KenS

I think when trying to study information and its relation to mathematical truth, we must start off practical and should be talking about provability in formal systems of logic. I don't actually know of any rigorous connections between the two notions, but I can think of an argument that "mathematical truths contain zero information" might be false based on indirect connections between existing work on proof theory and information theory. But I don't want to give that interpretation yet because I would like to first ask Skatche if he wanted to elaborate on his statement a little better or point to some references for us to read.

The philosophical question is interesting too, and I would agree that a set theory without the axiom of infinity seems pretty adequate for describing our experiences of reality. I'm not sure if its the most harmonious, however...

It seems Skatche is roughly talking about what is called semantic entailment in logic and I would partially agree with your criticism... since mathematical truth is considered to be more than just that, it includes axioms that you feel good about accepting. However, I'm not sure where reality comes into the picture when considering the definition of mathematical truth.