Here’s a fun one:
- Anyone who knows basic maths knows that 2+2=4.
- If someone knows that 2+2=4, then that person believes that 2+2=4.
- The known proposition in premises 1 and 2 (i.e. that 2+2=4) can be replaced by a very large number of other propositions (e.g. that 2+3=5 or that 5-1=4) while maintaining the truth of the premises.
- Therefore, anyone who knows basic maths has a very large number of beliefs (countably-many?).
- Regular people do not have a large number of occurent beliefs.
- Therefore, many of the beliefs of regular people are non-occurent.
I’ve heard a few people complain that this idea of a non-occurent or implicit belief is non-sensical or elusive. If you’re one of those people, which premise do you reject?