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The Indefinability of “One”

Goldstein, Laurence (2002) The Indefinability of “One”. Journal of Philosophical Logic, 31 (1). pp. 29-42. ISSN 0022-3611. (doi:10.1023/a:1015077403773) (KAR id:7928)


Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials - to be entia non grata - and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of defining the number one in terms drawn only from logic and set theory, is a doomed enterprise. The starting point is Russell's Theory of Descriptions, which purports to supply a quantificational analysis of definite descriptions by adjoining a uniqueness clause' to the formal rendering of indefinite descriptions. That theory fails on at least two counts. First, the senses of statements containing indefinite descriptions are typically not preserved under the Russellian translation. Second (and independently), the uniqueness clause' fails to trim 'some' to 'one'. The Russell-Whitehead account in Principia Mathematica fares no better. Other attempts to define 'one' are covertly circular. An ontologically non-embarrassing alternative account of the number words is briefly sketched.

Item Type: Article
DOI/Identification number: 10.1023/a:1015077403773
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
B Philosophy. Psychology. Religion
Divisions: Divisions > Division of Arts and Humanities > School of Culture and Languages
Depositing User: Laurence Goldstein
Date Deposited: 25 Sep 2008 09:51 UTC
Last Modified: 09 Mar 2023 11:30 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Goldstein, Laurence.

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