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AN “i” FOR AN i: SINGULAR TERMS, UNIQUENESS, AND REFERENCE

Published online by Cambridge University Press:  25 January 2012

STEWART SHAPIRO
STEWART SHAPIRO*
Affiliation:
Department of Philosophy, The Ohio State University and Department of Logic and Metaphysics, Arché Research Centre, University of St Andrews
*
*DEPARTMENT OF PHILOSOPHY, THE OHIO STATE UNIVERSITY, 350 UNIVERSITY HALL, 230, NORTH OVAL MALL, COLUMBUS, OH 43210, USA, DEPARTMENT OF LOGIC AND METAPHYSICS, ARCHÉ RESEARCH CENTRE, UNIVERSITY OF ST ANDREWS, ST ANDREWS, FIFE, SCOTLAND KY16 9AL. E-mail: shapiro.4@osu.edu
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Abstract

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of −1 are indiscernible: anything true of one of them is true of the other. So how does the singular term ‘i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 3 , September 2012 , pp. 380 - 415
Copyright
Copyright © Association for Symbolic Logic 2012

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