I thank Michael Zimmerman for helpful comments on this essay.

The Platonic case strikes many as too easy to be characterized as agenuine moral dilemma. For the agent's solution in that case is clear;it is more important to protect people from harm than to return aborrowed weapon. And in any case, the borrowed item can be returnedlater, when the owner no longer poses a threat to others. Thus in thiscase we can say that the requirement to protect others from seriousharm overrides the requirement to repay one's debts byreturning a borrowed item when its owner so demands. When one of theconflicting requirements overrides the other, we do not have a genuinemoral dilemma. So in addition to the features mentioned above, in orderto have a genuine moral dilemma it must also be true thatneither of the conflicting requirements is overridden(Sinnott-Armstrong 1988, Chapter 1).

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The second argument that generates inconsistency, like thefirst, has as its first three premises a symbolic representation of amoral dilemma.

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Moral dilemmas, at the very least, involve conflicts between moral requirements. Consider the cases given below.

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And like the first, this second argument shows that the existence ofdilemmas leads to a contradiction if we assume two other commonlyaccepted principles. The first of these principles is that‘ought’ implies ‘can’. Intuitively this saysthat if an agent is morally required to do an action, it must bepossible for the agent to do it. We may represent this as

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Intuitively, PD just says that if doing A brings aboutB, and if A is obligatory (morally required), thenB is obligatory (morally required). The firstargument that generates inconsistency can now be stated. Premises(1), (2), and (3) represent the claim that moral dilemmas exist.

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The other principle, endorsed by most systems of deontic logic, saysthat if an agent is required to do each of two actions, she is requiredto do both. We may represent this as

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So if one assumes that ‘ought’ implies ‘can’and if one assumes the principle represented in (5)—dubbed by somethe agglomeration principle (Williams 1965)—then again acontradiction can be derived.

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Intuitively this principle just says that the same action cannot beboth obligatory and forbidden. Note that as initially described, theexistence of dilemmas does not conflict with PC. For as described,dilemmas involve a situation in which an agent ought to do A,ought to do B, but cannot do both A and B.But if we add a principle of deontic logic, then we obtain a conflictwith PC: