74358 Rush.pdf (209.15 kB)
What is wrong with Cantor's diagonal argument?
journal contributionposted on 2023-05-17, 09:17 authored by Rush, PA, Brady, R
We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the LEM is instrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it.
Publication titleLogique Et Analyse
Department/SchoolSchool of Humanities
PublisherNational Centre for Logical Investigation
Place of publicationBelgium
Rights statementCopyright 2008 Logique Et Analyse