Sunday, May 10, 2009

Drawing Lines (Part IV): Mathematics and Theology

At first sight, this seems to be an odd choice of disciplines between which to draw a line. Surely it is obvious that the two have nothing in common? Well, not so fast...

Here's a list of what they do have in common. Both of them
  • construct knowledge based on fundamental axioms which are supposedly self-evident but unproven and nevertheless taken to be true;
  • use rigorous logic to derive secondary propositions from those axioms;
  • claim to explain the underlying structure of reality;
  • handle entities which the human mind cannot visualise nor find material analogy for;
  • have been shown to have questions for which there are no answers;
  • can be demonstrated to obey Gödel's Incompleteness Theorems (or at least, their extension to sets of logical propositions);
  • seem to be obsessed with numbers and symbols;
  • have a long tradition of philosophy and religious conceptualisation;
  • have been considered necessary disciplines for the pursuit of an ordered life.
So... what don't they have in common? Actually, that part is pretty easy. Theology prefers words to numbers. Ha, yes, I was only teasing. Theology of course requires the existence of God as axiomatic. Mathematics requires the existence of a universe in which things remain consistent (but unprovably so). The two are not quite the same thing, I suppose.

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Afterword: As BL has pointed out, there is an entertaining episode in the history of mathematics, involving mathematicians David Hilbert and Paul Gordan. Hilbert's work on the Basis Theorem elicited Gordan's response, "Das ist nicht Mathematik. Das ist Theologie." If that were the case, Gordan was to recant eventually, for he later said, "Even theology has its merits."

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4 Comments:

Blogger boonleong said...

Mathematics allows for alternative sets of axioms to "create a strange new universe" (eg non-Euclidean geometry, or non-standard analysis, or even logic with more than two truth values). Does theology?

Sunday, May 10, 2009 7:58:00 pm  
Blogger Trebuchet said...

boonleong, of course it does; one need only look at how in the history of theology (whether Christian or otherwise), certain contestable axioms give rise to completely different nodes on a 'religion tree', in which only one axiom is changed. For example, Mormonism and mainstream Protestantism.

When I say theology, I mean theology. I don't mean a specific kind. It is like when I say mathematics, I am not talking specifically of using a Riemannian geometry instead of an Euclidean one.

Monday, May 11, 2009 12:09:00 am  
Blogger boonleong said...

I just remembered Paul Gordon's comment on David Hilbert's proof of his Basis Theorem: "Das ist nicht Mathematik. Das ist Theologie."

:)

Tuesday, May 12, 2009 4:02:00 pm  
Blogger Sze Zeng said...

Hi AMC,

This is good stuff! Indeed, there are so much similarity between math and theology.

Thanks for sharing this. And Merry Christmas to you and family!~

Tuesday, December 25, 2012 5:07:00 pm  

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