(Note: I'm going to address your questions in reverse order, as the second one is easier to answer by far. I'll go into more detail on why the first one is so hard to answer below.)
Could one be just as justified believing that, say, what actually happened is the opposite of what one's memories say?
Certainly, if you decide to ignore probability theory, Occam's Razor, and a whole host of other things. It's not advisable, but it's possible if you choose your axioms that way. If you decide to live your life under such an assumption, be sure to tell me how it turns out.
If there is no why, is any set of axioms better than any other?
At this point, I'd say you're maybe a bit confused about the meaning of the word "better". For something to be "better" requires a criterion by which to judge that something; you can't just use the word "better" in a vacuum and expect the other person to be able to immediately answer you. In most contexts, this isn't a problem because both participants generally understand and have a single accepted definition of "better", but since you're advocating throwing out pretty much everything, you're going to need to define (or better yet, Taboo) "better" before I can answer your main question about a certain set of axioms being better than any other.
Certainly, if you decide to ignore probability theory, Occam's Razor, and a whole host of other things. It's not advisable, but it's possible if you choose your axioms that way. If you decide to live your life under such an assumption, be sure to tell me how it turns out.
Why would one need to ignore probability theory and Occam's Razor? Believing that the world is stagnant and that the memories one is currently thinking of are false, and that the memory of having more memories is false, seems to be a simple explanation to the universe.
...At this point, I
Standard methods of inferring knowledge about the world are based off premises that I don’t know the justifications for. Any justification (or a link to an article or book with one) for why these premises are true or should be assumed to be true would be appreciated.
Here are the premises:
“One has knowledge of one’s own percepts.” Percepts are often given epistemic privileges, meaning that they need no justification to be known, but I see no justification for giving them epistemic privileges. It seems like the dark side of epistemology to me.
“One’s reasoning is trustworthy.” If one’s reasoning is untrustworthy, then one’s evaluation of the trustworthiness of one’s reasoning can’t be trusted, so I don’t see how one could determine if one’s reasoning is correct. Why should one even consider one’s reasoning is correct to begin with? It seems like privileging the hypothesis, as there are many different ways one’s mind could work, and presumably only a very small proportion of possible minds would be remotely valid reasoners.
“One’s memories are true.” Though one’s memories of how the world works gives a consistent explanation of why one is perceiving one’s current percepts, a perhaps simpler explanation is that the percepts one are currently experiencing are the only percepts one has ever experienced, and one’s memories are false. This hypothesis is still simple, as one only needs to have a very small number of memories, as one can only think of a small number of memories at any one time, and the memory of having other memories could be false as well.