Utilitarianism

Clearly, “odd” means “unusual” in the first premise, but it means “not even” in the second premise. Consequently, both premises are true, even though the conclusion is false, so the argument is not valid.

Let’s consider another, more serious, example. In Utilitarianism (1861), John Stuart Mill claims to “prove” that “happiness is a good” with the following argument:

The only proof capable of being given that an object is visible is that people actu- ally see it. The only proof that a sound is audible is that people hear it. In like manner the sole evidence it is possible to produce that anything is desirable is that people actually desire it. . . . [E]ach person, so far as he believes it to be attainable, desires his own happiness. This, however, being a fact, we have not only all the proof which the case admits of, but all which it is possible to require, that happiness is a good.

Mill has sometimes been charged with committing a transparent fallacy in this passage. Specifically, the following argument is attributed to him:

(1) If something is desired, then it is desirable. (2) If it is desirable, then it is good.

(3) If something is desired, then it is good.

Mill never presents his argument in this form, and it may be uncharitable to attribute it to him. Still, whether it is Mill’s way of arguing or not, it provides a good specimen of a fallacy of equivocation.

The objection to this argument is that the word “desirable” is used in dif- ferent senses in the two premises. Specifically, in the first premise, it is used to mean “capable of being desired,” whereas in the second premise, it is used to mean “worthy of being desired.” If so, the argument really amounts to this:

(1*) If something is desired, then it is capable of being desired. (2*) If something is worthy of being desired, then it is good.

(3) If something is desired, then it is good.

This argument is clearly not valid. To make the charge of equivocation stick, however, it has to be shown that the argument is not valid when the mean- ing of the word “desirable” is used in the same sense in the two premises. This produces two cases to be examined:

(1*) If something is desired, then it is capable of being desired. (2**) If something is capable of being desired, then it is good.

(3) If something is desired, then it is good.

We now have a valid argument, but the second premise is not true, for some- times people are capable of desiring things that are not good. The second way of restoring validity takes the following form:

(1**) If something is desired, then it is worthy of being desired. (2*) If something is worthy of being desired, then it is good.

(3) If something is desired, then it is good.