References
G. Boolos, ‘The iterative conception of set’, The Journal of Philosophy 68 (1971), 215–231.
A. Church, ‘Schröder's anticipation of the simple theory of types’, The Journal of Unified Science (Erkenntnis) 9 (1939), 149–152.
N. Cocchiarella, ‘A second order logic of variable-binding operators’, Reports on Mathematical Logic 5 (1975), 3–18.
N. Cocchiarella, ‘The theory of homogeneous simple types as a second order logic’, Notre Dame Journal of Formal Logic 20 (1979), 505–524.
N. Cocchiarella, ‘Frege, Russell and Logicism: a logical reconstruction’, forthcoming in Frege Synthesized, L. Taimien and J. Hintikka, eds, D. Reidel, Dordrecht.
N. Cocchiarella, Logical Investigations of Predication Theory and the Problem of Universals, vol. 2 of Indices, Bibliopolis Press, Naples, 1984.
G. Frege, The Basic Laws of Arithmetic, translated by M. Furth, University of California Press, Berkeley, 1964.
G. Frege, Posthumous Writings, eds. H. Hermes, F. Kambartel and F. Kaulbach; translated by P. Long and R. White, Blackwell, Oxford, 1979.
G. Frege, Translations from the Philosophical Writing of Gottlob Frege, eds. P. Geach and M. Black, Blackwell, Oxford, 1952.
A. Fraenkel, Y. Bar-Hillel, and A. Levy, Foundations of Set Theory, North-Holland, Amsterdam, 1973.
D. Gallin, Intensional and Higher-Order Modal Logic, North-Holland, Amsterdam, 1975.
K. Gödel, The Consistency of the Continuum Hypothesis, Princeton University Press, Princeton, 1940.
L. Henkin, ‘Completeness in the theory of types’, Journal of Symbolic Logic 15 (1950), 81–91.
R. Jensen, ‘On the consistency of a slight(?) modification of Quine's New Foundations,’ Synthesé 19 (1968), 250–263.
G. Kreisel, ‘Two notes on the foundations of set-theory’, Dialectica 23 (1969), 93–114.
R. M. Montague, Formal Philosophy, ed. R. H. Thomason, Yale University Press, New Haven, 1974.
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.
W. V. O. Quine, Mathematical Logic, Harvard University Press, Cambridge, 1958.
W. V. O. Quine, Set Theory and Its Logic, Harvard University Press, Cambridge, 1963.
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.
B. Russell, and A. Whitehead, Principia Mathematica, Cambridge University Press, 1913.
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.
E. Specker, ‘Typical ambiguity’, in Logic, Methodology and Philosophy of Science, eds. E. Nagal et al., Stanford University Press, 1962, pp. 116–124.
H. Wang, ‘A formal system of logic’, Journal of Symbolic Logic 15 (1950), 25–32.
H. Wang, From Mathematics to Philosophy, Humanities Press, New York, 1974.
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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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DOI: https://doi.org/10.1007/BF00542647