- Dans : DAVID HILBERT’S LECTURES ON THE FOUNDATIONS OF MATHEMATICS AND PHYSICS, 1891-1933 - 2009 (N° 5)

- Pages : 375 à 434
- DOI : 10.1007/b12915_4
- Date de création : 04-01-2011
- Dernière mise à jour : 24-02-2015

In this Chapter, the authors present two sets of lecture notes by Hilbert in which he reflects on epistemological consequences of modern physics. The opening passages of both lectures set the theme in almost identical words as a reflection on the role of mathematics in the exact sciences. Indeed, both lectures cover similar ground and deal with epistemological implications of general covariance such as time-reversal invariance and the need to formulate what Hilbert calls a “principle of objectivity,” the independence from coordinates for all meaningful statements in physics. The second set of lectures takes the theme further and discusses the implications of what Hilbert called the “world equations,”* i.e*., the field equations of his 1915 communication on the “Foundations of Physics.” Hilbert considered the question of completeness of physical theory and introduced the concept of “accessorial” laws, arguing that in a proper sense such laws no longer exist in modern physics based on general relativity and quantum theory. This contention is discussed in its philosophical implications in an attempt to position Hilbert’s axiomatic method in distinction to Kantian apriorism and against Poincaré’s conventionalism.

In this Chapter, the authors present two sets of lecture notes by Hilbert in which he reflects on epistemological consequences of modern physics. The opening passages of both lectures set the theme in almost identical words as a reflection on the role of mathematics in the exact sciences. Indeed, both lectures cover similar ground and deal with epistemological implications of general covariance such as time-reversal invariance and the need to formulate what Hilbert calls a “principle of objectivity,” the independence from coordinates for all meaningful statements in physics. The second set of lectures takes the theme further and discusses the implications of what Hilbert called the “world equations,”* i.e*., the field equations of his 1915 communication on the “Foundations of Physics.” Hilbert considered the question of completeness of physical theory and introduced the concept of “accessorial” laws, arguing that in a proper sense such laws no longer exist in modern physics based on general relativity and quantum theory. This contention is discussed in its philosophical implications in an attempt to position Hilbert’s axiomatic method in distinction to Kantian apriorism and against Poincaré’s conventionalism.