Experimental Logics, Mechanism and Knowable Consistency
Article first published online: 27 APR 2012
© 2012 Stiftelsen Theoria
Volume 78, Issue 3, pages 213–224, September 2012
How to Cite
Kaså, M. (2012), Experimental Logics, Mechanism and Knowable Consistency. Theoria, 78: 213–224. doi: 10.1111/j.1755-2567.2012.01133.x
- Issue published online: 22 AUG 2012
- Article first published online: 27 APR 2012
- experimental logics;
- knowable consistency;
- Lucas-Penrose thesis
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 (or in practice ) rather than . 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.