[FOM] FOM Digest, Vol 151, Issue 16

Andrei Popescu A.Popescu at mdx.ac.uk
Tue Jul 21 12:43:54 EDT 2015

Dear Arnon, 

>> It seems to me that there are a lot of people who simply *want* to keep the liar paradox alive.

Let me add my own 2 cents at keeping it alive. How about rotating the sentence with 90 degrees (so to speak), obtaining:

"This sentence is meaningless." 

where "meaningless" means "does not have a truth value"?  

Now, performing to this sentence a similar analysis to the one for the standard liar paradox, we obtain that the sentence is meaningless. 
But this makes the statement true, a fortiori meaningful.   


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Subject: FOM Digest, Vol 151, Issue 16

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Today's Topics:

   1. Re: The liar "revenge"? (Arnon Avron)


Message: 1
Date: Tue, 21 Jul 2015 00:05:16 +0300
From: aa at tau.ac.il (Arnon Avron)
To: Josh Cole <jcolend at gmail.com>
Cc: Foundations of Mathematics <fom at cs.nyu.edu>,
	nweaver at math.wustl.edu,	Arnon Avron <aa at tau.ac.il>
Subject: Re: [FOM] The liar "revenge"?
Message-ID: <20150720210516.GB25357 at localhost.localdomain>
Content-Type: text/plain; charset=us-ascii

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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End of FOM Digest, Vol 151, Issue 16


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