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Elements of a phenomenological justification of logical principles, including an appendix with mathematical doubts concerning some proofs of Cantor on the transfiniteness of the set of real numbers. (English) Zbl 1025.03006

According to the author, “there are two main objections against epistemological foundation of logical principles: 1. Every argument for them must necessarily make use of them. 2. Logical principles cannot be abstracted from experience because they imply elements of meaning that exceed in principle our finite experience (like universality & necessity)” [p. 250], and, in opposition to these objections, he argues in favor of Husserl’s thesis “that logic needs a theory of experience as a foundation” [ibid.]. In an appendix be “presents some mathematical doubts concerning the proofs by Cantor of the transfiniteness of the set of real numbers” [ibid.].

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03E10 Ordinal and cardinal numbers
00A30 Philosophy of mathematics
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