FOM: The Liar
neilt at mercutio.cohums.ohio-state.edu
Tue Aug 20 11:40:54 EDT 2002
On Mon, 19 Aug 2002, charles silver wrote:
> It also seems to me that there should be a
> "simple" answer to the faults of the Liar--one that does not require
> much technical machinery at all.
This is rather vague. What counts as technical machinery? And, more
importantly, what would count as too much of it?
Here's a suggestion about the Liar and related paradoxes. Keep them in the
language, but don't be bothered by them. Note that the 'proofs' of
absurdity to which they give rise cannot be reduced to normal form. Hence
absurdity has not really been proved.
Insist that for a sentence to be asserted, it must have a proof in normal
form; and for a sentence to be denied, it must have a reductio in normal
form. Use also a relevant, paraconsistent logic in which one cannot pass
from absurdity to an arbitrary proposition, but with which one *can*
prove, for any sequent valid in the orthodox sense, some valid subsequent
thereof. Then live well.
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