Suppose Alice believes p. Does it follow that Alice disbelieves not-p? Or would she have to believe not-not-p to disbelieve not-p? (Granted, in both classical and intuitionistic logic, not-not-p follows from p.)
Maybe this is a merely verbal question about “disbelieves”.
Or could it be that disbelief is a primitive mental state on par with belief?
4 comments:
Why would that follow? Couldn’t Alice believe P and not-P? Don’t people sometimes believe contradictory things without realizing it? In which case, she would believe not-P and disbelieve not-P, which sounds odd to me.
It doesn't seem odd to me to say that someone who contradicts themselves might believe and disbelieve the same thing. But perhaps we do need to complicate the account of disbelief, and say that to disbelieve p you need to believe either the negation or the negand of p AND not believe p. (The term "negand" isn't much used. It's one of my favorite words.)
By your initial claim, to believe p you need to disbelieve not-p. But as previously pointed out, some believe p & believe not-p. So, a corollary of your claim is that some disbelieve not-p & believe not-p. By your account of disbelief, to disbelieve p you need to not believe p. By the corollary & your account of disbelief, some don’t believe not-p & believe not-p. Contradiction.
The suggestion in my comment is an alternative to the suggestion in my post. The two aren't meant to go together. Am I missing something?
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