What are your axioms?

[palou]

Zkuq said:

palou said:

There can be not justification without an axiom, though. If you are convinced by an argument, there has to be an axiom that is responds to better than your previous beliefs. As said, take any topic, and just imagine yourself a 3-year old that asks "but why" each time you justify your previous stance, until there's nothing left to justify with.

For most people, that is probably just not true. People are far from logical. They might seem logical at first glance but a closer look often reveals contradictions. I try to avoid them personally by adjusting my views to be consistent, but being human, I'm not sure it's even possible to achieve a logically consistent whole in practice. Following your 'why' route, I might be able to come up with some so-called axioms, but if I were to try to find all of my so-called axioms, I'd be surprised if at least some of them weren't contradicting each other in some way. Obviously correcting them might be possible, but it complicates things a lot. Life is complex, and breaking it down to a set of axioms I can really trust seems either ridiculously difficult or impossible. I can probably quite easily find a lot of general guidelines I feel very strongly about, but to call them axioms? No way. Perhaps in the context of this discussion, you'd be ready to call those general guidelines axioms due to how strongly I feel about them, but I'm definitely not.

It's not about how strongly you feel about them, it's simply the fact that you would be unable to justify them any further that makes them an axiom. Mathematicians don't feel anything, at all, about their axioms - just say that in the context that the following are true, and make their conclusions there on out. Note also that an axiom doesn't necessarily have to be true (or rather, they are automaticaly true, by their own definition) in any context, just non-contradictory with other axioms. They also don't have to be complete, it's fine if they can't resolve some problems (note that it's technically impossible for a set of axioms to be both complete and coherent.) 

 

I use a cheap cop-out, only 1, fairly weak, axiom. No contradictions, but really limited capacity to evaluate situations.

 

I'd be interested in hearing what these not-axioms you carry around are, though.