[FOM] Concerning proof, truth, and certainty in mathematics

Robert Lindauer rlindauer at gmail.com
Mon Aug 2 19:47:59 EDT 2010

On Mon, Aug 2, 2010 at 12:29 PM, Monroe Eskew <meskew at math.uci.edu> wrote:

> Vaughan,
> Are there writings that one might call "formal theology"?  Are there
> theological theorems and open problems?  I once read an essay by a
> Catholic Cardinal that was much more philosophically careful and
> sophisticated than typical religious talk, but I have never seen
> something like you describe--theology which differs from mathematics
> only in subject matter.
> Best,
> Monroe


There are of course many formal theological systems dating from both
in western and eastern thought:

The summa theologica:

Spinoza's Ethics:

And Patanjali's "How to know God" (more practical so perhaps less
obviously formal, but certainly intended as a step-by-step guide for
achieving a certain result, but more like an applied
mathematics-for-engineering style, as long as you're comparing).

While modern theologists tend not to formalize -in the same way as
mathematicians- their arguments, that they are formalizable as axioms,
definitions, inference rules and theorems is generally thought to be
self-evident, for those theologists who like this kind of approach.

There are good reasons for why many theologists have tended away from
mathematical-formalisms: a recognition of the effectiveness of a
dialectical critique of any axiomatic approach, the consequent
wistfulness for transcendental theology.

I hope the parallel opposing attitudes in mathematical practice are
clear enough.

(Perhaps the thought that it is sufficient to produce arguments that
are formalizable in theory even if no such proof is produced in
reality, is something they have in common as disciplinary activities).

As for "open theological problems":

I think there are many many such things, including foundational ones,
again very parallel to those found in foundational-mathematics:
a) is there any such thing as "God"? (formalists versus realists)
b) does the word "God" have a single meaning? (irrealism versus realism)
c) what is the nature of God's infinitude (power, knowledge, goodness,
etc.) "Can God make a rock he can not destroy?"
d) how can humans have relations with God?

While philosophers have been more likely to study these questions,
they are in the end, theological questions just as

i) "Are there any such things as numbers?"
ii) "What constitutes being a number?" or
iii) "what is the nature of mathematical infinity?" or
iv) "how can finite, inconsistent beings have absolute knowledge of
mathematical truths?"

are, in the end, both philosophical and mathematical questions.

A good place to look into current lively topics is here:



Robbie Lindauer

ps - because Theology is also meant to be practical, there are much
more interesting things done in other methods , for instance, in
Liberation Theology,which because generally dialectical in nature tend
to resist formalism in the same way that a survey of "all the truths
of mathematics" would also resist formalization.

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