The following is plausible:
- x disbelieves p if and only if x believes not-p.
But suppose Jones believes snow is white. Then, surely, he disbelieves that it's not the case that snow is white. But then by (1) he has to believe that it is not the case that it's not the case that snow is white. But very few people have such double-negative beliefs, and there is no need to saddle Jones with it.
Now believing not-p is sufficient for disbelieving p. But it's not necessary. Perhaps then:
- x disbelieves p if and only if x believes a negation or negand of p.
(Negative propositions of the form not-
p have
p as their negand. Other propositions don't have negands.) But it seems that believing
p to be false may also be sufficient for disbelief, even if you do not burden your mind with the further first-order belief that not-
p. So:
- x disbelieves p if and only if x believes a negation or negand of p or x believes that p is false.
But this is really messy...
