Re: Mathematical properties

George Andrews (andrewsg@letu.edu)
Sun, 01 Mar 1998 13:23:40 -0600

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Jan de Koning wrote:

> ... 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.

Are you saying Russell did not prove that 1+1=2? Or are these rebuttals
referring to his famous(infamous?) paradox? Additionally, How can you be so
sure of my obstinacy? Do we know each other? Finally, I presume your keyboard
finger positioning was just a tad off; what a difference a couple of "l"s make!
What is it that you would like to convince me of? By your closing remarks, we
may actually share many views in common.

> 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.

Thank you for the references, for I am very interested in the interactions
mathematical thought and theology. However, I doubt if many people would
consider foundational mathematics theology; especially in light of recent
postmodern developments in the the philosophy of mathematics. However,
many-including myself-would certainly find mathematical thought fecund with
analogies to the divine and even many-again including myself-would avow
Dooyeweerd's claim that all theoretical thought is religious. But the question
I thought was under consideration was what a mathematical property was?
Perhaps, you are addressing this via theistic arguments and I have missed your
point.

> 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.

Is not the notion of a ãhigher lawsphereä an attempt to abstract the notion of
abstraction itself? And what is "counting" if not applied to physical objects?
The Peano postulates produce the ãnaturalä numbers but ãcountingä is an
application of them. What is gained by the introduction of ãhigher and lower
lawspheresä.

Yes, physics is "more"; hence, the ontological chasm of scientific knowledge.
But is this not what Tom Pearson was originally questioning by asking:

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??

Sincerely;

George

--
George Andrews Jr.
Assistant Professor Physics
LeTourneau University
andrewsg@letu.edu

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Jan de Koning wrote:

... 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.

Are you saying Russell did not prove that 1+1=2? Or are these rebuttals referring to his famous(infamous?) paradox? Additionally, How can you be so sure of my obstinacy? Do we know each other? Finally, I presume your keyboard finger positioning was just a tad off; what a difference a couple of "l"s make! What is it that you would like to convince me of? By your closing remarks, we may actually share many views in common.

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.
Thank you for the references, for I am very interested in the interactions mathematical thought and theology. However, I doubt if many people would consider foundational mathematics theology; especially in light of recent postmodern developments in the the philosophy of mathematics. However, many-including myself-would certainly find mathematical thought fecund with analogies to the divine and even many-again including myself-would avow  Dooyeweerd's claim that  all theoretical thought is religious. But the question I thought was under consideration was what a mathematical property was? Perhaps, you are addressing this via theistic arguments and I have missed your point.
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.
Is not the notion of a ãhigher lawsphereä an attempt to abstract the notion of abstraction itself? And what is "counting" if not applied to physical objects?  The Peano postulates produce the ãnaturalä numbers but ãcountingä is an application of them. What is gained by the introduction of  ãhigher and lower lawspheresä.

Yes, physics is "more"; hence, the ontological chasm of  scientific knowledge. But is this not what Tom Pearson was originally questioning by asking:

Sincerely;

George

--
George Andrews Jr.
Assistant Professor Physics
LeTourneau University
andrewsg@letu.edu
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