Dissatisfied with earlier attempts by Gottlob Frege and Bertrand Russell, Ludwig Wittgenstein (1889-1951) attempted to elucidate the nature of logical truth in his Tractatus Logico-Philosophicus (1922). Wittgenstein was concerned with the relation between language and the world and the logical and mathematical ramifications of this relation (Blackburn 390, Bunnin and Yu 739). In the Tractatus, Wittgenstein asserted that in order to describe reality, logic is necessary, but not sufficient and, in so doing, put forth what has come to be known as the picture theory of meaning (Rohmann 430). In his picture theory of meaning, Wittgenstein argued that language mirrors reality. Whether the picture theory of meaning collapses with Wittgenstein’s rejection of the metaphysics of logical atomism of the Tractatus is disputed among philosophers, but there is a consensus that Wittgenstein abandoned the theory in his later philosophy (Bunnin and Yu 531).
Wittgenstein’s exposition of his later philosophy appears in his posthumously published Philosophical Investigations (1953.) In the Philsophical Investigations, Wittgenstein turns his attention from the subject matter of the Tractatus to the workings of ordinary language, the philosophy of psychology and the philosophy of mathematics. The later Wittgenstein rejects his earlier unified theory of meaning in favor of an explanation based on a diversity of “language games” governed by rules and constituting a form of life. His later approach did not insist on an account of meaning as a psychological or abstract entity, but instead focused on the use of words and sentences (Bunnin and Yu 738-739).
The difference between Wittgenstein’s earlier philosophy and his later philosophy are striking, yet philosophers disagree about the significance of these differences in terms of how to read Wittgenstein’s intent regarding purpose, methodology and philosophical outcome. Differing interpretations have brought about heated debate in metaphyics, epistemology and philosophy of mind (Bunnin and Yu 739). Although Wittgenstein’s criticism of the Tractatus in the Philosophical Investigations was aimed not at the doctrines or theses of the Tractatus, but at the suppositions behind them, Wittgenstein intended the Philosophical Investigations to be read in the context of the Tractatus so that his criticism of it could be readily understood (“Wittgenstein, Ludwig Josef Johann,” Hacker 961).
The Picture Theory of Meaning
Wittgenstein opened the Tractatus by giving a metaphysics of a world consisting of atomic facts, completely independent of one another, but Wittgenstein gave no examples of what he considered to be atomic facts. He claimed that they existed, but not that he had identified them (“Wittgenstein, Ludwig Josef Johann,” Urmson 395). Next, Wittgenstein stated that all complex propositions are truth-functional relations among these atomic propositions, that each atomic proposition consists in unanalyzable names designating simple objects, and that the sense of any one of these propositions is the state of affairs it depicts (Bunnin and Yu 738).
An understanding of Wittgenstein’s terse, abstract metaphysics is key to understanding his picture theory of meaning, which immediately follows it in the Tractatus. The main theses of the Tractatus are that the structure of language consists in complex propositions consisting of atomic propositions, which in turn consist of names and that the language-to-world connection is a picturing relation. Thus, when one thinks of what is the case in the world, facts, one’s thoughts picture these facts, and since propositions are expressions of thoughts, these too are pictures of facts (Grayling 36).
The picture theory of meaning was inspired by Wittgenstein’s reading in the newspaper of a Paris courtroom practice of using models to represent the then relatively new phenomenon of automobile accidents (Grayling 40). Toy cars and dolls were used to represent events that may or may not have transpired. In the use of such models it had to be stipulated which toys corresponded to which objects and which relations between toys were meant to represent which relations between those objects (Glock 300). Another source of inspiration for the picture theory of meaning was the introduction to Heinrich Hertz’s Principles of Mathematics. Wittgenstein’s picture theory of meaning gives pictures much broader metaphysical and logical importance than Hertz did, but similarities between the two notions are still evident (Finch 13).
Before Wittgenstein developed his picture theory of meaning, Russell’s theory of judgment had laid a foundation upon which Wittgenstein was able to build. Russell had already determined that names were simple and propositions composite, that relations between the components of propositions represented facts and that propositions represented reality by depicting truly or falsely how things are, not by standing for something. What had not yet been determined was how we can say how things are not and the possibility of falsehood, i.e., that a proposition can have meaning even when the state of affairs it depicts does not obtain (Glock 299).
The components of any model or picture are multiple and each goes proxy for the components of the state of affairs depicted. The structure of the picture is the arrangement of its components. The logical form of the structure of a picture must be shared with the state of affairs it depicts. Therefore, the components of the picture must be equinumerous and combinable with the state of affairs the picture depicts such that the picture can mirror all possible combinations in that state of affairs (Glock 300).
All of these features are present in propositional representation. A proposition pictures, or describes, reality by depicting a state of affairs. Atomic propositions are simple, their components being unanalyzable names. These names go proxy for simple objects to which they are correlated and which give them meaning. The state of affairs, or possible combination of objects, a proposition depicts is its sense. Facts represent facts, simple names represent simple objects and relations represent relations (Glock 301).
The essence of the picture theory of language is that what shows what logically simple names, or primitive signs, stand for is the way they are used in propositions. Without the logical framework of propositions, these signs are meaningless. While the meaning of a sign is the object it goes proxy for, it is impossible to elucidate this meaning without a proposition that shows the connection between the name and the object it goes proxy for (Hunnings 47).
Thus, Wittgenstein establishes the theses of the Tractatus, namely that only those propositions that picture reality are significant, that is, only factual propositions are significant. This conclusion inevitably follows from Wittgenstein’s theory that it is only by picturing reality that propositions acquire sense, or meaning. And since reality is the sum of all facts, or states of affairs, be they those that obtain or those that do not, talking or thinking about anything that falls outside of the realm of facts is, quite literally, nonsenical, since such talk or thought does not depict anything. From this it follows that, as Wittgenstein himself points out in the Tractatus, the propositions that he has used to state his theory are also senseless. As for logic, its propositions are sometimes true, sometimes false, depending on the truth-values of their constituent atomic propositions, but this only yields tautologies and contradictions. Therefore, these propositions also lie outside of what is the case, or the world, and thus have no sense (Grayling 44-6).
The Possibility of Falsehood in the Picture Theory of Meaning
The strength of the picture theory of meaning lies in the fact that it explains the possibility of falsehood, or how propositions can be false and still be meaningful. When propositions are true, they correspond to reality, but when they are false, this doesn’t invalidate their meaningfulness despite the fact that they don’t correspond to reality. Whereas Russell’s dual-relation theory of judgment had failed to solve this problem, Wittgenstein’s picture theory of meaning succeeded in doing so (Glock 298). His solution was that propositions depict possibilities by nature of the fact that their components are combined in a certain way. The possibility of such a combination is assured by the components of the propositions mirroring the things they go proxy for and not by an additional logical form (Glock 299).
It is not necessary for facts to correspond to propositions as a whole in order for them to depict. All that is necessary is that there be a one-to-one correlation between the components of the propositions and those of the facts they depict in the world and for components of the former to be in relation to the components of the latter in isomorphic manner. Thus, the given relation between the components of the picture represents the like relation between the corresponding things, regardless of whether this fact obtains. To make a false proposition is simply to combine existing components in a way that they are not combined in reality (Glock 299-300). In other words, it is not the components of the proposition that do not correspond to reality, but the manner in which they are combined. Such propositions present states of affairs that represent possible situations. Wittgenstein maintained that propositions represented possible states of affairs by describing them. (Finch 3). Pictures simply represent logical possibility (Finch 10). Such representation is possible because the propositions themselves cannot be negated; all that can be negated is whether or not they obtain in reality (Finch 65).
The Breakdown of the Picture Theory of Meaning
The Tractatus reduced all logical complexity to propositional calculus and all propositions to truth-functions of atomic ones. Such atomic propositions must be logically independent of one another, which made the nature of the atoms they were built on evasive (Blackburn 390). Ultimately, Wittgenstein’s picture theory of meaning broke down with his realization that the atomic propositions he had posited were untenable. Wittgenstein himself attacked the core doctrine of his picture theory of meaning, isomorphism. He realized that neither propositions nor the possible states of affairs they depict, which he had argued shared a definite logical form, have atomic components. Once the idea of atomism is taken out of the picture, saying that a proposition and what it depicts have something in common only states an internal relation. In his later philosophy, Wittgenstein continued to sustain this internal relation in referring to “pictoriality” in propositions, but rejected the picture theory of meaning. Wittgenstein no longer saw the relation between thought and reality as a metaphysical one between a proposition and facts in the world, but simply as a grammatical one (Glock 303).
Despite its breakdown, the Tractatus contributed a great deal to modern philosophy. Firstly, the Tractatus gave rise to the atomist and foundationalist traditions, the idea that philosophy should seek to discover hidden logical structures through analysis, the quest for a logically perfect language, the logico-metaphysical conception of language and logical form to mirror the logical structure of the world. Neverhteless, the later Wittgenstein rejected these contributions outright in his Philosophical Investigations. Secondly, it authoritatively and decisively dealt with errors of Frege and Russell. Thirdly, it instigated a change in direction in modern analytic philosophy known as the “linguistic turn” while laying the ground for Wittgenstein’s own later conception of philosophy as outlined in the Philosophical Investigations. Fourthly, it layed the foundation for Wittgenstein’s later Remarks on the Foundations of Mathematics, his magnum opus on the nature of logical necessity and logical truth (“Wittgenstein, Ludwig Josef Johann,” Hacker 960-961).
The Trouble with the Tractatus
In the Philosophical Investigations, Wittgenstein rejected his earlier view that the meaning of a word was its reference. His view in the Philosophical Investigations was that there did not have to be a one-to-one semantical correspondence between words and the world. He came to the realization that this misconception stemmed from the supposition of ostensive definition. He then conceded that neither are all words precisely defined or analyzable according to necessary and sufficient conditions of application, nor do they need to be. The idea of preciseness of definition was, therefore, unintelligible. Because in ordinary language there need not be an absolute criterion of correctness, impreciseness is not a defect. The Cartesian and Empiricist ideal of final analysis also pursued by Wittgenstein’s contemporaries, G.E. Moore and Russell, is a chimera (“Wittgenstein, Ludwig Josef Johann,” Hacker 961). Different words work in different ways. While we could shoehorn every word into the mold of naming something, this conflation would only serve to undermine diversity rather than yielding a useful insight (Craig 1063). Words do not cease to function and become meaningless because they are not rigorously restricted by rules (Craigh 1064).
The Nature of Logic in the Philosophical Investigations
Wittgenstein argued, in the Philosophical Investigations, that the terms “simple” and “complex” are relative. That is, they depend upon context and point of view. Therefore, the idea that every meaningful sentence analyzed will ultimately reveal underlying simples is misguided (Craig 1064). There are a multitude of predicates that do not name simples. These predicates clearly are not by necessity analyzable into “simpler” predicates. Any attempt to pursue this kind of analysis will likely only uncover what Wittgenstein terms “family resemblance” in the Philosophical Investigations (Craig 1064). There are many concepts, among them key philosophical ones such as “number” and “proposition” that share this family resemblance according to the Philosophical Investigations. This contrasts sharply with the Wittgenstein’s view in the Tractatus that all propositions shared a common essence he called propositional form. Furthermore, and also in contradistinction to the Tractatus, Wittgenstein demonstrates in the Philosophical Investigations that he was mistaken in his supposition that the core function of propositions was to describe states of affairs. He came to realize that not all propositions describe and that there are a variety of distinct logical ways in which those that do describe do so. He concluded that the idea that the meaning of a sentence stems from the meanings of its constituent parts was mistaken and that truth does not depend on correspondence between propositions and facts (“Wittgenstein, Ludwig Josef Johann,” Hacker 961).
Hence, the core idea of the Tractatus, that representation had to correspond to reality by depicting, through its logical structure, the logical structure of the world, was mistaken. Rather than being true or false or in any way answerable to reality, rules for the use of words determine their meaning. Grammar is independent of the world rather than metaphysically bound to it. Thus, that red is a color is not necessary or metaphysically true. While the early Wittgenstein would have argued, in accordanced with the Tractatus, that the symbols or language used to describe colored things showed that red was a color, these symbols or language are actually mere rules to say that anything that can be said to be red can also be said to be colored. What appeared in the Tractatus to be logico-metaphysical coordination between language and reality turns out to be nothing more than grammar. Whereas the early Wittgenstien tried to show that what made the proposition p true was that fact that p, the later Wittgenstein came to the conflicting conclusion that “the proposition that p” is simply “the proposition that is true if it is a fact that p.” There was not logico-metaphysical relation after all, just grammar. Consequently, the puzzle of intentionality of thought and language are also clarified through grammar, rather than through corespondence between words and facts in the world (“Wittgenstein, Ludwig Josef Johann,” Hacker 961). Thus, Wittgenstein concluded that the idea of clear logico-metaphysical and logico-syntactical structures is an illusion (Craig 1064).
Meaning through Rule Following in Language Games in the Philosophical Investigations
In the Philosophical Investigations, Wittgenstein emphasized that language is practical in nature. It takes its meaning from context, not from logico-syntactical structure. He argued, in contradistinction to his earlier philosophy, that words were not fixed in meaning, but could be used as needed in language games and that through their use in language games they derived their meaning (Rohmann 431). Wittgenstein further argued that meaning can only be explained by explaining word usage. Meaning is thus what is understood when language is used. Thus, meaning stems from the ability to use language correctly. Meaning is demonstrated when an expression is used correctly, when correct use is explained and when interlocutors appropriately respond to use. In addition to formal definition, there are various forms of explanation including, but not limited to, ostenstion, paraphrase, contrastive paraphrase, exemplification and explanation by examples. Thus, Wittgenstein shows that while ostensive definition appears to link words to the world, what it really does is give an example to be applied in the correct definition of a word. The example is a part of the form of representation, and thus is not linked to reality, or what it represents (“Wittgenstein, Ludwig Josef Johann,” Hacker 961). Language users act in accordance with these examples, which shows that the link between rules and behavior is conditioned and conventional. Thus, Wittgenstein shows, rule-following is central to language use. Furthermore, if we accept that thought is delimited by language, then rule-following is also crucial to our lives as thinking beings (Craig 1046).
According to Wittgenstein’s later philosophy, images alone cannot guarantee certain behavior nor the suitability of a particular standard of assessment. Images are not sufficient for explaining meaning since they are nothing more than examples or rules that convey meaning, not meaning itself. Neither are images necessary for explainig meaning, as meaning can occur without them. Usually, when a language user responds to a given expression, he does so decisevely and without deliberation or any inner reference. (Craig 1065). What is necessary for their to be meaning is for the langauge user to fix on a particular similarity among examples, rather than any other and to associate that particular similarity with the rule. This idea contrasts directly with Wittgenstein’s view in the Tractatus that a linguistic expression that does not correlate to a definite combination of simples is meaningless. Moreover, since a simple is to be directly apprehended as being what it is, the representation of a simple is cognizance of a self-interpreting item, whether via direct cognition or by having in mind something which encapsulates its nature. However, the idea of rule-following seems to render this manner of apprehension unintelligible (Craig 1065). Thus, according to Wittgenstein’s later philosophy, his earlier picture theory of meaning and the world of definite connected facts made up of perceptible simples it presupposes are unintelligible (Craig 1065). Meaning can only be eludicated by the manner in which words and sentences are used in the form of life (“Wittgenstein, Ludwig Josef Johann,” Hacker 961).
The invariable, inflexible relationship between language and the world expounded in the Tractatus shows that Wittgenstein thought language had to be narrowly defined (Blackburn 390). His later philosophy contradicts this view. In it, Wittgenstein attacks the idealism and logical necessity of the Tractatus that gave rise to notions of an ideal, logical language (Finch 244-45). Apart from the later Wittgenstein’s notion of pictoriality, all that was left of the picture theory of meaning was a comparison between propositions and literal pictures (Glock 303). This gave a new theory of meaning, but left the original question of logical necessity unanswered.
Although Wittgenstein discovered the suppositions behind the Tractatus to be erroneous, the Tractatus still had a profound effect on philosophy by calling into question traditional approaches to it. The basis of Wittgenstein’s new approach is his reformulated concept of language as an indeterminate number of social activities or language games, each with its own distinct way of using language to serve its purpose. While it may still hold that language can be used in a manner similar to the picture theory of meaning outlined in the Tractatus, there are various other ways in which language is used. Wittgenstein lists a number of them including giving orders, asking, thanking, cursing, greeting and praying in paragraph 23 of the Philosophical Investigations and concludes by remarking: “It is interesting to compare the multiplicity of tools in language and the ways they are used, the multiplicity of kinds of word and sentences, with what logicians have said about the structure of language (including the author of the Tractatus Logico-Philosophicus)” (“Wittgenstein, Ludwig Josef Johann,” Urmson 396).
Even though, according to Wittgenstein, we learn the rules that govern language games through practice, not by theoretical instruction, we are apt to err in being influenced by one or two particular views on the way language is used and oversimplify these views at well, resulting in a misconception of meanings of words as dependent on ostensive definition. Then, we are puzzled when this attempt to force varying uses of language into one oversimplified model causes us to misunderstand the workings of our own conceptual tools. Another tendency that leads to philosophical puzzlement is the vain search for a common feature in all things called by the same name. Such a feature need not exist in Wittgenstein’s view, only family resemblance. Most of Wittgenstein’s later philosophy consists of applying this way of doing philosophy to a vast array of philosophical problems and seeking connections between them, circumscribed by the description of actual and possible language use in varying contexts (“Wittgenstein, Ludwig Josef Johann,” Urmson 396-397).
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