# TWO VERSIONS OF HUME S LAW

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1 DISCUSSION NOTE BY CAMPBELL BROWN JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE MAY 2015 URL: COPYRIGHT CAMPBELL BROWN 2015

2 Two Versions of Hume s Law MORAL CONCLUSIONS CANNOT VALIDLY BE INFERRED from nonmoral premises this principle, commonly called Hume s law, presents a conundrum. 1 On one hand, it seems obviously true, and its truth is often simply taken for granted. On the other hand, an ingenious argument by A. N. Prior seems to refute it. My aim here is a resolution. I shall argue, first, that Hume s law is ambiguous, admitting both a strong and a weak interpretation; second, that the strong interpretation is false, as shown by Prior s argument; and, third, that the weak interpretation is true. 1. Two Hume s Laws Hume s law, more precisely, states that no argument can satisfy all of three conditions: 1. The argument is valid. 2. The conclusion of the argument is moral. 3. The premises are not moral. The third condition is what is sometimes called a plural predication. Its subject the premises is grammatically plural. Generally, plural predications may be read in two ways. On a distributive reading, a property is ascribed to each member of a group or collection individually, as in The pencils are green, which ascribes greenness to each pencil. On a collective reading, a property is ascribed to the group or collection as a whole, as in The pencils are scattered, which ascribes being scattered not to each pencil (a single pencil cannot be scattered), but to the whole collection of pencils. 2 Hume s law may thus be interpreted in two ways, as the third condition is read either distributively or collectively. An argument is valid just when the premises jointly imply the conclusion. 3 The distributive reading may thus be stated as follows: HL1. If φ!,, φ! jointly imply ψ, and ψ is moral, then at least one of φ!,, φ! is moral. 1 The origin of Hume s law is a famous passage in Hume (1978, III. i. 3). Other terms could be used instead of moral, e.g., ethical or normative. 2 For more on plural predication, see McKay (2006). 3 By saying that φ!, φ! jointly imply ψ, I mean that ψ is a logical consequence of φ!, φ!. Every interpretation that makes all of φ!, φ! true also makes ψ true. I assume that negation, conjunction and disjunction are interpreted classically.

3 To state the collective reading, we need to say what it is for the premises of an argument to be collectively nonmoral. I take this to mean that the conjunction of the premises is nonmoral. 4 This makes the collective reading equivalent to the thesis that the moral sentences are closed under the inverse of implication: HL2. If φ implies ψ, and ψ is moral, then φ is moral. Notice that HL1 is logically stronger, implying but not being implied by HL2. 2. The Distributive Reading Is False (or Trivial) HL1 has this absurd consequence: Either no sentence is moral or all nonmoral sentences are logically consistent with each other. This is shown by what is essentially Prior s argument (1960: 201-2). Let m be a moral sentence, and let n be a nonmoral sentence whose negation, n, is also nonmoral. 5 Now consider the disjunction n m. Is this moral or not? If it is, then HL1 has this counterexample: n, therefore n m. If it is not, then HL1 has this counterexample: n, n m, therefore m. In either case, HL1 is false. The only way out, for the defender of HL1, is to claim that sentences such as m and n cannot both exist. 6 But this is not an attractive escape route. Were there no moral sentences, then Hume s law would be quite trivial. One of the three conditions it claims to be jointly unsatisfiable would be unsatisfiable on its own (the second condition above). And surely some nonmoral sentences are inconsistent with each other. It would be absurd to say, for example, that either Grass is green or Grass is not green is moral. So HL1 is at best trivial, but most likely false. Some philosophers defend explicitly distributive readings of Hume s law. For example, Greg Restall and Gillian Russell prove the following: 4 This is to adopt a form of singularism. A singular entity, the conjunction, is taken to stand in for a plurality, the premises. I do not mean to endorse singularism across the board, but it seems plausible in this case. For more on singularism, arguments for and against, see McKay (2006). 5 Given HL1, the statement that φ is inconsistent with some nonmoral sentence is equivalent to the statement that φ is nonmoral. 6 Perhaps there is another way. Some respond to Prior s argument by saying that being moral is not a property of sentences, but a relation between sentences and arguments (Pigden 1989; Schurz 1997). The sentence n m is moral in the second counterexample given above, but not in the first. Elsewhere, I have tried to explain what is mistaken in this view (Brown 2014). Here I simply set it aside. I claim only that if being moral is a property, not a relation, then the distributive reading of Hume s law is refuted by Prior s argument. I also set aside solutions that involve abandoning classical logic. 2

4 If Σ is a satisfiable set of sentences, each of which is descriptive, and A is normative, then Σ A. 7 (The phrase each of which signals a distributive reading.) But this version of Hume s law is not the one stated above, the one that, I think, Prior attacks. Prior is concerned with arguments from the nonmoral to the moral (he says non-ethical and ethical ), where these are assumed to be exhaustive categories. Otherwise, his argument would simply present a false dilemma by assuming that n m must be either moral or nonmoral. Restall and Russell, however, are concerned with arguments from the descriptive to the normative, where these are not exhaustive (for example, n m is neither descriptive nor normative). 3. The Collective Reading Is True HL1 results from combining three principles: P1. If φ is moral, and φ is equivalent to ψ, then ψ is moral. P2. If either φ is moral or ψ is moral, then φ ψ is moral. P3. If φ ψ is moral, then either φ is moral or ψ is moral. It is straightforward to show that HL1 entails the conjunction of P1, P2 and P3. To show the converse, suppose that φ!, φ! jointly imply ψ, and that ψ is moral. Let φ be the conjunction (φ! φ! ). Since ψ is moral, φ ψ is moral [from P2]. But since φ implies ψ, φ is equivalent to φ ψ. So φ is moral [from P1]. So at least one of φ!, φ! is moral [from P3]. If HL1 is false, as I have argued, then so is either P1, P2 or P3. I shall argue that P3 is the false one; P1 and P2 are true. This is in effect to argue for HL2, since it is equivalent to the conjunction of P1 and P2. I begin with what seems to me a near truism: A moral sentence is one that says something moral. Elsewhere I have proposed an account of what it is to say something moral (Brown 2014). Here I hope we can get by with an intuitive grasp of that notion. Consider, for example, the tautology, Either lying is wrong or lying is not wrong. Despite its containing the moral term wrong, this sentence does not say anything moral. In an intuitive sense, tautologies do not say anything at all; they are empty or vacuous, without content. So a fortiori they say nothing moral. The assumption that a moral sentence must say something moral is, therefore, incompatible with the naive view that moral sentences are just those that contain moral vocabulary. But that view is implausible, anyway, and it would make Hume s law plainly false. P1 follows immediately. Logically equivalent sentences say the same thing. Thus if one is moral, i.e., says something moral, then so is the other. To show that P2 is true and P3 is false, a further premise is required. 7 Restall and Russell (2010: 255). 3

5 P2 is the converse of P3. P2 says that having a moral conjunct is sufficient for a conjunction to be moral; P3 says that this is necessary. Why, then, should this be sufficient but not necessary? The reason, I suggest, is this: A conjunction can say more than is said by either of its conjuncts, but cannot say less. To illustrate, consider the property of being offensive. The sentence You are either a genius or an idiot is not offensive. Nor is the sentence You are no genius ; it is compatible with your being of quite respectable intelligence. But the conjunction, You are either a genius or an idiot, and you are no genius, is offensive. The reason is that the conjunction says something extra, over and above what is said by either conjunct, namely, that you are an idiot. The offensiveness results only from the two conjuncts combining together; it is not present in either on its own. So a conjunction can say more than its conjuncts. But it cannot say less. You are an idiot remains offensive whatever it is combined with. There are funny cases like You are an idiot and by idiot I do not mean someone of low intelligence. But here the conjoined sentence has the effect of subverting the normal meaning of the offensive sentence. So this is not a mere conjunction, in the relevant sense. A moral sentence, I have said, is one that says something moral. Two things follow. First, if a conjunction cannot say less than its conjuncts, and one of its conjuncts says something moral, then the conjunction, too, must say something moral. So P2 is true. Second, if a conjunction can say more than its conjuncts, then a conjunction might say something moral even when its conjuncts do not. So P3 is false A Problem and a Pragmatic Solution HL2 implies that if any sentence is moral then every contradiction is moral, because a contradiction implies everything, including any moral sentence. So, for example, Grass is green and grass is not green is moral according to HL2 (assuming some sentence is moral). Granted, this is an odd result. Still, I think we can live with counting contradictions as a degenerate case of moral sentences. We know that contradictions are funny things anyway. Everything follows from them, for one thing. Is there any great harm in adding being moral to the list of their unusual properties? This does not threaten Hume s law, because the only thing that implies a contradiction is a contradiction. There is, however, a more serious worry. The sentence, All Australians are morally depraved, seems moral. 9 If it is moral, then, according to P2, so 8 Another analogy may be helpful. Being moral, on the view I am suggesting, is like being heavy. A whole may be heavy though none of its parts is heavy. But if a part is heavy then the whole must be heavy also. Having a heavy part is sufficient but necessary for a whole to be heavy. 9 This sentence is modeled on Prior s All New Zealanders ought be shot. The latter is less suitable for my purposes, because it is naturally given the wide-scope reading, It ought to be 4

6 too is the conjunction, All Australians are morally depraved and no Australians are morally depraved. But this is equivalent to There are no Australians, which seems clearly nonmoral. The solution, I think, is to say that the first sentence is not moral, after all. Appearances to the contrary can be explained pragmatically. An utterance of this sentence typically has a conversational implicature that is moral, namely, that some Australians are morally depraved. 10 This is why the sentence may seem moral, though in fact it has no moral content. Suppose I say to you, All Australians are morally depraved. You assume that I, in conformity with Grice s Maxim of Quality, would not say this unless I had some justification for believing it to be true (Grice 1989). But what justification could I have? Clearly, I could not know this a priori. The concept of moral depravity is not contained in that of being an Australian, or anything like that. 11 Could I have some a posteriori justification, without ever having encountered an Australian? Possibly. Perhaps I have sufficient evidence to establish inductively that, say, all humans are morally depraved, and I have inferred from this that all Australians (none of whom I have ever met) must also be morally depraved, since I know they are all human. In that case, however, because you assume that I conform to Grice s Maxim of Quantity, you would expect me to say, more informatively, All humans are morally depraved. Only one possibility remains: I have observed enough Australians to infer that all are morally depraved. But then there must exist some Australians for me to have observed. Thus, my utterance implicates that some Australians are morally depraved. Well, perhaps there is one other possibility. I might have come to believe this on the basis of reliable testimony. But this only pushes the problem back a step. How can I be justified in trusting this testimony unless the person providing it has observed an Australian? She might believe it on testimony, too. But obviously this cannot go on forever. If anyone is in a position to legitimately say, All Australians are morally depraved, someone at some time must have observed at least one Australian. the case that all New Zealanders are shot. Karmo (1988) interprets it this way, for example. This reading would introduce unnecessary complications. 10 Why think that Some Australians are morally depraved is moral if All Australians are morally depraved is not? What difference can a quantifier make? The answer, I think, is that only existential quantification carries ontological commitment. Only the Some form of the sentence entails the existence of moral stuff, the instantiation of moral properties. I develop this view in Brown (2014: 62-63). 11 So the view I am offering predicts, for example, that whereas All Martians come from Mars does not implicate that there are any Martians, All Martians have three legs does implicate this. That seems right to me. 5

7 5. Conclusion Which is the real Hume s law? It seems likely that what most people have in mind, under this title, is closer to HL1 than HL2. The former is perhaps the simpler and more obvious interpretation. The problem with HL1, as we have seen, is that it is false (or at best trivial). But now we can explain why it seems to be true. It bears a very close resemblance to another principle, HL2, which, as I have argued, is true. University of Glasgow Philosophy Department 6

8 References Brown, C. (2014) Minding the Is Ought Gap, The Journal of Philosophical Logic, 43(1): Grice, H. P. (1989) Studies in the Way of Words, Cambridge, Mass.: Harvard University Press. Hume, D. (1978/1739) A Treatise of Human Nature, second edition, Oxford: Oxford University Press. Karmo, T. (1988) Some Valid (but No Sound) Arguments Trivially Span the Is Ought Gap, Mind 97(386): McKay, T. (2006) Plural Predication, Oxford: Oxford University Press. Pigden, C. (1989) Logic and the Autonomy of Ethics, Australasian Journal of Philosophy 67(2): Prior, A. (1960) The Autonomy of Ethics, Australasian Journal of Philosophy, 38(3): Restall, G. and Russell, G. (2010) Barriers to Implication, in C. Pigden, ed., Hume on Is and Ought, London: Palgrave Macmillan, pp Schurz, G. (1997) The Is-Ought Problem: An Investigation in Philosophical Logic, Dordrecht: Springer. 7

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