Mathematical properties

Tom Pearson (
Sat, 14 Feb 1998 12:25:58 -0600 (CST)

At 12:42 PM 2/12/98 -0500, Jan de Koning wrote:

>About math.: I disagree. Everything has mathematical (numerical and
>spatial) properties. Denying that these properties exist does not make
>them going away. 2+2=4 is not an idealization of reality. That is just a
>"real" observation. Even saying "Three in One" is a real mathematical
>statement, not an idealization, and I thank God for that.

I find these comments fascinating, largely because I am feeble when it comes
to mathematics. But they leave me with questions. Can someone explain to
me what a "mathematical property" is? Since you say that "everything" has
them, I assume this means that these are properties of "things," including
physical objects. Ordinarily, a property is something that belongs to, or
is expressed by, a substance of some sort. So what kind of a thing is a
"mathematical property" belonging to a physical substance? Or are these
mathematical properties simply assigned to a physical substance for the
purpose of giving it a particular kind of description?

And what does it mean to say that "2+2=4" is a "real" observation? Just
what is being "observed"? Is it the case, for instance, that numbers have
an independent existence apart from the objects they measure? This sounds
to me like Pythagoreanism/Platonism redux, which were mostly efforts to
create a stable metaphysics. But does this metaphysics still play a role in
modern science? Does it serve as a specific type of link between science
and Christian theology?

Well, you can see my questions here rapidly dissolve into murk. It reminds
me that my most serious regret about my undergraduate education was that I
didn't study more mathematics. Having worked through the last couple of
books by Roger Penrose left me wondering if I had really understood all of
his claims, since there is a mathematical basis for most of them.

Can anybody help me get straightened out on this stuff?

Tom Pearson

Thomas D. Pearson
Department of History & Philosophy
The University of Texas-Pan American
Edinburg, Texas