Moral skepticism (or moral scepticism) is a class of metaethical theories all members of which entail that no one has any moral knowledge. Many moral skeptics also make the stronger, modal, claim that moral knowledge is impossible. Moral skepticism is particularly opposed to moral realism: the view that there are knowable, objective moral truths.
Defenders of some form of moral skepticism include David Hume, J. L. Mackie (1977), Max Stirner, Friedrich Nietzsche, Richard Joyce (2001), Michael Ruse, Joshua Greene, Richard Garner, Walter Sinnott-Armstrong (2006b), and the psychologist James Flynn. Strictly speaking, Gilbert Harman (1975) argues in favor of a kind of moral relativism, not moral skepticism. However, he has influenced some contemporary moral skeptics.
Forms of moral skepticism
Moral skepticism divides into three subclasses: moral error theory (or moral nihilism), epistemological moral skepticism, and noncognitivism. All three of these theories share the same conclusions, which are:
- (a) we are never justified in believing that moral claims (claims of the form "state of affairs x is good," "action y is morally obligatory," etc.) are true and, even more so
- (b) we never know that any moral claim is true.
However, each method arrives at (a) and (b) by different routes.
Moral error theory holds that we do not know that any moral claim is true because
- (i) all moral claims are false,
- (ii) we have reason to believe that all moral claims are false, and so, because
- (iii) since we are not justified in believing any claim we have reason to deny, we are not justified in believing any moral claims.
Epistemological moral skepticism is a subclass of theory, the members of which include Pyrrhonian moral skepticism and dogmatic moral skepticism. All members of epistemological moral skepticism share two things in common: first they acknowledge that we are unjustified in believing any moral claim, and second, they are agnostic on whether (i) is true (i.e. on whether all moral claims are false).
- Pyrrhonian moral skepticism holds that the reason we are unjustified in believing any moral claim is that it is irrational for us to believe either that any moral claim is true or that any moral claim is false. Thus, in addition to being agnostic on whether (i) is true, Pyrrhonian moral skepticism denies (ii).
- Dogmatic moral skepticism, on the other hand, affirms (ii) and cites (ii)'s truth as the reason we are unjustified in believing any moral claim.
Finally, Noncognitivism holds that we can never know that any moral claim is true because moral claims are incapable of being true or false (they are not truth-apt). Instead, moral claims are imperatives (e.g. "Don't steal babies!"), expressions of emotion (e.g. "stealing babies: Boo!"), or expressions of "pro-attitudes" ("I do not believe that babies should be stolen.")
Moral error theory
Moral error theory is a position characterized by its commitment to two propositions: (i) all moral claims are false and (ii) we have reason to believe that all moral claims are false. The most famous moral error theorist is J. L. Mackie, who defended the metaethical view in Ethics: Inventing Right and Wrong (1977). Mackie has been interpreted as giving two arguments for moral error theory.
The first argument people attribute to Mackie, often called the Argument from Queerness, holds that moral claims imply motivation internalism (the doctrine that "It is necessary and a priori that any agent who judges that one of his available actions is morally obligatory will have some (defeasible) motivation to perform that action" ). Because motivation internalism is false, however, so too are all moral claims.
The other argument often attributed to Mackie, often called the Argument from Disagreement, maintains that any moral claim (e.g. "Killing babies is wrong") entails a correspondent "reasons claim" ("one has reason not to kill babies"). Put another way, if "killing babies is wrong" is true then everybody has a reason to not kill babies. This includes the psychopath who takes great pleasure from killing babies, and is utterly miserable when he does not have their blood on his hands. But, surely, (if we assume that he will suffer no reprisals) this psychopath has every reason to kill babies, and no reason not to do so. All moral claims are thus false.
Epistemological moral skepticism
All versions of Epistemological Moral Skepticism hold that we are unjustified in believing any moral proposition. However, in contradistinction to moral error theory, epistemological moral skeptical arguments for this conclusion do not include the premise that "all moral claims are false." For example, Michael Ruse  gives what Richard Joyce  calls an "evolutionary argument" for the conclusion that we are unjustified in believing any moral proposition. He argues that we have evolved to believe moral propositions because our believing the same enhances our genetic fitness (makes it more likely that we will reproduce successfully). However, our believing these propositions would enhance our fitness even if they were all false (they would make us more cooperative, etc.). Thus, our moral beliefs are unresponsive to evidence; they are analogous to the beliefs of a paranoiac. As a paranoiac is plainly unjustified in believing his conspiracy theories, so too are we unjustified in believing moral propositions. We therefore have reason to jettison our moral beliefs.
There are two different opinions that follow from moral skepticism.
Amoralism is the idea to drop morality.
Criticisms of moral skepticism come primarily from moral realists. The moral realist argues that there is in fact good reason to believe that there are objective moral truths and that we are justified in holding many moral beliefs. One moral realist response to moral error theory holds that it "proves too much" — if moral claims are false because they entail that we have reasons to do certain things regardless of our preferences, then so too are "hypothetical imperatives" (e.g. "if you want to get your hair-cut you ought to go to the barber"). This is because all hypothetical imperatives imply that "we have reason to do that which will enable us to accomplish our ends" and so, like moral claims, they imply that we have reason to do something regardless of our preferences. 
If moral claims are false because they have this implication, then so too are hypothetical imperatives. But hypothetical imperatives are true. Thus the argument from the non-instantiation of (what Mackie terms) "objective prescriptivity" for moral error theory fails. Russ Shafer-Landau and Daniel Callcut have each outlined anti-skeptical strategies. Callcut argues that moral skepticism should be scrutinized in introductory ethics classes in order to get across the point that "if all views about morality, including the skeptical ones, face difficulties, then adopting a skeptical position is not an escape from difficulty." 
- Moral Skepticism (Stanford Encyclopedia of Philosophy)
- D. Brink, "Moral Realism and the Skeptical Arguments from Disagreement and Queerness," Australasian Journal of Philosophy 62 (1984)
- Joyce, Richard (2001). The Myth of Morality, Cambridge University Press.
- M. Ruse, Taking Darwin Seriously (Oxford: Basil Blackwell, 1986)
- Daniel Callcut, “The Value of Teaching Moral Skepticism,” in Teaching Philosophy Volume 29, Number 3 (Sept 2006), p.231, paper online at http://philpapers.org/archive/CALTVO-2
- Butchvarov, Panayot (1989). Skepticism in Ethics, Indiana University Press.
- Gibbard, Allan (1990). Wise Choices, Apt Feelings. Cambridge: Harvard University Press.
- Harman, Gilbert (1975). "Moral Relativism Defended," Philosophical Review, pp. 3–22.
- Harman, Gilbert (1977). The Nature of Morality. New York: Oxford University Press.
- Joyce, Richard (2001). The Myth of Morality, Cambridge University Press.
- Joyce, Richard (2006). The Evolution of Morality, MIT Press. (link)
- Lillehammer, Halvard (2007). Companions in Guilt: arguments for ethical objectivity, Palgrave MacMillan.
- Mackie, J. L. (1977). Ethics: Inventing Right and Wrong, Penguin.
- Sinnott-Armstrong, Walter (2006a). "Moral Skepticism", The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.). (link)
- Sinnott-Armstrong, Walter (2006b). Moral Skepticisms, Oxford University Press.
- Olson, Jonas (2014) Moral Error Theory: History, Critique, Defence, Oxford University Press.
- Moral skepticism at PhilPapers
- Walter Sinnott-Armstrong. "Moral Skepticism". Stanford Encyclopedia of Philosophy.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
- Richmond Campbell. "Moral Epistemology". Stanford Encyclopedia of Philosophy.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
- Henry S. Richardson. "Moral Reasoning". Stanford Encyclopedia of Philosophy.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
- Moral skepticism at the Indiana Philosophy Ontology Project