This is what I mean when I say that hypotheses are "axioms", and physical experiments are "conclusions".
I see. You're right that philosophers pretty much never do anything like that. Except experimental philosophers, but thus far most of that stuff is just terrible.
"In the framework that I'm working in..."
That's a good framework with with to approach any philosophical text, including and especially the Platonic dialogues. I just wanted to stress the fact that the dialogues aren't treatises presented in a funny way. You're supposed to argue with Socrates, against him, yell at his interlocutors, try to patch up the arguments with premises of your own. It's very different from, say, Aristotle or Kant or whatever, where its a guy presenting a theory.
In the field of philosophy, from my limited knowledge, I think that these discussions lead to conclusions that we need to believe as "truth"
Would you mind if I go on for a bit? I have thoughts on this, but I don't quite know how to present them briefly. Anyway:
Students of Physics should go into a Physics class room or book with an open mind. They should be ready to learn new things about the world, often surprising things (relative to their naive impressions) and should often try to check their prejudices at the door. None of us are born knowing physics. It's something we have to go out and learn.
Philosophy isn't like that. The right attitude walking into a philosophy classroom is irritation. It is an inherently annoying subject, and its practitioners are even worse. You can't learn philosophy, and you can't become an expert at it. You can't even become good at it. Being a philosopher is no accomplishment whatsoever. You can just do philosophy, and anyone can do it. Intelligence is good, but it can be a hindrance too, same with education.
Doing philosophy means asking questions about things to which you really ought to already know the answers, like the difference between right and wrong, whether or not you're in control of your actions, what change is, what existing is, etc. Philosophy is about asking questions to which we ought to have the answers, but don't.
We do philosophy by talking to each other. If that means running an experiment, good. If that means just arguing, fine. There's no method, no standards, and no body of knowledge, unless you say there is, and then convince someone, and then there is until someone convinces you otherwise.
Scientists and mathematicians don't hate philosophy. They tend to love philosophers, or at least the older ones do. Young scientists and mathematicians do hate philosophers, and with good reason: part of being a young scientist or mathematician is developing a refined mental self-discipline, and that means turning your back on any froo-froo hand wavy BS and getting down to work. Philosophy is the most hateful thing in the world when you're trying to be wrong as little as possible. But once that discipline is in place, and people are confident in their ability to sort out good arguments from bad ones, facts from speculation, philosophy starts to look like fun.
The second part of your post is terrific. :)
What do I mean by "morality isn't logical"? I mean in the same sense that mathematics is logical but literary criticism isn't: the "reasoning" we use to think about morality doesn't resemble logical reasoning. All systems of logic, that I'm aware of, have a concept of proof and a method of verifying with high degree of certainty whether an argument constitutes a proof. As long as the logic is consistent (and we have good reason to think that many of them are), once we verify a proof we can accept its conclusion without worrying that there may be another proof that makes the opposite conclusion. With morality though, we have no such method, and people all the time make moral arguments that can be reversed or called into question by other moral arguments. (Edit: For an example of this, see these posts.)
Without being a system of logic, moral philosophical reasoning likely (or at least plausibly) doesn't have any of the nice properties that a well-constructed system of logic would have, for example, consistency, validity, soundness, or even the more basic property that considering arguments in a different order, or in a different mood, won't cause a person to accept an entirely different set of conclusions. For all we know, somebody trying to reason about a moral concept like "fairness" may just be taking a random walk as they move from one conclusion to another based on moral arguments they encounter or think up.
In a recent post, Eliezer said "morality is logic", by which he seems to mean... well, I'm still not exactly sure what, but one interpretation is that a person's cognition about morality can be described as an algorithm, and that algorithm can be studied using logical reasoning. (Which of course is true, but in that sense both math and literary criticism as well as every other subject of human study would be logic.) In any case, I don't think Eliezer is explicitly claiming that an algorithm-for-thinking-about-morality constitutes an algorithm-for-doing-logic, but I worry that the characterization of "morality is logic" may cause some connotations of "logic" to be inappropriately sneaked into "morality". For example Eliezer seems to (at least at one point) assume that considering moral arguments in a different order won't cause a human to accept an entirely different set of conclusions, and maybe this is why. To fight this potential sneaking of connotations, I suggest that when you see the phrase "morality is logic", remind yourself that morality isn't logical.