(1) because they seem obviously true
I don't see how this is evidence.
(2) because we don't actually have the option of not adopting them
Why can't we? Can't we simply have no beliefs at all?
(3) because in practice it turns out that assuming them gives what seem like good results.
What makes you think it has good results? Don't you need to except the axioms in order to show that they have good results? E.g. You see that you follow the axioms and have a good life, but doing so assumes you know your percepts, your memory of using the axioms and being fine is true, and that your current reasoning about this being a good reason to believe these axioms is valid.
Can't we simply have no beliefs at all?
I dare say you can in principle have no conscious beliefs at all. Presumably that's roughly the situation of an ant, for instance. But your actions will still embody various things we might as well call beliefs (the term "alief" is commonly used around here for a similar idea) and you will do better if those match the world better. I'm betting that I can do this better by actually having beliefs, because then I get to use this nice big brain evolution has given me.
...Don't you need to accept the axioms in
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.