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The Mathematical Philosophy of Giuseppe Peano

Published online by Cambridge University Press:  14 March 2022

Hubert C. Kennedy
Hubert C. Kennedy*
Affiliation:
Providence College
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Abstract

Because Bertrand Russell adopted much of the logical symbolism of Peano, because Russell always had a high regard for the great Italian mathematician, and because Russell held the logicist thesis so strongly, many English-speaking mathematicians have been led to classify Peano as a logicist, or at least as a forerunner of the logicist school. An attempt is made here to deny this by showing that Peano's primary interest was in axiomatics, that he never used the mathematical logic developed by him for the reduction of mathematical concepts to logical concepts, and that, instead, he denied the validity of such a reduction.

Type
Research Article
Information
Philosophy of Science , Volume 30 , Issue 3 , July 1963 , pp. 262 - 266
Copyright
Copyright © Philosophy of Science Association 1963

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References

[1] Black, M., The Nature of Mathematics (Paterson, N. J.: Littlefield, Adams & Co., 1959).Google Scholar
[2] Burali-Forti, C., ”Una questione sui numeri transfiniti”, Rend. del circolo mat. di Palermo, Vol. xi (1897).Google Scholar
[3] Cassina, U., Critica dei Principi della Matematica e Questioni di Logica (Roma: Edizioni Cremonese, 1961).Google Scholar
[4] Cassina, U., Dalla Geometria Egiziana alla Matematica Moderna (Roma: Edizioni Cremonese, 1961).Google Scholar
[5] Cassina, U., ”Su la logica matematica di G. Peano”, 1933 (in 3, 331–342.)Google Scholar
[6] Dedekind, R., Essays on the Theory of Numbers (La Salle, Illinois: Open Court Pub. Co., 1948).Google Scholar
[7] Enriques, F., Natura, Ragione e Storia (Torino: Edizioni Scientifiche Einaudi, 1958).Google Scholar
[8] Geymonat, L., Filosofia e Filosofia della Scienza (Milano: Feltrinelli, 1960).Google Scholar
[9] Geymonat, L., ”I fondamenti dell'aritmetica secondo Peano e le obiezioni ‘filosofiche’ di B. Russell” (in 10, 51–63.)Google Scholar
[10] In Memoria di Giuseppe Peano, ed. Terracini, A. (Cuneo, Italy: Presso il Liceo Scientifico Statale, 1955).Google Scholar
[11] Kennedy, H. C., “An Appreciation of Giuseppe Peano”, Pi Mu Epsilon Journal, Vol. 3, No. 3, 107–113.Google Scholar
[12] Peano, G., Arithmetics Principia, Nova Methodo Exposita, 1889 (in 17, II, 20–55.)Google Scholar
[13] Peano, G., Formulario Mathematica, Riproduzione in facsimile dell' edizione originale, con introduzione e note di Ugo Cassina (Roma: Edizioni Cremonese, 1960).Google Scholar
[14] Peano, G., (Estratto) “I fondamenti dell' aritmetica nel Formulario del 1898” (in 17, III, 215–231.)Google Scholar
[15] Peano, G., ”Importanza dei simboli in matematica”, 1915 (in 17, III, 389–396.)Google Scholar
[16] Peano, G., ”Notations de Logique Mathématique” (Introduction au Formulaire de Math.), 1894 (in 17, II, 123–176.)Google Scholar
[17] Peano, G., Opere Scelte, ed. Ugo Cassina, 3 vols. (Roma: Edizioni Cremonese, 1957–59).Google Scholar
[18] Peano, G., ”Sul concetto di numero”, 1891 (in 17, III, 80–109.)Google Scholar
[19] Peano, G., ”Sui fondamenti della geometria”, 1894 (in 17, III, 115–157.)Google Scholar
[20] Peano, G., ”Sul paragrafo 2 del Formulario, t. II: Arithmetica”, 1898 (in 17, III, 232–248.)Google Scholar
[21] Russell, B., The Principles of Mathematics (Cambridge, 1903).Google Scholar
[22] Vailati, G., Il Metodo della Filosofia (Bari, Italy: Editori Laterza, 1957).Google Scholar