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LANGUAGE not be at all so clear whether some complicated mathematical formula contains a hidden contradiction And if it does so, we shall not be able to discover this by logical investigation (e.g by deriving a reductio ad absurdum) unless sentences containing it are assured of a truth-value The Picture Theory of the Proposition In the Tractatus Logico-Philosophicus Wittgenstein built upon Russell’s theory of descriptions in order to analyse the descriptions of complex objects ‘Every statement about complexes’, he wrote, ‘can be resolved into a statement about their constituents and into the propositions that describe the complexes completely.’ Consider the following sentence (not one of Wittgenstein’s own examples): Austria-Hungary is allied to Russia That sentence was untrue when Wittgenstein wrote the Tractatus because Austria-Hungary was at war with Russia It is not true now for a quite different reason, because the political unit called ‘Austria-Hungary’ no longer exists If we follow the lead of Russell, we will say that in both cases the sentence is meaningful but false The two possibilities of falsehood are clearly parallel to those for ‘The sovereign of X is male’ ‘Austria-Hungary’ can be looked on as a definite description, roughly, ‘the union of Austria and Hungary’ If we follow Wittgenstein and analyse the sentence on the lines of Russell’s theory, we get: For some x and some y, x ¼ Austria and y ¼ Hungary and x is united to y and x is allied to Russia and y is allied to Russia Or more simply we can say that ‘Austria-Hungary is allied to Russia’ means ‘Austria is allied to Russia and Hungary is allied to Russia, and Austria is united to Hungary’ In the Tractatus Wittgenstein built a great deal of metaphysics on the possibility of analysis of this kind But in philosophy of language, he wrote, ‘Russell’s merit is to have shown that the apparent logical form of a proposition need not be its real form.’ 132
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