Re: Mathematical properties

Jan de Koning (
Sat, 21 Feb 1998 12:38:41 -0500

In answer to George Andrews:

I was afraid of that. I said I would have to give a philosophy lecture to
prove my point. Now I would have to answer to Bertrand Russell, using
Hilbert, Poincare, Cantor, Brouwer, Dooyeweerd and Vollenhoven. Well, I am
sorry, but I do not have the time to do that completely. If requested I
will give some study references written in Dutch, English, German and
French. For now, just this: the distinction real - abstract is really not
nearly suffucient, since it throws things togeteher which have totally
different properties, and thus confuses the discussions. To refute Russel
many more than three hundred pages have been written. I will just writea
few sentences, and am fukky convinced that they are not nearly enough to
convince George.

God created the universe, the earth and all that is therein. Vollenhoven
was convinced of that and thought, if God did create everything, than God
is involved with everything as well. So as a Theological candidate he
wrote his Theological doctoral thesis on : The Foundations of Mathematics
from a Theistic Point of View." (in Dutch, Amsterdam 1918.) That book has
some 450 pages. He studied mathematics under Brouwer (whom he criticized
in his dissertation) who wrote in English in 1912 in an American journal,
but I cannot find the reference at the moment. Brouwer was the father of
Intuitionism, a word that Vollenhoven took over while criticizing its
content (which makes talking about it even more difficult.) V. confesses
to be influenced by Poincare. I mention these names to make research
somewhat easier if you want to know where I come from. I had philosphy
from Vollenhoven in 1942, while studying mathematics in Amsterdam for a
little while (untill the Germans made studying impossible.) V.wrote in
1932 a small book titles (translated) The Necessity of a Christian Logic,
in which he discussed the mathematical theories of the Polish school.

V. (a pupil of Kuyper) wanted to stress very much God's sovereignty over
all of life, all of creation. He divided life, studying of life and so on
in thirteen spheres of law, saying right away, that there might be more or
less: numerical, spatial, physical , . . . , juridical, ethical, pistical
(service of God or not) all bound together and directed out of your heart
(for humans), which was directed towards or away from God. If it was away
from God our Lord Jesus could bend it back through the Holy Spirit to be
directed towards God again. (He said much more here.) All these
law-spheres are irreducible. Numbers are not spaces. Things are not
animals, etc. etc. However, things, animals etc. charactrized by a
"higher" law-spheres have attributes belonging to the lower spheres as
well. The main characteristic of each law sphere is different, though.

In this context talking about real and abstract is impossible. At most you
can say that "things" in a higher lawspere have attribute belonging to a
lower lawspere. Counting does not change when you go to physical objects.
Actually the physical lawsphere was split in two by later adherents to this
theory. Others follow a slightly different order in the "higher" law
spheres. Still, I claim that physics may use a lot of applied ,athematics,
but physics is much more than mathematics.

Enough for now,

Jan de Koning
Willowdale, Ont.