I’ve thought a lot about axioms (things believed to be true without proof) in the context of personal philosophy. The only one I’ve come up with so far, for myself, personally, is “I can derive accurate information about reality via my senses.” Not necessarily perfect, and not necessarily complete, but, on the whole, over time, accurate. Call this Axiom 1.
(Actually, I also include, for completeness, “I exist”. Some philosophers get touchy about this one. Call this Axiom 0.)
What axioms do you have, if any, that do not follow from this one?
As an example, I’ve considered adding to the list “Both inductive and deductive reasoning can yield valid statements about reality”, but I haven’t, because I believe you can show empirically (by observing reality with your senses) that this is true.
Update: Wikipedia points out that “observations themselves do not establish the validity of inductive reasoning, except inductively. In other words, observations that inductive reasoning has worked in the past do not ensure that it will always work.” In more other words, induction cannot empirically prove itself. So maybe I do have to include induction, and possibly deduction, in an axiom.