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FREGE MEETS ZERMELO: A PERSPECTIVE ON INEFFABILITY AND REFLECTION

Published online by Cambridge University Press:  01 August 2008

STEWART SHAPIRO  and
GABRIEL UZQUIANO
STEWART SHAPIRO*
Affiliation:
The Ohio State University and University of St Andrews
GABRIEL UZQUIANO*
Affiliation:
University of Oxford
*
*THE OHIO STATE UNIVERSITY COLUMBUS, OH 43210, USA AND UNIVERSITY OF ST ANDREWS ARCHÉ E-mail:shapiro.4@osu.edu
†UNIVERSITY OF OXFORD PEMBROKE COLLEGE OXFORD OX1 1DW, UK E-mail:gabriel.uzquiano@philosophy.ox.ac.uk
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Extract

1. Philosophical background: iteration, ineffability, reflection. There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, first-order Zermelo–Fraenkel set theory with the axiom of choice (ZFC): the iterative conception and limitation of size (see Boolos, 1989). Each strand provides a rather hospitable environment for the hypothesis that the set-theoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case.

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Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Special Issue 2: Mathematical Methods in Philosophy , August 2008 , pp. 241 - 266
Copyright
Copyright © Association for Symbolic Logic 2008

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