EDIT: Thanks to whoever corrected "valid" to "proper statement". The original title used "valid" which means something else entirely, so it's appreciated.
First time poster, so apologies if anything amiss or terminology wrong. I searched but didn't seem to find anything addressing this question directly.
By ~C I mean negation of C. By -> I mean the conditional connective
Currently studying logic, and learning about truth tables. It stumped me that the following sentence is contingent because it seems to imply C is the case if C is not the case -- which seems it will always be false. If anything, it seemed a contradiction.
However looking at the definition of conditional I can see it's defined to be true unless a true hypothesis leads to a false conclusion. And that made more sense if we had, for instance, C -> ~A, since I guess if C was false we can't imply anything about ~A being true.
The problem is it seems we can imply something in this case (namely that if C is true then ~C is false) which led we to wonder if it even makes sense for the conclusion to be the negation of the hypothesis in a conditional. Or even more broadly, can the conclusion reference the negation of the hypothesis in any way, since it seems that C -> (~C v B) or something would suffer the same problem. But C -> C seems to make sense (and trivially so) and C -> (C v B) seems to make sense too, and less trivially.
In trying to make sense of it, I concocted the following examples:
C = It is dry C -> ~C
It is dry if it is not dry --> seems obvious contradiction by logic alone, independent of the truth value of C, but by the rules of formal logic it's contingent?
A = It is raining C = It is dry C -> ~A
It makes sense that if it is not dry, we can't say anything about whether or not it's raining.