[FOM] The liar "revenge"?
Chris Scambler
cscambler at gmail.com
Tue Jul 21 05:50:07 EDT 2015
> 1) Would you agree that Eiffel tower is not true?
> 2) Would you agree that the number 7 is not yellow?
> 3) Would you agree that the liar sentence is not yellow?
> 4) Would you agree that "This sentence is true" is not true?
> 5) Would you agree that 1/0 is not less
> than 7, and also not greater than 7?
> 6) Would you agree that the liar sentence is not less
> than 7, and also not greater than 7?
>
Let's think about 1): "Eiffel tower is not true". Naively at least, truth
is a predicate much like yellow (as you intimate in your list of
questions). Some things are in the extension of the predicate, others
aren't. As you perceive, only well-formed, meaningful sentences of the
language in question fall under the extension of true. Now it seems
reasonable to say that
(TRANS) x does not fall under the extension of F iff it is not the case
that Fx
Since Eiffel tower is not a well-formed, meaningful sentence of English,
it does not fall under the extension of true. Whence, by TRANS(parency of
"falls under the extension of") it is not the case that Eiffel tower is
true. This should not be confused, however, with the claim that Eiffel
tower is false, for obvious reasons. Compare 2), that number 7 is not
yellow. Since only concrete objects fall under the extension of yellow, by
TRANS it is not the case that 7 is yellow. But it does not follow that the
number 7 has some other colour.
Now I suppose one might challenge the view that truth is just an ordinary
predicate of things like yellow or what have you. But this would need to be
well motivated; it certainly seems like truth is exactly such a predicate.
Or one might challenge (TRANS), since it is easy to see that it too leads
to liar-like paradox by considering the predicate employed meaningfully in
its left hand side. But then that would be to accept that liar-like
paradoxes present some difficulties, which I take it is not something you
are interested in doing.
Even given this, however, in the case of the Liar sentence I do not think
that the meaninglessness argument as presented in Weaver stands up. Let L
be the Liar. By what has been said, the assumption of L's meaninglessness
indeed entails it cannot be in the extension of "true". Whence by TRANS, L
is not true. But we cannot then say that this is what L itself says, since
by supposition it is meaningless - i.e., it says nothing. Thus we simply
arrive at the view that L is not true, because like Eiffel tower it is not
the sort of thing that can be true.
One might say something like: by definition we have that L if and only if L
is not true. But this biconditional is itself meaningless if L is, like
"table if and only if table is not true" and so cannot be used in the
formal argument to establish L's purported "truth".
The conclusion - that L is not true, but not paradoxical - is I think
wrong. But this is because it sets out from the assumption that the Liar is
meaningless, which I think is itself pretty obviously wrong. Nevertheless,
I think this is the proper conclusion one who thinks the Liar is
meaningless should arrive at.
Best,
Chris
>
>
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