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Frege's double correlation thesis and quine's set theories NF and ML

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References

  1. G. Boolos, ‘The iterative conception of set’, The Journal of Philosophy 68 (1971), 215–231.

    Google Scholar 

  2. A. Church, ‘Schröder's anticipation of the simple theory of types’, The Journal of Unified Science (Erkenntnis) 9 (1939), 149–152.

    Google Scholar 

  3. N. Cocchiarella, ‘A second order logic of variable-binding operators’, Reports on Mathematical Logic 5 (1975), 3–18.

    Google Scholar 

  4. N. Cocchiarella, ‘The theory of homogeneous simple types as a second order logic’, Notre Dame Journal of Formal Logic 20 (1979), 505–524.

    Google Scholar 

  5. N. Cocchiarella, ‘Frege, Russell and Logicism: a logical reconstruction’, forthcoming in Frege Synthesized, L. Taimien and J. Hintikka, eds, D. Reidel, Dordrecht.

  6. N. Cocchiarella, Logical Investigations of Predication Theory and the Problem of Universals, vol. 2 of Indices, Bibliopolis Press, Naples, 1984.

    Google Scholar 

  7. G. Frege, The Basic Laws of Arithmetic, translated by M. Furth, University of California Press, Berkeley, 1964.

    Google Scholar 

  8. G. Frege, Posthumous Writings, eds. H. Hermes, F. Kambartel and F. Kaulbach; translated by P. Long and R. White, Blackwell, Oxford, 1979.

    Google Scholar 

  9. G. Frege, Translations from the Philosophical Writing of Gottlob Frege, eds. P. Geach and M. Black, Blackwell, Oxford, 1952.

    Google Scholar 

  10. A. Fraenkel, Y. Bar-Hillel, and A. Levy, Foundations of Set Theory, North-Holland, Amsterdam, 1973.

    Google Scholar 

  11. D. Gallin, Intensional and Higher-Order Modal Logic, North-Holland, Amsterdam, 1975.

    Google Scholar 

  12. K. Gödel, The Consistency of the Continuum Hypothesis, Princeton University Press, Princeton, 1940.

    Google Scholar 

  13. L. Henkin, ‘Completeness in the theory of types’, Journal of Symbolic Logic 15 (1950), 81–91.

    Google Scholar 

  14. R. Jensen, ‘On the consistency of a slight(?) modification of Quine's New Foundations,’ Synthesé 19 (1968), 250–263.

    Google Scholar 

  15. G. Kreisel, ‘Two notes on the foundations of set-theory’, Dialectica 23 (1969), 93–114.

    Google Scholar 

  16. R. M. Montague, Formal Philosophy, ed. R. H. Thomason, Yale University Press, New Haven, 1974.

    Google Scholar 

  17. W. V. O. Quine, ‘New foundations for mathematical logic’, American Math Monthly 44 (1937), 70–80; reprinted with additions in From a Logical Point of View, Harvard Univ. Press, 2nd ed., Cambridge, 1961.

    Google Scholar 

  18. W. V. O. Quine, Mathematical Logic, Harvard University Press, Cambridge, 1958.

    Google Scholar 

  19. W. V. O. Quine, Set Theory and Its Logic, Harvard University Press, Cambridge, 1963.

    Google Scholar 

  20. B. Russell, ‘On some difficulties in the theory of transfinite numbers and order types', Proc. of London Math. Soc. (1906); reprinted in Essays in Analysis, ed. D. Lackey, Braziller, New York, 1973.

  21. B. Russell, and A. Whitehead, Principia Mathematica, Cambridge University Press, 1913.

  22. E. Specker, ‘The axiom of choice in Quine's New Foundations for Mathematical Logic’, Proc. of the Nat. Acad. of Sciences 39 (1953), 972–975.

    Google Scholar 

  23. E. Specker, ‘Typical ambiguity’, in Logic, Methodology and Philosophy of Science, eds. E. Nagal et al., Stanford University Press, 1962, pp. 116–124.

  24. H. Wang, ‘A formal system of logic’, Journal of Symbolic Logic 15 (1950), 25–32.

    Google Scholar 

  25. H. Wang, From Mathematics to Philosophy, Humanities Press, New York, 1974.

    Google Scholar 

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Cocchiarella, N.B. Frege's double correlation thesis and quine's set theories NF and ML. J Philos Logic 14, 1–39 (1985). https://doi.org/10.1007/BF00542647

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