Numbers and Relations

Erkenntnis 49 (1):93 - 113 (1998)
Authors
Byeong-uk Yi
University of Toronto, St. George
Abstract
In this paper, I criticize John Bigelow's account of number and present my own account that results from the criticism. In doing so, I argue that proper understanding of the nature of number requires a radical departure from the standard conception of language and reality and outline the alternative conception that underlies my account of number. I argue that Bigelow's account of number rests on an incorrect analysis of the plural constructions underlying the talk of number and propound an analysis of numerical sentences, such as "Quine and Goodman are two", that conforms to the natural understanding of the plural constructions. The analysis leads to the account of number according to which natural numbers are properties, i.e., one-place relations: the number two, for example, is the property indicated by "to be two", which, I argue, is a one-place predicate that can combine with plural terms like "Quine and Goodman"
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DOI 10.1023/A:1005402021225
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Citations of this work BETA

The Logic and Meaning of Plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
The Logic and Meaning of Plurals. Part I.Byeong-Uk Yi - 2005 - Journal of Philosophical Logic 34 (5-6):459-506.
Reference to Numbers in Natural Language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
What Are Numbers?Joongol Kim - 2013 - Synthese 190 (6):1099-1112.

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