Proofs of the Cantor-Bernstein Theorem by Arie Hinkis

Author:Arie Hinkis
Language: eng
Format: epub
Publisher: Springer Basel, Basel

Poincaré’s move can be described in Lakatosian terms (1976 I.4.c) as “strategic withdrawal” to safe harbor, which decreases mathematical content.

Incidentally, Poincaré regarded the origin of non-predicative definitions in the tacit assumption of an actual infinity (1906b p 316; cf. 1906a p 18, 25), an infinite set which serves as the domain of discourse. Signs of this infiltration of the actual infinity Poincaré saw in the use of the word all which he italicized in both his proofs of CBT described above. Thus in the second proof, even if we drop the word ‘inductive’ from the proof, it will still not be acceptable by Poincaré because actual infinite collections are assumed in it, such as the collection of all An.

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