Piero Martinetti and the Concept of Number.

Author/s Umberto Bottazzini
Publishing Year 2022 Issue 2022/3 Language Italian
Pages 11 P. 373-383 File size 167 KB
DOI 10.3280/SF2022-003002
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In 1927 Martinetti published an article on the concept of number with the aim of explaining and deepening the correspondence between the form of time and the arithmetic only mentioned by Kant, in particular in the Prolegomena. In order to establish the gnoseological foundation of the concept, Martinetti examines three theories: the empirical theory, the conceptual theory and lastly the critical theory. The first theory, according to Martinetti shared by most mathematicians, argues that number is the result of a process of abstraction from the data of experience. The second theory considers number to be a purely logical concept. Finally, the third theory, of Kantian origin, bases the arithmetic on the pure intuition of time. In what follows, the theses supported by Martinetti are critically compared with the arguments presented by mathematicians and logicians of his time, and in particular with the intuitionist concepts of Brouwer and Weyl.

Keywords: Keywords: number, time, Kant, Brouwer, empirism, logicism, intuitionism.

  1. Il numero: P. Martinetti, Il numero, «Rivista di filosofia», 18 (1927), pp. 158-78 (citato dal volume P. Martinetti, Saggi filosofici e religiosi, a cura di L. Pareyson, Bottega d’Erasmo, Torino 1972).
  2. - Argentieri 2015: Niccolò Argentieri, Introduzione a P. Martinetti, Il numero, Lit edizioni, Roma 2015-ebook Castelvecchi, 2015.
  3. - Brouwer 1907: L.E.J. Brouwer, On the Foundations of Mathematics, in Id., Collected Works, vol. 1, North-Holland, Amsterdam 1975.
  4. - Enriques 1922: Federigo Enriques, Per la storia della logica, Zanichelli, Bologna 1922.
  5. - Fano 1915: Giorgio Fano, Sui fondamenti della geometria, «Rivista di filosofia», 7 (1915), 4, pp. 391.
  6. - Frege 1884: Gottlieb Frege, Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl, Koebner, Breslau 1884.
  7. - Husserl 1891: Edmund Husserl, Philosophie der Mathematik, Psychologische und logische untersuchungen, C.E.M. Pfeffer, Halle-Saale 1891.
  8. - Natorp 1910: Paul Natorp, Die logischen Grundlagen der exacten Wissenschaften, Teubner, Leipzig 1910.
  9. - Russell 2010: Bertrand Russell, Principles of mathematics, Routledge, London 2010.
  10. - Weyl 1967: Hermann Weyl, Filosofia della matematica e delle scienze naturali, Boringhieri, Torino 1967.
  11. - Weyl 2012: H. Weyl, Levels of infinity, Dover Publications, Inc., 2012.
  12. - Wundt 1880: W. Wundt, Logik: eine Untersuchung der Principien der Erkenntniss und der Methoden wissenschafticher Forscung, 2 B.de, Verlag von Ferdinand Enke, Stuttgart 1880.

Umberto Bottazzini, Martinetti e il concetto di numero in "RIVISTA DI STORIA DELLA FILOSOFIA" 3/2022, pp 373-383, DOI: 10.3280/SF2022-003002