[FOM] Davis's honor Roll

[A.P. Hazen]

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?)
---
Allen Hazen
Philosophy Department
University of Melbourne
Interests: historical minutiae, etc.