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HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

GIORGIO VENTURI · UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência

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Author / responsible party
GIORGIO VENTURI
Publisher
UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência
ISSN
2317-630X
ISSN
2317-630X
Language
English

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Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

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APA 7

VENTURI, G. (s. f.). HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS. https://doi.org/10.1590/0100-6045.2015.V38N2.GV

MLA

VENTURI, GIORGIO. "HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS.". https://doi.org/10.1590/0100-6045.2015.V38N2.GV.

Chicago

VENTURI, GIORGIO. s. f. "HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS.". https://doi.org/10.1590/0100-6045.2015.V38N2.GV.

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VENTURI, G. s. f, HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS, UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência, available at: https://doi.org/10.1590/0100-6045.2015.V38N2.GV [Accessed 6 Aug. 2026].

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Title
HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
Author / contributors
GIORGIO VENTURI
Publisher
UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência
ISSN
2317-630X
ISSN
2317-630X
Language
English

Subjects

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Hilbert; Axioms; Intuitions; Axiom of Completeness; Frege; Reference of axioms; Cesar's problem; Foundations of geometry; Proof theory; Grundlagen der Geometrie
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