Logic and the Tractatus

In Hans-Johann Glock & John Hyman (eds.), A Companion to Wittgenstein. Chichester, West Sussex, UK: Wiley-Blackwell. pp. 291–304 (2017)
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This chapter provides us with an appropriate way in to the logic of the Tractatus. Whitehead and Russell's Principia Mathematica was an attempt to vindicate “logicism”, the claim that truths of mathematics were disguised truths of logic. To overcome Russell's paradox, Russell had introduced the “theory of types”, stratifying sets, and with that the properties of sets. The resulting system was too weak to generate number theory without the addition of further axioms, including the “Axiom of Reducibility”. This chapter examines the logical apparatus of language, “the logical constants” starting with what at one point Ludwig Wittgenstein calls his “fundamental thought” that the logical constants do not stand for anything. Wittgenstein stresses that operations are quite different from Russellian propositional functions. Wittgenstein's task is to introduce a single logical constant that is truth‐functional and in terms of which the whole of standard Fregean logic can be defined.



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