Re: Logic and math and the world

From: Craig Franck (craig.franck_at_verizon.net)
Date: 10/22/04 

Date: Fri, 22 Oct 2004 23:58:25 GMT

"Acid Pooh" wrote

> "Craig Franck" wrote

> > I'm not sure. It was mentioned in an essay by John D. Barrow called "What
> > is Mathematics?". Since he was referring to "most people," I imagine what he
> > meant by the world being logical is it was coherent as opposed to an "Alice in
> > Wonderland"-type world. The world is full of "patterns of regularity," which
> > is what math excels at describing.
> >
> > Another major issue was, while all math refers to itself, a small subset refers to
> > things in the real world.
>
> I'm not sure what you mean by this. I mean, I narrowed down what you
> might mean in the second part -- (i) some parts of mathematics can
> serve as models (in the non-logical sense) for phenomena in the
> physical world, or (ii) some physical phenomena can serve as a model
> (in the logical sense) for some bits of mathematics. I'll assume you
> meant the first. But what does the first part mean?

I meant the first, but the second formulation seems to follow from the first.
Most of us acquire basic competence in arithmetic from real-world examples.

By the first part I mean A = A refers to itself, and F = ma refers to itself as
well as the entities (possibly somewhat abstract) F, m, a, and a relation that
holds.

"Referring to itself" is perhaps an odd way of saying A = A can be translated
into the sentence "The statement 'A equals A' is always true, and 'A' need not
refer to anything other than itself as a mathematical symbol."

> > One possible explanation that is offered for this is logic and math refer to the
> > simplest possible relations of abstract entities, and the world, to be, must
> > consist of a set of relations of actual entities. So there is an intersection of
> > math and the real world.
>
> Are you sure you mean the same kind of set in both cases? If so, this
> locks you into a Platonic ontology. Blech. :-)

I suppose for two sets to have an intersection, they must contain the same
kinds of things. I believe math and physical relations are of a different
logical type. Math is representational, while physical entities are themselves. 

-- 
Craig Franck
craig.franck@verizon.net
Cortland, NY

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