[FOM] The liar "revenge"?

Arnon Avron aa at tau.ac.il
Mon Jul 20 17:05:16 EDT 2015

Making an argument much longer, with several steps, does not
make it any more compelling, if the crucial point
remains as weak as before. In the case of Cole's reply,
I skip all the five first steps and go directly to the
sixth one:
> 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.

So again I read that a meaningless sentence asserts something, which is
a contradiction in terms. A meaningless sentence does not assert
anything, and does not say anything. Period. This is the meaning 
of "meaningless".

 Well, if people prefer that instead of saying that the liar sentence
is  meaningless I'll say that it does not assert anything,
(or that it does not say anything) then fine - as long as the
answer would not be again something of the type:
"if it does not assert anything then it is true, because this
is precisely what it asserts"... With such a logic
I simply cannot cope.

Let me add here the following comment. It seems to me that there are
a lot of people who simply *want* to keep the liar paradox alive,
and to see it as an unbreakable paradox.  I see
little point in arguing with them if all they can do is to repeat
arguments that like the "proofs" of the existence of god,
convince only those who want to be "convinced" (and in fact 
are convinced of what the argument "proves" well before hearing it...). 
But those people should better be aware that any conclusion
they reach from the "paradox" will be completely irrelevant to
mathematicians who do not see a real problem with the liar - that is,
practically all mathematicians. Indeed, the liar is known 
for two thousands years or so, and (as far as I know) 
mathematicians never really care about it. The story was completely
different when they faced Russel's paradox (or the other
"logical paradoxes") - and for good reasons. 


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