Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 01/18/05 

Date: 18 Jan 2005 21:46:13 GMT

 <tchow@lsa.umich.edu> wrote:
>Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote:
>
>>If I must put this
>>more succinctly I would say "semantic connections" or "intentions".
>>
>>I can easily see that you (or Torkel) might consider most of these
>>things to be irrelevant for a mathematical cconcept of meaning.
>
>They seem to be irrelevant for any theory of meaning, mathematical or
>otherwise. Consider the traffic example. Again I would say that according
>to common sense, we know what the directions *mean* without having any
>knowledge of whether the directions are correct or not. In fact, I have to
>know what they mean before I can even begin to evaluate whether they are
>correct. Until I know what they mean, I'll be stuck on square one. "What
>did he say? Did you catch what he said? What did he mean by `turn
>right'?" When I finally understand what is being said, *then* I can go
>about deciding whether or not it's true.

Hmm..then how do you analyse the knights/knaves statements?
When a knave (always tells falsehoods) says "to get to town, take the left
fork", I take that statement to really mean "do not take the left fork".

(sorry if I am being obtuse, not getting the point)

>>So I take this analogy to mean that you (and the common sense and/or
>>philosophical concept) consider "meaning" to be simply translation,
>
>Not at all. I was just using an example to illustrate a point about
>meaning, namely that it does not have anything to do with whether the
>statement is true or with any grounds for believing it.
>
>>But given this now, I am still unsure what it is then that you take to
>>be the meaning of "sqrt(2) is irrational".
>>What about "sqrt(4) is irrational" (sic)?
>
>It means that if you take any two integers a and b, and then compute a^2
>and 4b^2, then you will get two distinct integers.
>
>>What about Goldbach's conjecture? (as Torkel pointedly mentioned)
>
>It means that if you take all primes and list all pairwise sums, then every
>even integer greater than 2 can be found somewhere in that list.

To me, both of these sound -exactly- like translation. So I don't get
your "not at all".

Also, they both sound, as with the "il pleut/it's raining" example, very
circular, that is one could ask what your statements mean and then give
very legitimately the original.

>Surely one needs to understand the meaning of a conjecture before one can go
>about looking for a proof.

informally I get that but ... is that meaning beyond the translation into
constituent formalized parts?

>Alice: "I'm trying to prove that every Hodge class on a projective
> nonsingular algebraic variety over C is a rational linear
> combination of classes of algebraic cycles."
>Bob: "What on earth does that mean?"
>Alice: "Beats me. If I knew what it meant then I'd be able to prove it."
>Bob: ??!

:) OK, that makes sense to me but I don't know how to reconcile it with
your examples before.

Mitch

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