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A DEFENSE OF LOGICISM

Part of: Philosophical aspects of logic and foundations General and miscellaneous specific topics

Published online by Cambridge University Press:  07 April 2025

HANNES LEITGEB Open the ORCID record for HANNES LEITGEB [Opens in a new window] ,
URI NODELMAN Open the ORCID record for URI NODELMAN [Opens in a new window]  and
EDWARD N. ZALTA Open the ORCID record for EDWARD N. ZALTA [Opens in a new window]
HANNES LEITGEB
Affiliation:
MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS UNIVERSITÄT MÜNCHEN MUNICH GERMANY E-mail: [email protected]
URI NODELMAN
Affiliation:
PHILOSOPHY DEPARTMENT STANFORD UNIVERSITY STANFORD, CA 94305 USA E-mail: [email protected] E-mail: [email protected]
EDWARD N. ZALTA
Affiliation:
PHILOSOPHY DEPARTMENT STANFORD UNIVERSITY STANFORD, CA 94305 USA E-mail: [email protected] E-mail: [email protected]
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Abstract

We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this framework is part of logic, (c) showing how the denotations for predicates and individual terms of an arbitrary mathematical theory can be viewed as logical objects that exist in the framework, and (d) showing how each theorem of a mathematical theory can be given an analytically true reading in the logical framework.

Keywords

logicismphilosophy of mathematicsreductionobject theory

MSC classification

Primary: 00A30: Philosophy of mathematics
Secondary: 03A05: Philosophical and critical
Type
Article
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 1 , March 2025 , pp. 88 - 152
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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