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Syntax, Semantics, and the Problem of the Identity of Mathematical Objects

Published online by Cambridge University Press:  01 April 2022

Gian-Carlo Rota ,
David H. Sharp  and
Robert Sokolowski
Gian-Carlo Rota
Affiliation:
Department of Mathematics Massachusetts Institute of Technology
David H. Sharp
Affiliation:
Theoretical Division Los Alamos National Laboratory
Robert Sokolowski
Affiliation:
School of Philosophy The Catholic University of America
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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.

Type
Research Article
Information
Philosophy of Science , Volume 55 , Issue 3 , September 1988 , pp. 376 - 386
Copyright
Copyright © 1988 by the Philosophy of Science Association

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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.

References

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