Advertisement

Studia Logica

, Volume 88, Issue 2, pp 195–213 | Cite as

Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’

  • M. Randall HolmesEmail author
Article

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.

Keywords

New Foundations symmetry Rieger-Bernays permutation methods 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bernays P. (1954). ‘A system of axiomatic set theory VII’. Journal of Symbolic Logic. 19: 81–96CrossRefGoogle Scholar
  2. 2.
    Crabbé Marcel (1982). ‘On the consistency of an impredicative subsystem of Quine’s NF’. Journal of Symbolic Logic 47, 131–136CrossRefGoogle Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    reference for setlike from Forster.Google Scholar
  5. 5.
    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.
  6. 6.
    Grishin V.N. (1969). ‘Consistency of a fragment of Quine’s NF system.’ Sov. Math. Dokl. 10: 1387–1390Google Scholar
  7. 7.
    Hailperin T. (1944). ‘A set of axioms for logic’. Journal of Symbolic Logic 9:1–19CrossRefGoogle Scholar
  8. 8.
    Holmes M. Randall (1994). ‘The set theoretical program of Quine succeeded (but nobody noticed)’. Modern Logic. 4: 1–47Google Scholar
  9. 9.
    Jensen Ronald Bjorn (1969) ‘On the consistency of a slight (?) modification of Quine’s ‘New Foundations”. Synthese 19, 250–263CrossRefGoogle Scholar
  10. 10.
    Quine W.V.O. (1937). ‘New Foundations for Mathematical Logic’. American Mathematical Monthly 44: 70–80CrossRefGoogle Scholar
  11. 11.
    Quine, W. V. O., Mathematical Logic, second edition, Harvard, 1951.Google Scholar
  12. 12.
    Rieger L. (1957). ‘A contribution to Gödel’s axiomatic set theory’. Czechoslovak Mathematical Journal 7: 323–357Google Scholar
  13. 13.
    Scott, Dana, ‘Quine’s individuals’, in E. Nagel (ed.), Logic, methodology and philosophy of science, Stanford, 1962, pp. 111–115.Google Scholar
  14. 14.
    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.Google Scholar
  15. 15.
    Wang, H., Logic, Computers, and Sets, Chelsea, 1970, pp. 406.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsBoise State UniversityBoiseUSA

Personalised recommendations