To obtain paradoxes, it is you that would need access to more proofs than I do.

From an evidence-based point of view, as a contrapositive of the usual argument against P=0 and P=1, we can say that if it's possible to convince me that a statement might be false, it must be that I already assign it probability strictly <1.

As you may have guessed, I also don't agree with the point of view that I can be convinced of the truth of any statement, even given arbitrarily bizarre circumstances. I believe that one needs rules by which to reason. Obviously these can be changed, but you need meta-rules to describe how you change rules, and possibly meta-meta-rules as well, but there must be something basic to use.

So I assign P=1 to things that are fundamental to the way I think about the world. In my case, this includes the way I think about probability.