ONT Re: Model Theory
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
JA = Jon Awbrey
JC = John Collier
JA: Aside from that, my point is that there are many different kinds of meaning
besides the straightforward denotative sort -- just for instance, there is
the "functional" meaning of rites and rotes, in the original sociological
sense of the word "functional", not the more recent inversion of it.
So, the fact that you tried to use this example to illustrate some
point means that it had some meaning to you, otherwise there would
have been no quantum of motivation sufficient to the attempt.
JC: I would agree that there is meaning in my giving the example, but
I would not agree the there is meaning in the example itself.
JA: It is my interest to classify the dimensions of meaning that actually are.
This is just a routine component of a greater objective, one that a wise
person once described in the following wise:
JA: quoting JC:
| I think it is important to understand what scientists are actually doing,
| not just what they think they are doing, or what they are trying to do.
JC: I can agree with this, and still disagree that there is any meaning
in the example. I do think there is meaning in Propositional Calculus
that can be discovered despite its having many disparate uses.
JC: Wittgenstein says that "meaning is use", and one would
hope that this symmetrically implies that use is meaning.
But I am not at all sure that this tells us anything more
about where meaning comes from than we knew already. Some
things have to be just root normative. Use itself isn't.
If it were in itself, then everything would become means,
and there would be no ends. There has to be a point where
we say "We can stop here.", not merely because we are tired.
But I would guess that you know this.
JA: As did both Achilles and the Tortoise.
JC: Another case is the smile of the Chesire cat from the Alice books.
It makes sense of a sort in the context of the Dodgson's nonsense books,
but specifically because it is nonsense. It does have connotative meaning,
but this is always contextual. I realize you may well reply that all meaning
is contextual, but my position all along has been that it is not for complete
logical systems.
JA: I no longer have the context that I'd need to know what the particular interpreter
I am addressing intends by the words "complete logical system", as he has pulled
the rug of my prior assumptions out from under me with that last phoney example.
Mathematics is filled with all sorts of mathematical objects and systems that
are little more than a "set with a modest provision of structure" (SWAMPOS).
You can pick any old SWAMPOS at random and call it a "logic" if you wish --
so what? Unless we take the question seriously "What is a logic for?"
it is all just so much chasing of will o'th' wisps.
JC: That may be true. I suspect it is important or maybe even necessary for explaining
why logic is meaningful to us, though I suspect that we have built in intuitions of
what and what is not meaningful logic and mathematics. I also believe that logic
and mathematics are the study of the same thing, and that the limits of logic and
of mathematics are identical (I am a logicist, unless this position can be shown
to be incoherent). On the other hand, I am not at all certain that logic is
"for" anything, though I am quite certain that we can use it for many things.
That can help us to understand what logic is.
JC: I would say similar things for other systems that involves values other than
truth and falsity. Basically, what I am saying is that I believe the values
themselves can have creative power. Logic is our key to the value of truth,
and also to the emptiness of falsity. As such, I think it stands outside of
any particular uses we might make of it. These are not values we give it,
but values we find in it. At least, so it seems to me.
JC: There various people I have cited were cited not as authorities per se
in our dispute, but as evidence that there are logicians who do not
take the meaningless formalism view of mathematics and logic.
JA: I am confused now -- was I supposed to be defending Formalism?
JC: Not in the least. You were presenting an alternative, I thought.
However there has always been an alternative. You have to show your
position to be not only a solution to the defects of formalism, but that
in some way it responds to problems with a Platonic or transcendental view
of logical and mathematical truth.
JA: No thanks, I already had the eyesore-morphic argument with behaviorism.
Some people are just plane content living in Flatland, and nothing
will chase them out of that Paradys once they have got
their gnosis glued to that mere.
JC: Jon, it is your own two-dimensional view conflationary view of logicism that
is the problem. As I said before, you have constructed a straw man, at least
so it appears to me. I see the view that you are rejecting as 'richer' than
your own view as I have seen it so far, not more impoverished. But perhaps
we are talking past each other somehow, in which case my warning is still
justified.
You have suspected me of not reading what I read several times already --
and that's alright -- suspicion of one another's hermeneutics can lend
a ruddy instincture to inquiry -- but at least when you pose it that
way you reduce it to a simple empirical matter, that is, if we count
reaching out to a library shelf to see if the ismatists in question
wrote what they wrote a form of empirical test, which it can be.
Back to the ScareQuo, and the Yellow Brick Road ...
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤