Journal article
Logicism and the Problem of Infinity: The Number of Numbers
Philosophia mathematica, Vol.19(2), pp.167-212
06/01/2011
DOI: 10.1093/philmat/nkr008
Abstract
Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects. This paper argues that the problem of infinity is based on a metaphysical prejudice in favor of numbers as objects - a prejudice that mathematics can get along without.
Details
- Title: Subtitle
- Logicism and the Problem of Infinity: The Number of Numbers
- Creators
- Gregory Landini
- Resource Type
- Journal article
- Publication Details
- Philosophia mathematica, Vol.19(2), pp.167-212
- Publisher
- Oxford Univ Press
- DOI
- 10.1093/philmat/nkr008
- ISSN
- 0031-8019
- eISSN
- 1744-6406
- Number of pages
- 46
- Language
- English
- Date published
- 06/01/2011
- Academic Unit
- Philosophy
- Record Identifier
- 9984397938302771
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