Re: Platonism

From: J.E. (troubled6man_at_yahoo.com)
Date: 11/28/04 

Date: 27 Nov 2004 15:53:35 -0800

examachine@gmail.com (Eray Ozkural exa) wrote in message news:<320e992a.0411261232.41252e2e@posting.google.com>...

[snip]

> So, reality of mathematical statements seems quite like the reality of
> physical statements! They are theoretical. They are first and foremost
> thoughts (to us!). They can be derived from thought experiments or
> empirical observations. This might be an easier route for you to
> answer. In exactly which fashion can we distinguish physical
> statements from mathematical statements?

Physical statements have a material model that is very much like a
mathematical model. What makes a physical statement is that certain
parts of the model correspond to observations, and the specifically if
you can find a model where the parts that match up to observations DO
match up to past observations, then the other observations will IF
CHECKED also match observations. That match up is called the physical
theory. Mathematics has no "mathematical theory" and is not "checked"
in that same way. But the first part of the two acticvities are no
different that I can tell.
 
> The only answer I can find is that (in current mathematics)
> * They don't have to directly correspond to physical systems, they can
> talk about certain mental constructions with desirable properties such
> as abstractness which are not *directly* derived from sensory
> experience or empirical trials e.g. graph theory. A graph is an
> abstract concept. But it is wrong to say that graphs do not exist in
> the real world. They certainly do, especially when programmed on a
> computer!

Graphs, if said to exist the way you claim, would seem to be physical
claims. Comparison with observation is the physical theory. So once
you assert "my mathematical thought is real" then it sounds to me like
you had a physical though (which is a terrible word because it sounds
like physically had a thought, which is something else true, but
totally different).
 
> But unfortunately there can be cases in mathematics that are not even
> *indirectly* derived from observations, that are solely the result of
> thought experiments and are indeed incompatible even with the basic
> features of our universe.

I disagree that it is as indirect as you claim. Mathematicians are
interested in patterns as much physicists are. If they are more
interested in the patterns of material models that no one has figured
out how yet to relate to any scale or coarseness of physical
experience, then there isn't anything wrong with that. They aren't
"bad physicists" because they didn't claim that they had a physical
theory to go with their material model.

> I don't find this a desirable thing, because
> I find these to be misleading thought experiments. I suggest we put
> them aside until we can find a use for them.

I disagree. If we don't have a good stock of material models, then
what if someone has an idea for a physical theory, why should we force
them to create material models that OTHERS would have enjoyed making.
That sounds arbitrary.
 
[snip]

> By the way, another view that I might regard good enough would be some
> kind of mathematical instrumentalism, that might say that "exist" is
> used only as a figure of speech in mathematics, which is precisely
> what I'm suggesting is the current practice. IOW, this "exist" has
> *nothing* to do with "exist" in the ordinary sense... Which is perhaps
> what you want to say... Are you an instrumentalist of some sort? But
> we should beware, when we say that, we are really coming to
> mathematical solipsism that I talked of a while ago! That does not
> seem desirable either!

You did ask earlier about *most* mathematicians, so I'd like to add my
two cents. Most mathematicians when they say "exist" have an
axiomatic system (like ZFC) in mind, and mean that they are
considering a formla with the symbol E flipped backwords in it. I
believe it might be called formalism, and it is fairly common IMO.

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