[FOM] 23 syllables

[Bill Greenberg]

Take (1,2,) as premises,

1) Des('Het', Het) <-> Het=Het                                   Premise	
2) -(G)(Des('Het',G) <-> Het=G)                                 Premise

We then have the following:

3) Des('Het', Het)        				                                 1
4) (EG)-(Des('Het',G) <-> Het=G))      			                    2
5) -(Des('Het',G) <-> Het=G)                                        		4,EI
6) (Des('Het',G) & -Het=G) v (Het = G & -(Des('Het',G))       5
7) -(Het = G & -(Des('Het',G))
         3, Leibniz's Law
8)  Des('Het',G) & -Het=G
          6,7
9)  Des('Het', Het) & Des('Het',G) & -Het=G                           2,8

Do you accept (9)?  If not, which of (1,2) is false?

Best regards,
WIlliam J. Greenberg

On 12/7/06, Hartley Slater <slaterbh at cyllene.uwa.edu.au> wrote:
> At 4:00 AM -0500 7/12/06, Henri Galinon wrote:
> >And
> >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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