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 (Bunnin and Yu 739, Blackburn 390). 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. However, Wittgenstein was not concerned with ontology, per se. He believed that the language used in this sort of metaphysical inquiry simply mirrored the logical structure of its subject matter, making the inquiry itself unnecessary by virtue of the impossibility of its very nature (Hunnings 2-3). Wittgenstein’s picture theory of meaning succeeded in explaining the possibility of falsehood, but ultimately broke down due to its reliance on the atomic propositions it posited, which proved to be untenable.
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 (Rée and Urmson 395). Next, Wittgenstein stated that all 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, ones 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 consituent 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
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). In a Hertzian sense, 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 Theory
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).
The invariable, inflexible relationship between language and the world expounded in the Tractatus shows that Wittgenstein thought language had to be one way or another (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. While Wittgenstein’s picture theory of meaning succeeded in explaining the possibility of falsehood, it failed to explain the nature of logical truth because of the untenability of the atomic propositions it posited.
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