Those arguments don't do anything to show that those beliefs are likely to be true. The connections between epistemic justification and practical justification are philosophically very interesting, and these are questions that epistemologists sometimes investigate. And that is the notion we will be focusing on in this class. Pascal's argument does not enable him to know that God exists. The mountain climber's reasoning does not enable him to know that he can successfully jump the crevasse.
Some notions are what philosophers call factive notions.
If you can see that P is the case, it seems like P has to really be the case. For me to be able to see that you are nervous, you have to really be nervous. Otherwise, I can't see that you are nervous. If I discover that you are dishonest, you have to really be dishonest. Otherwise, I can't discover that you are dishonest.