From: Remko Muis (firstname.lastname@example.org)
Date: Thu Sep 04 2003 - 08:33:22 EDT
Here's a little Dutch contribution:
"The real world rarely or never precisely complies with our "astoundingly overwhelmingly beautiful" mathematical representations."
True enough, but isn't that just because are mathematical models are too simple? There seems to be no reason to suppose that real phenomena in general are too complex to fit our equations.
By the way, I do not believe that either God, or man, did create mathematics. I don't even understand what one means when one says that He, or we, did. Did God really create the natural numbers? (I read Kroneckers famous statement in one of the previous contributions) Or do we mean that He defined numbers such that they obey Peano's axioms? If so, did He use a first-order or a second-order language to do so?
It's not my purpose to make fun of these ideas, but my worry concerns the supposed possibility that God could have chosen to create different mathematics. Presumably, creating is a free act of a Creator, not something that he couldn't do otherwise. Now it seems that the only criterium for any mathematical theory is that it be consistent. Could God have created natural numbers such that they do not obey Peano's axioms? It seems to me every property that any number has is an essential property of it, and that it is impossible that God could have chosen to give that particular number other properties than it has according to "our" mathematics.
If one would reply to this by rejecting the criterium of consistency as a criterium of what is possible for God to create, maybe by arguing that God is not subject to the laws of logic, then the worry becomes even greater: if the laws of logic do not apply to God, can we still meaningfully speak and think of Him, or even believe in Him?
In my view, mathematics is the description of structures that might be regarded as possible patterns of physical systems, that can either be instantiated or not. It cannot be reduced to logic, but is very much akin to it. If mathematics turns out to be beautiful (indeed it is!), that's just the way it is. Must every beauty come from God?
Institute for History and Foundations of Mathematics and the Natural Sciences
Utrecht, The Netherlands
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