It isn’t a Shotgun
December 26, 2006 § 38 Comments
An Examined Life has up another post on the development of doctrine. I made the following comment in the combox there:
My only objection – and it is important to understand how narrow an objection it is – is to this claim:
Ultimately, however, anything that is accepted as de fide will have some deductive proof following from other irreformable doctrines and the theorems that can be derived from them.
I object to this claim precisely because it is in the same class of claims as David Hilbert’s postulate (disproven by Godel) about mathematics: that every mathematical truth must admit of a deductive proof from primordial axioms. (In our logic we substitute “is de fide” for “is true” in the metalanguage, and the game is immediately over**). (I am leaving out what would be a nontrivial discussion of the implications of ruling out abstract reasoning capable of performing Peano arithmetic here, but this is after all just a combox).
Specifically, I do not object to this claim:
My second assumption is that whatever the Church teaches, at any time in history, will be logically compatible with everything else the Church has ever taught, or ever will teach, at any point in her history.
There is a difference between a relatively weak assertion of logical compatiblity (inductive inferences are not ruled out by a requirement for logical compatibility) and the strong assertion of the existence of a deductive proof for every theorem (where inductive inferences, and indeed all inferences which are not a matter of mechanical application of the [some] rules of logic, are ruled out).
And interestingly, both of our “stakes in the game” here are the same: we are both attempting to understand DD in a way which avoids logical contradiction. If my understanding is correct, insisting on the existence of a deductive (solely deductive) proof for every theorem results in a logical contradiction.
** I didn’t say this in the comment at AEL, but this can be expressed unambiguously at the formal level by making every statement take the form “It is de fide that X”.