Mathematics, the empirical facts, and logical necessity

Erkenntnis 19 (1-3):167 - 192 (1983)
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Abstract

It is argued that mathematical statements are "a posteriori synthetic" statements of a very special sort, To be called "structure-Analytic" statements. They follow logically from the axioms defining the mathematical structure they are describing--Provided that these axioms are "consistent". Yet, Consistency of these axioms is an empirical claim: it may be "empirically verifiable" by existence of a finite model, Or may have the nature of an "empirically falsifiable hypothesis" that no contradiction can be derived from the axioms

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Citations of this work

Non-ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.

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References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Set theory and the continuum hypothesis.Paul J. Cohen - 1966 - New York,: W. A. Benjamin.
The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory.Kurt Gödel - 1940 - Princeton university press;: Princeton University Press;. Edited by George William Brown.

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