The Indefinability of “One”

Journal of Philosophical Logic 31 (1):29-42 (2002)
  Copy   BIBTEX

Abstract

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,998

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Incomplete descriptions.Marga Reimer - 1992 - Erkenntnis 37 (3):347 - 363.
Descriptions: An Annotated Bibliography.Berit Brogaard - 2010 - Oxford Annotated Bibliographies Online.
Issues in the Semantics and Pragmatics of Definite Descriptions in English.Barbara Abbott - 2008 - In Nancy Hedberg & Jeanette Gundel (eds.), Reference: Interdisciplinary Perspectives. Oxford University Press. pp. 61-72.
Descriptions: Points of Reference.Kent Bach - 2004 - In Marga Reimer & Anne Bezuidenhout (eds.), Descriptions and beyond. New York: Oxford University Press. pp. 189-229.
The King of France Restored.Max Rosenkrantz - 2007 - Metaphysica 8 (2):149-163.
Sharvy's theory of definite descriptions revisited.Berit Brogaard - 2007 - Pacific Philosophical Quarterly 88 (2):160–180.
What Russell Couldn't Describe.Fredrik Haraldsen - 2013 - Australasian Journal of Philosophy 91 (3):459-473.

Analytics

Added to PP
2009-01-28

Downloads
107 (#164,504)

6 months
16 (#157,013)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Laurence Goldstein
PhD: University of St. Andrews; Last affiliation: University of Kent

Citations of this work

No citations found.

Add more citations

References found in this work

Tractatus logico-philosophicus.Ludwig Wittgenstein, G. C. M. Colombo & Bertrand Russell - 1990 - New York: Routledge. Edited by C. K. Ogden.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.

View all 26 references / Add more references