ESSAY 6.2 On the Triviality of Hume's Law: a Reply to Gerhard Schurz Charles Pigden 1. No-Ought-From-Is: Three Factions Hume's famous 'observation' concerning is and ought is one of the most talked-about single paragraphs in the entire history of philosophy. Though a little neglected in Hume's own day it gradually acquired the status of a superstar text, so that nowadays even those who know next to nothing about Hume's ethics, know about the alleged barrier between is and ought. The discussion reached a pitch in the middle years of the Twentieth Century but the Is/Ought passage continues to be a focus for meta-ethical debate, down to the present day. Some (like Bentham) think it expresses a profound truth; some (like Reid) think it is true but not profound; and some think that it cannot be profound because it is not true. Gerhard Schurz in his magisterial (1997) The Is-Ought Problem (to which this paper is largely a response) argues that Hume's No-Ought-from-Is thesis is both true and profound whereas I belong to the true-but-not-profound party. (See Pigden, 1989.) To be more precise, I think that Hume's No-Ought-From-Is thesis (when appropriately modified) is an instance of a profound truth (that in logic you cannot get out what you haven't put in) but not a particularly profound instance of that truth. Thus the fact that you cannot get a non-vacuous ought from an is is on a par with the fact that you cannot get (non-vacuous) 'hedgehog'conclusions from 'hedgehog'-free premises. No-Ought-from-Is does not express an important fact about the nature of morality but a fact about the nature of logic. However, the unimportance of the No-Ought-from-Is thesis is itself important and its non-profundity profound. For on my reading, No-Ought-from-Is poses no threat to naturalism and affords no argument for non-cognitivism. And this is important because it is widely believed to do both. Schurz, on the other hand, thinks that Hume's No-Ought-From-Is thesis (again when appropriately modified) is not a particular instance of a more general truth but an oughtspecific thesis, or at least a thesis specific to a class of modal or sentential operators of which 'ought' is one. You cannot get an ought-relevant ought from an is because of certain features of the moral concepts, which features are imperfectly represented in the many systems of deontic logic. Since No-Ought-From-Is holds in virtue of specific features of the moral concepts, this suggests that moral discourse is in some sense special, and that its peculiarities 213 require a specific explanation. For this reason Schurz's No-Ought-from-Is does pose a threat to naturalism and may even afford an argument for non-cognitivism. Schurz (as of 1997) does not consider himself a non-cognitivist but he does subscribe to some typically non-cognitivist sentiments. He equates normative statements with prescriptive statements (Schurz, 1997, pp. 5-6) and thinks that ethical argument 'cannot lead to "one truth" among possible positions' since there is 'a multitude of different but equally possible moral attitudes' (p. 3) Furthermore, 'it is not 'the function of ethical norms and values to explain or predict the factual conduct of humans, but to guide and improve it' (p. 279). This constellation of opinions strongly suggests non-cognitivism. So. why doesn't Schurz consider himself a non-cognitivist? a) Because he associates non-cognitivism with the view that a logic of norms is impossible (a view which he vehemently rejects); and b) because in his semantics normative statements can take the values 1 and 0, 'true' and 'false' even though they may not be either true or false in the ordinary senses of those words (pp. 16-17). Thus Schurz might be sympathetic to the inference-to-the-best-explanation that I shall sketch in §8, an argument designed to prove what he tends to take for granted, namely that moral judgments are prescriptive not descriptive, designed to guide conduct not to state facts (pp. 5-6). This argument fails on my reading of No-Ought-From-Is, but might succeed on his. The chief purpose of this paper is to defend my view against Schurz (especially as expressed in The Is-Ought Problem) and the chief point at issue is whether what Hume has to say is true and profound or merely true. But both our views are best understood as responses to the neither-true-nor-profound party as represented by the late Arthur Prior. But before going on to Prior I had better revert to Hume. 2. Hume Explained What exactly is Hume getting at in his famous paragraph? The answer, I suspect, is that what he is getting at is not very exact by modern standards. What he seems to be saying is something like this: You cannot derive a conclusion concerning 'ought' (or for that matter any other moral word) from 'ought'-free (or non-moral) premises. The reason is that 'ought' and its relations have a distinctively moral content they express some new relation or affirmation and that in logic you cannot get out what you haven't put in. If this new relation or affirmation does not appear in the premises which ex hypothesi it does not, being new then it cannot appear in the conclusion of a valid deductive inference. The vulgar systems of morality attempt to derive the moral (propositions connected by an ought or an 214 ought not) from the non-moral (propositions about the being of God or observations concerning human affairs) and for logical reasons this simply can't be done. Thus the vulgar moralists are exposed as logical incompetents at best and charlatans at worst. Misled by their moralistic zeal they have perpetrated something akin to a pious fraud by purporting to conjure moral rabbits out of non-moral hats by means of logic alone. But so far this argument only tells against those who attempt to deduce the moral from the non-moral. Some think that Hume is attempting to make a more controversial point. If we confine ourselves to pure logic it seems that we cannot derive conclusions about unmarried men from premises about bachelors. For example, it does not follow as a matter of logical consequence that because Fritz is a bachelor that Fritz has no wife. For it is possible to interpret the premise 'Fritz is a bachelor' in such a way that 'Fritz is a bachelor' is true whereas 'Fritz has no wife' is false, if we interpret 'bachelor' to mean married man (or assign 'bachelor' the same extension as 'married man'). A sentence X is only a logical consequence of a set to sentences K if K cannot be true and X false however we interpret the non-logical vocabulary in K and X. Nevertheless, it is generally agreed that 'Fritz is a bachelor' entails that Fritz has no wife. because (given the actual meaning of 'bachelor') it is analytic that bachelors have no wives. (I myself have some doubts about this but they are not germane to the present argument. See Pigden, 1987.) Now, some think that Hume is not just making the logical point that no conclusions concerning ought and ought not can be logically derived from premises concerning is and is not (i.e. that no conclusion about what ought to be can be a logical consequence of premises about what is) rather he is making the stronger point that no conclusions about what ought to be can be entailed by premises about what is. In other words, he is denying the existence of analytic bridge principles linking the moral and the non-moral, Is and Ought. The trouble with this interpretation is that it is plainly false. For Hume subscribes to just such an analytic bridge principle. He suggests a definition of 'obligation' ('when the neglect or nonperformance of [an action] displeases us after a [certain] manner, we say that we lie under an obligation to perform it' (T, 3.2.5.4/517)) and explicitly defines the related concept of a virtue in terms of the reactions of an ideal spectator. 'The hypothesis we embrace is plain. It maintains that morality is determined by sentiment. It defines virtue to be whatever mental action or quality gives to a spectator the pleasing sentiment of approbation; and vice the contrary.' (EPM, App. 1.10/289.) Thus in Hume's view it is analytic that a mental action or quality which gives to a (suitably qualified) spectator the pleasing sentiment of approbation is a virtue. Hence claims about virtues are entailed by 215 claims about the reactions of suitably qualified spectators. Indeed, Hume uses this supposed analyticity to do what Schurz (1997, chs 11 and 12) considers highly problematic he justifies an ethical theory (namely that 'PERSONAL MERIT consists altogether in the possession of mental qualities, useful or agreeable to the person himself or to others') by appealing to the empirical facts (namely that 'mental qualities, useful or agreeable to the person himself or to others' 'give to a [suitably qualified] spectator the pleasing sentiment of approbation'). As Hume himself puts it, having set up the analytic bridge principle (that virtue is 'whatever mental action or quality gives to a spectator the pleasing sentiment of approbation'), 'we then proceed to examine a plain matter of fact, to wit, what actions have this influence.' (EPM, App. 1.10/289). Of course this empirical justification only works on two conditions: a) that Hume's supposedly analytic BP is correct and b) that human beings do in fact share a moral sense so that we are ideally disposed to approve and disapprove of the same things. Neither condition seems very plausible to me, but that's another story! From now on I take Hume to be a proponent of the Logical Autonomy of ethics, the thesis that you cannot logically derive moral conclusions from non-moral premises, ought from is. I do not take him to be arguing for the Semantic Autonomy of ethics, the thesis that moral conclusions are not entailed by non-moral premises. I am fortified in this reading by the fact that Hume often appeals to the conservativeness of logic roughly the claim that you cannot get out what you haven't put in to prove a skeptical point. After all, his critique of induction rests (partly) on the simple observation that no set of premises about what has been can justify a conclusion about what will be since what will be involves some new relation or affirmation. (See Heathcote, Essay 3.1, Pigden, Essay 3.4 and Russell, Essay 4.) Thus the premises about what has been can be true and the conclusion about what will be, false. In my book Hume is the proponent of the comparatively weak thesis that ethics is logically autonomous. Yet even this weak thesis appears to be false. 3. Arthur Sells the Pass. In his youth the New Zealand philosopher Arthur Prior was a standard-bearer for the trueand-profound party. But in 1960 he recanted and went over to the neither-true-nor-profound faction. He devised as set of counterexamples which purport to prove that the Logical Autonomy of ethics is false and that you can derive moral conclusions from non-moral premises. All the inferences are logically impeccable and in each case what appear to be moral conclusions follow from obviously non-moral premises. The inferences are as follows: 216 (A) l. Tea-drinking is common in England. Therefore: 2. Either tea-drinking is common in England or all New Zealanders ought to be shot. (B) l. There is no man over 20ft high. Therefore: 2. There is no man over 20ft high who ought to sit in an ordinary chair. (C) l. Undertakers are church officers. Therefore: 2. If church officers ought to be reverent, undertakers ought to be reverent . (Prior Essay 1.1.: this volume) (A) is simply an instance of ∨-Introduction i.e.: A ⊩ A ∨ B. (B) is a quantified variant of the principle ~A ⊩ ~(A & B), viz ~(∃x)(Fx) ⊩ ~(∃x)(Fx & Gx). (C) (which I have simplified) is an instance of the following inference schema: (x)(Fx ⊃ Gx) ⊩ (x)((Gx ⊃Hx) ⊃ (Fx ⊃ Hx)). Since each of these inferences is valid it seems that we can indeed get an Ought from an Is. 4. The Gospel According to Pigden or Hume on the New Zealand Plan Still you can't help feeling that there is something fishy about these inferences and that they are not really concerned with duties at all. Consider the following parallel inferences. (A)' l. Tea-drinking is common in England. Therefore: 2. Either tea-drinking is common in England or all New Zealanders are hedgehogs. (B)' l. There is no man over 20ft high. Therefore: 2. There is no man over 20ft high who is a hedgehog. (C)' l. Undertakers are church officers Therefore: 2. If church officers are hedgehogs, undertakers are hedgehogs. 217 Here we have what appear to be hedgehog-related conclusions from non-hedgehog premises. Here too the words 'hedgehog' and 'hedgehogs' occur essentially in a certain sense. If (A)'2, (B)'2 and (C)'2 were all true, it would not be possible to uniformly replace the words 'hedgehog' and 'hedgehogs' with grammatical equivalents without risk of a change in truthvalue. The truth of these propositions does not guarantee the truth of the relevant substitution instances. Just because there is no man over 20ft high who is a hedgehog, it does not follow that there is no man over 20ft high who is a hero. The absence of 20ft high human hedgehogs does not guarantee the absence of 20ft high human heroes. But 'risk' is the operative word in this connection. For under certain conditions it is possible to replace the 'hedgehogs' with random grammatical equivalents without prejudice to the truth-values of the resulting propositions namely when the premises of the arguments are true. So long as there is no man over 20ft high, then not only is there no man over 20ft high who is a hedgehog but there is no man over 20ft high who is a hero. If there are no giant humans at all, then there are no giant human hedgehogs and no giant human heroes either. So although the 'oughts' and the 'hedgehogs' in the conclusions are essential in one sense, they are inessential in another. Given the premises they can be (uniformly) replaced salva veritate i.e. without affecting the truth of the resulting conclusions. Which means that in the context of the inferences they can be (uniformly) replaced salva validitate, i.e. without prejudice to the validity of the resulting inferences. Now the fact that we can substitute 'hedgehogs' for 'oughts' in the conclusions of these inferences without affecting their validity, suggests that these words play no essential part in the argument. Given the premises, any old thing would do. Nor is this all. The second set of examples brings out something important about the first. They are not just counterexamples (or apparent counterexamples) to the No-OughtFrom-Is Thesis. They are counterexamples (or apparent counterexamples) to the conservativeness of logic. The conservativeness of logic is the admittedly metaphorical thesis that in logic you cannot get out what you haven't put in. Yet in the first set of inferences we have what appear to be ought-related conclusions from 'ought'-free premises just as in the second set we have hedgehog-related conclusions from 'hedgehog'-free premises. So if Prior's examples refute No-Ought-From-Is, they also refute the conservativeness of logic. This suggests and I say no more that the one is simply an instance of the other. If this is correct, then the way to vindicate Hume's Is/Ought principle is to vindicate conservativeness. 218 That is my strategy. First I develop the concept of inference-relative vacuity. An expression a predicate or a propositional variable in the first instance occurs vacuously in the conclusion of an inference K ⊩ X iff it can be uniformly replaced with any expression of the same grammatical type salva validitate, i.e. whilst preserving the validity of the resulting inference K ⊩ X'. The offending 'oughts' in (A)2, (B)2 and (C)2 are vacuous in this sense as are the 'hedgehog's in (A)'2, (B)'2 and (C)'2. This explains our uneasy feeling that the conclusions are not really concerned with either obligations or hedgehogs. For example, the following inference (A'') is just as valid as the original (A) and for exactly the same reason.: (A'') l. Tea-drinking is common in England. Therefore: 2. Either tea-drinking is common in England or all New Zealanders ought NOT to be shot. We then clarify or redefine the concept of conservativeness as follows: In logic (firstorder predicate logic at any rate) no predicate or propositional variable can appear nonvacuously in the conclusion of a valid inference unless it appears in the premises. In other words, you can't get anything non-vacuous out that you have not put in. This claim is susceptible of proof. (See Pigden,1989, pp. 136-137, the Introduction and Salwen, Essay 5.1, this volume.) Indeed as Schurz points out it is a simple consequence of the uniform substitution theorem (Schurz, 1997, p. 5). But if no predicate or propositional variable can occur non-vacuously in the conclusion of a valid inference unless it appears in the premises, it follows that no 'ought' can appear non-vacuously in the conclusion of a valid inference unless it appears in the premises provided and this is an important proviso that the 'ought' appears either as a predicate or as the component of a sentence or subsentence whose internal structure is irrelevant to the validity of the inference. There is another proviso which is at least equally important. The proof of conservativeness only applies to 'ought' if 'ought' is not regarded as a logical constant (or a logical symbol). I treat 'ought' as a schematic expression: that is an expression whose interpretation is allowed to vary when determining logical consequence. Logical constants as their name suggests are given a constant interpretation. What '&', '~' and the quantifiers mean is not allowed to vary from model or to be more precise, their interpretations are only allowed to vary within certain well-defined parameters. (For example, in different models the quantifiers take different 219 domains.) They must not be interpreted in such a way as to invalidate the theorems of the logic in question. Now it is only if it is not regarded as a logical constant (in this sense) that the proof of conservativeness applies to 'ought'. For in the sense that I have defined it, logic is only conservative with respect to the non-logical vocabulary. However, if I am granted these two provisos, the proof of conservativeness vindicates the autonomy of ethics in a slightly amended form. Instead of No-Ought-From-Is, we have the admittedly less pithy NoNon-Vacuous-Ought-From-Is. More pedantically we say that an 'ought' cannot occur nonvacuously in the conclusion of a valid inference unless it appears in the premises. Schurz challenges both my provisos. He regards 'ought' as a sentential operator rather than a predicate and he also regards it as a logical constant (or more precisely a logical symbol). That is, he believes there are logical principles governing the 'ought' operator and thus that there are principles peculiar to and pervasive of all moral or normative reasoning. For him (though not for me) deontic logic the supposed logic of norms is a genuine subject. We will return to these issues later. For now, let us suppose that I am right and that 'ought' is neither a sentential operator nor a logical constant and that the Logical Autonomy of ethics is an instance of the conservativeness of logic. What are the consequences for metaethics? 5. Naturalism and Autonomy Let us start with naturalism. Naturalism is the name of a family of doctrines which share the following features: 1) They are realist. They hold that moral judgments are truth-apt, factstating, true or false (and hence that non-cognitivist theories such as emotivism and prescriptivism are false) and that some (non-negative atomic) moral judgments are true. 2) They are reductionist (in a very large sense of the word): though some moral judgments are true, no specifically moral facts or properties are required to make them true. We can have moral truth without 'queer' non-natural facts or properties, without adding any irreducibly moral entities to our pre-existing ontologies. Naturalists differ between themselves about the facts, properties and relations required to underwrite the principles of morality. There are theistic naturalists, for whom morality is a matter of divine commands, ideal observer or response-dependent naturalists, like Hume, who reduce ethics to the reactions of an ideal observer or define it terms of some (usually human) response, utilitarian naturalists, who think morality reduces to facts about pleasure and pain, Aristotelian naturalists who resort to supposed facts about biological functions and human flourishing and (nowadays) Kantian or rationalistic naturalists who want to found morality on facts about what it is reasonable to do. 220 What binds them together is the shared belief that we can have moral truth without metaphysical spooks and moral facts without the non-natural fancies of a G.E. Moore. (See Pigden, 1991.) Some philosophers seem to think that the Logical Autonomy of ethics is incompatible with naturalism. Because you can't get an Ought from an Is they conclude that there must be something special about both ought-judgments and the facts (if any) to which they correspond. The logical gulf between the moral and the non-moral is the outward and visible sign of a deep ontological divide. . But this is a mistake. So long as you confine yourself to logic alone, you cannot derive hedgehog conclusions from 'hedgehog'-free premises not even if the premises deal with the exploits of erinaceous europeus or the doings of small spiny creatures with an unhealthy penchant for tarmac. Yet nobody concludes that there is something special about either hedgehog-judgments or the corresponding hedgehog facts. The Logical Autonomy of hedgehog talk does not betoken a deep ontological divide between hedgehogs and the rest of the animate creation. But famous philosophers, including the young Bertrand Russell, have drawn the corresponding conclusion in the case of the moral 'ought'. (See Russell, 1999, chs 3-7.) However, it might appear that although the truth of No-Ought-From-Is is quite compatible with the truth of naturalism, the falsehood of No-Ought-From-Is would imply the falsehood of non-naturalism and hence the truth of naturalism. To deal with this issue we need to make some distinctions. There are three forms of the autonomy of ethics, Logical, Semantic and Ontological. Logical Autonomy we have dealt with already. It is the thesis that logic alone won't allow you to derive moral conclusions from non-moral premises. With the appropriate modifications I believe this to be true. Semantic Autonomy is the thesis that moral words and phrases are not synonymous with non-moral words and phrases and more generally that there are no analytic bridge principles (true by definition) linking the moral and the non-moral. Finally Ontological Autonomy is the thesis that for moral judgments to be true there must be peculiarly moral facts and properties (of the kind envisaged by G.E.Moore, WD. Ross and others) to make them true. It is thus the reverse of naturalism. Now, Logical Autonomy does not imply Semantic Autonomy, nor does Semantic Autonomy imply Ontological Autonomy. You cannot non-vacuously derive hedgehog conclusions from premises in which the word 'hedgehog' does not appear, but this does not demonstrate that 'hedgehog' is not synonymous with 'erinaceous europeus' (as indeed it is). You cannot non-vacuously derive ought-conclusions from premises in which the word 'ought' does not appear, but it does not follow (though it may, of course, be true) that 'ought' 221 and its relations are not synonymous with any non-moral words. Similarly, the Semantic Autonomy of ethics does not imply Ontological Autonomy (at least not without an extra dose of argument). 'Water' (which names the drinkable substance that falls out of the sky as rain and is found in lakes and rivers) is not synonymous with 'H2O' (which names the compound composed of two hydrogen atoms to one oxygen atom). This is shown by the fact that it was a major discovery that water is H2O, not something that people realized by reflecting on their concepts. Nevertheless water is H2O (at certain temperatures and pressures) despite the fact that the two terms are not synonymous. As Frege would put it, the two symbols have different senses but the same reference. But what goes for 'water' presumably goes for 'good' and 'ought'. Just because 'good' is not synonymous with any naturalistic predicate, it does not follow that goodness is not identical with any naturalistic property. So the situation looks like this: (with the slashed arrows representing non-entailments) Logical Autonomy does not imply Semantic Autonomy, which does not imply Ontological Autonomy, but Ontological Autonomy implies the falsehood of naturalism and vice versa. However, it may be that the reverse entailments hold. Suppose a) that Ontological Autonomy is true and b) that our moral language is more or less in order, i.e. that it does not embody some ghastly naturalistic confusion. Then these two together would appear to imply Semantic Autonomy. For if a special realm of sui generis moral facts or properties are required to make moral judgments true and the language of morals reflects that fact, then moral predicates cannot be synonymous with non-moral predicates. If c) moral predicates are not synonymous with non-moral predicates and if d) logic is conservative, then these two together would appear to imply Logical Autonomy. For if an 'ought' occurs non-vacuously in the conclusion of a valid inference, it must contain non-natural semantic content. But if 222 logic is conservative, where can this content have come from, if not from the premises? Thus the situation seems to be like this: Thus if Logical Autonomy is false, the conjunction of Semantic Autonomy and the conservativeness of logic is false. And since we can take the conservativeness of logic as read, this would appear to mean that Semantic Autonomy is false. But since Ontological Autonomy plus the apparently innocuous assumption that moral language is in order together imply Semantic Autonomy, if Semantic Autonomy is false then Ontological Autonomy is probably false too! But if Ontological Autonomy is false then naturalism is true. So although the truth of Logical Autonomy does not imply the falsehood of naturalism, the falsehood of Logical Autonomy would appear to imply the truth of naturalism. So the fact that it is not false would appear to give it a certain amount of importance, though only at one remove. But if you have been attentive you will have noticed the qualifications scattered through the preceding paragraph – 'seems', 'appears' and so on. They are there for a reason. Crucial to the argument I have just sketched is the thesis that Semantic Autonomy and the conservativeness of logic together entail Logical Autonomy. Hence if Logical Autonomy is false, the conjunction of the two is false. But though the conjunction does imply Logical Autonomy, all the work is being done by just one of the conjuncts, namely the conservativeness of logic. And this is not surprising since the autonomy of ethics simply is the conservativeness of logic in its ethical incarnation. Thus if (per impossibile) Logical Autonomy were false, conservativeness would be false, in which case Semantic Autonomy might remain unaffected. But if the falsehood of Logical Autonomy is compatible with the truth of Semantic Autonomy, it is compatible with the truth of Ontological Autonomy (though it is not clear whether in such a weird and impossible scenario the notion of kinds of facts, properties or propositions would make sense). And if the falsehood of Logical Autonomy is compatible with the truth of Ontological Autonomy, it is compatible with the falsehood of naturalism. 223 Thus the truth of Logical Autonomy does not entail the falsehood of naturalism and the falsehood of Logical Autonomy would not entail the truth of naturalism (except in the sense that in that impossible situation all distinctions between types of facts, properties and propositions might break down). Naturalism, it seems, is logically independent of the NoOught-From-Is thesis. Whether No-Ought-From-Is is true or false, naturalism could be false or true. Which is one reason to suppose that its subversive potential is not as great as Hume and his would-be followers have supposed. Some of the vulgar systems of morality might be able to get away with it after all. 6. Non-Cognitivism, No-Ought-From-Is and the Inference to the Best Explanation But there is another reason why No-Ought-From-Is is supposed to be a world-shattering thesis. It has been used not only to refute naturalism but to underwrite non-cognitivism, the anti-realist thesis that moral judgments are not primarily true or false since their role is not to state facts but to express emotions or prescribe action. Somehow the fact that you cannot derive moral conclusions from non-moral premises is supposed to show, or at least suggest, that moral judgments are not primarily descriptive, but emotive, prescriptive or whatnot. But how exactly is the argument supposed to work? Since Hakan Salwen and I have discussed this matter at length in Essays 5.1 and 5.2, I can afford to be brief. The argument is best construed as an inference to the best explanation. For ease of exposition, I will formulate the argument so as to take account of both Prior's problem and my solution, though those who hint at some such argument would appear to be oblivious of both. 1) You can't derive an ought from an is. That is, you cannot non-vacuously derive moral conclusions from non-moral premises. 2) The best explanation of 1) is a) that logic is conservative – a new relation or affirmation cannot appear nonvacuously in the conclusion of a valid inference unless it appears in the premises; and b) that since moral judgments are not designed to state facts but to express emotion or prescribe action [insert non-cognitivist theory of choice] moral words always express 'a new relation or affirmation' Therefore (probably) 224 3) The role of moral judgments is not to state facts but to express emotion or prescribe action [insert non-cognitivist theory of choice]. This argument is formally respectable (though of course not deductively valid). But formally respectable though the argument may be, on my reading of No-Ought-From-Is it is a complete failure. For an inference to the best explanation fails if there is a better explanation to hand and in this case there is. The following is a better, because simpler explanation of 1): 2') Logic is conservative – that is you cannot non-vacuously derive Fconclusions [conclusions containing predicates of kind F] from non-F premises [premises which don't contain predicates of kind F]. Since logic is conservative in this sense, it follows that no moral conclusion – no conclusion in which the moral words appear non-vacuously – can be derived from premises in which they don't. But this explanation entails absolutely nothing about the nature of moral judgments or the meaning of the moral vocabulary. It's a purely formal thesis holding in virtue of the conservativeness of logic. Just as the deliverances of reason are supposed to be motivationally inert, so the deliverances of general logic are meta-ethically inert. And NoOught-From-Is is simply an instance of the conservativeness of logic. Thus No-Ought-FromIs provides no support whatsoever for non-cognitivism whether abductive or deductive. This explains my paradoxical pronouncements at the outset. I said that No-OughtFrom-Is is not a very profound truth but that its non-profundity is itself profound. It is not profound because it cannot, as some have supposed, be used to refute naturalism or support non-cognitivism. However, the fact that it cannot be used to do these things is itself a profound and important point. 7. The Gospel According to Schurz or Hume on the Austrian Plan However, this elaborate structure of argument rests on two provisos, both of which might be false: a) that 'ought' should be construed as a predicate and b) that 'ought' is not a logical constant. Gerhard Schurz challenges them both. For him, 'ought' is both a sentential operator a symbol that attaches to pre-existing sentences to form new sentences – and a logical constant in the relaxed sense of the word defined above. He is a bit vague about the principles governing the constant but he thinks it likely that they are captured by some among 225 the family of deontic logics devised over the last fifty years since G.H von Wright's pioneering paper of (1951). Since he thinks that there may well be logical relations between 'ought' and the modal operators – in particular, that it may well be a logical truth that OughtImplies-Can – he investigates the issue in the context of multi-modal 'alethic-deontic' logics. For although Schurz disputes my understanding of the No-Ought-From-Is principle, he does believe that Hume's famous passage expresses a profound truth, a truth that he proves (with a few reservations and restrictions) for a wide range of alethic-deontic logics. This is what he calls the Generalized Hume Thesis (or GH, for short). If 'ought' is a logical constant then it can appear non-vacuously in the conclusion of a valid inference even if it does not appear in the premises. After all, most logics contain theorems as the standard deontic logics definitely do and the theorems of a deontic logic follow from any set of propositions whatsoever, including the empty set. Thus in most deontic logics we have K ⊩D ~(OA & ÕA) for any set of premises K including the set that contains nothing at all. And it is clear that the 'oughts' in this inference cannot be replaced by any grammatical equivalents salva validitate i.e. without prejudice to the validity of the inference. (For example, if we replaced the 'O' operators in the conclusion with the '◇' of possibility we would arrive at an alethic falsehood.) Nevertheless the No-Ought-From-Is thesis can be saved but in an amended form. The basic idea is that no substantial 'oughts' - 'oughts' enjoining some duties as opposed to others – can be derived from ought-free premises. The idea, perhaps, goes back to Prior's Christchurch colleague, J.M. Shorter, who pointed out that the 'oughts' in Prior's counterexample are all 'subject to a certain futility' – 'they are quite useless for anyone who wants to decide what concrete action he ought to perform' (See Shorter, Essay 1.2, this volume). The problem with Shorter's response is that he had no proof that all the counterexamples to No-Ought-From-Is would be futile in this sense. Well, Schurz has supplied such a proof. I cannot in a short paper or even in a long one – do justice to the logical ingenuity required to establish this thesis across such a wide range of logics. But I can explain what the Generalized Hume Thesis amounts to. Suppose you have a mixed conclusion X following from a (possibly empty) set of ought-free premises K. Then the conclusion will be ought-irrelevant in a certain sense. That is, it will be possible to 226 uniformly replace all the n-place predicates within the scope of the ought-operators with any n-placed predicates whatsoever, including more complex predicates. (It is convenient in this context to regard propositional variables as zero-place predicates.) Suppose, for example, that from a consistent set of ought-free premises it were possible to derive the following sentence (in fact, of course, it isn't): If it is necessary that power corrupts, then we ought to eschew power. If this sentence did indeed follow from a consistent set of ought-free premises, then the following sentence would also follow: If it is necessary that power corrupts, then we ought NOT to eschew power. Thus no substantial ought, no ought which tells anyone to perform a particular action as opposed (for instance) to its opposite can be derived from ought-free premises. Instead of Hume's No-Ought-From-Is or my No-Non-Vacuous-Ought-From-Is, we have No-OughtRelevant-Ought-From-Is. Deontic logic cannot get you from non-moral premises to a substantive moral conclusion. (It is 'utterly impotent in this particular'.) It is not the 'oughts' themselves, the ought-operators occurring in the conclusion of such an inference that are replaceable salva validitate. Rather, it is the predicates occurring in the scope of those operators that are replaceable. (This, if you like, is the difference between GH on the Austrian Plan and GH on the New Zealand Plan. I think that the ought-operators should be treated as schematic and therefore that they are replaceable salva validitate in the conclusion of a valid Is-Ought inference. For Schurz the ought-operators themselves are logical symbols, and therefore not repaceable salva validitate, and it is the predicates governed by the ought-operators that can be replaced by random grammatical equivalents.) The Generalized Hume Thesis (GH) only holds in those alethic-deontic logics which do not include Bridge Principles. A Bridge Principle is a thesis that includes at least one schematic letter which appears both inside and outside the scope of a deontic operator. One of the most plausible examples of such a principle is Ought-Implies-Can: OA ⊃ ♢A 227 Now, it looks as if admitting such principles would open the floodgates to Is/Ought inferences. But Schurz has another interesting result. The most plausible BPs those which bid fair to being a) truths and b) truths of logic are Ought-Implies-Can and the Must-Ought principle, □A ⊃ OA, which is equivalent in 'normal' alethic-deontic logics to the Necessary Means-Ends principle, □(A ⊃ B) ⊃ (OA ⊃ OB). It turns out that if we add these principles to the aletheic-deontic mix, all the Is-Ought inferences that are thereby licensed are practically trivial in a certain sense. If you can infer a conclusion containing a clause OA from ought-free premises then you can also infer a corresponding conclusion containing the clause A. This means that you can only infer that under certain circumstances something ought to be the case if you can also infer that under those circumstances it is the case. Thus even with these Bridge Principles a version of Hume's thesis can still be demonstrated, namely No-Non-Practically-Trivial-Ought-from-Is. 8. Meta-ethical Worries Now, a proof is a proof is a proof. So naturally I don't deny any of this. That is I don't deny that if 'ought' is treated a) like a sentential operator and b) like a logical symbol, then you can get a non-vacuous ought from an is. And I certainly don't deny indeed I rejoice in the fact that even so, it can still be demonstrated that you can't get an ought-relevant ought from an is. So what exactly is my complaint? First of all I don't believe in deontic logic. It's leading principles are false, bordering on the nonsensical and even when they are true, they don't seem to me analytic. With the possible exception of universalizability, I don't believe that there are any non-trivial principles peculiar to and pervasive of all moral or deontic reasoning. As the young Prior put it 'the "logic of ethics" is not a special kind of logic, nor a special branch of logic but an application of it'. Deontic logic comes from disregarding this dictum and in my view it is a mistake. However, I shall reserve this polemic for the final section. For now I want to concentrate on the meta-ethical issues. For in my opinion the Austrian Plan is bad news for he kind of meta-ethic that I believe in. Let me declare my interest. I am both a descriptivist and an error theorist. I think moral judgments are truth-apt and that the truth they are apt for is a full-blooded affair not the namby-pamby minimalist property beloved by Horwich (1998) and Blackburn.(1993). I am thus a foe to non-cognitivism even in its latter-day expressivist variant. But I think that all moral judgments are false, or at least that all non-negative atomic moral judgments are 228 false (see Pigden 2007a). In this I am at one with John Mackie (1977) and Richard Joyce (2001). Thus I am also a foe to moral realism, the thesis that there are honest–to-goodness moral truths. Suppose we concede that 'ought' is a logical symbol and that No-Ought-From-Is, in so far as it is true, is not a truth of general logic, not an instance of the conservativeness of logic, but a truth that holds in virtue of special features of the deontic concepts. What are the consequences for meta-ethics? What does this tell us or what does this suggest about the nature and status of moral judgments? Well, the thesis that 'ought' is a logical symbol knocks out certain kinds of non-cognitivism those extreme forms of emotivism that deny the possibility of genuine moral reasoning for instance. Thus Stevenson, and maybe Ayer, should definitely resist Schurz.. But more sophisticated non-cognitivists those that don't deny the possibility of logical connections between moral judgments can afford to rest easy. Indeed, my chief beef with Schurz's twin theses is that they may afford an argument for noncognitivism. However, the argument, if it can be constructed, will be abductive not deductive, and at first sight, the twin theses would appear to be compatible with all the major forms of descriptivism including the error theory. Whether the truthmakers for moral claims are natural, non-natural or non-existent, there can still be 'logical' truths holding in virtue of the meaning of the word 'ought'. An analogous situation holds with respect to the Peano Axioms so long as these are given an if-thenist reading. ('If there are numbers, then Zero is a number', etc.) Whether numbers are natural (as the Aussie Aristotelians like Armstrong (1997) and Bigelow (1988) believe), non-natural (as the Platonists believe), or non-existent (as Field (1989) believes), it can still be the case that if there are numbers, the successor of any number is a number etc. But just as the mathematical anti-realist cannot concede the categorical claim that zero is a number (since it implies the existence of zero), so there are some 'logical' principles that the moral anti-realist cannot concede. For whether Schurz's first thesis (that 'ought' should be treated is a logical constant) is incompatible with the errortheory depends upon the alleged principles governing the ought-operator. Most deontic logics include the following rule ⊢A ⇒ ⊢OA (from A is a theorem, infer that it is obligatory that A is a theorem'). It is thus a bizarre feature of the standard deontic logics not only that the well-known theorems of propositional logic are obligatory, but that the far more dubious theorems of deontic logic are obligatory 229 too. This is much more of a problem for the error theory than non-cognitivism. 'Hurrah for ~(A & ~A)!' or 'Let ~(A & ~A) be the case!' are admittedly strange things to say (after all, what choice do we have?), but most of us, I suppose, would be prepared to raise a cheer for the truths of logic so long as we believed them to be truths. But however much he applauds the truths of logic, an error theorist can't say that they are obligatory since he does not believe that there is such a thing as being obligatory for the truths of logic to be. Nor do obligatory truths of logic sit well with some of the leading brands of naturalism. Would a suitably qualified observer feel a pleasing sentiment of approbation for ~(A & ~A)? Is it in accordance with a virtuous character to make it the case that ~(A & ~A)? I don't think so! To my mind, this illustrates the pitfalls of treating words like 'ought' as logical symbols in the first place. There is always a risk of smuggling in substantial indeed false or nonsensical assumptions by excluding as impermissible interpretations in which those assumptions are false. (In a logic L, K ⊩L X, iff there is no permissible interpretation of K ∪{X} such that K is true and X false. Thus the tighter the semantics the fewer the permissible interpretations the looser the consequence relation and the more dubious stuff you are entitled to infer.) The upshot of all this is that Schurz's first thesis – that 'ought' should be regarded as a logical operator is only consistent with the error theory if the principles governing the ought-operator do not allow us to infer that theorems are obligatory. But it is only with this restriction that the thesis is at all plausible. What about No-Ought-Relevant-Ought-From-Is? No-Ought-Relevant-Ought-FromIs, like No-Non-Vacuous-Ought-From-Is, is quite compatible with naturalism, since naturalism, whether ontological or semantic, does not imply that you can logically derive an ought from an is, even if logic is extended so as to include the dubious principles beloved by deontic logicians. And of course, nobody supposes that any kind of No-Ought-From-Is is incompatible with either non-naturalism or the error theory. But the idea that No-Ought-From-Is, in so for as it is true, rests upon special features of the moral concepts – even if they are features shared by many other more-or-less modal sentential operators might afford an abductive argument for non-cognitivism. So although Schurz's verion of No-Ought-From-Is is compatible with the major brands of descriptivism, this thesis does tend to call them into question. Remember the inference to the best explanation discussed above? The idea was that the best explanation of the fact that you can't get an ought from an is was a) that logic is conservative and b) that since moral judgments are non-cognitive, moral words are fundamentally unlike natural words. Since this is the best explanation of an established fact, it is probably true, in which case, moral 230 judgments are non-cognitive. This argument failed because there was a better explanation of No-Ought-from-Is available, namely the conservativeness of logic. But if 'Ought' should be treated as a logical operator, that 'better' explanation is no longer available. For deontic logic is not conservative with respect to 'ought' since you can get a non-vacuous ought from an is. However, the first (non-cognitivist) explanation is not available either since that two relied on the notion that logic is conservative with respect to 'ought'. Why is it then that you can't get an ought-relevant ought from an is? What feature common to such a vast range of logics explains this singular fact? Now I am not so much sleeping with the enemy as working for the enemy here, so I can't be expected to give of my best. But it seems to me that the explanation should go something like this. In deontic logic, the value of OA at a world α is not determined by the characteristics of α itself, but by the characteristics of the worlds which are 'ideal' with respect to α. It is for this basic reason that no ought-free but contingent description of a set of worlds K can imply that A as opposed to ~A ought to be with respect to those worlds. For an ought-free set of propositions K can only imply an ought-involving proposition X, if given the truth of K, X would hold whatever worlds were ideal with respect to the K worlds. Now if this is even roughly right, then this feature too needs to be explained. That is, we need to explain why it is that in all the plausible deontic logics the value of OA at a world α is determined not by that nature of that world but by the worlds which are ideal with respect to it. And the best explanation might be that the function of moral judgments is not to say how things are but to prescribe how they are desired to be. Philosophers hitherto have attempted to interpret the world in various ways. The point of moral judgments however is to change it. Thus if we accept that 'ought' is a logical word and with it Schurz's conception of No-Ought-From-Is, this paves the way for a two-tiered inference-to-the-best-explanation for some kind of non-cognitivism. And for an error–theorist like me, that is ample reason to dislike it. To dislike it, yes, but not to reject it. After all, non-cognitivism might be true and the error theory false. To defend descriptivism (including my heretical nihilist variant), I need to show that deontic logics are no logics since their leading theorems are not analytic. This won't falsify No-Ought-Relevant-Ought-From-Is, of course, but it will reduce it to metaethical irrelevance. It will be an interesting fact about moralities with certain structural features that you can't get an ought-relvant ought from an is. But since those structural features will be optional for systems of moral thought, this won't tell you anything about the nature of morality 231 9. Smooth Operator But before I get on to this, there is something I need to clear up. I said earlier on that my edifice of meta-ethical argument rests on two provisos a) that 'ought' should be construed as a predicate and b) that 'ought' is not a logical constant (or a logical symbol). This was what Schurz thought when he criticized my (1989) paper in The Is-Ought Problem (1997). But as he now realizes (after a cozy chat at Erfurt) this is a mistake. Though I do require proviso b) I can afford to relax proviso a). The fact is that I am not sure whether 'ought' is a predicate or a sentential operator. But so long as it is not a logical constant, my argument works either way. Of course if 'ought' is a non-logical sentential operator, it cannot be accommodated within the predicate calculus. For predicate logic is officially blind to anything which occurs within the scope of a non-logical sentential operator. (It is not officially blind to everything that occurs within the scope of a logical sentential operator since the negation sign is precisely that.) The solution is an operator logic of the kind devised by Steven T. Kuhn (1981). In that logic there is room for sentential operators like the 'O' and the 'P' of deontic logic or the modal operators, '□' and '◇'. However, these are not treated as logical expressions but as schematic variables. That is, when it comes to determining logical consequence, their interpretations are allowed to vary. (Thus we have a loose semantics and a tight consequence-relation.) What we would normally think of as modal or deontic logics can be formulated as theories within the topic-neutral framework of operator logic. What used to be theorems within a logic reappear as theses within a theory. If, in a modal logic, M, X is a consequence of K, in the topic-neutral operator logic O, X is a consequence of K plus the axioms of M. The impulse behind operator logic is a motive of candor. The operator logician feels that the dubious principles of a modal or deontic logic should not be buried in the logical machinery or allowed to determine a consequence relation by ruling out certain interpretations as impermissible, but should be stated upfront as premises. Now as Schurz notes, in Kuhn's operator logic, the uniform substitution theorem holds. Which means that no (non-logical) sentential operator can appear non-vacuously in the conclusion of a valid inference, unless it appears in the premises. So if 'ought' is such an operator, we have no non-vacuous ought from is. Indeed, this continues to hold even if the operator logic is augmented with some very minimal modal principles. But there is another point worth noting. Lloyd Humberstone has proved that in any logic subject to a compositional semantics, no expression which is s-schematic for the logic 232 in question (that is no expression that is not a logical symbol) can appear non-vacuously in the conclusion of a valid inference unless it appears in the premises (Pigden 1989, pp. 144145, Humberstone 1985). Thus whatever the grammatical category of 'ought' even if it belongs to a category as yet undreamt of so long as it is not a logical expression, we have No-Non-Vacuous-Ought-From-Is Thus the dispute between Schurz and myself turns on a point of philosophic principle. Is 'ought' a logical expression and are any of the deontic logics genuine logics? If it is, then my version of No-Ought-From-Is is false. (Which also means that No-Ought-From-Is is not a truth of general logic.) If it is not, then Schurz's version of No-Ought-From-Is, though true, is relatively trivial since it simply represents a structural feature of some systems of moral thought. 10. Dissing Deontic Logic Now obviously I don't have the space for a detailed demolition job on deontic logic. So I shall confine myself to criticizing some of the chief theorems of the leading systems. But I pick my targets carefully. The theorems in question are of crucial importance (they often appear as axioms) and if they are deleted (and deleted for good so that they can't be rederived from other theorems!) then the logics in question will be in tatters. Remember that although I believe some deontic theorems to be false, the key point is that they are not analytically true. To prove that a principle is not analytic you don't need a true counterexample, but only a conceivable one. Thus you may think that in the true system of morals (whatever that may be) there are no tragic dilemmas, no situations from which you cannot escape without wrong-doing. But so long as such situations are conceivable then a logic which excludes them cannot be analytically true. And a logic whose principles are not analytically true is not a true logic. Many deontic logics include the principle ~(OA & ÕA) (It is not the case that it ought to be the case that A and it ought to be the case that not-A), . But counterexample Orestes was obliged to kill Clytemnestra (because she had murdered his father) and obliged not to kill her (since she was his mother). (Aeschylus, 1953, Oresteia pp. 124131.) Many deontic logics include the principle 233 OA ⊃ PA (If A is obligatory then A is permitted). But counterexample Orestes was obliged to kill Clytemnestra (because she had murdered his father) but not permitted to kill her (which is why he was pursued by the furies). ). (Aeschylus, 1953, Oresteia pp. 124131.) Some deontic logics (minimal deontic logics) allow for the possibility of tragic situations they are not excluded by the logic but include the following theorem: (OA & ÕA) ⊃ OB (If A is obligatory and not-A is obligatory then anything whatsoever is obligatory.) But counterexample Orestes was obliged to kill Clytemnestra (because she had murdered his father) and obliged not to kill her (since she was his mother) but he wasn't obliged to kill Electra, even though she was his accomplice. Nor was he obliged to tap-dance his way through Mycenae singing sea-shanties. I have already complained about the fact that in most deontic logics tautologies are obligatory, a claim which, to my mind, borders on the nonsensical. Some deontic logicians have the grace to be embarrassed about this, and in Chellas's logic D, it is not a feature (Chellas 1980, ch. 6). But even in his logic, it turns out that if anything whatever is obligatory, the tautologies are too. Which means that only the error theory can save him from deontic absurdity. Though I don't believe in obligations, it seems to me ridiculous to suppose that it is analytic that if anybody ought to do anything, the tautologies ought to be. This diatribe so far would meet with the approval of paraconsistent logicians. Indeed, it is derived, in part from the polemics of Routley and Plumwood (1984). But even they require the following principle (K) sometimes known as agglomeration if their deontic logic is to be of any interest: (OA & OB) → O(A & B) (If A is obligatory and B is obligatory, then it is obligatory that A and B. I use the arrow rather than the horseshoe because the conditional operator in the Routley/Plumwood system is non-classical.) This seems to me false as the following counterexample shows. I assume Ought-Implies-Can, although it is not analytic since it is rejected in some systems of ethics 234 such as those of Luther and Calvin (Pigden, 1990). Nevertheless, it is certainly a conceivable and even a plausible principle. I ought to be (and can be) a better father. I could devote more time and attention to my children and it would be a good thing if I did. I ought to be (and can be) a better husband. I could devote more time and attention to my wife and it would be a good thing if I did. I ought to be (and can be) a better philosopher. I don't always do justice to my talents and am easily distracted. I should stick to my schedule of reading one article on meta-ethics every day. I ought to be (and can be) a better teacher. I should devote more brain space to attending to my students and remembering their names rather than going around in a philosophic daze. I ought to be (and can be) a better member of my Party. I believe in the cause and there is no denying that in the last few years I have been slacking off. I ought to be (and can be) a better runner, walker and swimmer and weight-lifter. I am much too inclined to stay up late and lie in bed in the mornings not doing my exercises. I ought to be (and can be) a better graphic artist. I'm certainly no genius, but I do have a respectable talent and I and I can hardly claim to have pushed that talent as far as far as it will go. And I ought to be (and can be) a better member of Amnesty International. Swimming the Dunedin Harbor once a year to raise funds is really not enough. But although these things are true, or at least plausible, what is not the case is that I ought to be a better father, a better husband, a better philosopher, a better teacher, a better athlete, a better party member, a better artist and a better member of Amnesty, for to do all that would be quite impossible, more than flesh and blood could stand. Hence the principle (K), otherwise known as agglomeration, is not analytic. In recent years, deontic logicians have become increasingly embarrassed by the contentious theorems and there is a tendency to meet this concern by discarding theorem after theorem and devising more and more minimal deontic logics1. These are steps in the right direction, but to my mind they don't go far enough. The real lesson to be learned from this sorry series of logical misadventures, is not that the deontic logics devised so far are insufficiently minimal, but that the whole enterprise is misconceived from the start. The reason that nobody so far has managed to discover a satisfactory deontic logic is a simple one – there is no such thing to be discovered. 11. The Triumph of Triviality or Vulgarity Run Rampant Whatever the grammatical category of 'ought' turns out to be, it is not a logical symbol since there are no significant structural principles peculiar to and pervasive of all systems of moral 235 thought. The leading theorems of deontic logic where they are not actually false are not analytically true. But if 'Ought' is not a logical word, then my variant of No-Ought-From-Is is demonstrable – you can't get a non-vacuous ought from an is. But this holds for the simple reason that no non-logical word of any kind can appear in the conclusion of a valid inference unless it appears in the premises. No Ought-From-Is is simply an instance of the conservativeness of logic, the thesis that in a valid inference you don't get out what you haven't put in. As such it can afford no support, whether abductive or deductive, either for non-cognitivism, or for any other meta-ethical theory. It is meta-ethically inert. Truisms acquire importance by being denied, but in the absence of such denials, Hume's thesis is true but trivial. The vulgar systems of meta-ethics, whichever they turn out to be, remain unsubverted. 236 NOTES 1. In a forthcoming paper in Nous, Lou Goble shows how very difficult it is to develop a 'Goldilocks' deontic logic which is neither too strong allowing us to derive arbitrary obligations from deontic dilemmas of the form (OA & ÕA) nor too weak failing to underwrite inferences of the form O(F v S), ÕF ⊩ OS but just right. (When you read his excellent paper you are reminded of a physician who prescribes a drug to deal with a disease, only to find the drug has undesirable side-effects. She prescribes another drug to counteract the side-effects only to find that the second drug either inhibits the therapeutic effects of the first drug or has side-effects of its own. So she prescribes a third drug ...) Goble comes up with a logic which though not quite just right is not as obviously too strong or too weak as many of its rivals. In a paper read at the Fourth World Conference on Paraconsistency in Melbourne in 2008, 'An Adaptive Logic for Normative Conflicts' Joke Meheus of Ghent argued that the only Goldilocks solution to the problems of deontic logic would be an adaptive, and therefore non-monotonic logic. Obviously my brand of No-Ought-From-Is would not hold for such a logic, but maybe Schurz's would.