These are excellent answers and I don't see any that I significantly disagree with. Joshua's list of short summary terms would be a good direct one-on-one comparison with Rand's. Here are my comments on that list (Joshua in bold; my comments italicized):
1. Metaphysics: Atomic Materialism (one kind of philosophical naturalism) << I think "atomic materialism" probably is a good summary term. "Materialism" is helpful for denying "supernaturalism" and "atomic" is helpful for stressing that reality is made up of innumerable separate components and not some kind of mystical single substance.
2. Epistemology: the Canon: Sensations, Feelings, and Anticipations. << Yes this too seems like a good summary, and indicates the proper place of reason by omission.
3. Ethics: Hedonism* << Since Epicurus did not use this term, and since it doesn't have an agreed-upon definite meaning, and since what is agreed upon may not be Epicurean, I would probably look for another word or term. I would say that Epicurean ethics involves maximizing the pleasure and minimizing the pain of the person under consideration, rather than measured by some larger group of people. Pleasure and pain are feelings and need no further definition. while "maximization" is not a matter of time, and does not reference either the immediate moment or "over the long run" (
"And even as men choose of food not merely and simply the larger portion, but the more pleasant, so the wise seek to enjoy the time which is most pleasant and not merely that which is longest." - Letter to Menoeceus) Presumably the "most pleasant" involves "purity" and "intensity" rather than "duration." I do not see how this can be measured outside by a third party, so presumably this is a matter for individual determination. This boils down to "maximize pleasure and minimize pain both mental and physical.
4 Politics: [theory or practice?]
4a: theory of politics: Arises by human convention.
4b: practice of politics: N/A (unrelated to the questions that concern the Epicurean.) <<< Yes I agree that the important points here have to refer to the "justice" doctrines, indicating that there is no absolute best system.. Period - full stop. These PD's indicate that convention / agreement can be involved, but NOT necessarily, as those who refuse to participate are outside of justice. Thus the bottom line is that politics is determined by the people involved whether arrived at by agreement or by force or by any other method.
