TY - JOUR

T1 - Hilbert's sixth problem

T2 - Between the foundations of geometry and the axiomatization of physics

AU - Corry, Leo

N1 - Publisher Copyright:
© 2018 The Author(s) Published by the Royal Society. All rights reserved.

PY - 2018/4/28

Y1 - 2018/4/28

N2 - The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue 'Hilbert's sixth problem'.

AB - The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue 'Hilbert's sixth problem'.

KW - Axiomatization

KW - David Hilbert

KW - Physics

UR - http://www.scopus.com/inward/record.url?scp=85045554125&partnerID=8YFLogxK

U2 - 10.1098/rsta.2017.0221

DO - 10.1098/rsta.2017.0221

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C2 - 29555796

AN - SCOPUS:85045554125

SN - 1364-503X

VL - 376

JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

IS - 2118

M1 - 0221

ER -