The indefinability of “one”
Journal of Philosophical Logic 31 (1):29 - 42 (2002)
| 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. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,631 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesBerit Brogaard (2007). Descriptions: Predicates or Quantifiers? Australasian Journal of Philosophy 85 (1):117 – 136.
Zoltán Gendler Szabó (2005). The Loss of Uniqueness. Mind 114 (456):1185 - 1222.
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 Russell's Theory of Types, 1901–1910: Its Complex Origins in the Unpublished Manuscripts.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.
Stephen Schiffer (2005). Russell's Theory of Definite Descriptions. Mind 114 (456):1135-1183.
Berit Brogaard (2010). Descriptions: An Annotated Bibliography. Oxford Annotated Bibliographies Online.
ST Kuhn (2000). Embedded Definite Descriptions: Russellian Analysis and Semantic Puzzles. Mind 109 (435):443-454.
Marga Reimer (1992). Incomplete Descriptions. Erkenntnis 37 (3):347 - 363.
Laurence Goldstein (2002). The Indefinability of ÂOneâ. Journal of Philosophical Logic 31 (1):29-42.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads6 ( #145,407 of 548,969 )Recent downloads (6 months)1 ( #63,511 of 548,969 )How can I increase my downloads? |
My notes
Discussion
