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Syntax, Semantics, and the Problem of the Identity of Mathematical Objects
Published online by Cambridge University Press: 01 April 2022
Abstract
A plurality of axiomatic systems can be interpreted as referring to one and the same mathematical object. In this paper we examine the relationship between axiomatic systems and their models, the relationships among the various axiomatic systems that refer to the same model, and the role of an intelligent user of an axiomatic system. We ask whether these relationships and this role can themselves be formalized.
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- Copyright © 1988 by the Philosophy of Science Association
Footnotes
The authors wish to thank Professors Hilary Putnam and John A. Wheeler for their valued comments on this paper.
Work supported by the U.S. Department of Energy.
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