyable “realm of the meaningful” by once and for all characterizing all the kinds of admissible expressions and all their admissible combinations (as, for example, the early Carnap (1964) had envisaged), then our reading of Wittgenstein has led us to agree with those who are convinced that this goal is misconceived. There is no “realm of meaning” that could be characterized once and for all in its totality, and certainly epistemological theories about the forming of all knowledge on the basis of “sense data” are hopelessly unconvincing and not at all something with which the later work of Wittgenstein would be compatible. To agree with him on this point is an easy step to take on the basis of the considerations developed in these pages. And if one chose to use the term “immodest” to criticize such a position, this would be in full accord with Wittgenstein. From the perspective developed in this book, an “immodest” project of this kind is clearly an illusion. Indeed, our discussion has provided many reasons why such a project is impossible to realize.

But it should be noted that this concept of immodesty is different from Dummett’s concept of full-bloodedness; it is not the opposite of his concept of “modesty.” To reject the project of a formal account of a purported “totality of the meaningful” (let alone to attempt to do this on the basis of a sense data theory) does not mean to accept recourse to psychological concepts as the last word in a philosophical account of meaning. This can be seen when we put the question differently and ask whether Wittgenstein’s account, as interpreted in the foregoing chapters (regardless of whether or not we want to call it a “theory”) is or is not of epistemological relevance. Can it be of help in critical reflections about purported insights and explanations? The answer emerging from our discussions is clearly affirmative. Although anyone who has understood the process or activity of projection as explained in this book will see that it is an illusion to speak of a surveyable realm of the meaningful, or to imagine that this realm could ever be circumscribed by means of rules which could function as a basis for epistemological legislation, this in no way vitiates the fact that Wittgenstein’s account of meaning is (and is meant to be) of the highest epistemological relevance in many of the particular cases he discusses. He corrects mistakes; he destroys illusions about non-existent foundations and pseudo-explanations, perhaps most strikingly in the case of his so-called “Philosophy of Psychology.” In this area we can also see how he avoids circularity precisely by refusing to take psychological concepts for granted. So the account of meaning he offers is not “pure” because it is of epistemological relevance, and it is (on Dummett’s understanding of these words) not modest but “full blooded,” since it has something to say about what the understanding of a linguistic expression consists in, without recourse to unexamined mental entities like “concepts” but with recourse to what he has called “language games.”

The epistemological relevance of Wittgenstein’s work and his opposition to “dismissive quietism” is sometimes underestimated because it is not always fully appreciated that his investigations are normative. Unfortunately, Wittgenstein himself has contributed to this misconception that all he has to say is purely descriptive. For example, he writes that philosophy “leaves everything as it is” (§ 124), and “Philosophy just puts everything before us, and neither explains nor deduces anything.” (§ 126) But we should not read such sentences in isolation. To do so would be to neglect the important distinction he makes between those contexts in which language works and those contexts in which it “goes on holiday.” (§ 38) Only where language works can we “leave it as it is.” And much of the energy that a philosopher working in Wittgenstein’s spirit has to invest goes into determining on which side of this divide a particular usage of language belongs: is it a case in which language works or in which it goes on holiday? Wittgenstein (2005, 302e (§ 87)) also explicitly states this normative interest when he says he would “rectify mistakes.”

From the above considerations we can conclude that what is today perhaps most commonly called a “theory of meaning” (i.e., one where there is a robust sense of “theory” not exemplified in Wittgenstein’s work) will in most cases be “pure” in Rorty’s sense (i.e., it will have no direct epistemological concerns) and can (in Dummett’s sense) only be a modest one, since it does not explain what “being in command of a concept” consists in. It typically treats a logical system of the kind developed by Frege as a point of comparison to shed light on some aspects of natural languages. Aspects of language that might be brought into focus by such a comparison are those that we have here called the “calculus” side of language (the side to which our “algebraic understanding” applies). From the considerations set forth in this book we can see that such a theory will concern itself with what Wittgenstein calls “surface grammar,” that is, with similarities among expressions that can be “taken in by the ear.”[8] It is clear that this level does not suffice in terms of answering epistemological questions.

If, on the other hand, our topic is “Wittgenstein’s account of meaning,” our reading of his texts clearly indicates that what he is doing cannot be classified as “modest” in Dummett’s sense, but must be termed “full blooded.” In other words, it does not take psychological entities like “concepts” for granted but (in speaking about the mastery of “language games”) gives an account of what the “knowledge of a concept” consists in. Furthermore, it makes clear what is meant by the mastery of complex forms of expression by (among other things) offering genealogical accounts, that is, by “…finding and inventing intermediate links.” (§ 122; Wittgenstein’s emphasis) Without recourse to “psychological entities” (which would introduce the danger of circularity by speaking of “inner semantic” processes in order to explain the linguistic activities), Wittgenstein is therefore able to show what the mastery of simple expressions entails and what steps are involved in the expansion of these expressions. Here it is important to note that his genealogical stories (as he explicitly states) are not meant to lead to an imagined “whole,” a complete “realm of the meaningful.” Such an attempt, he said, will “only lead to injustices.”[9] Instead, Wittgenstein is aiming to achieve what he calls “surveyability” or an “overview” (§ 122)[10] of areas of linguistic usage, which, although restricted, nevertheless exhibit systematic relations (in a broad sense) whose workings are characteristic of the functioning of natural languages. So his treatment of meaning is normative and, by being so, of the greatest epistemological relevance; it helps us to distinguish cases in which we “said and meant something” from cases in which we only “said something,” but in which a careful and often lengthy activity of reflection reveals that (despite appearances) we failed to mean anything. In this respect, his account is not “pure” in Rorty’s sense.

How, then, should we answer the question posed by the title of this chapter? Does our close reading of Wittgenstein’s later work in the end justify the claim that his work constitutes a contribution to a theory of meaning? My own answer is this: we at least find a highly relevant contribution to the issue of what we could possibly mean by the phrase “theory of meaning.” My message for the modest quietists of different schools is (among other things) that there is more to learn about the calculus side of language in Wittgenstein’s writings than some of them seem to think, and also about the systematic side (in a broader sense) of the ways of using our imagination. It seems to me worthwhile to understand in detail why the calculus side of language exists, but can cover so little ground, why the calculus picture must fail if it is taken as a guiding one in the endeavor to understand all of the basic workings of natural languages, and to understand the workings of the counterpart of this side of language, the part that engages our capacity for imagination. As we have seen, this understanding involves some extended reflections and, regardless of whether one chooses to call these reflections a “theory,” Wittgenstein’s work shows at length how we can proceed here without circularity. I am aware that some readers (on the “quietist” side in its non-dismissive version) and certainly Wittgentstein himself, would, even if they accept what has been worked out in this book, prefer not to speak of a “theory” here.

My message for the defenders of a calculus type of theory is that the close reading as exercised in this book shows in detail why a theory of meaning of the sort Dummett has envisaged cannot be realized, but also shows that this does not force on us the admittedly absurd conclusion that we learn the sentences of our native languages one by one. To find the way out of Dummett’s impasse (“Frege or no serious philosophical treatment of meaning at all”) one must recognize that (even in the domain of Frege’s Sinn) we have to rely on two kinds of human understanding: the hermeneutic ability to understand situations (“imagination”) and the algebraic ability to get the forms right (“calculation”). If we are willing to follow Wittgenstein in adopting a diachronic perspective, that is, one that takes into account that (ontogenetically and phylogenetically) our linguistic competence has evolved in time, then we can see that these two types of understanding have to be understood as constantly interacting, and that in the course of these interactions it is the hermeneutic side that has the last word.

As we have shown, it takes some prolonged effort to formulate and argue for such a picture of language. And it may well be the case that some readers would happily call this kind of work the construction of a “theory.” For those who do, there is a clear sense in the phrase “Wittgenstein’s later theory of meaning.” In his later work, we indeed find important contributions to a “theory of meaning” in this broad sense: we get a substantial, systematic, and detailed picture of the workings of natural language and of the kind of competence that is involved in mastering it. Wittgenstein himself surely was no “dismissive quietist.” But at the same time, he shows us why we cannot hope to develop a theory of meaning in the strict sense of an axiomatic-deductive system. This is why, for readers who follow Wittgenstein’s stricter use of the term “theory,” the answer to the question hinted at in the title of this chapter has to be negative: Wittgenstein’s later work does not offer any building blocks for an axiomatic-deductive theory of meaning. Personally I do not want to quarrel about words; I hope to have shown that Wittgenstein has important and as yet under-appreciated contributions to offer both sides.

In the aphoristic writings of the dramatist Heinrich von Kleist (1964, p. 71) we find the following remark: “One could distinguish two classes of people, on the one hand there are those who are at home with metaphors, on the other are those at home with formulas. Those at home in both areas are very few; they do not form a class.” This book aims to increase the number of people who are at home on both sides.

Notes

1 Millikan (1984, 2004); Dretske (1981).

2 See above, pp. 55 and 64, n. 6.

3 Cf. McDowell (2009). Both Conant and McDowell clearly speak against the “dismissive” variant of quietism, but both sympathize with Wittgenstein’s doubts that there could be “philosophical theories” involving postulated hidden entities. Sometimes the word “quietism” is used to signify a position abstaining from grand metaphysical theories. In this sense Wittgenstein is a quietist. But as we have seen, this does not prevent him from engaging in philosophical work – and leaving plenty of it for us, for now as well as for the future. Cf. Stekeler-Weithofer (2012).

4 See above, p. 148.

5 See above, pp. 162 and 164, n. 2.

6 Cf. the quote above, p. 113.

7 See Introduction, p. 2.

8 See above, p. 98.

9 See above, p. 113.

10 The German term is “Übersicht.”

References

Blackburn, Simon (1993) Review of Paul Johnston, Wittgenstein and Moral Philosophy. Ethics, 103: 588–590.

Brandom, Robert (2008) Between Saying and Doing: Towards an Analytic Pragmatism, Oxford: Oxford University Press.

Carnap, Rudolf (1964) The Logical Syntax of Language, London: Routledge and Kegan Paul.

Chomsky, Noam (1957) Syntactic Structures, Den Haag: Mouton.

Conant, James (1996) On Wittgenstein’s philosophy of mathematics. Proceedings of the Aristotelian Society, 70: 195–222.

Dretske, Fred I. (1981) Knowledge and the Flow of Information, Cambridge MA: MIT Press.

Dummett, Michael (1987) Reply to John McDowell, in Michael Dummett (ed. Barry M. Taylor), Dordrecht: Nijhoff, pp. 253–268.

Dummett, Michael (2007) Reply to John McDowell, in The Philosophy of Michael Dummett (The Library of Living Philosophers, vol. XXXI), (eds Randalle E. Auxier and Lewis Edwin Hahn), Chicago: Open Court, pp. 367–381.

Kleist, Heinrich von (1964) Anekdoten, Kleine Schriften (ed. H. Sembdner), Bd. 5, München: Deutscher Taschenbuch Verlag.

McDowell, John (1998) In defence of modesty, in J. McDowell, Meaning, Knowledge, and Reality, Cambridge MA: Harvard University Press, pp. 87–107.

McDowell, John (1998a) Another plea for modesty, in McDowell, Meaning, Knowledge, and Reality, Cambridge MA: Harvard University Press, pp. 108–131.

McDowell, John (2007) Dummett on truth conditions and meaning, in The Philosophy of Michael Dummett (The Library of Living Philosophers vol. XXXI), (eds Randalle E. Auxier and Lewis Edwin Hahn), Chicago: Open Court, pp. 351–366.

McDowell, John (2009) Wittgensteinian “Quietism.” Common Knowledge, 15: 365–372.

Millikan, Ruth G. (1984) Language, Thought, and other Biological Categories: New Foundations for Realism, Cambridge MA: MIT Press.

Millikan, Ruth G. (2004) Varieties of Meaning, Cambridge MA: MIT Press.

Rorty, Richard (1980) Philosophy and the Mirror of Nature, Oxford: Blackwell.

Stekeler-Weithofer, Pirmin (2012) Against Quietism. Wittgenstein Studien 3: 233–244.

Wittgenstein, Ludwig (2005) The Big Typescript: TS 213, German-English Scholar’s Edition (ed. and trans. C. Grant Luckhardt and Maximilian A.E. Aue), Oxford: Blackwell.

Index

aggregate complexity

ambiguity

analysis/synthesis

assertion sign

assumption

Augustinian picture

axiomatic-deductive theory

Blackburn

Brandom

calculation/calculus

Carnap

chess

Chomsky

color square language

complex expressions

component action/expression/situation

Conant

concept/object

conceptual notation/concept script

context principle

creativity, see also imagination

Davidson

demonstrative teaching, see ostensive teaching

depth grammar, see surface/depth grammar

derivation of sentence meanings

describing

Dummett, Chapter

epistemology

explicitness/implicitness, see implicitness/explicitness

form of representation

form/content in logic

Fregen, Chapter

full-blooded theory, see modest/full-blooded theory

function of word in sentence

fundamental logical relationship (Frege)

generality

grammar (traditional)

grammar (Wittgenstein)

grammatical fiction

grammatical rule

grammatical sense

illocutionary act/force/role

image, see picture

imagination

implicitness/explicitness

injustice

innumerable kinds of expressions

judgeable content

judgment stroke, see assertion sign

kinds of expressions

Kleist

language game

Locke

logical form/role

McDowell

meaning body

mental process

metaphor

microscope

modest/full-blooded theory

name

naturalism

nominalism

normativity

notation

numerals

object/concept, see concept/object

ostensive teaching

overview

paradigm

part/whole relationship

parts of speech

philosophy

picture

point of an utterance

projection

propositional content

psychology

pure philosophy of language, see epistemology

quietism

Rorty

rule

Russell

Searle

secondary meaning

semantic function/role/structure

sense

simile

speech act theory

standard form

standing for

Stenius

subject/predicate

substitution

surface/depth grammar

syntactic metaphor

synthesis, see analysis/synthesis

systematic theory

theory of meaning

thought

transference

unity of complex expressions

unsaturatedness

use

utterance meaning, see point of an utterance

Waismann

word/sentence