[FOM] Intuitionists and excluded middle

[Hartley Slater]

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)
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Url: http://www.philosophy.uwa.edu.au/staff/slater