Antinomicity and the axiom of choice. A chapter in antinomic mathematics

Florencio G. Asenjo



The present work is an attempt to break ground in mathematics proper, armed with the accepting view just described. Specifically, we shall examine various versions of antinomic set theory, in particular the axiom of choice, keeping the presentation as intuitive as possible, more in the manner of a nineteenth century paper than as a thoroughly formalized system. The reason for such a presentation is the conviction that at this point it should be the mathematics that eventually determines the logic, rather than the other way around.

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F. G. Asenjo, “The Idea of a Calculus of Antinomies”, La Plata, 1953.

F. G. Asenjo, “A Calculus of Antinomies”, Notre Dame Journal of Formal Logic, VII, 1966., p. 103.

F. G. Asenjo and J. Tamburino, “Logic of Antinomies”, Notre Dame Journal of Formal Logic, 1975.

F. G. Asenjo, “Formalizing Multiple Location”, [in:] Non-Classical Logics, Model Theory, and Computability, edited by A. I. Arruda, N. C. A. da Costa, and R. Chuaqui, North Holland, Amsterdam, 1977, pp. 25–36.

F. G. Asenjo, “Toward an Antinomic Mathematics”, in [17].

F. G. Asenjo, “Continua Without Sets”, Logic and Logical Philosophy, 1993, Vol. 1, pp. 95–128.

M. J. Beeson, Foundations of Constructive Mathematics, Springer-Verlag, Berlin, 1985.

E. W. Beth, The Foundations of Mathematics, North Holland, Amsterdam, 1958.

G. Frege, “A critical elucidation of some points in E. Schroeder’s Algebra der Logic”, [in:] Translations from the Philosophical Writings of Gottlob Frege, edited by P. Geach & M. Black, Oxford, 1977, pp. 86–106.

K. Gödel, “Russell’s Mathematical Logic”, The Philosophy of Bertrand Russell, edited by P. A. Schilpp, Tudor, 1944.

J. van Heijenoort, From Frege to G¨odel, Harvard University Press, Cambridge, 1967.

T. Jech, The Axiom of Choice, North Holland, Amsterdam, 1973.

A. Kolmogorov, “On the principle of excluded middle”, in [11].

E. Mendelson, Introduction to Mathematical Logic, Wadsworth, Monterey, 1987.

G. H. Moore, Zermelo’s Axiom of Choice, Springer-Verlag, New York, 1982.

J. von Neumann, “An Axiomatizaton of Set Theory”, in [11], pp. 421–423.

Paraconsistent Logic: Essays on the Inconsistent, edited by G. Priest, R. Routley, and J. Norman, Philosophia Verlag, Munich, 1989.

A. Robinson, Introduction to Model Theory and to the Metamathematics of Algebra, North Holland, Amsterdam, 1965.

H. Rubin & J. Rubin, Equivalents of the Axiom of Choice, North Holland, Amsterdam, 1963.

B. Russell, An Enquiry into Meaning and Truth, Allen & Unwin, London, 1940.

A. N. Whitehead and B. Russell, Principia Mathematica, 1927.

D. Wrinch, “On Mediate Cardinals”, American Journal of Mathematics, 1923, Vol. 45, pp. 87–92.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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