Topic: GENERAL LOGIC
Some more curious inferences
By Jeffrey Ketland
Nominalism denies the existence of numbers, sets and functions. But a widely discussed problem concerns whether nominalism can account for the applicability of mathematics. This is the indispensability argument against nominalism, associated with Godel, Quine and Putnam. Above we examined examples of the application of mathematics to relationships of logical consequence. It seems to me that the `speed-up' phenomenon under discussion suggests a modified version of the indispensability argument, based now on unfeasibility considerations. Presumably the nominalist does not wish to deny the validity of the inferences I, I{2}, and I{3} under consideration. But there is no feasible direct verification for the above inferences, and the short mathematical derivations involve practically indispensable assumptions about numbers, sets and functions. So, how might a nominalist account for our knowledge that such inferences are valid? After all, the anecdotal evidence is that even nonmathematicians find I{2} and I{3} `obvious'.
Source: Analysis Preprints
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OFFTOPIC NOTE:
Setting aside the problems Ketland mentions above, Everett could try to write a Nominalist Semantics for Pirah?, for that would be consistent with Everett's recent works. Nevertheless, in such case any claim Everett made in the case of Pirah? would have to be valid for other natural languages, and, of course, his views would not easily convince those who do not accept nominalism.
Posted by Tony Marmo
at 00:01 BST
Updated: Wednesday, 27 October 2004 00:00 BST
