Experimental Logics, Mechanism and Knowable Consistency
Författare och institution:
Martin Kaså (Institutionen för filosofi, lingvistik och vetenskapsteori)
Publicerad i:
Theoria, 78 ( 3 ) s. 213–224
ISSN:
0040-5825
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2012
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
In a paper published in 1975, Robert Jeroslow introduced the concept of an experimental logic as a generalization of ordinary formal systems such that theoremhood is a Pi-0-2 property(or in practice Delta-0-2) rather than Sigma-0-1. These systems can be viewed as (rather crude) representations of axiomatic theories evolving stepwise over time. Similar ideas can be found in papers by Putnam (1965) and McCarthy and Shapiro (1987). The topic of the present article is a discussion of a suggestion by Allen Hazen, that these experimental logics might provide an illuminating way of representing "the human mathematical mind". This is done in the context of the well-known Lucas-Penrose thesis. Though we agree that Jeroslow's model has some merit in this context, and that the Lucas-Penrose arguments certainly are less than persuasive, some semi-technical doubts are raised concerning the alleged impact of experimental logics on the question of knowable self-consistency.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Algebra och logik ->
Matematisk logik
HUMANIORA ->
Filosofi, etik och religion ->
Filosofi ->
Logik
HUMANIORA ->
Filosofi, etik och religion ->
Filosofi ->
Teoretisk filosofi
Matematik ->
Algebra och logik ->
Matematisk logik
HUMANIORA ->
Filosofi, etik och religion ->
Filosofi ->
Logik
HUMANIORA ->
Filosofi, etik och religion ->
Filosofi ->
Teoretisk filosofi
Nyckelord:
experimental logics, Jeroslow, knowable consistency, Lucas-Penrose thesis
Postens nummer:
162441
Posten skapad:
2012-08-22 15:08
Posten ändrad:
2012-08-28 15:38