Skip to main content
SpringerLink
Log in

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

  • Published:
Studia Logica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bernays P. (1954). ‘A system of axiomatic set theory VII’. Journal of Symbolic Logic. 19: 81–96

    Article  Google Scholar 

  2. Crabbé Marcel (1982). ‘On the consistency of an impredicative subsystem of Quine’s NF’. Journal of Symbolic Logic 47, 131–136

    Article  Google Scholar 

  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.

  4. reference for setlike from Forster.

  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. Grishin V.N. (1969). ‘Consistency of a fragment of Quine’s NF system.’ Sov. Math. Dokl. 10: 1387–1390

    Google Scholar 

  7. Hailperin T. (1944). ‘A set of axioms for logic’. Journal of Symbolic Logic 9:1–19

    Article  Google Scholar 

  8. Holmes M. Randall (1994). ‘The set theoretical program of Quine succeeded (but nobody noticed)’. Modern Logic. 4: 1–47

    Google Scholar 

  9. Jensen Ronald Bjorn (1969) ‘On the consistency of a slight (?) modification of Quine’s ‘New Foundations”. Synthese 19, 250–263

    Article  Google Scholar 

  10. Quine W.V.O. (1937). ‘New Foundations for Mathematical Logic’. American Mathematical Monthly 44: 70–80

    Article  Google Scholar 

  11. Quine, W. V. O., Mathematical Logic, second edition, Harvard, 1951.

  12. Rieger L. (1957). ‘A contribution to Gödel’s axiomatic set theory’. Czechoslovak Mathematical Journal 7: 323–357

    Google Scholar 

  13. Scott, Dana, ‘Quine’s individuals’, in E. Nagel (ed.), Logic, methodology and philosophy of science, Stanford, 1962, pp. 111–115.

  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.

  15. Wang, H., Logic, Computers, and Sets, Chelsea, 1970, pp. 406.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Boise State University, Boise, ID, USA

    M. Randall Holmes

Authors
  1. M. Randall Holmes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Randall Holmes.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-008-9107-8

Keywords

Search

Navigation