by agingjb » May 3rd, 2010, 9:00 am
Hmm. I would have said that, in mathematics, infinity can be given (many) well-defined axiomatic bases, free of paradox but often with undecidable questions within the axiomatic basis. (Actually it might be better to say infinities - and infinitesimals).
For the believer of course all these systems are implicit in the mind of the Deity - which implies a sort of Platonism.
But as for theology, I would have said that rational debate is possible but that it will soon become clear that there are aspects of the Divine that transcend any formal or informal language. It is up to the theologian and philosopher to clarify meaning as far as possible. I would not, for instance, speak of "logic" but of "logics".
An example: the word "necessary" will soon arise, but a glance at a text on Modal Logic will reveal that there many (actually an infinite number of) formal systems - all consistent - with variations in the precise meaning of "necessary".