When a normative moral theory collides with our beliefs, we must change either our beliefs or our theory. It is not always clear which we should change; but it is clear that we must change something. I shall consider two collisions between utilitarianism and what we believe, or are supposed to believe. About the first collision, I am going to say that the belief is false and that therefore there is no call to change utilitarianism. About the second, I am going to say that if the belief is true, utilitarianism cannot be changed to accommodate it; I shall leave it open, though, whether the belief is true. The two collisions are related, though different. They both concern the utilitarian thesis about self-sacrifice.
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