What axioms do you begin with, or what assumptions do you make about the universe? I think this could be a really interesting thread, if everyone behaves. I think the following is a good place to start:
I'm sure we all have more than that. We'll assume these three. Tell us what other assumptions you make, or if you don't like the ones I've started with feel free to argue against them. I began with these because I think they're pretty basic and most people would accept them.

My boot sequence ...

An external (mind independent) world exists

Our sense organs can provide generally accurate information about this world.

Our memory facilities are generally reliable and can be trusted more often than not.

Our built-in instincts about memories and perceptions (for example reasoning abilities) are generally reliable and can be trusted (as otherwise we would be extinct already).

Other minds exist, with similar conditions applied.

To allow simplified encoding of high level information, we can group a set of similar perceptions under a common abstract model (like 'tree', 'cat', 'book').

Our language is generally consistent and meaningful, and can generally be understood by other minds, and allow the transmition of information.

"Truth" is a measure of the correspondence between a statement (in language) and reality. It can be assigned a positional representation or value between 0 and 1, for example.

...

I think axioms are very useful, but i am not at all sure you can prove something with them, in a way that is as logically sound as in math. I mean that, two people may well be able, with the same axioms, to reach a different conclusion. The axioms do not seem mathematically strict that way.
Regardless, it is probably a good idea to state "axioms" because i think it will still make your views much clearer, and although the logic to its conclusion is probably still subjective, it does restrict much what is still reasonable.

I do not think i can give a set of axioms i will find satisfying for longer then this moment, right now. What i still miss is axioms of what is considered "a good thing" and a "bad thing", basically, what values morals are based on.
My axiom my morals are based on:
-Could not find a good definition of want. :-/, basically it is rather arbitrary, and based on a beings instincts, culture, i guess.
-Define good as the collective of what conscious creatures want, weighed by their "level of consciousness".
-Axiom: I want is a weight of getting "what i want" and increasing good.
Not that "level of consciousness" is rather vague too :-/, need it to deal with animals, of course.

You certainly can't prove anything without them I doubt it. I could be wrong, but my suspicion is that if we began at the same place, most of us would arrive at the same place as well. Of course, that's pure speculation, and impossible to test.Precisely my point.

I'll add a couple:

--The world is not 100% deterministic. My choices matter, even if only a little.

--The universe is basically what it appears to be. (rather than, say, a cruel joke, or someone's dream, or a science experiment of the gods, or--you get the idea)

--It is "good," in an absolute sense, to treat other people with kindness and empathy.

--It is not "good" to treat other people cruelly or badly or apathetically. No belief system that encourages such behavior is good.

The concept of "Ethical axioms" are really a denial of the concept of axiom, in that ethics are derived from a proper metaphysics and epistemology. Therefore, axioms must be metaphysical.

An analogy....Think of a house. Axioms are the foundation, epistemology is the first floor. One does not get to ethics until we are in the upstairs bedroom (so to speak). Axioms are in the basement, but the upstairs bedroom would not exist without them.

How can you have your standard of "good" be external? Would you say that ethics would be unimportant if you were the only man on an island. By your standard, they would be non-existent.

Also see my previous comment regarding axioms.

Please be careful in your assumptions.

Buddhists assume that: There is no self, no "me," no "I." I am not inherently existing.

This is not the opposite of what you posted but is certaintly different. Buddhists do not believe the law of Identity and some may argue Existance.

Hence Buddhism may be safely dismissed from the pantheon of rational philosophies. Thanks for pointing that out.

IMO, you are misunderstanding Buddhism though. To actually understand these kinds of statements requires a gestalt shift in thinking.

for example see reification:
Gestalt psychology - Wikipedia, the free encyclopedia

Buddhism is not as interested in stating what appears obvious as much as forcing these shifts in perception. Which is "better" is a matter of opinion, as two opposite views may be functionally equivalent

I did not say it was "better" or "worse". I implied (pretty obviously) that it was non-rational, as evidenced by its rejection of the Law of Identity, and should be recognized as such.

External to what?

Also, I wasn't saying that *was* my standard of good; I was saying that it *fell into* the category of "good."

There may be other "good," I'm just mentioning one part.

Well, again, I was not attempting to give a general definition of ethics. I was giving one of my personal axioms. It's good to treat people well--that's something I take as an axiom.

On an island, I guess there would still be ethics of a kind: I would treat animals with respect? At least, those I wasn't having to kill for food.

By the way, technically I can take anything I like for an axiom. Just because one of my axioms follows from one of yours, doesn't mean I can't take mine as an axiom anyway.

I can even take a falsehood for an axiom, if I like...it just makes for a noninteresting system.

But certainly my "it's good to treat others nicely" axiom is simple and clear, and I see no reason why I shouldn't accept it as an axiom by itself. Are you arguing that there is a small set of even simpler axioms that immediately imply mine? Or that mine is just false?

I'd be happy to take others, if they're simpler or more powerful, so long as mine still follows as a theorem.

I object to this, the world need not be deterministic for your choices to matter. I would rather have something like 'I can affect the world consistent to my goals'. If the universe is deterministic does not even need to enter this discussion in my view, it does not matter, the limited knowledge of the world makes things seem random/non-deterministic anyway.
This is why i tried to define good as something based on what other people want. Because that defines(for me) what is meant with kindness/empathy; being kind means that you balance your own 'want' with that of others. Here want is what people want not only at this moment, but also that they wont regret/feel miserable because of it. In other words, what people want is not what they say, or even think nor how they act.
It seems to me, that your definition does not take into account that different beings have different needs. I think it misses that we give different creatures different value. (Like i do not look down all day to save some ants, but do try not to eat too much meat, or hit people.)
My goal is that to make creatures get what they want, based on weighing for each creature. (weighing based on knowledge too) On a island then I would be the only creature to worry about, so i would do whatever i wanted.
Is is sensible to make an axiom about this? The very words "on the chance that one will be rewarded for such senselessness in an unseen, spiritual world." seems like reasoning that making decisions based on existence of an afterworld, is a bad idea because you should not make decisions based on things you do not know. Which would fall in the realm of logic. (or some other more fine-grained axioms perhaps)

@bns: that was my point, we are not sure that the same axioms lead to the same results in discussing. Perhaps because of hidden axioms, of course. (which we may be able to find, ofcourse)
@utabintarbo I am not sure if i understand, I do think that ethical axioms are even more subjective then the other ones, they are separate from "the other" axioms too. (btw, not having one of those three axioms does not mean someone is unreasonable.)

You may be right; perhaps that shouldn't really be an axiom.

Do you have an idea for a simpler axiom or two, from which this one would quickly follow as a result of logic?

With the axioms about treating others well...I thought about trying to formulate it about "what they want," but I found a couple of problems.

One, it might be bad to give them what they want, in some cases. Suppose my best friend wanted to kill himself...is it good or bad to help him? That's another debate for another thread, but I wanted to avoid the possibility altogether. Or possibly, if I'm raising a child I can't always give him what he wants, because he will turn into a spoiled and poorly adjusted adult. Also the child may want something very dangerous, like to play with fire. I wanted to avoid the possibility of all the above.

Two, how can I really know what someone wants? I have to use my own understanding or guess of what they would want.

So that's why I used terms like kindness and empathy. I'm trying to encapsulate the idea of, (a) trying to understand what people want, and then (b) trying to treat people accordingly, up to a point that does not harm them, or me, or someone else, etc.

...but without jumping through all the above hoops.

Which is why I chose non-determinism as an axiom.

What I'm trying to axiomatize my way out of, is the possibility that all things, even my decisions, are predetermined.

I may *think* I'm making choices, but really my choices are only a predictable result of biological processes, which in turn yada yada.

Screw that, in my universe. There exists free will.

External to yourself.

Then it does not qualify as an axiom. The topic is "What are your axioms?". Or am I incorrect in my reading?

Very well, if it meets the definition of axiom, and you can defend it.

As determined how? Telepathy? Are you a closet Betazoid perhaps?

@DChristopher Sorry, i missed the 'not'
You may have another reason to try to rule out determinism, but i think pre-determinedness is a reason not to have this discussion. Watching the road still prevents you from crashing your car, regardless of determinism. If a person were not to watch the road because he thought it was pre-determined anyway, the likelyhood of crashing his car would be higher. (likelyhood in a frequentists probability interpretation, if you wish) (btw i dont think the universe is deterministic.)

I will try make another iteration of the ethics-axiom idea, i will call 'want' 'feel' now, since it is closer to what i mean. Note that i also mean how they feel "averaged over time". (which has problem of how to average then)
Axiom: Goal is to make all creatures together feel as good as possible, with the importance of each creature weighed.
Now to try to atleast list problems about this:
-What is a creature?
-How is the importance of a creature weighed?
-How do you know how a creature feels.
Honestly, i do not know how to deal with these questions. Wether something is a creature is perhaps not so important, if it is not a creature, its importance is simply "zero". So what is the importance of a creature? Could try something like how complicatedly it behaves, or its nervous system. In practice though i am afraid, i just stick to what i associate with what i know about the creature, same for what the creature is feeling. Maybe a good approach is to give the creature the freedom to do what it wants, and assume that it will appease itself. (this is not passive, some one without food does not have the freedom to eat, giving him food is non-passive.)
-What is feeling (good)?
Well, i do not know how to deal with this one either. :/ It seems similar to the what is the meaning of life question.

I guess i will for now go pragmatist, and much like DChristopher, encapsulate these four question into judging case by case what creatures might be thinking and what "value" they have. In that sense, my axiom adds little, but it does rule out hate by the way. (unless perhaps it makes you feel damn good.)

Edit: Note that the axiom is more a goal to set, not a axiom at all.

I don't see why I can't. I assume, as an axiom, that there exists an external (to myself) standard of good. And I put "treating others well," perhaps defined more carefully but that's the gist, in the "good" category.

Why not? An axiom, according to your link, basically has no restrictions. The link says, "any starting assumption."

The definition of axiom is, "any starting assumption." So, pretty much anything meets that definition.

Also, I don't have to defend axioms; I get to assume them, without defense.

It's fair to argue that my axioms are somehow unappealing, and I might even agree and change them; but they don't have to be proven.

I'm going to add an axiom to my list: there is somehow a universal standard of "good," which is external to myself.

We can axiomatize goals, I think. We make some axiom that says what is good in general for creatures, if you like; then we make another axiom that says something like, "I should try to increase 'good.'"

I'm getting myself into semantic difficulties here, but basically I'm saying there is a universal "good." There is also, "good" restricted to individuals--wants or feelings or needs or something, being met, vaguely. Finally, pursuing such individual good is universally good and right.

Is this explanation making sense?

I like this formulation. Then, spoiling a child is also not giving the child freedom, because spoiling the child actually hampers them in the long run.

Also it could be argued that killing a suicidal friend hampers, rather than increases his freedom; and that helping the friend past the problem does the opposite.

Interesting viewpoint.