Hilbert’s Program: the Transcendental Roots of Mathematical Knowledge Cover Image

Hilbert’s Program: the Transcendental Roots of Mathematical Knowledge
Hilbert’s Program: the Transcendental Roots of Mathematical Knowledge

Author(s): Rossen Lyutzkanov
Subject(s): Philosophy
Published by: Институт по философия и социология при БАН
Keywords: philosophy of mathematics; transcendental philosophy; Hilbert’s program

Summary/Abstract: The design of the following paper is to establish an interpretative link between Kant’s transcendental philosophy and Hilbert’s foundational program. Through a regressive reading of Kant’s Critique of Pure Reason (1781), we can see the motivation of his philosophical project as bound with the task to expose the a priori presuppositions which are the grounds for the possibility of actual knowledge claims. Moreover, according to him the sole justification for such procedure is the (informal) proof of consistency and (architectonical) completeness. Hilbert tried to strip Kant’s philosophy of its last anthropomorphic vestiges which led to the formulation of his “finite standpoint” and the prooftheoretical methods for axiomatic reconstruction of classical mathematics. Therefore, contrary to the received view, the proofs of consistency and completeness which were envisaged as part of his metamathematical program were not conceived as a means to secure to epistemic basis of mathematical knowledge. Accordingly, the program itself was not confuted by Gödel’s theorems and remains as viable as ever.

  • Issue Year: II/2010
  • Issue No: 2
  • Page Range: 121-126
  • Page Count: 6
  • Language: English