[FOM] The liar "revenge"?

Till Mossakowski mossakow at iws.cs.uni-magdeburg.de
Tue Jul 21 03:16:16 EDT 2015

The liar sentence is not per se meaningless. See the following PhD 
thesis giving a meaning (in two-valued logic!) to such sentences:


Am 20.07.2015 um 23:05 schrieb Arnon Avron:
> 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.
> Arnon
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom

More information about the FOM mailing list