Abstract
A common objection to Quine’s set theory “New Foundations” is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set (a kind of symmetry) which motivates NF.
Similar content being viewed by others
References
Bernays P. (1954). ‘A system of axiomatic set theory VII’. Journal of Symbolic Logic. 19: 81–96
Crabbé Marcel (1982). ‘On the consistency of an impredicative subsystem of Quine’s NF’. Journal of Symbolic Logic 47, 131–136
Forster, T. E., Set Theory with a Universal Set, second edition, Clarendon Press, Oxford, 1995. NOTE: seek page refs for invariance of s.c., s.c. not a set, s.c. wellordered not a set.
reference for setlike from Forster.
Forster, T. E., ‘AC fails in the natural analogues of V and L that model the stratified fragment of ZF’, preprint, found at http://www.dpmms.cam.ac.uk/~tf or from the author.
Grishin V.N. (1969). ‘Consistency of a fragment of Quine’s NF system.’ Sov. Math. Dokl. 10: 1387–1390
Hailperin T. (1944). ‘A set of axioms for logic’. Journal of Symbolic Logic 9:1–19
Holmes M. Randall (1994). ‘The set theoretical program of Quine succeeded (but nobody noticed)’. Modern Logic. 4: 1–47
Jensen Ronald Bjorn (1969) ‘On the consistency of a slight (?) modification of Quine’s ‘New Foundations”. Synthese 19, 250–263
Quine W.V.O. (1937). ‘New Foundations for Mathematical Logic’. American Mathematical Monthly 44: 70–80
Quine, W. V. O., Mathematical Logic, second edition, Harvard, 1951.
Rieger L. (1957). ‘A contribution to Gödel’s axiomatic set theory’. Czechoslovak Mathematical Journal 7: 323–357
Scott, Dana, ‘Quine’s individuals’, in E. Nagel (ed.), Logic, methodology and philosophy of science, Stanford, 1962, pp. 111–115.
Specker, E. P., ‘The axiom of choice in Quine’s ‘New Foundations for Mathematical Logic’ Proceedings of the National Academy of Sciences of the U. S. A. 39 (1953), 972–975.
Wang, H., Logic, Computers, and Sets, Chelsea, 1970, pp. 406.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Holmes, M.R. Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’. Stud Logica 88, 195–213 (2008). https://doi.org/10.1007/s11225-008-9107-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-008-9107-8