Relativism is the view that the correct standard of right and wrong depends on (or is relative to) either the person applying it or the person to whom it is applied. In the former case, the view is called speaker-relativism, since it says that the correct moral standard depends on who is speaking. In its most extreme form, speaker-relativism amounts to the view that right and wrong are in the eye of the beholder, since it says that each person is correct in making moral judgments according to what seems right or wrong to him. But speaker-relativism also has less extreme forms, according to which the correct moral standard is determined by the speaker's culture, for example. On this version of the view, each person is correct in making moral judgments according to what his own culture deems right or wrong. Thus, a speaker-relativist might say that whereas we are correct to judge slavery wrong, the ancient Romans were correct to judge it differently, because their cultural standards were different.
The alternative to speaker-relativism is agent-relativism, the view that the correct moral standard depends on the person to whom it is being applied -- that is, the agent. Like speaker-relativism, agent-relativism allows for different versions, depending on whether the criterion of correctness is taken to be the agent's personal opinions, the standards of his culture, or whatever. An agent-relativist might say that whereas we would be wrong to hold slaves, the ancient Romans were not. (The speaker-relativist would require us to say that Roman slavery was wrong, though he would allow the Romans to judge otherwise.)
Neither view is at all plausible. Leaving aside the technical objections, we can reject both views on the grounds that they deny the universality of morality. Standards that varied from one speaker or agent to another simply wouldn't be moral standards; they would be cultural norms or personal preferences, not standards of right and wrong.
The problem comes in where you draw those lines. In theory, it could be anywhere. Consider the following example:
"Yesterday, April 25th, I jumped into a lake to save a drowning child."
Let's assume that was a paradigmatic "moral" act (I understand it is disputable, but let's just assume). What is the "universal" standard (in the Kantian sense) I just set? Is it to jump into lakes to save drowning children? That seems plausible. I could define it more broadly--jump into bodies of water to save drowning children. Now I can save children drowning in rivers as well as lakes. Perhaps the standard is to save drowning children, regardless of whether it is by jumping in or calling for help. Or maybe the standard is saving children, period, and it does not matter if the problem is that they are drowning or not.
All of these seem to be plausible, but which one we pick seems somewhat arbitrary and random. Moreover, I could draw the standard completely differently, perhaps the moral standard I just set was that I am morally obligated to jump into lakes (irrespective of the situation). One can also draw the lines narrowly, but this, if anything, makes the problem worse. Maybe the standard is that one is universally, eternally, and everlastingly obligated to jump into lakes to save children--on April 25th. Or better yet, that I, David Schraub, am universally and eternally obligated to jump into lakes to save drowning children on that date(/hour/minute/instant). This creates a universal standard, but not one that really matters in a transcendental sense. The lines are arbitrary and somewhat meaningless, where we place them is a matter of pure discretion.
This is problematic because moral universalism's most convincing warrant is its claim to predictability. That is, when I set up a moral standard, I am bound to abide by it regardless of the situation. Universalism allows us to set up moral categories, sorting actions into moral and immoral based on their similarity to the overarching standards. Murder is wrong universally, so my particular act of murder is wrong because it violates the standard. Situational exceptions are not permitted because the whole point of the standard is to transcend the particularities of the moment, otherwise we'd never have any methodology for decisionmaking beyond case-by-case analysis. Velleman asserts that "situational ethics" is different from moral relativism, and he may be right, but it seems that they are fatally interwoven. The "situation" which dictates moral choices is often heavily contingent upon the standing of the agent, thus situational ethics are often indistinguishable from the "agent-relativism" Velleman claims is ridiculous. Velleman cannot have it both ways--he can't say that we have set-in-stone universal standards AND claim that situationalism falls within that paradigm. Or rather, he can, but only if he admits that standards don't give us predictability in any real sense of the term, because the standard itself is arbitrary and almost definitely will shift in the face of unpredictable circumstances.
The way out might be to affirm, as a moral principle, pragmatism and flexibility. That is, set our moral standard to "case-by-case," and make it elastic. Then, when faced with choices, we balance between the competing values presented, such as predictability and efficiency, as well as more nuanced concepts like justice and dignity. Different (but seemingly comprarable) situations might then come out differently--but that is okay. Richard Delgado and Jean Stefancic explain in the context of Critical Race Theory that:
"Most mainstream scholars embrace universalism over particularity, and abstract principles and the 'rule of law' over perspectivism (an approach characterized by an emphasis on how it was for a particular person at a particular time and place). Clashing with this more traditional view, Critical Race Theory writers emphasize the opposite, in what has been termed the 'call to context.' For CRT scholars, general laws may be appropriate in some areas (such as, perhaps, trusts and estates, or highway speed limits), but political moral discourse is not one of them. Normative discourse (which civil rights is) is highly fact-sensitive, which means that adding even one new fact can change intuition radically. For example, imagine a youth convicted of a serious crime. One's first response may be to urge severe punishment. But add one fact-he was seen laughing as he walked away from the scene-and one's intuition changes: Even more serious punishment now seems appropriate. But add another fact-he is mentally impaired or he was abused as a child-and now leniency seems in order. Because civil rights is more like the latter case than the former (highway law), neutral universal principles like formal equality can be more of a hindrance than a help in the search for racial justice. For this reason, many CRT writers urge attention to the details of minorities' lives as a foundation for our national civil rights strategy." [Richard Delgado and Jean Stefancic, eds. Critical Race Theory: The Cutting Edge. Philadelphia: Temple University Press, 2000, pg. xvii-xviii]I'm not sure Velleman wants to live in that world, as it doesn't have the type of rigid moral taxonomy he seems to think is necessary for a functioning moral universe. But I don't see a better option. Recognizing the reality that there is no single moral standard that does not both encompass too much and too little, we have to find another option. Perspectivism (which is not the same as relativism, but very close to it and situational ethics) offers much promise in this regard.
Other people have written that any moral standard (situational or no) is necessarily arbitrary and unprovable, no matter how much we may "want" or "need" it. This might or might not be true, but it is irrelevant. We have to live some way, even if living means, as Max Weber put it, committing ourselves to "warring Gods and Demons" without any solace or hope that our choice can be "justified" in the abstract, metaphysical sense of the term. Choices have to be made, including the choice to judge or not to. I am equally unjustified in not judging as I am in judging. It is literally impossible to escape the vortex of morality (even if it is, paradoxically, totally beyond our grasp). Inaction is still a moral choice (think of bystanders in the Holocaust), so choose we must. Even if there is no morality "out there," it still becomes relevant. Without morality, none of our actions have meaning--including the action to create moral codes. Okay, so we created morality out of whole cloth--so what? There isn't a standard to tell us we can't. So we're back where we started, and I still assert that from that starting point, Perspectivism has a lot to offer moral theorists, even though it clearly doesn't offer the "universal standards" Velleman so clearly desires.