[FOM] 23 syllables

Hartley Slater slaterbh at cyllene.uwa.edu.au
Thu Dec 7 18:07:37 EST 2006

At 4:00 AM -0500 7/12/06, Henri Galinon wrote:
>here is our antinomy : the least number not specifiable in less than 
>nineteen syllables is specifiable in 18 syllables. I have just so
>specified it.

Certainly 'the least number not specificable in less than ninteen 
syllables' contains less than ninteen syllables.  But you have not 
shown that it specifies anything, and so specifies something in less 
than 19 syllables.  See the very end of my lengthy paper 'Epsilon 
Calculi', just published in the Journal of the IGPL. (Vol 14, No 4, 
2006, pp. 535-590).  I there discuss a formal treatment of the same 
paradox by Graham Priest, and isolate the corresponding fallacy in 
his reasoning.

A bit of a myth has grown up about 'The Logical Paradoxes' that they 
are quite intractable conundrums (that is indeed a major source of 
the idea behind Priest's paraconsistent logic).  But in many cases, 
if not all, the problem has merely been a too hasty logical analysis. 
If you do not believe me, try getting a contradiction from the 
following formal definition of Heterologicality, for instance:
Het'x' iff (EF)((G)(Des('x',G) <-> F=G).-F'x').
You will need the additional assumption that (G)(Des('Het',G) <-> 
Het=G) at one point, and so the contradiction which is then derivable 
merely means that this further assumption cannot be true..
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

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