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Key Theories of Ludwig Wittgenstein

Ludwig Wittgenstein (1889–1951) was the leading analytical philosopher of the twentieth century. His two philosophical masterpieces, the Tractatus Logico-philosophicus (1921) and the posthumous Philosophical Investigations (1953), changed the course of the subject. The first was the primary origin of the “linguistic turn” in philosophy and inspired both logical positivism and Cambridge analysis in the interwar years. The second shifted analytic philosophy away from the paradigm of depthanalysis defended in the Tractatus and cultivated by logical positivists and Cambridge analysts toward the different conception of “connective analysis,” which was a primary inspiration of Oxford analytic philosophy and dominated the third quarter of the century. Wittgenstein is unique in the annals of philosophy for having produced two equally influential, diametrically opposed, philosophies. His work, in both phases of his career, is marked by its originality, subtlety, and stylistic brilliance. By nature an aphorist, he strove to crystallize his thoughts in short and often gnomic remarks of great power, which make considerable demands upon his readers.

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Born in Vienna to a wealthy and cultured family of Jewish origin, he studied engineering in Berlin and Manchester. Attracted by the new logic of Frege and Russell and fascinated by its philosophical implications, he went to Cambridge to work with Russell in 1911. The work he did there marks the beginning of his seven years labour on the Tractatus. He served in the Austrian army during the First World War, completing his book while on active service. Convinced that he had solved the central problems with which he had been concerned, he abandoned philosophy and worked as a primary school teacher from 1920 to 1926. The next two years were spent designing and building a mansion in Vienna for his sister. The house, which still stands, is austerely beautiful. During these years, he came into contact with Moritz Schlick, the moving spirit behind the Vienna Circle, members of which had studied the Tractatus in detail. The book, and Wittgenstein’s conversations with Schlick, Waismann, and more briefly with Carnap and Feigl, exerted great influence upon the evolution of logical positivism.

In 1929 Wittgenstein returned to Cambridge to resume philosophical work. Although he had initially intended to continue working in the vein of the Tractatus, he rapidly found deep flaws in his first philosophy. Between 1929 and 1932 his thought underwent profound revolution. He undermined the supporting members of the edifice of his earlier ideas and laid the foundations for his new method and its application both to the range of problems in the Tractatus and to the philosophy of mathematics and philosophical psychology. Over the next decade and a half, he consolidated and developed his new ideas, which he communicated in his now legendary classes to his pupils in Cambridge. Through them, and through the circulation of their lecture notes, he revolutionized philosophy at mid-century. He was appointed to a chair at Cambridge in 1939. During the war, he worked first as a hospital orderly in London and later as a laboratory assistant doing research on wound shock in Newcastle. He completed the Philosophical Investigations in 1946, but did not publish it. In 1947 he resigned his chair in order to concentrate upon writing. He died of cancer in Cambridge in 1951, leaving behind a voluminous Nachlass of some 20,000 pages. The Investigations was published in 1953 and was immediately hailed as a masterwork. Over the next decades a further dozen unfinished works and four volumes of lecture notes taken by his students were published.

The first phase of Wittgenstein’s career consisted in responding to, and bringing to its zenith, an antecedent tradition of metaphysical and logical reflection upon the relationship between thought, language, and reality. The influences upon him were primarily Frege and Russell, but also Schopenhauer and the two philosopher-scientists Hertz and Boltzmann. Other general cultural influences that he acknowledged were the writings of Karl Kraus, Adolf Loos, Paul Ernst, and Otto Weininger. A later influence was Oswald Spengler. Some of these figures were influential largely in the manner of Rorschach spots – one or two sentences that they had written served Wittgenstein as seeds for the development of his own ideas. The second phase of Wittgenstein’s career, which culminated with the Investigations, is virtually without precedent in the history of philosophy. It arose, phoenix-like, out of the ashes of the Tractatus.

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The Tractatus Logico-philosophicus

Two general themes dominate the Tractatus. First is the nature of representation, the relation between thought, language, and reality, and the limits of thought and representation. Second is the nature of logic and logical truth. The two are intimately interwoven, since logic is conceived to be a condition of sense. The metaphysical presuppositions of logic are at the same time the metaphysical presuppositions of representation in general. Logic does not presuppose the existence of any logical facts or logical objects, let alone any logical experience, as Frege and Russell supposed. But it does presuppose that names have meanings and that propositions have sense. The meanings of simple (logically proper) names, which are the final residue of logical analysis, are simple sempiternal objects in reality. The sense of an elementary proposition, which is a combination of names in accord with logical syntax and which is logically independent of any other proposition, is the possible state of affairs that the proposition depicts and the existence of which it asserts.

The Tractatus opens by delineating a crystalline metaphysics. The world is the totality of facts, not of things. The totality of things (simple objects) of which the world consists constitutes the indestructible substance of all possible worlds. Because the Tractatus is a treatise on logic, Wittgenstein gives little clue in the book as to what kinds of items simple objects are – that would belong to a treatise on the application of logic. But it is clear from his notebooks, both before and after the writing of the book, that the kinds of things he had in mind are spatio-temporal points, simple unanalyzable perceptual qualities (minimally discriminable shades of color, sounds, degrees of hardness, etc.) as well as relations. Objects have both form and content. The form of an object consists in its combinatorial possibilities with other objects (a color can concatenate with a spatio-temporal point but not with a sound). The combinatorial possibilities of an object are its internal properties. These determine the ontological category of the object. Different objects that share the same form, e.g. different shades of color, belong to the same ontological category, e.g. color. The actual combinations of an object with other objects, e.g. a shade of color with specific spatio-temporal points, are its external, contingent properties. A possible concatenation of objects constitutes a state of affairs. The obtaining or non-obtaining of a state of affairs is a fact. The totality of positive and negative facts constitutes reality.

A representation of a state of affairs is a model or picture. In it, elements of the picture go proxy for the elements (objects) represented, and their arrangement in accord with conventions of representation represents the arrangement of the items in a possible state of affairs. Such a picture is true (or correct) if things in reality are arranged as it represents them as being. A picture must possess the same logical multiplicity as, and be isomorphic with, what it represents. Propositions are a special case of representation – they are logical pictures. It is of the essence of propositions not merely to be bivalent (i.e. either true or false, as Russell supposed) but to be bipolar – to be capable of being true and capable of being false. This insight lies at the heart of the Tractatus. In this way, propositions reflect the nature of what they represent, for it is of the nature of states of affairs that they may obtain or not obtain. An elementary proposition depicts an atomic state of affairs. It consists of simple names, which are the points at which language is connected to reality. The meanings of the simple names are the simple objects in reality for which they go proxy. The logico-syntactical form of a simple name mirrors the metaphysical form of the object in reality that is its meaning. So the logico-syntactical combinatorial possibilities of names mirror the metaphysical combinatorial possibilities of objects. Hence what can be described in language coincides with what is possible in reality. In this sense, the Tractatus espouses a form of modal realism. What is metaphysically possible in reality is languageindependent, but is necessarily reflected in what makes sense in language. The bounds of sense necessarily coincide with the limits of possible worlds.

Pace Frege, propositions are not names. They do not have a meaning, do not stand for or go proxy for things. Propositions are sentences in their projective relation to the world. They have a sense (or direction); they represent (point towards) a possibility in reality and say that it obtains. A proposition agrees or disagrees with reality, depending on whether it is true or false. It is true if things in reality are as it represents them as being, otherwise it is false. Its sense is independent of whether it is true or false. To understand a proposition is to know what is the case if it is true and also what is the case if it is false, and one can understand it without knowing whether it is true or false. In a proposition, what represents is the fact that its constituent names are concatenated as they are. A metaphysics of symbolism informs the Tractatus. Only simple names can stand for simple objects. Only relations can represent relations; so in the proposition “aRb” it is not “R” that says that a stands in the relation R to b, but rather thata” stands to the left of “R” and “b” to the right that says that aRb. And only facts (i.e. propositions) represent facts. The sense of a proposition, the state of affairs which it depicts, is a function of the meanings of its constituent names. Sense must be absolutely determinate, as otherwise the law of excluded middle will not apply (and the propositional sign will not express a bipolar proposition). Hence any vagueness in the propositions of ordinary language must be a feature of the surface grammar, which will disappear on analysis. Any indeterminacy must be determinately indeterminate and will be seen to be so on analysis, which will reveal the proposition in question to be analyzable into a disjunction of determinate possibilities. The essence of the proposition is given by the general propositional form, which is: “This is how things are,” i.e. the general form of a description of how things stand in reality. In general, the essence of words is to name objects in reality, and the essence of propositions is to describe how things stand.

The picture theory of thought and proposition gave a profound answer to the fundamental problems of the intentionality of thought and language. When one thinks that a is F, then the object of one’s thought is a – one’s thought reaches right out to a and to none other. One’s thought is intrinsically individuated by its content, e.g. that a is F. If one’s thought is true, then it reaches right up to reality, and does not fall short of what is the case, namely that a is F. What one thinks is precisely what is the case. Hence what one thinks cannot be a mental representation (e.g. an array of ideas in one’s mind or an abstract object such as a Fregean Gedanke), for then what one thinks would not be what is the case if one’s thought is true. Nevertheless, one’s thought may be false. But what one thinks (the content of one’s thought) remains the same whether one thinks truly or falsely. So how can one’s thought be identical with what is the case if it is true, and also be independent of what is the case – if one’s thought is false? Furthermore, what one thinks when one thinks falsely is precisely what is not the case. But if what one thinks when one’s thought is false does not actually exist, how can one think it? It seems that thought predetermines reality “give or take a Yes or No” – that there is a pre-established harmony between thought and reality. For if one’s thought is true then what one thinks is what is the case, and if one’s thought is false then what one thinks is that which is not the case. Accordingly, thought as it were prepares a mold for reality, leaving it but two options, to fill it or to leave it empty. What must thought and reality be like for this harmony to obtain? Further diffi- culties attend the intentionality of language. One gives expression to one’s thought by a sentence, e.g. “a is F,” and the name “a” refers precisely to a and no other, just as the sentence describes precisely what is the case if what one says is true. But how can mere signs, noises, or marks on paper represent something? How can one part of reality, as it were, represent something? How can signs reach beyond themselves and refer to a long vanished or future object and describe a state of affairs that is not present and indeed may never obtain?

The modal realist metaphysics of the Tractatus and the metaphysics of symbolism of the picture theory were tailored to resolve this battery of problems. What is represented by a true proposition is exactly the same as what is represented by a false one – namely a state of affairs (which may or may not obtain). What is asserted by a true proposition is exactly the same as what is denied by the assertion of its negation. This is possible because the proposition is a picture or model of reality, and internally related to what it represents, i.e. a state of affairs, irrespective of whether things are as it asserts them to be. Precisely because the names of which propositions on analysis consist go proxy for the objects that are their meanings and because their logico-syntactical form mirrors the metaphysical form of the objects, the combination of names in a proposition represents the possibility of the objects they stand for being correspondingly combined in a fact. In a proposition a (possible) state of affairs is put together experimentally. So a proposition is literally a model (picture) of a possibility. It is true if the possibility represented obtains, otherwise it is false. This explains how it is that what we think is the same irrespective of whether our thought is true or false. It also explains how it is that “p” and “~prepresent the same state of affairs, the former asserting its existence and the latter denying it. An immediate consequence is that negation does not characterize the sense of “~p,” i.e. it does not characterize that which is or is not the case and which is represented by “p.” It does not stand for something in reality (pace Frege and Russell, who conceived of the negation sign as standing for a function or logical object) which is a feature of what is the case. Negation is an operation, not a function. It, as it were, reverses the sense of a proposition. The assertion of “p” expresses agreement with what is represented, i.e. with the state of affairs represented, and says that it obtains; the assertion of “~p” expresses disagreement with what is represented, and says that it does not obtain. The proposition must guarantee the possibility of the fact the existence of which it asserts. It does so by virtue of sharing a logical form with what it represents and by virtue of its constituent names being connected to the constituents of the possibility represented. Whether things are as they are represented as being depends upon whether the state of affairs depicted obtains. The metaphysics of symbolism and the ontology of atomism ensure the harmony between thought, language, and reality. Thought and its expression have a content which is identical with what can be the case, and coincide with what is the case if they are true. The correlation of names and their meanings is psychological, effected by acts of meaning by such and such a name this ☞ object. We use the propositional sign as a projection of a possible situation. The method of projection is thinking the sense of the proposition, i.e. when we use the propositional sign “p” to say what we think, we think that p, so we mean by the sign the state of affairs that p, which is its sense. So the intentionality of language is extrinsic, derivative from the intrinsic intentionality of mental acts of meaning and thinking.

The logical analysis of propositions must terminate in elementary propositions which are logically independent of each other, i.e. have no entailments. Their truth depends only on the existence and nonexistence of atomic states of affairs. Elementary propositions can be combined to form molecular propositions by means of the logical connectives. These devices are not names of logical entities (as Frege and Russell supposed), but truth-functional operators which generate truth-dependencies between propositions. The logical connectives are interdefinable, and can be reduced to the single operation of joint negation. All possible propositions can be generated by means of joint negation of elementary propositions (the thesis of extensionality). All logical relations (of implication, incompatibility, or compatibility) result from the inner complexity of molecular propositions, i.e. the truth functional combination of their constituent propositions. The sense of a molecular proposition is a function of the senses of its constituent elementary propositions. It is determined by the truth functional form of their combination, which fixes the truth conditions of the molecular proposition, i.e. the conditions which the molecular proposition must satisfy in order to be true. There are two limiting cases of truth functional combination, namely tautologies and contradictions. These are the propositions of logic. Since negation is given by the mere bipolarity of the proposition and conjunction by the mere possibility of successive assertion, all the propositions of logic flow from the essence of the proposition as such. Tautologies and contradictions are limiting cases of truth-functional combination inasmuch as they are no longer bipolar. They have no truth conditions, for tautologies are unconditionally true and contradictions unconditionally false. They are well formed but degenerate propositions (in the sense in which a point is a degenerate case of a conic section). A tautology is true under every assignment of truth values to its constituent propositions, so it excludes no possibility; a contradiction is false under every such assignment, so it excludes every possibility. So they are both senseless; they have, as it were, zero sense. They say nothing at all. But this vacuous logical necessity is the only form of expressible necessity. So it cannot be argued that while the empirical sciences investigate the domain of contingent truth, philosophy is an a priori science which investigates the domain of necessity. The degenerate truths of logic are not a field in which pure reason alone can attain knowledge about reality, for to know the truth of a tautology is to know nothing about how things stand in reality.

This conception of logical truth was revolutionary. Psychological logicians (e.g. B. Erdmann) had argued that the laws of logic describe the ways human beings are constrained by the nature of their minds to think. Platonists (e.g. Frege) held that the laws of logic describe completely general logical relations between abstract entities which exist in a “third realm.” Russell believed that they describe the most general facts in the universe. It was thus held that logic had a proper subject matter of its own, that it was the science of the completely general, and that logical investigation could result in genuine knowledge. The Tractatus rejected all these views. The mark of a logical proposition is not, as Frege and Russell had supposed, absolute generality. Logical truths are tautologies, not generalizations of tautologies: either it is raining or it is not raining is as legitimate a logical truth as any, and “(p) (p ⁄ ~p)” is not even a well formed proposition (since it employs the formal concept of a proposition; see below). Moreover, all the propositions of logic say the same thing, namely nothing. So there is no logical knowledge to be attained, merely the transformation of one vacuous tautology into another. But different tautologies exhibit different patterns of internal relations between propositions.

Unlike the vacuous propositions of logic, metaphysical utterances are nonsense – they transgress the bounds of sense. For the categorial concept-words which occur in them – “object,” “fact,” “name,” “proposition,” “colour,” “space,” etc. – are not genuine concept-words but variables which cannot occur in a fully analyzed well formed proposition. They represent the constant form of their values. But what one tries to say by means of the pseudo-propositions of metaphysics, e.g. that space is three-dimensional or that red is a color, is shown by features (the forms of the constituent names) of genuine propositions, e.g. that a is located at point xl, ym, znor that that point is red. What is shown by a notation cannot be said. Truths of metaphysics are ineffable; and so too are truths of ethics, aesthetics, and religion. Just as kant circumscribed the limits of knowledge to make room for faith, Wittgenstein circumscribed the bounds of language in order to make room for ineffable metaphysics.

An immediate consequence is that there can be no philosophical propositions, i.e. propositions describing the essential natures of things or the metaphysical structure of the world. So the very propositions of the Tractatus itself are condemned as nonsense – as attempts to say what can only be shown. Their role was to lead one to a correct logical point of view. Once that is attained, one can throw away the ladder up which one has climbed. Hence philosophy is not a science. Indeed, it is not a cognitive discipline at all. The results of philosophy are not new knowledge, but philosophical understanding. The future task of philosophy is to monitor the bounds of sense, to clarify philosophically problematic sentences, and to show that attempts to say something metaphysical transgress the bounds of what can significantly be said.

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The Philosophical Investigations

The Investigations is the precipitate of sixteen years of reflection, which began with Wittgenstein’s dismantling of the edifice of the Tractatus. He had wanted the book to be published together with the Tractatus, so that the two styles of thought could be seen in juxtaposition. The contrast could not be greater. A considerable part of the Investigations is concerned explicitly or implicitly with criticizing fundamental commitments not only of the Tractatus but also of the whole tradition of philosophical thought of which it was the culmination, and replacing them by a profoundly different conception.

The idea that the meaning of a name is the object it stands for was misconceived. The very idea involves a misuse of the word “meaning,” for the meaning of a word is not an object of any kind. There is no such thing as the name-relation, and it was misconceived to think that the essence of words is to name something, for words have indefinitely many roles. Although words may be connected to reality in all manner of ways (one may stick a label on a bottle on which is written “Shake before use,” wear a name-label on one’s lapel, print the name of a book on its cover, hang an “Enter” notice on a door, etc.), none of them determines the meaning of a word; they presuppose it. Words are not connected to reality by semantic links at all. The supposition that they are derives from a misapprehension of ostensive definition, which connects a word with a sample, as when one explains what a color word means, e.g. “This ☞ 28bbb3347a932edf44620216dc402853 color is black.” But the sample invoked is an instrument of language and belongs to the means of representation, not to what is represented. For the ostensive definition does not describe anything, but gives a rule for the use of the word “black.” It is akin to a substitution rule, for instead of saying “My shoes are black” one can say “My shoes are this28bbb3347a932edf44620216dc402853 color” (employing the sample, ostensive gesture, and phrase “this color” in place of the word “black”). Ostensive definition provides no exit from language. The idea that all words are either definable by analytic definition in terms of necessary and sufficient conditions of application or indefinable was an illusion. There are many different ways of explaining words (e.g. by a series of examples together with a similarity rider, by paraphrase or contrastive paraphrase, by exemplification, by ostension) and not all words are or need to be sharply defined. The demand for determinacy of sense was incoherent, for vagueness is not always a defect and there is no absolute standard of exactness. The terms “simple” and “complex” had been misused, for they are relative not absolute terms, and what is to count as simple or complex must be laid down from case to case. We must not mistake the absence of any criteria of complexity for the satisfaction of the criteria of simplicity. We must recognize the existence of family resemblance concepts, which are united not by characteristic marks (necessary and sufficient conditions of application) but by partially overlapping similarities. In particular, we should note that many central philosophical concepts, such as proposition, name, language, number, have no essence, but are family resemblance concepts.

Accordingly, the idea of a general propositional form was illusory, confusing a humdrum propositional variable used, for example, for purposes of anaphoric reference, as in “He told me his tale, said that that was how things were, and asked for a loan,” with a general form of all propositions. (No one would be tempted to say that the phrase “that’s the way the cookie crumbles,” which colloquially serves a similar purpose, represents the general form of the proposition.) Propositions have no (non-trivial) common essence, for there are many different kinds of structure which we call “propositions”: avowals of experience (such as “I have a pain” or “It hurts”), avowals of intent, ordinary empirical propositions, hypotheses, expressions of laws of nature, logical and mathematical propositions, “grammatical propositions” (in Wittgenstein’s idiosyncratic use of this term) which are expressions of rules (such as “red is a color” or “the chess king moves one square at a time”), ethical and aesthetic propositions, and so on. The variegated members of this large family do not possess a shared essence; each kind of case must be scrutinized in its own right. Bipolarity is a feature of an important member of the family, but not a defining property of propositions as such. It was misconceived to suppose that the essential function of the proposition is to describe. For the roles of many kinds of propositions, such as logical and mathematical propositions or avowals of experience or many ethical propositions, are not to describe. Moreover, even when propositions have a descriptive role, one must bear in mind that there are many logical differences among descriptions, as is evident when one compares describing a scene with describing the impression of a scene, or describing what one imagines with describing what is the case, etc. Accordingly, it was misconceived to think of logic as flowing from the essential nature of the elementary proposition or as reflecting the logical structure of the world. Tautologies are indeed vacuous. They say nothing, but they are correlates of rules of inference, i.e. truth-value preserving rules for the transformation of propositions. They are autonomous, free-floating, and have no justification, neither ineffable nor effable. But they are held in place by the fact that they are constitutive of what we count as thinking, reasoning, and inferring.

A language is not a calculus of rules together with an array of inde- finable names from which all significant sentences (and their truth conditions) can be generated. It is a human institution embedded in a distinctive form of life, grafted upon natural forms of human behavior. It can be elucidated only by attending to the use of words and sentences in the stream of human life. The meaning of an expression is what is given by an explanation of meaning. Explanations of meaning, of a humdrum and familiar kind, explain the use of expressions, and as such constitute rules for the use of the explanandum (at least in the context in question). Hence, too, the meaning of an expression is what one understands when one understands an expression and knows what it means. Understanding is internally related to meaning. It is an ability, the mastery of the technique of the use of an expression. It is exhibited in using an expression correctly, in explaining what it means, and in responding appropriately to its use. These are severally criteria of understanding. Far from making the notion of truth and truth conditions central to the notion of meaning, Wittgenstein made the notions of use, explanation of meaning, and understanding pivotal.

The conception of depth analysis which informed the Tractatus is relegated to a minor role. Analysis can yield nothing that is not evident in the practices of the uses of words. For nothing can be hidden in the domain of grammar, i.e. the domain of the rules for the use of words which we follow in our linguistic practices. For there is no such thing as following (as opposed to acting in accord with) a rule with which we are unacquainted. Rules for the use of words are standards of correctness. They are given in explanations of meaning, appealed to in justification and criticism of use, and invoked in teaching. There is an internal relation between a rule and what counts as acting in accord with it (a fortiori as following it), which is exhibited in the normative practices of using an expression, evaluating the correctness of its use, correcting mistakes, explaining its meaning, etc. In place of depth analysis, what is requisite for philosophical elucidation is a description of the use of words, of their manifold connections and interconnections with other words, of the circumstances and presuppositions of use, of the consequences of their use and the manner in which they are integrated in human behavior. Such a description, a surveyable representation of the use of a word, will enable one to disentangle the web of the grammar of a word and to resolve philosophical problems.

Concepts are not correct or incorrect, only more or less useful. Rules for the use of words are not true or false. They are not answerable to reality or to antecedently given meanings. Instead, they determine the meanings of words. There is no semantic connection between words and world: grammar is autonomous. What appear to be necessities in the world, e.g. that red is a color or that nothing can be red and green all over, are not ineffable metaphysical truths. What we think of as categorial terms (formal concepts) have a perfectly decent use in our language, and can occur in well formed propositions with a sense, e.g. “Red is my favourite color,” “Look at the colors of the sunset.” What looked like ineffable metaphysical truths, e.g. that red is a color, that space is threedimensional, that the world is the totality of facts, are no more than grammatical propositions, i.e. expressions of rules for the use of their constituent terms in the guise of descriptions. “Red is a color” is a rule which entitles one to infer from the proposition that a is red that it is colored. The proposition that nothing can be red and green all over is the expression of a rule which excludes the form of words “is red and green all over” from use. That the world is the totality of facts is a (misleading) expression of the rule that what we call a description of the world consists of a statement of facts (not a list of things).

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The apparent harmony between language and reality, which lies at the heart of the problems of intentionality, requires no pre-established coordination between the logico-syntactical forms of any possible language on the one hand and the metaphysical form of the world on the other. Modal realism is chimerical, for what is logically possible is simply what makes sense, and that is laid down in language. It is correct that the proposition that p and the fact that p which makes it true are internally related, but internal relations are fixed in language. The “harmony” is orchestrated in grammar, in such intra-grammatical articulations as, for example, “The proposition that p” = “The proposition which is made true by the fact that p,” which are simply two different ways of referring to the same proposition. It is correct to say that if one’s thought is true then what one thinks is precisely what is the case, but that is not a kind of identity between distinct items, i.e. one’s thought and what is the case. It is merely to say that the thought that p is the thought which is made true by its being the case that p (and made false by its not being the case that p) – and that is a grammatical (substitution) rule. Thought and what makes it true make contact in language, not between language and reality. Far from the intentionality of language being derivative from the intrinsic intentionality of thought, the intentionality of thought is derived from the intentionality of its linguistic expression, and that resides in the practice of its use and explanation. In general, what appear to be necessary connections in reality or between language and reality are merely the shadows cast by grammar. Metaphysics is not a domain for cognitive investigations in philosophy, but a hall of mirrors which needs to be shattered if we are to see the world and our thought about it aright.

The dominant tradition of philosophy conceived of subjective experience as the foundation of knowledge and language alike. It seems that a person knows how things are with him, that he is experiencing this or that (a pain or a visual impression) immediately and indubitably, but must infer from his subjective experience how things are “outside” him. Hence, it appeared, the private is better known than the public, and mind is better known than matter. Language, it seemed, was rooted in private experience. For the fundamental indefinables of a language seem to be given meaning by association or private ostensive definition connecting words (e.g. names of perceptual qualities, as well as of mental operations, attitudes, and emotions) with experiences. The Investigations mounts a full-scale attack upon this venerable conception with a battery of objections known as “the private language arguments.”

One’s current experience is not an object of subjective knowledge. The ability to avow one’s pain does not rest on evidence, nor is it a form of perception. One may know that there is a tree in the quad in as much as one perceives it, but one does not perceive one’s perception of it. One does not find out or verify that one is in pain. There is no such thing as being ignorant of whether or doubting whether one is in pain. So saying that one knows or is certain that one is in pain makes no sense either, since there is no possibility of ignorance or doubt to be excluded. To say “I know I am in pain” is either merely an emphatic avowal of pain or a philosopher’s nonsense. The idea that the subject enjoys privileged access to his own experience, since no one else can have what he has when, for example, he is in pain, is misconceived. It assumes that the experiences, e.g. pain, of different people are at most qualitatively, but not numerically, identical. But that very distinction applies only to substances, not to experiences. Two people have the same pain if their pains tally in intensity and phenomenological features, and occur in corresponding parts of their bodies. Experiences are not kinds of private property, having an experience is not a relation between a person and an experience, and different people can have the same experiences. The only sense in which experiences may be epistemically private is that one may have a certain experience and neither exhibit the fact nor tell another about it. But if one screams in pain, there is nothing epistemically private about one’s pain, and if one tells another what one is thinking, there is nothing one knows which he does not.

The traditional picture of the “inner” was accompanied by an equally distorted picture of the “outer.” We often know what another experiences, whether he is in pain or cheerful, what he is thinking or imagining. Our knowledge rests on the evidence of what he says and does, but this is neither inductive nor analogical evidence. Pain behavior is a logical criterion for being in pain. A person’s avowal of pain is a behavioral expression of pain, which partly replaces the natural pain behavior onto which it is grafted when one learns the use of the word “pain.” To say “I think that p” or “I intend to V ” is an expression of thought or intent (not a description of a private episode), and such utterances are criteria for the ascription of thoughts and intentions to others. They are defeasible (e.g. by evidence of insincerity); but if undefeated, then any doubt is senseless and the criteria justify the third-person ascription for which they are grounds.

The behavioral criteria for the ascription of psychological predicates are partly constitutive of their meaning. Psychological predicates are not given their meaning by a private rule, an ostensive definition, in which a subjective experience or impression functions as a private sample. There can be no such thing as a logically private sample. Nor can there be any such thing as a rule which only one person can, logically, follow. A sensation or experience cannot fulfill the role of a sample, for not being perceptible even by the person whose sensation or experience it is, it cannot function as an object of comparison. Nor can there be any criterion of identity for the putative sample, for the alleged sample must be recollected, and there can be no independent criterion of correctness for what one’s memory calls up – whatever seems right to one is right, and that means that there is no right or wrong here.

Wittgenstein’s reflections in philosophical psychology not only undermine the traditional conception of the “inner” and the “outer,” they also transform traditional conceptions of thinking and its relation to language. Language is not a mere vehicle for language-independent thoughts, and sentences are not the mere outward, perceptible garb of thoughts. Intelligent speech is not an outer process of uttering words accompanied by an inner process of thinking. Speaking is not the upshot of a process of translating wordless thoughts into language. What makes speech intelligent, thoughtful, is no accompaniment; in particular, not an accompanying act or process of meaning something by one’s words. For meaning something is neither an act nor a process, and what one means is typically what one’s words mean. What renders speech thoughtful is the context of utterance, what was said or done before, and what is or might be said or done after, the reasons that the speaker might adduce for what he said and the consequences that he draws. Similarly understanding is not a process of interpreting dead signs (sounds impinging upon one’s eardrums). We no more hear mere sounds when we hear our mother tongue spoken than we see mere patches of color when we look around us. We hear intelligent speech, and experience the meanings of words. Interpretation (unlike deciphering) presupposes understanding, and is called for only when more than one way of understanding is in question. That is necessarily the exception to the rule.

The limits of thought are determined by the limits of the expression of thoughts. A dog may think it is about to be taken for a walk, since its behavior can express that expectation, but it cannot now think that it is going to be taken for a walk next week, for only linguistic behavior involving temporal reference can count as the expression of such a thought. The possession of a language not only extends the intellect, it also enlarges the trajectory of the will. A dog can now want a bone, but only a language user can now want to see Naples before he dies. It is not thought that infuses the signs of language with meaning, but the use of those signs in the stream of life.

The conception of philosophy propounded in the Tractatus was revolutionary, denying the possibility of any philosophical propositions and doctrines, characterizing the subject as a non-cognitive activity whose aim is the elucidation of propositions by analysis and the curbing of metaphysical pretensions. This conception of the subject is transformed and deepened in the Investigations. The notion of ineffable truths that can be shown but not said disappears together with the conception of analysis. But Wittgenstein continued to argue that philosophy is not a cognitive discipline, that there are no philosophical propositions or theses. If there were theses in philosophy, everyone would agree with them, for they would be no more than grammatical truisms – rules for the use of words with which we are perfectly familiar, even if we have to be reminded of them. That we know of others’ states of mind on the basis of what they do and say is news from nowhere; the task of philosophy is to disentangle the misconceptions that lead us to think that this is inadequate or impossible, to clear away the misconceptions that prevent us from accepting these rule-governed connections in the grammar of our language that are constitutive of the concepts in question. It is not the task of philosophy to reform the grammar of our language – it leaves it as it is. But that is not a form of philosophical quietism. On the contrary, it recognizes that philosophical problems arise inter alia from our existing language, replacement of which would merely mask, and not resolve, the problems. Nor is it a declaration of the impotence or unimportance of philosophy. The problems of philosophy reach as deeply into us as our very language. And their resolution will have profound effects on disciplines, such as mathematics or psychology, which are enmired in conceptual confusion. (Almost half of Wittgenstein’s later writings were concerned with the philosophy of mathematics. His philosophy of mathematics has not been discussed in this chapter due to limitations of length.) Wittgenstein’s later conception of philosophy is Janus-faced. On the one hand, philosophy is akin to therapy, a cure for the diseases of the understanding, which has a certain affinity with psychoanalysis (but without any analogue of the theoretical commitments of the latter). On the other hand, it is a quest for a surveyable representation of a segment of grammar, which will lay bare the conceptual network. The two are complementary. The task of philosophy is conceptual clarification and the dissolution of philosophical problems. Philosophy cannot add to our knowledge of the world. Its role is to contribute to our understanding of what we do and do not know.

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Further reading

The Philosophy of Ludwig Wittgenstein

Baker, G. P. and Hacker, P. M. S.: An Analytical Commentary on the Philosophical Investigations. Volume 1, Wittgenstein: Understanding and Meaning (Oxford: Blackwell, 1980)
——: An Analytical Commentary on the Philosophical Investigations. Volume 2, Wittgenstein: Rules, Grammar and Necessity (Oxford: Blackwell, 1985)
Glock, H. J.: A Wittgenstein Dictionary (Oxford: Blackwell, 1996).
Hacker, P. M. S.: Insight and Illusion: Themes in the Philosophy of Wittgenstein, rev. edn (Oxford: Clarendon Press, 1986; Bristol: Thoemmes Press, 1997).
——: An Analytical Commentary on the Philosophical Investigations. Volume 3, Wittgenstein: Meaning and Mind (Oxford: Blackwell, 1990).
——: An Analytical Commentary on the Philosophical Investigations. Volume 4, Wittgenstein: Mind and Will (Oxford: Blackwell, 1996).
——: Wittgenstein’s Place in Twentieth-century Analytic Philosophy (Oxford: Blackwell, 1996).
Hanfling, O.: Wittgenstein’s Later Philosophy (London: Macmillan, 1989).
Kenny, A. J. P.: Wittgenstein (Harmondsworth: Penguin, 1973).
Monk, R.: Wittgenstein: The Duty of Genius (London: Jonathan Cape, 1990).
Mounce, H. O.: Wittgenstein’s Tractatus: An Introduction (Oxford: Blackwell, 1981).
Schulte, J.: Wittgenstein: An Introduction (Albany: State University of New York Press, 1992).

Bibliography
Writings
Werkausgabe, Bände 1–8 (Frankfurt am Main: Suhrkamp, 1989).
Tractatus Logico-philosophicus (London: Routledge & Kegan Paul, 1921, 1961).
Philosophical Investigations, 2nd edn (Oxford: Blackwell, 1953, 1958).
Remarks on the Foundations of Mathematics, 3rd edn (Oxford: Blackwell, 1956, 1978).
The Blue and Brown Books (Oxford: Blackwell, 1958). Philosophical Grammar (Oxford: Blackwell, 1974).
Remarks on the Philosophy of Psychology, volumes I and II (Oxford: Blackwell, 1980).
Philosophical Occasions 1912–1951 (Indianapolis: Hackett, 1993).

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