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Publication Date: 2008-01-01
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Risteski, I. B., & García D., C. E. (2008). Sobre lo que hay en filosofía de las matemáticas. Discusiones Filosóficas, 9(12), 151–172. Retrieved from https://revistasojs.ucaldas.edu.co/index.php/discusionesfilosoficas/article/view/655
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Abstract
In this paper, we sketch roughly several moments that have a considerable influence on the development of the philosophy of mathematics. We illustrate the main problems of this discipline and discuss the import of the so called 'positiviness of mathematics'. By examining several approaches to this problem, we analyze ontological and epistemological questions which can help to clarify this complicated area.
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References
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CARNAP, R. (1931). "Die logizistische Grundlegund der Mathematik". En: Erkenntnis 2, pp. 91-106.
HEYTING, A. (1931). "Die intuitionistische Grundlegung der Mathematik". Erkenntnis 2, pp. 106-116.
VON NEUMAN, J. (1931). "Die formaliistische Grundlegung der Mathematik". Erkenntnis 2, pp. 116-122.
DEDEKIND, R. (1888). Was sind und was sollen die Zahlen. Brunswick.
BETH, E. W. (1955). "Semantik entialment and formal derivability". Mededeling van de Koninklijke Nederlandse Akademie van Watenschappen, Afdeling Letterkunde, N. R. 18, 309-342.
PRAWITZ, D. (1971). Ideas and results in proof theory. Proc. 2nd Scand. Logic Symp., North-Holland, pp. 235-309.
COMBÈS, M. (1971). Fondements des Mathématiques. Paris: Presses Univ.
QUINE, W. V. (1961). From a Logical Point of View. Harvard University Press, Cambridge
GÖDEL, K. (1947). "What is Cantor's continuum problem?" Amer. Math. Monthly 54, pp. 515-527.
BENACERRAF, B. & PUTNEM, H. (1964). Philosophy of Mathematics.Oxford.
GOODSTEIN, R. L. (1968). Existence in Mathematics. Amsterdam.
BELL, E. T. (1951). Mathematics Queen and Servant of Science. New York: McGraw-Hill Book Co. Inc.
SKOLEM, T. (1923). "Begründung der elementaren Arithmetik". Skripter utgit av det Norske Videnskaps-Akademie, I No. 6b, Oslo
KLEENE, S. C. (1967). Mathematical Logic. London: John Wiley & Sons.
LAKATOS, I. (1972). Problems in Philosophy of Mathematics. North-Holland.
TARSKI, A. (1995). Introduction to Logic and to the Methodology of Deductive Sciences. New York: Dover Pub. Inc.
MAMUZIC,Z. (1963). Klasicna - moderna - konstruktivna matematika. Uvodjenje mladih u naucni rad III, Matematicka biblioteka No. 20, Zavod za izdavanje udjbenika SR Srbije, Beograd pp. 9-37.
