Proofs of CBT in Principia Mathematica

  • Arie HinkisEmail author
Part of the Science Networks. Historical Studies book series (SNHS, volume 45)


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.


Inductive Argument Cardinal Number Previous Proof Inductive Proof Propositional Function 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.The Cohn Institute for the History and Philosophy of Science and IdeasTel Aviv UniversityTel AvivIsrael

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