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Experimental logics, mechanism and knowable consistency

Författare och institution:
Martin Kaså (Institutionen för filosofi, lingvistik och vetenskapsteori)
Publicerad i:
Sino-European Winter School in Logic, Language and Computation, Sun Yat-Sen University, Guangzhou, China, Dec. 3-18, 2010,
Konferensbidrag, refereegranskat
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 Π2 property (or in practise Δ2) rather than Σ1. 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 paper 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):
Matematik ->
Algebra och logik ->
Matematisk logik
Filosofi, etik och religion ->
Filosofi ->
Filosofi, etik och religion ->
Filosofi ->
Teoretisk filosofi
experimental logic, Jeroslow, knowable consistency, Lucas-Penrose thesis
Postens nummer:
Posten skapad:
2010-12-15 15:56

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