Think about it!

Try this out:
Can you build a consistent belief system where a statement is true only if it is false?

That is, the only rule is:
if (not S) then S

Kinda fun to think about. The system would first have to disprove a statement to then declare it consistent. Clearly you cant have such a system in FOL, but what if we use a higher order... Its fun to twiddle around with.