FOM: The Liar

charles silver silver_1 at
Mon Aug 19 16:05:10 EDT 2002

    The recent proposed solution to the Liar Paradox recommended by Till
Mossakowski, which is the PhD thesis of Andreas Beck, is very impressive.
I've read a fair amount of the work and it is both insightful as well as
technically interesting.   However, the consequence that one instance of
'This sentence is False' may be true while another instance is false, is not
acceptable, to my mind.   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.   I think the "simple" answer is that we've
expected something we shouldn't have expected in the first place.  Why
should we have expected the Liar to deliver a single truth-value when we go
to work on it?   Also, the Liar cannot really be said to be "inconsistent"
proof-theoretically, since there are no rules of inference in ordinary
language.  And, it also doesn't seem to make sense to assume that any
sentence(s) constructed in ordinary language should have a model.
Nevertheless, I still think Andreas Beck's work is impressive.   (His
comments on the other well-known proposed solutions are worth reading on
their own.)

Charlie Silver

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