[FOM] Davis's honor Roll
a.hazen at philosophy.unimelb.edu.au
Sun Jun 1 04:25:45 EDT 2003
Martin Davis writes:
>I'm fond of noting that the list of logicians who have seriously proposed
>formal systems that turned out to be inconsistent reads like an honor roll:
>Frege, Church, Curry, Quine, Rosser.
Well, it **ought** to be an honor roll! A foundational worker who
isn't at least running the risk of inconsistency isn't being general or
foundational enough. (So maybe it's a GOOD sign that proposed large
cardinal axioms have sometimes turned out to be inconsistent? Yes, I think
so. The only way the people studying these things could have been sure
of avoiding inconsistency would have been by proposing axioms which--
unlike large cardinal axioms-- didn't yield new "power". And no one is
interested in axioms like "There AREN'T any inaccessible cardinals.")
Anyway, Martin: Russell belongs on the list. His 1906 "substitutional
theory," combined with axioms he would likely have accepted about identity
conditions for propositions, is inconsistent: cf. Peter Hylton's article
in "Synthese" vol. 45 (1980).
(And, for another addition: didn't Martin-Löf overstep at one stage and
propose a type of types?)
University of Melbourne
Interests: historical minutiae, etc.
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