Re: Mathematical properties

Jan de Koning (dekoning@idirect.com)
Sat, 14 Feb 1998 15:58:03 -0500

At 12:25 PM 14/02/98 -0600, Tom Pearson wrote:
>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?

Actually, to be complete I would have to give a philosophy lecture, which I
don't have the time for. Since I wrote the sentence, I'll try. 1apple + 1
apple = two apples is a mthematical statement. The group lying on the
table then has the mathematical property that there are two members in that
group. They have a spatial (which is a mathematical concept too) property
that they need enough room to be in. They have hardness, which is a
physical property; they did grow on a tree, which is a biological property
etc. etc.

>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?

Assigning properties does not need to be a simple task, neither are
physical things the only things having "properties." You can have a creed
with 12 articles. Having a certain number of articles is a numerical
(mathematical) property. Assigning properties does not need to be simple
assigning.
>
>And what does it mean to say that "2+2=4" is a "real" observation? Just
>what is being "observed"?

See above.
> Is it the case, for instance, that numbers have
>an independent existence apart from the objects they measure?
Yes.

>This sounds
>to me like Pythagoreanism/Platonism redux, which were mostly efforts to
>create a stable metaphysics.

Why?

> 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?

Theology is often incorrectly defined in N.America. Often what is meant a
Christian philosophy. to answer your question: Yes. I heard a retired
(lady) engineering prof. from the University of Toronto last Wednesday and
Thursday, who definitely expressed the view that everything has a
philosophical background and we better make sure that we know which
philosphical background it is.

>
>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.

Penrose is not the best guide, when wanting to learn about math as a
Christian, though his books are very interesting, and yes there is a
mathematical side to all of them.. Unfortunately I cannot remember an
English book about the subject of philosophy of math from a Christian point
of view. If you read Dutch I'll give you some titles. Penrose and Kuyk
once had a debate about these matters, but I can't find the title now.
Besides, I can't remember what was said and why, so even if I could remeber
the circumstances, maybe I shouldnot recommend it. Basically your
questions are philosphical questions. I would recommend as a beginning
for getting a reply to your questions Kalsbeek, Contours of a Christian
Philosophy; I lent out two books but can't remeber the titles anymore. One
of them was by the late Peter Steen.

My teacher Prof. Vollenhoven wrote in 1932 a book :De Noodzakelijkheid
eener Christelijke Logica" + "The Necessity of a Christian Logic."
>
>Can anybody help me get straightened out on this stuff?
>
>Tom Pearson

I tried a little, but it will take more than a e-mail message to get the
"proper" background.

Jan de Koning
Willowdale, Ont.