1. Are some actions really, objectively wrong? The question is not, "Are some actions wrong according to the standards of my culture?" nor, "Are some actions wrong in the opinions of most people?" nor any such variation. Are some actions really wrong, meaning the actor cannot "opt out" of the ethical condemnation? Is any culture which says otherwise objectively in error?
Many people say No; actions may make us uncomfortable or be disapproved by a society or by the traditions of a culture, but there is no other meaning to "right" or "wrong". These people would say all rules ultimately are merely agreements we make among each other -- we "play ethics" like we play baseball, so that just like we could change the rules of baseball, nothing prevents us from reformulating our ethical systems.
The answer given here is absolutely fundamental. If ethics is not a serious subject -- if it is just a game the rules of which we are free to change -- then ethics cannot guide society; when society wants to do something different, it will simply change the rules of ethics.
It should be obvious that I am among those who believe that yes, an objective right and wrong does exist and apply to certain choices.
2. Assuming we agree that some actions are really, objectively wrong, do they constitute a coherent whole? If so, what are the basic principles around which these are organized?
At the very beginning of the Nicomachean Ethics, Aristotle says that the objective is happiness, then he notes immediately that people disagree about what "happiness" really means, a disagreement that certainly is still found today. Is happiness merely a life of pleasure, even if that means being "fat, happy, and stupid" -- even if it means being like the Eloi in H. G. Wells' "The Time Machine"? Or was Odin right to sacrifice one eye for wisdom? Does happiness consist primarily in what we experience, or in what we become -- so that for serious wrongdoing "the real and final punishment is having to be the person you are"?
And whose happiness are we talking about? Is it "every man for himself," or is it the happiness of the whole society? If it is the happiness of society, does that extend to the very old and the very sick? Does it extend to criminals? Does it extend to infants? The unborn? What about animals? Is it OK for a society to utterly crush an innocent person if that would increase the total happiness? If "it is expedient for us, that one man should die for the people, and that the whole nation perish not," does that make it right?
Although Aristotle's thinking has great merit, I think a better starting point comes from the two greatest commandments.
I. Thou shalt love the Lord thy God with thy whole heart and with thy whole soul and with thy whole mind.
II. Thou shalt love thy neighbour as thyself.
The advantages of such a formulation are threefold. First, ethics is immediately placed in a social context, which avoids the common pitfall of egocentricity. It is not really clear that "intelligent self-interest" can consistently avoid a tendency towards selfishness. Secondly, ethics is geared towards our neighbors -- specific people we actually meet -- not towards an airy abstraction like "mankind". Thirdly, because the First Commandment is oriented towards an eternal, immutable, and omnipresent God, the principles (if not the people studying or implementing them) are not limited to fads or provincialism. That is, I am not able to make the happiness of my own family, or nation, or race, or political party, or generation into the summum bonum without violating the First Commandment.
3. Can we know what these basic principles really are? If so, how?
Of course, the objection could be made that maybe universally applicable moral principles exist, but we cannot be sure what they are. One may be agnostic about ethics.
One objection is that even if a core of fundamental principles tends to recur in culture after culture, for most of these principles -- perhaps all -- at least one culture can be found that does not hold that principle. This is no doubt true, but it a statement of anthropology, not of ethics; it is about what people or cultures say, not about what actually is.
The traditional answer, which again I hold, is that we perceive whether actions are right or wrong with our consciences, just as we perceive positions, pressures, temperatures, etc. with our senses.
Our senses can be dulled -- for example, after spending an hour or more in a dimly lit room, we may not realize how dark it is, or after spending time in a smelly dormitory, we may not notice the smell. Our senses can also be deceived, especially in complicated situations where our attention is misdirected. In spite of this, we do not simply give up on our senses altogether, but we use reason to develop a consistent view of the world that is either consistent with our senses or at least provides reasons why our senses are occasionally unreliable.
Our consciences can similarly be dulled (when we habitually ignore our consciences) or deceived (mostly in situations in which multiple principles are in play simultaneously). The whole project of ethics is to develop a consistent moral worldview that is consistent with our consciences or at least provides reasons why our consciences are occasionally unreliable.