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LOPEZ-ESCOBAR, E. G. K. SETS, CLASSES AND THE PROPOSITIONAL CALCULUS. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 28, n. 2, p. 417–448, 2016. Disponível em: Acesso em: 10 jun. 2023.


The propositional calculus AoC, “Algebra of Classes”, and the extended propositional calculus EAC, “Extended Algebra of Classes” are introduced in this paper. They are extensions, by additional propositional functions which are not invariant under the biconditional, of the corresponding classical propositional systems. Their origin lies in an analysis, motivated by Cantor’s concept of the cardinal numbers, of A. P. Morse’s impredicative, polysynthetic set theory.


BOOLE, G. The Mathematical Analysis of Logic, 1847.

————. An Investigation of the Laws of Thought, 1854.

BOYER, C.B. A History of Mathematics. New York: John Wiley & Sons Inc., 1989.

BURRIS, S. Logic for Mathematics and Computer Science. New Jersey:

Prentice Hall, 1998.

CHUAQUI, R.B. Axiomatic Set Theory: Impredicative Theories of Classes. Vol. 51 of Notas de Matemtica. Amsterdam: NorthHolland, 1981.

KELLEY, J.L. General Topology. New York: Van Nostrand, 1955.

LAWVERE, F.W. “Continuously variable sets: Algebraic Geometry =

Geometric Logic”. Proceedings A.S.L. Logic Colloquium, Bristol 1973. Vol. 80 of Studies in Logic and the Foundations of Mathematics. Amsterdam: North Holland, pp. 135-156, 1975.

MAREK, W. On the Metamathematics of Impredicative Set Theory. Vol. 98 of Dissertationes Mathematicae. Warszawa: PWN, 1973.

MIRIMANOFF, D. “Les antinomies de Russell et de Burali-Forti et leprobl`eme fondamental de la th´eorie des ensembles”. L’Enseigement Mathematique, 19, 1917a.

————. “Remarques sur la th´eorie des ensembles et les antinomies cantoriennes I” L’Enseigement Mathematique, 19, 1917b

————. “Remarques sur la th´eorie des ensembles et les antinomies cantoriennes II” L’Enseigement Mathematique, 19, 1920.

MORSE, A.P. A Theory of Sets. Vol. 108 of Pure and Applied Mathematics. New York: Academic Press Inc., 1965.

————. A Theory of Sets. Vol. 108 of Pure and Applied Mathematics,

second ed. New York: Academic Press Inc., 1985.

RUSSELL, B. History of Western Philosophy. New York: Simon and Schuster, 1945.

SCHRODER, E. ¨ Vorlesungen ¨uber die Algebra der Logik. Vol. 1, Leipzig, 1890.

SPECKER, E. “La reponse de Dmitry Mirimanoff”. In: J. Casser and Henri

Volken (eds.), Logic and Set Theory in 20th century Switzerland, 2001.

WANG, H. From Mathematics to Philosophy. New York: Humanities Press,

————. A Logical Journey From G¨odel to Philosophy. Cambridge, MA:

The MIT Press, 1996.


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