The idea that a consistent utilitarian would go mad with worry about the various effects of his actions is perhaps closely connected with a curious argument against utilitarianism to be found in [Kurt] Baier's book The Moral Point of View. Baier holds that (act) utilitarianism must be rejected because it entails that we should never relax, should use up every available minute in good works, and we do not ordinarily think that this is so. The utilitarian has two effective replies. The first is that perhaps what we ordinarily think is false. Perhaps a rational investigation would lead us to the conclusion that we should relax much less than we do. The second reply is that act utilitarian premisses do not entail that we should never relax. Maybe relaxing and doing few good works today increases threefold our capacity to do good works tomorrow. So relaxation and play can be defended even if we ignore, as we should not, their intrinsic pleasures.

(J. J. C. Smart, An Outline of a System of Utilitarian Ethics [Melbourne: Melbourne University Press, 1961], 40 [footnote omitted])

Note from KBJ: Baier's argument goes as follows:

1. If (act) utilitarianism is true, then we should never relax.

2. It's not the case that we should never relax.

Therefore,

3. It's not the case that (act) utilitarianism is true.

This is an instance of modus tollens, which is a valid (i.e., truth-preserving) argument form. No (act) utilitarian will accept the conclusion, so every (act) utilitarian must either reject the first premise or reject the second premise. Rejecting the first (conditional) premise of a modus tollens argument is called "grasping [or grabbing] the bull by the horn." One grasps the bull by the horn when one denies that his or her theory has the stated implication. It is a way of saying that the critic doesn't understand, or is not correctly applying, the theory. Rejecting the second (negated) premise of a modus tollens argument is called "biting the bullet." One bites the bullet when one accepts the allegedly repugnant (or painful)  implication of the theory. Smart mentions both strategies, though not by these names. Smart, like Peter Singer, is a notorious bullet biter. He sticks with his theory (act utilitarianism) even when it produces painful results (or results that go against the common moral consciousness). Note that in a given case, one can both grasp the bull by the horn and bite the bullet. (Perhaps we should call this strategy "grasping the bullet by the horn," or even, more hilariously, "biting the bull.") One is saying the following: "My theory doesn't imply that; but if it did, I'd accept it."

Note 2 from KBJ: One of the most common mistakes made by philosophers (even the best ones) is thinking that everyone must reply to an argument in the same way. The telltale sign that this mistake is being made is the use of "we," "our," and "us." When I see these words being used by the arguer, I want to scream, "Speak for yourself!" Every deductive argument can be viewed as an assertion, by the arguer, that a set of propositions—consisting of the premises of the argument and the negation of its conclusion—is inconsistent. Baier, for example, is claiming that the following set of propositions is inconsistent:

a. If (act) utilitarianism is true, then we should never relax.

b. It's not the case that we should never relax.

c. (Act) utilitarianism is true.

To say that a set of propositions is inconsistent is to say that it is impossible (logically) for all of the propositions to be true. The truth of any two of them, therefore, entails the falsity of the third. (Take a moment to satisfy yourself that this is the case.) Since the propositions can't all be true, everyone (or at least every rational person) must reject at least one of them. But there is no reason why everyone must reject the same proposition! Baier rejects c. Smart rejects a and b. Think of it this way. Baier is more confident of the truth of a and b than he is of c. Smart is more confident of the truth of c than he is of a or b. Isn't it ironic that many philosophers, whose lifeblood is arguing and criticizing, do not understand the nature of argumentation?