[FOM] Intuitionists and excluded middle

Hartley Slater slaterbh at cyllene.uwa.edu.au
Sun Oct 30 19:49:34 EST 2005

At 12:00 PM -0500 30/10/05, Michael Kremer wrote:
>Thus in
>Drago's argument, the intuitionist understanding
>of the logical connectives involved in LEM is
>tacitly presupposed, and so the argument as it
>stands simply begs the question against the
>classical logician.  The classical logician is
>quite happy to assert that either A or not-A
>without claiming to be able to decide which is the case.

Exactly so!  That is why 'the LEM', in Intuitionistic terms, is 
better symbolised as a modal thesis, of the form 'Lp v L-p', where 
'L' is 'it is decidable constructively that'.  Clearly *that* does 
not hold in general; and its not holding in general does not conflict 
with 'p v -p' invariably holding.  I previously referenced a recent 
article by J.Y.Beziau, which was about the propriety of such modal 
re-expressions (both in the Intuitionistic case, and in the dual, 
Paraconsistentist case, where there is again no conflict with 
classical logic, once the proper symbolisation is used).
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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