[FOM] The liar paradox

Annatala Wolf a.lupine at gmail.com
Thu Feb 16 13:07:21 EST 2017

I've read the paper, and I'm uncertain about the foundations of the
argument you're making. You argue that there is no axiomatization of truth
which blocks paradoxes and allows what you refer to as "ordinary
unparadoxical reasoning". But this seems to suggest you're working from the
assumption that what you refer to as "ordinary unparadoxical reasoning" is
itself a consistent deductive system.

Let me put it this way. A (real) paradox is a thing which cannot exist. So
how can we even converse about such a concept? We can do so because the
discussion itself is not inconsistent. There's nothing inconsistent at the
meta-level of thinking or reasoning about, describing, or even formally
defining a paradox. There is nothing inconsistent about the *sentence*
"this sentence is false": it exists. I just typed it.

When you use English "intuitively" to reason, it is easy to accidentally
use a definition of "truth" that changes or lifts in some circumstances and
is by itself innately inconsistent in others. For one example, in your
arguments you use "true" both as a symbol, and as the meaning you are
attempting to assign to that symbol. Those are not remotely the same thing.
Can you elucidate further about why this approach is logically valid?

On Thu, Feb 16, 2017 at 2:27 AM Nik Weaver <nweaver at math.wustl.edu> wrote:

> A while ago there was a discussion on this list about the seriousness
> of the liar paradox.  It seemed to be framed as a criticism of my
> book "Truth & Assertibility", which begins with a discussion of this
> topic (the question being, I think, why I would waste time on such a
> triviality).
> (Not all reactions to my book were negative.  May I mention that Math
> Reviews hailed my "fresh and productive approach" as "a major
> contribution"?)
> This is just to say that I have written a short paper on the subject
> titled "The liar paradox is a real problem".  It is available on the
> arXiv here:
> https://arxiv.org/abs/1702.03875
> The key takeaway: "whatever simple idea you have for an easy resolution
> of the liar paradox --- we've tried it, and it doesn't work."
> Nik Weaver
> Math Dept.
> Washington University
> St. Louis, MO 63130
> nweaver at math.wustl.edu
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom

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