John Mill's Proof Discussion

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On page 5 of Utilitarianism, Mill writes that although questions of ultimate ends are not amenable to direct proof, ;considerations may be presented capable of determining the intellect either to give or withhold its assent to the doctrine; and this is equivalent to proof.; In chapter 4 Mill attempts to provide the equivalent of a proof for the principle of utility-- the doctrine that happiness, and happiness alone, is desirable as an end. Mill divides the argument into two parts: (1) an argument to the conclusion that happiness is desirable, and (2) an argument to the conclusion that nothing else is desirable. (1). Mill argues: a. If anything is desired as an end, we have the only evidence we could have that it is desirable as an end. b. Happiness is desired as an end. c. Therefore, we have the only evidence we could have that happiness is desirable as an end. In support of a, Mill urges that just as the proof that anything is visible is that someone sees it, and just as the proof that anything is audible is that someone hears it, the proof that anything is desirable is that someone desires it. Objection: ;Kisible means ;capable of being seen,; and ;audible; means ;capable of being heard.; If anything is actually heard, then it must be capable of being heard. But ;desirable; does not mean ;capable of being desired.; It means ;worthy of being desired.; Hence from the fact that something is desired as an end it does not follow that this something is desirable as an end. Objection: Maybe happiness is desired and this is the only evidence we could have that happiness is desirable. From this it does not follow that happiness is desirable. We could equally well infer that since this evidence is inadequate to show that happiness is desirable, then by MillOs reasoning we cannot know that happiness is desirable. Maybe there is no knowledge to be had in this domain. (The argument indicates a problem with MillOs empiricism, the idea that the principles of...
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