David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Theoria 78 (3):213-224 (2012)
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
|Keywords||experimental logics Lucas‐Penrose thesis Jeroslow knowable consistency|
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References found in this work BETA
Roger Penrose (1994). Shadows of the Mind. Oxford University Press.
John R. Lucas (1961). Minds, Machines and Godel. Philosophy 36 (April-July):112-127.
John Lucas (2003). Minds, Machines and Gödel. Etica E Politica 5 (1):1.
Hilary Putnam (1965). Trial and Error Predicates and the Solution to a Problem of Mostowski. Journal of Symbolic Logic 30 (1):49-57.
Petr Hájek (1977). Experimental Logics and Π03 Theories. Journal of Symbolic Logic 42 (4):515 - 522.
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