In the literature one can see the increasing trend of supporting intuitionism through phenomenology. Brouwer’s pupil, Arend Heyting, is said to be a forerunner of this trend, as he used a phenomenological terminology in order to define intuitionist negation, by elaborating the first intuitionist logic. In this paper, the author tries to explore—with reference to the unpublished material stored in the Heyting archive—how much of Heyting’s general thought is compatible with phenomenology. In the conclusion she suggests that Heyting and Husserl, insofar as they both think consciousness must be the very beginning of knowledge, share a same antipsychologistic attitude which coexists with an attempt to overcome solipsism. Yet, the phenomenological concept of degree of evidence cannot be applied to Heyting’s scale of evidence (including small natural numbers, large natural numbers, infinitely proceeding sequences, the universal quantifier), on the one side because it is not clear if the latter is common and shared by all intuitionists, and, on the other side, because the former presupposes a revisable evidence that does not fit to Heyting’s viewpoint. Furthermore, Husserl’s and Heyting’s conceptions of the nature of mathematics and logic and of their relationship are essentially different. From an intuitionist viewpoint mathematics is the domain of evidence, while logic transcribes its regularities. From a phenomenological viewpoint, mathematics remains outside the domain of evidence. Apophantic logic coincides with mathematics (without either of them absorbing the other), but transcendental logic lies at a higher level.

Arend Heyting and Phenomenology: is the meeting feasible? / M. Franchella. - In: BULLETIN D'ANALYSE PHENOMENOLOGIQUE. - ISSN 1782-2041. - 3:2(2007), pp. 1-21.

Arend Heyting and Phenomenology: is the meeting feasible?

M. Franchella
Primo
2007

Abstract

In the literature one can see the increasing trend of supporting intuitionism through phenomenology. Brouwer’s pupil, Arend Heyting, is said to be a forerunner of this trend, as he used a phenomenological terminology in order to define intuitionist negation, by elaborating the first intuitionist logic. In this paper, the author tries to explore—with reference to the unpublished material stored in the Heyting archive—how much of Heyting’s general thought is compatible with phenomenology. In the conclusion she suggests that Heyting and Husserl, insofar as they both think consciousness must be the very beginning of knowledge, share a same antipsychologistic attitude which coexists with an attempt to overcome solipsism. Yet, the phenomenological concept of degree of evidence cannot be applied to Heyting’s scale of evidence (including small natural numbers, large natural numbers, infinitely proceeding sequences, the universal quantifier), on the one side because it is not clear if the latter is common and shared by all intuitionists, and, on the other side, because the former presupposes a revisable evidence that does not fit to Heyting’s viewpoint. Furthermore, Husserl’s and Heyting’s conceptions of the nature of mathematics and logic and of their relationship are essentially different. From an intuitionist viewpoint mathematics is the domain of evidence, while logic transcribes its regularities. From a phenomenological viewpoint, mathematics remains outside the domain of evidence. Apophantic logic coincides with mathematics (without either of them absorbing the other), but transcendental logic lies at a higher level.
filosofia della matematica del Novecento; intuizionismo; fenomenologia; A. Heyting
Settore M-FIL/02 - Logica e Filosofia della Scienza
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/42570
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