Rodin, Andrei (2014) On Constructive Axiomatic Method. [Preprint]

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Abstract

The formal axiomatic method popularized by Hilbert and recently defended by Hintikka is not fully adequate to the recent practice of axiomatizing mathematical theories. The axiomatic architecture of Topos theory and Homotopy type theory do not fit the pattern of the formal axiomatic theory in the standard sense of the word. However these theories fall under a more general and in some respects more traditional notion of axiomatic theory, which I call after Hilbert constructive. I show that the formal axiomatic method always requires a support of some more basic constructive method.

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Item Type:	Preprint
Creators:	Creators Email ORCID Rodin, Andrei andrei@philomatica.org
Keywords:	axiomatic method, constructivism, Euclid, Topos theory, Homotopy type theory
Subjects:	Specific Sciences > Mathematics
Depositing User:	Dr. Andrei Rodin
Date Deposited:	30 Aug 2014 00:22
Last Modified:	30 Aug 2014 00:22
Item ID:	10986
Subjects:	Specific Sciences > Mathematics
Date:	27 August 2014
URI:	https://philsci-archive.pitt.edu/id/eprint/10986

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