[FOM] The liar "revenge" - a last message

[Nik Weaver]

Arnon,

Thank you for your very clear message.  There will be no need for you to
repeat your point yet again: I understand it perfectly well.  In your
view liar-type sentences are not meaningful, and the fallacious step in
any paradoxical derivation involving such a sentence is the one where the
paradoxical sentence itself is consulted, as if it had something to say,
when in fact it does not say anything.

This solution is not as clean as you think it is.  If held to, it would
entail rejecting some basic deductive technique.  I will explain using
Quine's self-referential construction.  Consider the sentence

(*) "When preceded by its quotation is either not true or meaningless"
when preceded by its quotation is either not true or meaningless.

I have labelled this sentence (*).  Arnon, on your view we must affirm

(1) The sentence (*) is meaningless.

If you refuse to affirm sentence (1) then I will have to insist that
your position has changed.

I continue with the argument.  The next step is

(2) "When preceded by its quotation is either not true or meaningless"
when preceded by its quotation is meaningless.

And then comes

(3) "When preceded by its quotation is either not true or meaningless"
when preceded by its quotation is either not true or meaningless.

If both inferences, from (1) to (2) and from (2) to (3), are valid,
then we have proven (*).

In order to block the inference from (1) to (2) you would have to
curtail our ability to reason about simple syntactic constructions.
Preceding a string by its own quotation is a perfectly valid
syntactic operation.  To accept (1) but not (2) is to reject an
inference from "A is meaningless" to "B is meaningless" where A is
the label of some syntactic object and B is a syntactic construction
which produces the identical syntactic object.

Would you deny that preceding "When preceded by its quotation is either
not true or meaningless" by its quotation is a legitimate construction?

In order to block the inference from (2) to (3) you would have to
reject an inference from "B is meaningless" to "B is either not true
or meaningless".

So you see, your resolution of the liar-type paradoxes comes at the
cost of forcing us to reject elementary reasoning about simple
syntactic constructions.  I happen to think that is an issue of
pressing interest.  As to your more personal comments, I would simply
ask you to consider whether I have ever written about you or your work
in such a way.

best wishes

Nik