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: Tue, 18 Jan 2005 18:02:15 +0100

tchow@lsa.umich.edu wrote:
> Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote:
>
>>Not at all strange psychologically, or to force technical meaning on
>>this, modally.
>>
>>Back to the sqrt(2) example, what is the mathematical meaning of its
>>irrationality, -if one erases from our knowledge, its proof and/or
>>truth value-? We can surely use it hypothetically (it is well-formed).
>>I feel stuck in the "proof says it all"/"formality" vein, and I am
>>looking for some meaning outside of that point of view.
>
> I guess this all comes down to the fact that I have no clue at all about
> what you mean by "meaning." Your use of the term differs so far from
> anything I've ever seen, either in commonsense discourse or in philosophical
> writing, that I can't even guess what you mean by it.

Fair enough. I think I can describe what I ..uh.. mean by it.
And I think I can try to say what I think you mean by it.

> In particular, I
> don't understand what "psychologically" means,

By that I take the "meaning" of an statement to be that of an
utterance by an individual in a particular situation. Your example of
someone giving directions; the meaning of such utterances depends on
context (is the speaker trustworthy? do the speaker and hearer refer
to the same things?). For the sqrt(2) example, the meaning will
involve things like possible deductions ("incommensurable values
exist (namely sqrt(2)", "you can't calculate sqrt(2) using a finite
set of integer operations"), in addition to things like "I believe
'sqrt(2) is irrational' is true" or "I heard this statement and I'm
repeating it because I trust who said it before". 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.

> or what proof or truth has to do with meaning.

I agree with Torkel that it is uncontroversial that "truth is
involved with meaning", if their meanings are both watered down
terribly. And so I find it hard to believe that anyone would deny
this connection (like you just did, or Torkel at one point did)
unless there is a technical meaning of "meaning" that you are
demanding for our context.

> Suppose I'm learning French and someone says, "Il pleut" and I ask,
> "What does that mean?" The answer I want is that "Il pleut" means
> "It's raining." Once I know this, I know the meaning of "Il pleut."
> It is entirely irrelevant whether in fact it is raining, or whether
> I have any evidence that it is raining. Even if I have no way of
> telling whether or not it's in fact raining, this will not impede my
> ability to learn the meaning of "Il pleut." Nor will I need to rewrite
> my phrasebook once I find out that in fact it *is* raining.

So I take this analogy to mean that you (and the common sense and/or
philosophical concept) consider "meaning" to be simply translation,
or an assignment, or (I suppose more technically), a model. (I am
certainly using the word "meaning" in such a way in many places).

I see now from your analogy how neither truth nor proof (technically)
might have nothing to do with (your intended technical meaning of)
meaning (and changing the truth won't change the meaning) that, but
it seems...unfilling to me, it

Do you really mean that that the meaning of "sqrt(2) is irrational"
is given by its translation into the definitions of all those terms?
Where does the translation stop? Don't the atomic parts of the formal
language have meaning?

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)?
What about Goldbach's conjecture? (as Torkel pointedly mentioned)

What is this technical meaning of "meaning" that I am missing?
Is it just translation/assignment/morphism/formalization? 

-- 
Mitch Harris
(remove q to reply)

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