Definitional contradictions are impossible. For example, I can say that I will encounter a married bachelor, or a non-female vixen, with P=0. This doesn't actually say anything about the world; I could figure out that there are no married bachelors without leaving in my room, simply by knowing that bachelor is defined as "man who is not married." Mathematical truths (like 2+2=4) and non-contradiction (as mentioned deeper in this thread with the buttering of pancakes) are specific instances of definitional contradiction.

You're generally right, though. Truths that actually involve looking at the world, i.e. ones that are not inherently about language, cannot have P=0 or P=1.

Actually, certain truths about the self and "subjective" experience may also hit P=0 and P=1. It seems I can be certain of my existence, even if I can't be certain of what I am or what causes my existence. I can also be certain that there exists some X such that X exists. I also think I can be certain that it looks like there's a computer screen in front of me, that my knee feels slightly uncomfortable, and that I am literate. All of this seems to have P=1; the implied causes may be false - I may not actually have knees, for example - but I certainly do seem to be having the sense-experience. I don't think this contradicts your point in any practical sense, though.