Logicism, quantifiers, and abstraction

Abstract

With the aid of a non-standard (but still first-order) cardinality quantifier and an extra-logical operator representing numerical abstraction, this paper presents a formalization of first-order arithmetic, in which numbers are abstracta of the equinumerosity relation, their properties derived from those of the cardinality quantifier and the abstraction operator.

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G. Aldo Antonelli
University of California, Davis

Citations of this work

(Math, science, ?).M. Kary - 2009 - Axiomathes 19 (3):61-86.
Math, Science,?M. Kary - 2009 - Axiomathes 19 (3):321-339.

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