FOM: The meaning of truth
kanovei at wmwap1.math.uni-wuppertal.de
Mon Nov 6 13:13:17 EST 2000
> From: "charles silver" <silver_1 at mindspring.com>
> Date: Mon, 6 Nov 2000 06:52:37 -0800
> ... Kanovei's view,
> but unfortunately he seems unable to develop arguments for his
On the contrary I made my position extremely clear:
there is an opinion that it follows from a known Goedel's theorem
that there are mathematical statements true but not provable,
and I wrote that this is a misinterpretation of the theorem
and, basically, wrong, finally, I challenged the opponents to
present any math. sentence true but not provable.
Except for a few sharp but inconclusive remarks of Mr. Shipman
I only received a combination of claims that I am a "superfinitist"
and ridiculous references to "the Tarski truth predicate".
In other words "my position" is extremely clear: show me a sentence
or concede defeat. Which arguments do you expect ? Well, go further.
> preferring instead to joke about unicorns and the like.
I invented unicorns in order to expose meaninglessness of some
seriously presented claims by changing them to those of absolutely
the same logical structure but about unicorns, when the
meaninglessness becomes undisputable.
> he may be objecting to the claim that there's
> a *model*, the so-called "standard model", which has certain
> properties that can be ascertained.
After such a claim (that there is a "standard model") is made
precise, in correct scientific manner, that is, with explanation
how this model "there is", where, so to speak, it "is", et cetera,
I will "be objecting", not before, because so far there is nothing
> ... in establishing
> that there's at least one sentence, G ("This sentence is unprovable"),
> that is true but unprovable, this same model is alluded to. The
> model is singled out in order to establish what it is that the
> sentence G is true of.
I fancy what "of" at the end means, but the rest is just the
core of the problem.
> I am imagining that Kanovei objects
> to this reference to the "standard model" (as being similar
> to referring to unicorns),
Exactly, even worse, while we, educated people, think that we
might be able to recognize a unicorn be it unexpectedly demonstrated
(I think Mr. Shipman's remark), it is, mildly speaking, unclear how
the (ontological) "standard model" may look like.
> yet this reference is needed to
> establish the truth of G.
That's it !
> I would like Kanovei to address whether the above loose argument
> characterizes one aspect of his objection to the notion of Truth
If *truth of a mathematical sentence different from provability*
then, essentially, yes, basically, the only one aspect.
More information about the FOM