Consistency

There is a question I've never seen discussed. It's the question of evaluating how likely a given formalization of mathematics is of being consistent.

Results such as Gödel's and Cohen's are always stated under appropriate consistency assumptions.

So the question of knowing whether such consistency assumptions are realistic is inescapable.

This question can be posed in a slightly more precise form:

Let T be a mathematical theory. (I'm using Bourbaki's terminology.) Let L(T) be the length of the shortest proofs of a relation of the form "R and (not R)" if such proofs exist. Otherwise, say that L(T) is infinite.

For all practical purposes, the fact that L(T) is very large or is infinite makes no difference.

But I think that, for any reasonable mathematical theory, L(T) is much more likely to be very large than to be infinite.

It would be interesting to have a lower bound for L(T).