[FOM] The liar "revenge"?

[Josh Cole]

I like the way Weaver puts things in the paragraph in question. Here's a
longer form of the argument, intended to make clearer that the argument is
not circular.

Let's take the liar sentence to be, "This sentence is not true."

0. The key move is not to start with truth tables. Do not ask what are the
consequences of the sentence being true, or the consequences of it being
false. Inquire instead into what the sentence means; for we are suspicious
it might be neither true nor false, so that any analysis of the
implications of it being true or false would be misleading.

1. So first I approach the liar sentence in wonder. Gee, it is interesting
-- let's try to figure out what it might mean, and once we've got that
down, we might be in a position to say whether it is true or false.

2. Not having direct intuition into its meaning right off the bat, I try to
find its meaning by a close reading of it. It must mean something like,
"the words of the sentence now being uttered do not signify a truth."

3. Great! Now I just need to see what is signified by the words of the
sentence in question.

4. Wait! Step 3 really takes us back to our original question, the meaning
of the liar sentence.

5. I conclude I will never find a meaning to the sentence by this form of
analysis: we might view it as an infinite regress in a search for the
ultimate reference. Now, if the liar sentence had a meaning, surely it
would be susceptible to this kind of analysis, which carefully looks for
the reference of every phrase. So, I conclude that the liar sentence has no
meaning. At first it may look like the sort of string of words that would
have a meaning, but it is in reality not coherent. Sort of like, "Dog five
over blue times Johnson."

6. About to feel content with this "solution" to the paradox, an
unfortunate observation is made. A meaningless sentence is not true, in the
sense that it is not the case that a meaningless sentence makes an
assertion that is true. Thus, it seems the liar sentence is true after all,
since it asserts that a particular meaningless string of characters is not
true.

7. True, at this point, we could stop and have our contradiction: we've
argued the liar sentence to be meaningless and hence true, but a
meaningless sentence cannot possibly be true. Or we could continue, and
derive from the truth of the liar sentence its falsity.

It is not a circular argument, because we actually argue for the
meaninglessness of the sentence by an analysis of the words in it. Once
we've concluded it is meaningless, we claim that all meaningless sentences
are not true. Finally, based off of the words in the liar sentence and the
fact that it is not true, we argue that it is in fact true.

This is all very valuable, because one can be sorely tempted to dispense
with the liar sentence (and other similar sentences paradoxically
self-referential) by saying they are neither true nor false. It appears to
be very clean. Weaver's argument shows it is not as clean as one might at
first suspect.

Josh Cole

On Sun, Jul 19, 2015 at 12:41 PM, Arnon Avron <aa at tau.ac.il> wrote:

>
> I started today to read Weaver's new book "Truth & Assertibility",
> and already at the very first page I came across
> an argument that amazed me. It is not that it was the first time
> that I encounter that argument, but it is the first time
> I see it taken seriously by someone that I really respect (I hope
> that the rest of the book does not depend on it!). It
> runs as follows:
>
> "The first impression most people have about the liar sentence
> is that it is completely meaningless. But surely a meaningless
> sentence cannot also be true. So if it is meaningless
> then in particular it is not true, and that is just what
> it says of itself... which would make it true. We have
> reached a contradiction again."
>
> Well, to me it seems that Weaver could have shorten the
> "argument" by saying that if the liar sentence is meaningless,
> then since it is meaningful we have reached a contradiction again...
> Surely a meaningless sentence cannot say anything about
> anything, in particular not about itself (or anything else). So
> relying on what "it says of itself" depends on taking
> for granted that it is meaningful. Therefore the above  argument
> is hopelessly circular!
>
> I do wonder now if I am missing something here, and if so -
> what can it possibly be.
>
> Needless to say, for me the "liar sentences" of all types
> are indeed completely  meaningless, which is why I was never bothered
> by them (in contrast to the so-called logical paradoxes).
>
> Arnon Avron
>
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