David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 31 (1):29 - 42 (2002)
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
|Keywords||definition descriptions logicism mathematics one Russell|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Robert B. Brandom (1994). Making It Explicit: Reasoning, Representing, and Discursive Commitment. Harvard University Press.
Bertrand Russell (2005). On Denoting. Mind 114 (456):873 - 887.
Ludwig Wittgenstein (1922/1999). Tractatus Logico-Philosophicus. Dover Publications.
Neil Tennant (1997). The Taming of the True. Oxford University Press.
Gottlob Frege (1953/1968). The Foundations of Arithmetic. Evanston, Ill.,Northwestern University Press.
Citations of this work BETA
No citations found.
Similar books and articles
Berit Brogaard (2007). Descriptions: Predicates or Quantifiers? Australasian Journal of Philosophy 85 (1):117 – 136.
Marga Reimer (1992). Incomplete Descriptions. Erkenntnis 37 (3):347 - 363.
ST Kuhn (2000). Embedded Definite Descriptions: Russellian Analysis and Semantic Puzzles. Mind 109 (435):443-454.
Berit Brogaard (2010). Descriptions: An Annotated Bibliography. Oxford Annotated Bibliographies Online.
Barbara Abbott (2008). Issues in the Semantics and Pragmatics of Definite Descriptions in English. In Nancy Hedberg & Jeanette Gundel (eds.), Reference: Interdisciplinary Perspectives. Oxford University Press 61-72.
Kent Bach (2004). Descriptions: Points of Reference. In Marga Reimer & Anne Bezuidenhout (eds.), Descriptions and Beyond. Clarendon Press 189-229.
Stephen Schiffer (2005). Russell's Theory of Definite Descriptions. Mind 114 (456):1135-1183.
Francisco A. Rodriguez Consuegra (1989). Russell's Theory of Types, 1901–1910: Its Complex Origins in the Unpublished Manuscripts. History and Philosophy of Logic 10 (2):131-164.
Zoltán Gendler Szabó (2005). The Loss of Uniqueness. Mind 114 (456):1185 - 1222.
Laurence Goldstein (2002). The Indefinability of ÂOneâ. Journal of Philosophical Logic 31 (1):29-42.
Added to index2009-01-28
Total downloads44 ( #94,238 of 1,801,598 )
Recent downloads (6 months)14 ( #51,083 of 1,801,598 )
How can I increase my downloads?