Towards finishing off the axiom of reducibility
Philosophia Scientiae, Volume 1 (1996) no. 3, pp. 17-35.
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de Rouilhan, Philippe. Towards finishing off the axiom of reducibility. Philosophia Scientiae, Volume 1 (1996) no. 3, pp. 17-35. http://archive.numdam.org/item/PHSC_1996__1_3_17_0/

Aczel, Peter 1987 Non-well Founded Sets, CSLI Lectures Notes n° 14.

Church, Alonzo 1976 Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski, Journal of Symbolic Logic 41, 747-60. | Zbl

Chwistek, Leon 1921 Antynomie logiki formalnej, Przeglad Filozoficzny 24; 164-171 (english trans., "Antinomies of Formal Logic", in [McCall 1967]).

Chwistek, Leon 1922 Ueber die Antinomien der Prinzipien der Mathematik, Mathematische Zeitschrift 14, 236-243. | JFM

Chwistek, Leon 1929 Neue Grundlagen der Logik und Mathematik, Mathematische Zeitschrift 30. | JFM

Copi, Irving M. 1950 The Inconsistency or Redundancy of Principia Mathematica, Philosophical and Phenomenological Research 11, 190-199. | Zbl

Copi, Irving M. 1971 The Theory of Logical Types, London : Routledge and Kegan Paul.

Feferman, Solomon 1964 Systems of Predicative Analysis, The Journal of Symbolic Logic 29, 1-30. | Zbl

Gödel, Kurt 1944 Russell's Mathematical Logic, in [Schilpp 1944, 123-153] (reprinted. in [Gödel 1986-??, vol. II, 119-141])

Gödel, Kurt 1986-?? Collected Works (ed. by S. Feferman et alii), New York et Oxford : Oxford University Press, vol. I, Publications 1929-1936, 1986;vol. II, Publications 1938-1974, 1990; vol. III, Unpublished Essays and Lectures, 1995; vol. IV, forthcoming. | Zbl

Kleene, Stephen C. 1955a Arithmetical Predicates and Function Quantifiers, Transactions of the American Mathematical Society 79, 312-340. | Zbl

Kleene, Stephen C. 1955b Hierarchies of Number Theoretic Predicates, Bulletin of the American Mathematical Society 61, 193-213. | Zbl

Kleene, Stephen C. 1959 Quantification of Number-theoretic Functions, Compositio Mathematica 14, 23-40. | EuDML | Numdam | Zbl

Mccall, Storrs (ed.) 1967 Polish Logic 1920-1939, Oxford : Clarendon Press.

Mirimanoff, Dimitri 1917 Les antinomies de Russell et de Burali-Forti et le problème fondamental de la théorie des ensembles, L'Enseignement Mathématique 19, 37-52. | JFM

Myhill, John 1979 A Refutation of an Unjustified Attack on the Axiom of Reducibility, in [Roberts 1979].

Parsons, Charles 1990 Introductory note to 1944, in [Gödel 1986-??, vol. II].

Poincaré, Henri 1905-06 Les mathématiques et la logique, Revue de Métaphysique et de Morale 13 (1905), 815-835; 14 (1906), 17-34, 294-317 (abridged and modified version in [Poincaré 1908]). | JFM

Poincaré, Henri 1908 Science et Méthode, Paris : Flammarion.

Quine, Willard Van Orman 1963 Set Theory and its Logic, Cambridge, Mass : Harvard University Press (2nd ed. 1969). | Zbl

Ramsey, Frank Plumpton 1925 The Foundations of Mathematics, Proceedings of the London Mathematical Society, series 2, 25 (1926), 338-384 (paper read before the London Mathematical Society in 1925; reprinted in [Ramsey 1978]). | JFM

Ramsey, Frank Plumpton 1978 Foundations Essays in Philosophy, Logic, Mathematics and Economics (ed. by D. H. Mellor), London and Henley : Routledge and Kegan Paul.

Roberts, G. (ed.) 1979 Bertrand Russell, Memorial Volume, London : G. Allen and Unwin.

Rouilhan, Philippe De 1996 Russell et le cercle des paradoxes, Paris : P.U.F.

Russell, Bertrand 1907 The Regressive Method of Discovering the Premisses of Mathematics, published in [Russell 1973].

Russell, Bertrand 1908 Mathematical Logic as Based on the Theory of Types, American Journal of Mathematics 30, 222-262 (reprinted. in [Russell 1956]). | JFM

Russell, Bertrand 1910 Cf. [Whitehead and Russell 1910-27, vol. I, lst ed].

Russell, Bertrand 1956 Logic and Knowledge Essays 1901-1950 (ed. by R. C. Marsh), London : G. Allen and Unwin. | Zbl

Russell, Bertrand 1973 Essays in Analysis (ed. by D. Lackey), London : G. Allen and Unwin.

Schütte, Kurt 1960 Beweistheorie, Berlin : Springer. | Zbl

Wittgenstein, Ludwig 1913a Letter to Russell of September 5, 1913, in [Wittgentein 1961, 2nd ed., 123].

Wittgenstein, Ludwig 1913b Letter to Russell of the end of 1913, in [Wittgentein 1961, 2nd ed., 127-129].

Wittgenstein, Ludwig 1961 Notebooks 1914-1916 (ed. by G. H. von Wright and G. E. M. Anscombe, with an english trans. by G. E. M. Anscombe), Oxford : B. Blackwell (2nd ed. 1979).

Wittgenstein, Ludwig 1977 Culture and Value (ed. by G. H. von Wright, trans. by P. Winch), Oxford : B. Blackwell.

Zermelo, Ernst 1908 Untersuchungen über die Grundlagen der Mengenlehre, I, Mathematische Annalen 59, 261-281. | EuDML | JFM

Zermelo, Ernst 1930 Ueber Grenzzahlen und Mengenbereiche Neue Untersuchungen über die Grundlagen der Mengenlehre, Fundamenta Mathematicae 16, 29-47. | EuDML | JFM