Proofs of CBT in Principia Mathematica
In Principia Mathematica (PM, 1910–1913), the monumental treatise of A. N. Whitehead and B. Russell (together ‘WR’), the logicist movement obtained its most clear statement. The treatise contains four formulations of CBT with their proofs, which we will review below. The first two formulations appear in *73: In *73.85 the single-set formulation is given and in *73.88 the two-set formulation follows. The second formulation is proved by the first, in a standard fashion; the proof of first formulation is adapted from Zermelo’s proof in his paper on axiomatic set theory (1908a, see Chap. 23), which WR reference. It was, no doubt, because this proof avoids the notion of number that WR preferred it, for by *73 the notion of number was not yet introduced in PM. We present the first two formulations in Sect. 26.1 and their proofs in Sect. 26.2.
KeywordsInductive Argument Cardinal Number Previous Proof Inductive Proof Propositional Function
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