The principle of non-contradiction is that contradictory propositions cannot both be true, e. g. the two propositions "A is B" and "A is not B" are mutually exclusive.
However, whenever something is used as a criterion for truth (like the principle of non-contradiction), it suffers from the problem that it cannot justify itself. For example, if we believe that scientifically verified things are true, then there's the problem that the statement that "scientifically verified things are true" is itself not scientifically verified and therefore not true by its own standards, which, in turn, defeats the belief that scientifically verified things are true. This is, as far as I know, called the problem of the criterion.
But I was pondering on whether the following statements make the principle of non-contradiction self-evident or not:
- The principle of non-contradiction is valid.
- The principle of non-contradiction is invalid.
Are both of the above statements mutually exclusive? If so, then would that not mean that the principle of non-contradiction is self-evidently true?
I'm so confused. I feel like there's an error somewhere but I cannot pinpoint it if there is one.