- #1

nomadreid

Gold Member

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The old logicism in the form of a finite axiomatization of mathematics is of course dead, buried by Gödel et.al.

A naïve form of neo-logicism, which would try to reduce mathematics to a single logic, bumps against those holding or not to intuitionism, the limitations of first-order logic, and similar. Mathematics is not monolithic.

However, if we refer to logic (perhaps with uppercase: Logic) as a methodology to distinguish it from any specific logical system, where is the objection? That is, the idea of shifting around is enshrined in such ideas as Kripke semantics, many-worlds semantics, Belief Revision Semantics, etc. Is the only problem that one has not yet formalized all logical foundations of mathematics, or perhaps is the problem a gut feeling of strong Platonism bordering on mysticism? In other reasons, with a broad enough definition of Logic, is there any formal reason to reject neo-logicism in the same way that the Incompleteness Theorems gave a formal reason to reject classical logicism?