alligatortower asked: “What are your most important axioms?”

I had a really hard time answering this question - partially because I can’t make up my mind about what exactly an axiom is.

Axioms (which I am going to define for the moment as “self-evident propositions,” more on this below) suffer from the same kind of uncertain reality as any concept: Do they actually exist in the universe, or do they only exist in my mind? Maybe they don’t exist at all.

Plato thought that axioms were basically widely-held beliefs inherent to the human mind. Aristotle compared axioms to postulates that can’t ever be proven. Descartes agreed with Plato and introduced the cogito, which is pretty much rock solid as far as axioms go (although he tripped over his own shoelaces as soon as he tried to do anything with it). Kant thought that axioms were a priori principles of intuition that could lead us to moral truths.

Here’s the big problem with trying to come up with any kind of self-evident proposition, is that almost immediately you run in to these huge central questions like “what counts as being true?” From the way we talk about cable news or presidential debates, you might get the impression that it’s relatively straightforward to tell what’s “true,” but it turns out that trying to make rules to test if something is true or not is a notoriously slippery problem - after all, what do you use to test the rules?

You’ve got the correspondence theory of truth (beliefs are true insofar as they describe facts in the universe, if we agree on what counts as a fact, which we don’t, plus this doesn’t leave any room to discuss moral truth), various coherence theories of truth (beliefs are true if they match some set of propositions or values, which idealists like because they regard reality merely as something we believe in), and the pragmatic theories of truth (beliefs are true if they are useful; problematic for the obvious reasons).

So then even if you can make up your mind about that whole can of space-worms, you have another issue, which is, “once I decide on a rule for what counts as true, how do I know when that rule applies?” This is a problem so big it takes up roughly half of philosophy and involves, among other things, an insurmountable hypothetical argument about a cow that might prove we can’t really know anything at all.

Anyway - to answer your question - figuring out axioms without just randomly axiomatizing the things we already believe is pretty much the entire point of philosophy even though historically, almost nobody agrees on how to do this, or if it’s even possible, etc. Nevertheless, here’s what I’ve got, axiom-wise:

I exist
Other people exist (debated)

P.S. Personal opinion here: Kant’s “Act only according to that maxim by which you can also will that it would become a universal law” is up there, axiomatically speaking, but who knows. I need a nap.