Does reductive proof theory have a viable rationale?

Authors
Citation
S. Feferman, Does reductive proof theory have a viable rationale?, ERKENNTNIS, 53(1-2), 2000, pp. 63-96
Citations number
49
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Philosiphy
Journal title
ERKENNTNIS
ISSN journal
0165-0106 → ACNP
Volume
53
Issue
1-2
Year of publication
2000
Pages
63 - 96
Database
ISI
SICI code
0165-0106(2000)53:1-2<63:DRPTHA>2.0.ZU;2-C
Abstract
The goals of reduction and reductionism in the natural sciences are mainly explanatory in character, while those in mathematics are primarily foundati onal. In contrast to global reductionist programs which aim to reduce all o f mathematics to one supposedly "universal" system or foundational scheme, reductive proof theory pursues local reductions of one formal system to ano ther which is more justified in some sense. In this direction, two specific rationales have been proposed as aims for reductive proof theory, the cons tructive consistency-proof rationale and the foundational reduction rationa le. However, recent advances in proof theory force one to consider the viab ility of these rationales. Despite the genuine problems of foundational sig nificance raised by that work, the paper concludes with a defense of reduct ive proof theory at a minimum as one of the principal means to lay out what rests on what in mathematics. In an extensive appendix to the paper, vario us reduction relations between systems are explained and compared, and argu ments against proof-theoretic reduction as a "good" reducibility relation a re taken up and rebutted.