Is Any Set Theory True?

This paper draws its title from the recent symposium of which it was part; it attempts to respond to the question raised by that title, taking current work in set theory into account. To this end the paper contrasts set theory with number theory, examines a severe brand of set-theoretic realism that...

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Bibliographic Details
Published in:Philosophy of science 1969-09, Vol.36 (3), p.271-279
Main Author: Ullian, Joseph S.
Format: Article
Language:English
Subjects:
Axioms
Continuum hypothesis
First order theories
Intuition
Mathematical set theory
Methodology/Methodologies/ Methodological (see also Method)
Number theory
Physical theory
Sensory perception
Theory/Theories/Theorem/ Theorizing
Visual perception
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Summary:This paper draws its title from the recent symposium of which it was part; it attempts to respond to the question raised by that title, taking current work in set theory into account. To this end the paper contrasts set theory with number theory, examines a severe brand of set-theoretic realism that is suggested by a passage from Godel, and sketches a first-order way of looking at the results about competing extensions of Zermelo-Fraenkel set theory. A formalistic sentiment may be detectable in some portions of the paper.
ISSN:0031-8248
1539-767X
DOI:10.1086/288256