Re: Math and religion - is the very topic crankish?
- From: "mensanator@xxxxxxxxxxx" <mensanator@xxxxxxx>
- Date: 9 Nov 2006 09:34:05 -0800
John Coleman wrote:
Greetings
Obviously, mathematics is not a religion, which is why I didn't post
this as a response to the "Math as Religion" thread as I had originally
intended. I teach at a Catholic university, and when students here want
to pray, they go to the chapel and not to the Math/CS department. I
really wouldn't know what to do if any student turned to me for
religious advice - it's not my area of expertise to say the least.
But - There is no denying that a religious undertone can be detected in
many of the (non-crankish) discussions of foundational issues involving
Platonism, constructivism or finitism of various sorts and infinity.
For example,Cantor himself was interested in how his philosophy of the
infinite related to the notion of infinity in Scholastic philosophy
and he carried out correspondence with German Thomistic philosophers
(as is described, for example, in Joseph Dauben's "George Cantor: His
Mathematics and Philosophy of the Infinite". Also, see Dauben's
description of Cantor's views on God and infinity on pages 228-232 for
a clear example of the religious nature of some of Cantor's
philosophy).
Cantor had to overcome a lot of resistance to his views, and it is no
wonder that he adopted a shotgun approach of combining mathematical,
philosophical and theological arguments. It is significant that by the
early 20th century, theological discussion faded from the scene as far
as mathematical set theory is concerned and with the formulation of
precise axioms like ZFC it became just another branch of mathematics
(albeit one with foundational implications). Arguing that set theory is
religious because Cantor had religious views of infinity is like
arguing that physics is religious since Newton had religious views of
how God ran the universe. One should not commit the genetic fallacy.
Nevertheless, Cantor's case shows that it is not intrinsically
irrational to think that there is some link between the notion of
infinity and the notion of God, and that this link might have some role
to play in the philosophy of mathematics.
A more recent example of explicitly theological themes arrising in
mathematics is Errett Bishop's Constructivist philosophy. Particularly
interesting is a paper he wrote called "Schizophrenia in Contemporary
Mathematics" (Contemporary Mathematics, Volume 39, 1985):
"Our [constructivist] point of view is to describe the mathematical
operations that can be carried out by finite beings, man's mathematics
for short. In contrast, classical mathematics concerns itself with
operations that can be carried out by God. For instance, the above
number n_0 [0 if Riemann Hypothesis is true, 1 otherwise] is
classically a well-defined integer because God can perform the infinite
search that will determine whether the Riemann hypothesis is true...
You may think that I am making a joke, or attempting to put down
classical mathematics, by bringing God into the discussion. This is not
true. I am doing my best to develop a secure philosophical foundation,
based on meaning rather than formalistics, for current classical
practice. The most solid foundation available at present seems to me to
involve consideration of a being with non-finite powers -- call him God
or whatever you will -- in addition to the powers possessed by finite
beings." (page 9). Chapter 1 of Bishop's "Foundations of Constructive
Analysis" contains a similar argument. Ironically, Paul Halmos in his
autobiography says something to the effect that Bishop was a brilliant
mathematician "until he got religion [constructivism]." (or words to
that effect - I don't have Halmos' book before me).
Another example of a theological theme in philosophy of mathematics is
Edward Nelson's radical finitism. In his "Predicative Arithmetic" he
writes:
"We are creatures (Kronecker had it backwards), not too much older than
an infant in a crib, and we still feel the urge to count on something
when we count. The infant counts on its fingers, the mathematician on w
[omega] - but the infant at least nows its fingers to exist. The
mathematician's attitude towards w has in practice been one of faith,
and faith in a hypothetical entity of our own devising, to which are
ascribed attribtes of necessary existence and infinite magnitude, is
idolatry" (pg 80)
See "Ad Infinititum -The Ghost in Turing's Machine: Taking God out of
Mathematics and Putting the Body Back In" by Brian Rotman for similar
thoughts (although, Rotman's work strikes me as crankish since it is
based on "semiotics" - a philosophical type of linguisitics. He quotes
Derrida at the very beginning of chapter 1 - which does not bode well
for the rigor of the subsequent argument).
As far as Platonsim goes - many thinkers have felt that a commitment
to naturalism (the negation of theism) renders Platonism at the very
least implausible, which is perhaps one of the reasons why formalism
has been (officially) such a popular viewpoint in the philosophy of
mathematics. Penelope Maddy in "Realism in Mathematics" has a good
discussion of the problem, as well as what seems to me an adequate
defense of Platonism within the context of naturalism. Nevertheless,
even though she doesn't explicitly talk about God, the effort she must
undergo to find a naturalistic basis of Platonism is tacit admission
that it is not easy to completely disentangle Platonism from theism.
I don't have any real point beyond the observation that asking if there
is a relationship between religion and mathematics does not
*automatically* render you a crank. On the other hand - there is little
reason to doubt that most of those who do so on sci.math are cranks.
So, cranks, take note: the mathematicians like Bishop and Nelson I
quoted above have *earned* the right to raise such questions. They have
made major contributions to mathematics both before and after their
conversion to constructivism/finitism. Also - they are both willing and
able to rigorously spell out their assumptions and to see what follows.
Once you have even 1% of the accomplishments of someone like Nelson,
you might find someone taking you seriously as well.
So, having 0% of the accomplishments means you can't
have a rigorous argument?
-John Coleman
.
- Follow-Ups:
- Re: Math and religion - is the very topic crankish?
- From: John Coleman
- Re: Math and religion - is the very topic crankish?
- References:
- Math and religion - is the very topic crankish?
- From: John Coleman
- Math and religion - is the very topic crankish?
- Prev by Date: Re: MathCAD problem need help please
- Next by Date: Re: Conjecture on thread length
- Previous by thread: Math and religion - is the very topic crankish?
- Next by thread: Re: Math and religion - is the very topic crankish?
- Index(es):
Relevant Pages
|
