The philosophical significance of Gödel's Dialectica interpretation
Bibliographic Data
| ID | 10346944 |
|---|---|
| Authors | Stephen Mackereth (0000-0001-8150-9658, Society of Fellows and Department of Philosophy Dartmouth College Hanover New Hampshire USA, corresponding author) |
| Year | 2025 |
| Volume | 111 |
| Issue | 2 |
| Pages | 423-450 |
| Publication date | 2025-07-04 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Philosophy and Phenomenological Research (JOURNAL) |
| Journal identifiers | ISSN: 0031-8205 • E-ISSN: 1933-1592 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/phpr.70027 |
| OpenAlex | W4412043176 |
| Language | EN |
| References cited | 32 |
Hilbert's Program in the 1920s aimed to give finitary consistency proofs for infinitary mathematics, thus putting infinitary mathematics on a more secure footing. There is a popular narrative that Hilbert's Program was decisively refuted by Gödel's incompleteness theorems in 1931. However, Gödel himself, in a remarkable paper of 1958, pursues a modified version of Hilbert's Program: he presents his Dialectica interpretation as a new, Hilbert‐style consistency proof for arithmetic based on “an extension of the finitary standpoint,” and he clearly regards this proof as epistemologically significant. In this essay, I explain and assess the epistemological project that Gödel sets out in his Dialectica paper. Ultimately, I argue that the Dialectica interpretation is best understood, not as a consistency proof, but as a way of assigning a constructive meaning to arithmetic
Epistemology · Interpretation (philosophy · Linguistics · Critical Theory and Philosophy · Phenomenology and Existential Philosophy · Philosophy · Philosophy, Science, and History
| Citation velocity | historical |
|---|---|
| Highly cited | No |