Elijah Millgram

Copyright © 2017 Elijah Millgram.
All Rights Reserved.

Hume on Practical Reasoning (Treatise 463-469)*
By Elijah Millgram

From Iyyun 46, July 1997: 235-265. Electronic posting with the kind permission of the editor of Iyyun.

The claim that "'is' does not entail 'ought"' is so closely associated with Hume that it has been called 'Hume's Law'.1 The interpretation of the passage in Hume's Treatise of Human Nature that is the locus classicus of the claim is controversial. But the passage is preceded by three main bodies of argument, and, on the working assumption that the passage in question is closely connected to the argumentation that leads up to it, I will here examine the third of these, running from T 463:7 to 469:18.2

While interpretations have differed from one another, they have agreed in attributing to Hume uncharacteristically weak arguments.3 I propose to show that Hume's arguments are both stronger and more interesting than has been allowed. But -- I will argue -- they exploit and consequently depend upon a semantic theory that contemporary philosophers are no longer able to accept.

Hume must be assigned a good deal of the responsibility for making " 'is' does not entail 'ought' " part of philosophers' (and not just philosophers') commonsense. If I am right both about Hume's influence and about the presuppositions of his arguments, then the interest of these conclusions is not merely historical. Today Hume's Law is a philosophical near-truism, and the burden of proof is taken to rest squarely on the shoulders of its opponents. But if Hume's Law is inherited from Hume, and was originally accepted on the basis of arguments that we can no longer find acceptable, this may require a reassessment of just where the burden of proof may be presumed to lie.


It will be helpful to have a rough outline of Hume's semantic theory in front of us, and I will accordingly begin by summarizing it and indicating some of its consequences. If mental items (perceptions, in Hume's terminology) have contents, these must come from somewhere. Hume looks for their source and finds it in a surprisingly familiar place: to determine the content of a mental item, follow the causal chain it terminates back to its origin. "Ideas," says Hume, "always represent the objects or impressions from which they are deriv'd."4 An idea derives its content from the idea(s) or impression(s) that caused it, and impressions derive their contents (when they have any) from whatever caused them. Thus my idea of golden mountains is about golden mountains in virtue of being derived from ideas of gold and of mountains; and these are about gold and mountains because (let us suppose) at some time or other I have had impressions of gold and of mountains from which these ideas are derived. To be sure, causation itself is not enough: my mental entities are not about all the things that caused them. In modern theories, this difficulty is usually met by incantations of the phrase, "causal chain of the appropriate type"; Hume's way of addressing this problem -- determining that resemblance must be added to causation to transfer content -- has, at any rate, the merit of being more substantial than contemporary alternatives.5 We can label this part of his view the causal resemblance theory of mental content.6

At least part of the account I have just given should be familiar under the name 'the theory of ideas'. My description is intended to bring into focus the following point. The 'theory of ideas' is usually thought of as a doctrine in what we would today call philosophy of mind; and so the temptation is to blame aspects of Hume's views that are derived from it on an outmoded empirical psychology. But Hume's philosophical psychology is, like our own, hardly empirical at all. He does not discover what the contents of the mind are by, say, cutting open heads and looking. Rather, like contemporary philosophers of mind, he derives his theory of the mind from his theory of representation; just as contemporary philosophers, who take content to be borne by propositions, find the mind to be stocked with propositional attitudes, so Hume, who takes content to be borne by resemblance, finds the mind stocked with impressions and ideas. The explanatory account is semantic, not psychological: it is a view about how, and under what conditions, representation is possible.

The causal resemblance theory of content has two important consequences, corresponding, more or less, to the two conditions it imposes on representation. First, because we may not have examined the resemblance-preserving chain that is responsible for an idea having the content it does, we may be in error as to what the contents of our ideas are. (Hume accordingly devotes much of the Treatise to establishing what the contents of our ideas are in philosophically important cases.) An idea can be simple or complex. If complex, its content is determined by the way its structure relates simple ideas. If an idea is simple, its content is determined by the impressions and objects it derives from and resembles. It follows that one can establish the content of an idea by analyzing its structure, if it is complex, and by tracing the relevant chains of resemblance-preserving causation back to their origins. In doing so, one can discover what it really was that one was thinking about when one entertained and used an idea -- a surprising claim, since it might turn out that what one was actually thinking about was not at all what one took oneself to be thinking about.7 In the next section I will examine two instances of this use of the causal resemblance theory.

A second consequence of the theory is to be found in Hume's understanding of mathematical reasoning, i.e., deduction or demonstration.8 Hume's theory of content is, indirectly, a theory of what contents of thought are possible: if content is borne by resemblance, thoughts can have only those contents for which resemblance can be responsible. Contents must be, roughly, pictures of what they represent. ('Roughly', because we have other modalities of perception than the visual; we hear, taste, smell, and feel. So not all ideas are literally pictorial.) Because thought is the mental manipulation of contents, Hume's understanding of thinking in general, and deductive thinking in particular, is shaped and constrained by his pictorial theory of content, just as ours is presumably shaped and constrained by our propositional theory of content. That is, since in Hume's view all reasoning consists in the manipulation of ideas, which Hume tends to think of as something like mental pictures, deductive reasoning must be reconstructed as the manipulation of (roughly) mental pictures.9 The general shape of Hume's pictorial view of deductive arguments is nicely rendered by Harrison:10

two and two are four -- an a priori necessary truth, discoverable by reason -- can be known to be true by comparing our idea of, say, two spots and another idea of two spots, and seeing that they must be equal in number to our idea of four spots.11
We should bear in mind that in Hume's day the foremost deductive science was geometry, in which the reasoning was explicitly pictorial.12 And, of course, the deductive techniques codified by Frege were not available to show how propositionally oriented forms of deduction could be powerful tools of inference -- something the syllogistic was most definitely not. So Hume's thinking of deduction as something done with pictures was not nearly as far-fetched as it would be today. In sections 3-4 we will see how Hume's discussion of the view that morality might be a demonstrative science is controlled by his pictorial understanding of deductive argument.


The stated aim of the stretch of argument we are examining is to show that beliefs about what ought and ought not to be done -- about 'the boundaries of right and wrong' -- cannot be arrived at by reasoning. Later I will say a little about the role of this claim in Hume's larger argument. For now, we need only note that the considerations Hume allows himself in these arguments are not morality-specific, and so do not apply only to beliefs containing a 'moral ought'. (I will call the beliefs with which Hume is concerned 'deontic beliefs'; I mean the term to cover beliefs naturally expressed using a 'should' or an 'ought' whether or not they contain a 'moral ought'.)

The argumentation is organized by a familiar dilemma:13

If the thought and understanding were alone capable of fixing the boundaries of right and wrong, the character of virtuous and vicious either must lie in some relations of objects, or must be a matter of fact, which is discovered by our reasoning. (T 463)

The two tines of Hume's standard fork are subsidiary arguments to the effect that moral beliefs (or more generally, deontic beliefs, that is, judgments of what ought to be done) cannot be the conclusions of deductive reasoning (reasoning about relations of objects), and that they cannot be the conclusions of what we can call empirical or experimental reasoning (reasoning about matters of fact). I will treat the second tine first; it runs as follows:

Take any action allow'd to be vicious: Wilful murder, for instance. Examine it in all lights, and see if you can find that matter of fact, or real existence, which you call vice. In which-ever way you take it, you find only certain passions, motives, volitions and thoughts. There is no other matter of fact in the case. The vice entirely escapes you, as long as you consider the object. You can never find it, till you turn your reflexion into your own breast... (T 468f)

Now on a first reading, this argument should seem to beg the question. Why not say that you do perceive the vice?14 It seems unlikely that an opponent will agree that he does not perceive it in the imagined situation. To see why Hume thinks that this claim is legitimate we must bring to bear his semantic theory. If I judge some state of affairs to be virtuous or vicious, I must have an idea of vice or virtue. What is the content of this idea? Hume's way of addressing this question is to invoke what I am calling the causal resemblance theory of mental content.

There are similar applications of this technique elsewhere in the Treatise, and it will be useful to first consider one of these: Hume's treatment of necessity is suitably explicit. He asks:

What is our idea of necessity, when we say that two objects are necessarily connected together. (T 155, italics Hume's)
We make judgments to the effect that two objects are, or are not, necessarily connected. What is the content of the idea of necessary connection? Hume turns to the causal chain of ideas and impressions from which the idea in question is derived:
Upon this head I repeat what I have often had occasion to observe, that as we have no idea, that is not deriv'd from an impression, we must find some impression, that gives rise to this idea of necessity, if we assert we have really such an idea. (T 155)
Hume considers the two objects that we might have thought were the other end of the causal chain, and concludes that the impression of necessary connection is not derived from them. One reason for this may be a picture of the physical mechanisms that mediate sensation and the information they are able to convey; light carries information about the colors and (perhaps) the spatial dispositions of objects, but not about necessitation.15 Hume also has a further argument. The derivation must not be merely causal: the derived idea or impression must resemble its cause. So we need to examine the putative cause to see whether we can find an aspect of it that resembles the idea under consideration. Hume says:
I turn my eye to two objects suppos'd to be plac'd in that relation; and examine them in all the situations, of which they are susceptible.
He immediately discovers the spatial relation of contiguity and the temporal relation of succession, both of which have their correlates in his ideas; but no feature resembling the full force of necessary connection is apparent in the objects, since a similar-looking pair of objects could prove to be only coincidentally connected.16 So the objects cannot be the source of the entire content of the idea.

The content of the idea of necessary connection must derive from something in the circumstances in which the judgment of necessary connection is made: if not from an external impression, then from an internal one.17 Examining the surrounding circumstances reveals that the repeated observation found to give rise to such judgments

produces a new impression, and by that means the idea, which I at present examine. For after a frequent repetition, I find, that upon the appearance of one of the objects, the mind is determin'd by custom to consider its usual attendant, and to consider it in a stronger light upon account of its relation to the first object. 'Tis this impression, then, or determination, which affords me the idea of necessity. (T 155f)

Tho' the several resembling instances, which give rise to the idea of power, have no influence on each other, and can never produce any new quality in the object, which can be the model of that idea, yet the observation of this resemblance produces a new impression in the mind, which is its real model.18

Notice the role played by resemblance in this account -- over and above that of the resemblance between instances of causally interacting objects that Hume mentions in the just-quoted passage. While the mental impression from which our ideas of causation are derived is itself caused by the objects we naively take the idea to be about, semantic content is only transferred between resembling links of the causal chain. The impression of determination does not resemble the external objects, so, even though it is caused by them, it does not derive its content from them; consequently, the impression of determination terminates the semantic chain. In short, applying Hume's semantic views shows the content of our idea of necessity to be (in part) derived from an impression of reflexion rather than the 'necessarily connected' objects themselves. It follows from this that necessary connection is not any matter of fact about the objects, and so that empirical reasoning about the objects will not establish their necessary connection.

The reasoning is similar, albeit more terse, in Hume's discussion of the case of wilful murder. We make moral judgments, such as those regarding virtue and vice.19 What are the contents of the ideas involved in those judgments? The content of an idea (of, say, vice) must be derived, directly or indirectly, from some impression. Can this content be derived from impressions of vicious events? On considering a vicious event (wilful murder), Hume decides that it cannot. As in the argument about necessary connection, Hume's view is probably shaped in part by a conception of the mechanisms involved in sensation: sound and light convey information about, for example, color, but not, at any rate in the same way, about vice.20 More importantly, a derived idea must resemble its cause. What, in the murder, resembles the idea of vice, with its felt repugnance, motivating power and disapproval? Quite evidently, nothing. But when "you turn your reflexion into your own breast, [you] find a sentiment of disapprobation, which arises in you, towards this action" (T 468f). This sentiment does possess the requisite felt qualities, and must therefore be the source of the idea's content. Notice again the role played by resemblance in terminating the causal chain with the "sentiment of disapprobation" rather than with the non-resembling event acknowledged to have caused the sentiment. The murder causes the sentiment, but since the sentiment doesn't resemble the murder, the sentiment doesn't derive its content from the murder; and consequently ideas that derive their content from the sentiment cannot be thereby deriving their content from the murder itself.

The conclusion is

that when you pronounce any action or character to be vicious, you mean nothing, but that from the constitution of your nature you have a feeling or sentiment of blame from the contemplation of it.21
Since vice is not a matter of fact about the 'vicious' object, you cannot establish that an object is vicious by experimental reasoning about the object. But viciousness, recall, was just an example of a moral (or deontic) fact. Generalizing, the conclusion of the argument is that moral (or deontic) facts cannot be established by experimental reasoning that is solely about the objects that are the putative subject-matter of those facts.

Now we might wish to resist Hume's analysis on the grounds that the 'sentiment of disapprobation' cannot possibly capture the full force of the idea of vice. (In what way, we might ask, does disapprobation resemble vice?) It is clear enough what Hume thinks the feeling supplies: if part of the idea of vice is that it is (something like) repulsive, that can be accounted for by appealing to an actual feeling of revulsion.22 The problem here is that if 'disapprobation' is something on the order of a feeling of revulsion in the pit of one's stomach, it will not have the richness needed to reconstruct the cognitive role of the idea of vice; but if, on the other hand, it is sufficiently complex -- if it is disapprobation -- then it will have too much cognitive content to be construed as derived from an impression of reflection, that is, from something on the order of a feeling of revulsion in the pit of one's stomach. These problems are a good place to dig in one's heels; however, for our present exegetical purposes, we need only consider whether they should give rise to second thoughts about our reconstruction of Hume's argument. And here parity considerations settle the issue. It is just as implausible that a feeling of determination could account for whatever content the idea of necessity has over and above constant conjunction. (How does a feeling of determination -- perhaps something, as James might have thought, like a tension in the upper chest -- resemble necessity?) But Hume's treatment of necessity is given at much greater length, and it is clear that he accepts just this analysis. So we should not be surprised that he accepts a similar analysis in the case of vice as well.


We've just finished reconstructing one horn of a dilemma. If moral or deontic beliefs can be arrived at by reasoning, they must be arrived at either by experimental reasoning or by deductive reasoning. We have seen Hume's argument that they cannot be arrived at by experimental reasoning. Hume presents two further arguments to the effect that they cannot be arrived at deductively, or, in his language, cannot consist in 'relations of objects'. These arguments are intertwined in the text, and commentators often fail to distinguish between them.

The first argument in the anti-deductivist horn of Hume's dilemma aims at showing that the relations of objects that a moral or deontic fact would consist in cannot even be specified. (If they cannot be specified, "thought and understanding" cannot be "alone capable of fixing [their] boundaries" (463).) Since much of this argument has been adequately discussed, I will, in surveying those parts of it that have, provide just enough detail to frame the part that has not. Hume first points out that these relations have never actually been specified (T 463:25ff); this fact puts the burden of proof squarely on the shoulders of his opponent. (Hume remarks, " '[t]is impossible to refute a system, which has never yet been explain'd" (T 464:15f).) Moreover, he insists that the relations in which deontic facts allegedly consist must be specified in terms of the four relations of "[r]esemblance, contrariety, degrees in quality, and proportions in quantity and number" (T 464:4f, italics deleted); and it is (he will argue in a moment) very unlikely that deontic facts could be specified using only these relations. This restriction is not as question-begging as it might sound.23 First, Hume claims, no one has ever proposed any other relation to play this role (T 464:10-15). And second, recall that these relations are supposed to play a role in deductions or demonstrations, and that Hume's understanding of deduction is pictorial. Since deductive reasoning is to be reconstructed as the manipulation of mental pictures, the relations in question must be the kind of relations that can be used in a deduction, pictorially conducted: that is, in a deduction that proceeds in roughly the manner of the proofs of Euclidean geometry. This explains why it is reasonable to restrict the allowable relations to the four Hume mentions; and even if he has overlooked one or two, it is implausible that relations relevantly similar to these could suffice to specify the moral or deontic facts.

Hume supports the implausibility claim with an argument.

As moral good and evil belong only to the actions of the mind, and are deriv'd from our situation with regard to external objects, the relations, from which these moral distinctions arise, must lie only betwixt internal actions, and external objects... (T 464:21-465:1).24
But it is very unlikely that the allowable relations will suffice to rule in all the situations of moral import while ruling out those to which morality is irrelevant. Hume supports the point with a well-known illustration:
To put the affair, therefore, to this trial, let us chuse any inanimate object, such as an oak or elm; and let us suppose, that by the dropping of its seed, it produces a sapling below it, which springing up by degrees, at last overtops and destroys the parent tree: I ask, if in this instance there be wanting any relation, which is discoverable in parricide or ingratitude? (T 467:2-8)
There are obvious differences between oaks and persons, and between their respective relations; but the problem is to capture these differences in terms of the allowable relations, those that could plausibly play a role in pictorially executed deductions. Hume is quite right to think that it is unlikely that they can be captured in this way; once again, if Hume's opponent claims that moral (or more generally, deontic) facts can be specified in terms of relations of ideas, the burden of proof is squarely on him.

But burden of proof arguments, no matter how plausible, are not decisive. After all, perhaps some very complicated, not at all obvious way of combining relations of the allowable kinds will allow one to distinguish situations in which morality has a purchase from those in which it does not. Hume accordingly concludes his argument against the specifiability of the moral relations with a circularity argument that "deserves to be weigh'd, as being, in [his] opinion, entirely decisive" (T 468:19f). The circularity argument, running from T 467:24 to 468:20, purports to show that it is not merely unlikely that the requisite specifications be produced: it is in fact impossible.

The circularity argument invokes a further fact (presented as an opponent's objection) about what such a specification would have to express. We know what the relevant difference is between inanimate objects, plants and animals, on the one hand, and persons, on the other: people (should) know better:

I would fain ask any one, why incest in the human species is criminal, and why the very same action, and the same relations in animals have not the smallest moral turpitude and deformity? ... this action is innocent in animals, because they have not reason sufficient to discover its turpitude; but... man, being endow'd with that faculty, which ought to restrain him to his duty, the same action instantly becomes criminal to him... (T 467:24-32)

Hume's reply is that

this is evidently arguing in a circle. For before reason can perceive this turpitude, the turpitude must exist; and consequently is independent of the decisions of our reason, and is their object more properly than their effect. (467:33-36)
Hume's appeal to circularity here should be puzzling. The problem, it will be recalled, is to specify the relevant moral features of situations in a way that allows of moral demonstrations or deductions; Hume, then, is claiming that such a specification cannot be given because it would be circular. But not all circularity is vicious. It is true enough that circularity of a kind may be found here: on the proposed view, a moral fact holds of a situation if and only if certain 'relations of objects' can be found in the situation; one (not the only one) of these must be an awareness (or the capability of having an awareness) of those relations obtaining.

But why is this any worse than than circularities like these? An individual is a member of The Rule Club only if he knows the rules of the club, and these rules contain clauses stating that they apply only to members. One might feel proud of, among other things, one's appropriate pride in oneself; and one might even believe that one is not worthy of pride if one does not esteem oneself properly. Again, perhaps part of being intelligent is recognizing that, and how, one is. There is nothing wrong with these circularities; what then is wrong with the similarly circular specification of vice?25 To the best of my knowledge, this difficulty has been entirely overlooked by Hume's commentators.

Now in more recent times, philosophical resistance to seemingly innocuous circularity has been motivated by features of the technical apparatus used to reconstruct representation and reasoning. (I have in mind uses of the theory of types; of course, the circularity that motivated the theory of types was not itself innocuous.) The possibility of analogy suggests that to explain Hume's circularity argument, it may be once again helpful to turn to his semantic views. What requirements, we should ask, do these views impose on the reconstruction of the distinction between persons (who are aware of the morality-relevant relations in their situations) and animals (who are not)?

Content is, on Hume's view, a matter of (causally controlled) pictorial resemblance. For a person to be aware of the relations of objects that make, say, a certain moral response appropriate is for that person's mind to contain an idea of those relations: that is, for there to be in his mind an idea that pictorially resembles those relations (and is causally connected to them in the appropriate way). Very crudely expressed, being aware of the relevant relations of objects involves, among other things, having a picture of those relations in your head.26

But what must this picture look like? One of the facts it must picture is that you are (or could be27 ) aware of the relevant relations: this is, Hume points out, what is acknowledged to be the relevant difference between persons and animals or trees. So the picture must picture the fact that you (could) have a picture in your head; and not just any picture, but that very picture itself. Now content is, to reiterate, a matter of pictorial resemblance; to picture the fact that you have this very picture in your head, the picture must contain itself. And of course the smaller, contained picture (since it is identical to the larger, containing picture) must contain within itself a still smaller copy of itself, and so on, ad infinitum -- much like those pictures on the labels of cans that show the can itself, with a picture of the can on the label, that shows a still smaller picture of the can... In short, on Hume's semantic views, the circularity turns out to involve a infinite regress within the representation of the putative moral fact.28 (Of course, one need not crudely think of ideas as literally in the head; and, recall, not all ideas are visual. But the regress remains when these expository conveniences are left behind.)

Still, just as not all circularity is vicious, not all regresses are vicious either. Why is Hume unable to find this one acceptable? We are going to have to speculate, since Hume does not explicitly discuss the matter; but there are two considerations that come to mind. The first is simply that such a representation is not well-suited to be an element of a pictorially-understood deduction. The second, which would be in Hume's view decisive, has to do with what we could call the possible granularity of a mental representation. Hume devotes Part II of Book I of the Treatise to arguing that our ideas of space and time are not infinitely divisible. Without reviewing Hume's arguments on this point, we can say that Hume's view was that infinitely nested representations of the kind we are considering are just not possible, since nesting of this kind would require a kind of infinitely fine detail that our ideas cannot have. Hume took this position very seriously; this is indicated by both the length and location of his treatment, which suggest that Hume saw it as central to his account, and by the fact that, on the basis of this claim, Hume was willing to adopt the extremely counterintuitive position that Euclidean geometry is only approximately true.29

Recall our current location in Hume's move tree. The task of the second horn of the dilemma is to show that deontic facts are not demonstrable -- that morality cannot be thought of as a mathematical science. (It is interesting to see how much more time Hume commits to this horn of the dilemma than to the other, empirical, horn; we can get some comparative sense from this of how live the two options were felt to be in Hume's day.) We have just seen his first argument (or rather, a short series of connected arguments) for that conclusion; its (or their) point was that the premises from which a moral demonstration would proceed cannot be specified, and that the proofs that the mathematical moralist hopes for cannot be so much as begun. This argument has been seen to turn on Hume's pictorial understanding of representational content. On the one hand, the argument is much tighter than commentators have taken it to be; on the other, once we see how it works, it becomes clear that this is not an argument that can be appropriated by a contemporary moral philosopher.


The horn of the dilemma which argues against the deducibility of deontic beliefs contains a second argument (T 465:17-466:11, 15-18), which commentators have given particularly bad treatment. Some have simply ignored it, some have mistaken it for a part of the previous argument (easy to do because they share an illustration), and most have taken it to be a hopeless argument for a plausible conclusion.30

The argument runs as follows:

According to the principles of those who maintain an abstract rational difference betwixt moral good and evil, and a natural fitness and unfitness of things, 'tis not only suppos'd, that these relations, being eternal and immutable, are the same, when considered by every rational creature, but their effects are also suppos'd to be necessarily the same... (T 465:18-24)
'Tis one thing to know virtue, and another to conform the will to it... even in human nature no relation can ever alone produce any action; besides this... it has been shown... that there is no connexion of cause and effect... of which we can pretend to have any security by the simple consideration of the objects... we cannot prove a priori, that these relations, if they really existed and were perceiv'd, would be universally forcible and obligatory. (T 465:27-29; 466:1-7, 15-18)

The large structure of the argument is clear: it is a Modus Tollens with two premises:

  1. If moral conclusions can be derived through reasoning about relations of ideas or objects, then "their effects are... necessarily the same."
  2. The effects are not necessarily the same.
Leaving open for the moment just what these moral conclusions are, just what these effects are, and what they are effects of, note that from these premises it will follow that moral conclusions cannot be derived through reasoning about relations of ideas, or, as we might put it today, that morality is not a priori, or analytic, or conceptually true. The difficulty is that it is hard to see what Hume might mean by the premises so as to make them plausible, and the argument sound.

Now the first premise, that the effects (whatever they are) are necessarily the same, need not be Hume's, since the premise is introduced as how things stand "[a]ccording to the principles of those who maintain an abstract rational difference betwixt moral good and evil" (T 465:18-21). Interpreters have accordingly assumed that the argument is merely directed against actual opponents who did in fact accept (1). But this view has two difficulties. First, as we shall see, the argument would then be directed against straw men31 -- even if these particular straw men actually happened to exist. (We will see in a moment that it is not plausible to suppose that they did.) Second, it would fail to do the work required by Hume's larger argument. In order to show that morality is not established by a priori reasoning, it does not suffice to show that people who think it is, and who also happen to believe (1), are mistaken. We must, rather, construe Hume as arguing that anyone who believes that morality is established by a priori reasoning is committed to (1), and therefore is mistaken. Hume's own language supports this point: "[a]ccording to the principles of those... ," he says; not 'according to those... '.

Why anyone would believe (1) should seem obscure when one considers just what the necessarily following effects must be if the argument is to go through. Commentators who try to take (1) as explicitly acknowleged by Hume's opponents appeal to the following passage:

'Tis one thing to know virtue, and another to conform the will to it. In order, therefore, to prove that the measures of right and wrong are eternal laws, obligatory on every rational mind, 'tis not sufficient to show the relations upon which they are founded: We must also point out the connexion betwixt the relation and the will; and must prove that this connection is so necessary, that in every well-disposed mind, it must take place and have its influence... (T 465:27-35)
On the basis of this passage, the effects in question are taken to be motivational, i.e., to be an acknowledgement of the action's obligatoriness or an urge to perform the action.32 These effects are taken to be effects of doing the demonstrative reasoning. They are supposed to be effects of relations of ideas, in a very concrete sense: the ideas are the ideas of the agent, and their effects are the choices or intentions or motivations of the agent. But this construal is mistaken.

In order for the Modus Tollens to be valid, the effects in question must be not merely motivations, but actions, for (2) claims that actions are what do not necessarily follow: "no relation can ever alone produce any action."33 And this claim is supported not by any fact specific to human reason or motivation, but by appeal to general facts about causation. Now no-one should find it plausible that actions necessarily follow upon appreciation of an a priori demonstration that some action is right -- not even Hume's rational intuitionist opponents. Bluntly put, an agent may be hit over the head before he gets a chance to carry out the action. (Recall also that Hume's Christian opponents believed in the possibility of sin, which, on their view, involves knowing the right, but not acting on it.) In short, for the argument to be valid, the effects must be actions rather than just motivations; the principle of charity consequently requires that we refrain from identifying the effects of the 'relations' as motivations alone, even though it is implausible to attribute this view to Hume's opponents.

There is another reason for thinking that the effects in question should not be thought of as motivational, having to do with what I take the function of the arguments we have been examining to be. Hume is arguing against practical reasoning, against the notion that action can be correct or incorrect in the light of reason for or against it. He has already argued that neither the action, nor the passion that mediates the transition from theoretical conclusion to action, can be mistaken; consequently there is no room for describing such transitions as reasoning. This is (part of) the force of his earlier claim that reason is and ought only to be the slave of the passions.34 Now suppose that an opponent does not accept this claim, but insists that an agent's action can be rationally required by certain beliefs he holds.35 Hume can concede this without conceding that practical reasoning is possible. For even if holding a belief can rationally require action, there is still no room for practical reasoning unless the belief that compels action can itself be arrived at by reasoning. And the purpose of the body of argument that this paper is examining is to show that deontic beliefs cannot be arrived at by reasoning.

So the argument we're looking at has work to do in Hume's larger argument; and if I am right about its role, then this is the wrong place for taking the effects in question to be simply motivational. For Hume has already argued that reason does not motivate, and has also argued that because reason does not motivate, deontic beliefs cannot be arrived at by reasoning (T 457:6-458:18). It is now time for him to concede the possibility of motivating beliefs, if only for the sake of argument, and show that even if some beliefs did motivate, this would not show that there was such a thing as practical reasoning. These role-directed considerations favor construing Hume's argument as not depending on the claim that reason does not motivate. On the conventional interpretation, however, this is the force of (2).36

The effects, then, are not simply motivations, but actions. But if the effects are actions, we have to explain why the proponent of the view that relations of ideas ground morality is committed to the claim that the actions that follow upon particular relations of ideas must always be the same. To do this, we must return to Hume's semantic theories.

Recall that what the contents of deductively manipulated ideas are must be compatible with the causal resemblance theory. And restrictions on what these contents can be may constrain which deductive inferences are possible. Thus, for example, because Hume takes there to be a limit to the precision of one's mental pictures, he is willing to conclude that Euclidian geometry is only approximately true. His semantic analysis of the contents of geometrical ideas constrains the consequences of admittedly deductive argument.37

Now consider an alleged inference from relations of objects to (something like) the appropriateness of an action. We must picture, first, the relevant relations of objects, and, second, the appropriateness of a particular action. (Call these picture1 and picture2; we have already seen Hume's argument that you are not going to be able to render picture1.) Now how is picture2 to depict the appropriateness of an action? How would a picture of an action differ from a picture of an action's appropriateness? All the picture can do is depict the action's being done. Therefore, the content of the ensuing judgment must be, that the action is done. (This, of course, is Hume's opponents' problem; not Hume's. Hume can analyze appropriateness by adjoining to picture2 a non-representational feeling of (say) approval. This is because Hume is not committed to the feeling's being deduced from picture1. But his opponents do not have this option; only pictures can be deduced from pictures by comparison of ideas.)38

On Hume's general views about conceptual possibility and necessity, if picture2 is demonstrable or deducible from picture1, then what picture2 depicts is necessitated by what picture1 depicts.39 Since what picture2 will depict is an action, Hume's opponents, by virtue of their claim that morality is established deductively, are committed to the claim that action ensues necessarily on the occurrence of those relations of objects that make it appropriate. This makes Hume's response -- that there are no such necessary connections -- reasonable.

Recall Hume's unusual way of putting his standard fork, using the locution 'relations of objects' instead of 'relations of ideas'.40 The relations of objects are mirrored by the relations of ideas that represent those objects. Deductions proceed from initial relations of ideas to further relations of ideas; these latter relations of ideas, however, mirror relations of objects: if the initial relations of ideas correctly mirrored the objects they represent, then so do the latter. Therefore, if from a representation of a situation it were possible to deduce a representation of a certain action occurring in that situation, this would show that in such a situation, that action would, necessarily, occur. This feature of deduction is not specific to Hume's pictorial conception of it; the same holds for our propositional conception: if from a statement representing a given state of affairs it is possible to deduce a further statement that in that state of affairs some action will occur, this shows that in the actual state of affairs the action will, necessarily, occur.

Here's an illustration of the difficulty Hume takes his opponents' views to have. (I'm going to modify the one Hume gives; his illustrates both this argument and the one immediately preceding it, which makes it messy to untangle.) Consider what a deductive demonstration of the evil of parricide would have to look like. The premise of this deduction would be a representation of the relevant relations of objects. (For expository purposes, we can imagine this as, say, a picture of a father and his child. Of course, an idea capable of capturing the notion of parenthood would have to be complex in the extreme, and to the extent that it involved specifically causal notions would be partially non-representational for reasons that Hume discusses elsewhere. I propose to ignore these complications for the present.) The conclusion of the deduction would be a picture, the force of which would be that parricide is evil, or ought not to be done. How could a picture have this force? The closest we can come is a picture of someone doing what he ought, i.e., not murdering his father. So the conclusion of the demonstration would be, not that people ought not to murder their fathers, but that they do not murder their fathers. But whether people murder their fathers or not is a contingent matter, not amenable to being settled a priori.

Now that we have accounted for Hume's emphasis on effects that are actions, we can fine-tune the view to accommodate effects and necessary conditions that are motivational as well. It might be suggested that for action to follow, the agent has to recognize that it is required: the agent must "know virtue" (T 465:28). Furthermore, the agent must have the right moral character: he must be "well-disposed" (34). And finally, what is required in some cases may be not actually action, but rather the attempt or the motivation: what can be morally required is only that the agent "conform the will", that "in every well-disposed mind, [the connexion betwixt the relation and the will] must take place and have its influence" (23, 34f). We can now see that these qualifications, which Hume gracefully concedes, are irrelevant to the argument. If these are what morality requires, his deductivist opponents are committed to their necessarily occurring in the appropriate situation; but motivation and attempts, even on the part of well-disposed agents, are as contingent as action. We have now accounted for the passages that seemed to support the conventional reading of the argument.41

To recapitulate: Because deductive relations, pictorially understood, can hold only between contents that can be pictured, someone who claims that morality is deductive can at best mean that pictures of actions can be deduced from pictures of situations that (morally) require them. This would entail that (morally) appropriate actions necessarily occur in the situations that (morally) require them. The fact is they do not, at any rate, not necessarily. Therefore, morality cannot be deductive. Moreover, since the argument was not morality-specific, it establishes more generally that deontic facts cannot be arrived at by deductive reasoning.42

It is well-known that pictorial theories of thought have difficulty accounting for what we think of as logical connectives, such as negation:43 how is one to distinguish a picture of some state of affairs from a picture of its negation? What is important as regards the present point is that this difficulty extends to what we regard as modal and deontic operators. How is one to distinguish a picture of a state of affairs' holding from a picture of its necessarily holding? How is one to distinguish a picture of a state of affairs' holding from a picture of its being obligatory?44 It cannot be done using the representational elements of the picture. The easiest way to see this is to imagine trying to use a picture of a state of affairs to represent the necessity or obligatoriness of that state of affairs by modifying the representational elements of the picture -- perhaps by scrawling "Necessary" or "Obligatory" across the top. The attempt is bound to fail: what one will get is not a picture of necessity, but a picture of, say, a landscape marred by peculiar skywriting. But if the representational elements of the picture cannot be used to distinguish obligation from fact, the remaining option is to adjoin to the picture a non-representational impression; and this is what Hume does.45


The passage generally read as claiming that 'is does not entail ought' (T 469:19-470:4) is often considered to be a mere afterthought to the previous argument,46 a further independent but very brief argument presented as a rhetorical question: Hume professes not to understand transitions from 'is' to 'ought', and demands an explanation. We are now prepared to take a position on the force of that rhetorical demand.

If the passage is read on its own, it is extremely weak, just because no argument is presented. Hume's opponent is likely to think he has an account (e.g., one that appeals to divine will, or fitness in relations of objects or ideas), and the mere rhetorical question will not (and should not) carry conviction.47 I suggest that a better reading of the 'is-ought' passage would take it as a corollary to the previous argument; this is dictated by, at least, the principle of charity. By seeing just how the previous argument supports the claim we will be able to explain just what its force is supposed to be -- on the assumption that the most reasonable interpretation is the one supported by the arguments Hume actually gives.

The arguments we have already seen are supposed to have established that judgments of obligation involve ideas whose contents derive, not from the situation that supposedly generates the obligation, but from the sentiments of the observer. Consequently, reasoning from a description of such a situation to such a judgment will involve the introduction of such a sentiment-derived idea. But reason is conservative, in that the conclusion of an inference can only contain elements contained in its premises; as Hume puts it elsewhere (describing it as one of two "very obvious principles"), "reason alone can never give rise to any original idea" (T 157:18-20). So one cannot arrive at 'ought-judgments' by reasoning about circumstances.

The point is this. Since the idea derived from the sentiment is ipso facto not derived from the situation being examined, it will not appear in a description of the situation. If the premises of an argument are the description of that situation, the idea needed in the argument's conclusion will not appear in the premises, and, since reason is conservative, cannot figure in the argument's conclusion.

The 'is-ought' passage can now be seen to be, not an afterthought, but an argument that relies on the conclusions of the immediately preceding arguments. And the force of its conclusion is just what it sounds like: 'is' does not entail 'ought'. Specifically, you can't start with a description of some situation and reason your way to claims about what, in that situation, ought to be the case.

The 'is-ought' passage does not itself invoke the considerations, deriving from the causal resemblance theory of mental content, whose importance for the previous arguments I have been emphasizing. But it does invoke the conclusions of arguments that do turn on those considerations, and so we should see the causal resemblance theory of mental content as underwriting Hume's acceptance of the eponymous law, that " 'is' does not entail 'ought' ". We are not yet fully equipped to assess the degree of this dependence, since we have surveyed only one of the three bodies of argument that lead up to the 'is-ought' passage; were the others to prove not to turn on causal resemblance considerations, it would be possible to surrender the causal resemblance theory and still have Hume-supplied reasons to accept Hume's Law. I will not here anticipate the outcome of examining these other arguments.


We've reconstructed a few of Hume's arguments on the subject of practical reasoning, and found them to be a good deal better than commentators usually acknowledge them to be. We've also found them to rest, at least in part, on a body of semantic theory that is no longer acceptable today. What does this buy us? Well, first, it's nice to know that Hume repays close reading; that, on examination, his arguments turn out to be tight and ingenious attempts to arrive at dramatic (if unlikely) conclusions, rather than boring, bad arguments for obviously true conclusions. Second, it may be worth rereading other arguments in the Treatise in light of these reconstructions; perhaps they too will turn out to be dependent on Hume's semantic views in interesting ways. Third, as I suggested at the outset, this interpretation may have consequences for contemporary moral philosophy: I take it that the presumption that the burden of proof rests on opponents of Humean views about practical reasoning is in part due to the historical influence of the arguments we have been considering. But if this is right, finding these arguments to depend on a body of semantic theory that we no longer believe puts modern philosophers who believe Hume's Law on the spot: they must be prepared to show that they have not merely inherited Hume's Law, but that they can adduce good reasons for it. That " 'is' does not entail 'ought' " may, today, seem obvious; but if this obviousness is an effect of the arguments we have been examining, a defence of Hume's Law should not appeal to its obviousness.

There is a fourth moral to draw from our discussion of Hume's arguments. Consider the question of the penumbra of commitments surrounding the causal resemblance theory. The puzzle here is that several aspects of the causal resemblance theory do not seem to get anything like the amount of explicit consideration that they deserve, given their central role in Hume's arguments. For example, while the pictorial view of deduction seems essential for reconstructing several of the arguments, the Treatise lacks the kind of discussion of pictorial deduction that we might hope for and think warranted by the uses to which the view is put. (While there is an extended discussion of geometry early on in the Treatise, this reads like an application of the view to a branch of mathematics, rather than a treatment of the view itself.) Or again, consider the argument discussed in section 4, against the deductivist view of morality. The argument turns on a very straightforward consideration: that the would-be conclusion of such an argument cannot be fully represented, and so cannot be the conclusion of a demonstration. So why doesn't Hume simply say this?48 Now as a matter of fact, he does say something very much like this elsewhere; I take it that this is more or less the force of T 415:23-33 and 458:12-22. But even granting this, why does the later argument express such an uncomplicated consideration in such a convoluted manner?

What I think is happening is this. Much of the causal resemblance theory was, in Hume's time, a widely-held view (remember 'the theory of ideas'); and Hume accordingly takes many of its commitments for granted. He does not feel that they need discussion, in roughly the way that a twentieth-century philosopher writing a treatise on mind or morality would be unlikely to feel that the propositional understanding of deduction needs discussion. And because of this, he does not see how much work these commitments are doing in his arguments. They are the platitudinous and frequently suppressed premises without which the argument does not make sense, but which are not worth spelling out for a contemporary and sophisticated audience. One doesn't tend to think that the dialectical work is being done by one's platitudinous premises, and so one frames one's arguments so as to highlight the premises one takes to be substantive. However, from a distance of two hundred and fifty years or so, it is precisely the platitudinous and often suppressed premises that seem to be the hinges on which the arguments turn.

The moral, then, is that we should take very seriously the thought that we are in Hume's position ourselves. Like Hume, we take for granted and rely on semantic theories; and the arguments we construct -- whether for updated versions of Hume's Law or for other claims -- will tend to depend on those theories in ways that are not obvious to us. It is worth remembering how likely it is that, in two hundred and fifty years, our current semantic theories will appear merely quaint. For this reason it is worth taking special pains to avoid, where possible, having one's arguments in moral philosophy depend on the apparatus supplied by contemporary philosophy of language.


*Thanks to Annette Baier, Alyssa Bernstein, Hilary Bok, Lindy Cassidy, Cora Diamond, Steve Engstrom, Don Garrett, Hillel Millgram, Robert Nozick, Hilary Putnam, Geoff Sayre-McCord, Tim Scanlon, Candace Vogler and Margaret Wilson, who read and commented on earlier drafts of this paper. I'm also grateful to Sanford Shieh for helpful discussion, and to an audience at Brown University for questions and objections.[back]

1. Hare 1963, 108.[back]

2.Hume 1888/1978 and Hume 1777/1978 will be cited by T and E, respectively, followed by page number, and, where this is useful, line numbers; T 5:6-8 would refer to Hume 1888/1978, page 5, lines 6-8. The 'is-ought' passage is at T 469. The first stretch of preceding argument (T 457:5-459:10) recapitulates points made at T 413-417, and cannot be adequately discussed without considering those passages as well; limitations of space prevent me from doing that here. The second (T 459:11-463:2) deploys considerations that are morality-specific, and are for this reason also best treated separately. [back]

3. I will discuss some of these interpretations in the text and footnotes below. For now, we may note that my assessment of the reconstructed arguments as weak is typically shared by the commentators who have advanced those reconstructions. Stroud, for example, wraps up his account of the arguments I will consider in sections 3 and 4, below, by remarking that "[i]t need hardly be said that this argument is not completely decisive", attributing the arguments' not fully spelled-out shortcomings to "the vagueness and imprecision of the views Hume is arguing against" -- and to "unjustifiable restrictions on what is demonstrable" (1977, 175f). Fogelin ends up describing the arguments in question as "embarrassingly weak" (1985, 127). Harrison states that "[n]ot only does Hume's proof of the conclusion that morality is not susceptible of demonstration fail... ; his conclusion is also false, and rather obviously false at that" (1976, 49). [back]

4. T 37:29-31. " '[T]is impossible perfectly to understand any idea, without tracing it up to its origin, and examining that primary impression, from which it arises" (T 74f; cf. also 74:36-75:1; 83:11-29 could be construed as involving an extremely long chain of this kind). Abstract ideas are trickier but are treated by Hume as derivative from the straightforward case: T 17ff, esp. 17:17-20; 20:9-13; 22:11-24; 24:24-26; 34:30-35.

The causal analysis of reference may seem to sit uncomfortably with Hume's subsequent discussions of causation and of external objects. I do not think this difficulty can be explained away, say, by somehow combining the accounts -- I think that they really are incompatible. And I do not think that Hume was unaware of this: in fact, I suspect that eliciting such incompatibilities was part of Hume's philosophical project (the part that justifies calling Hume a skeptic). (For discussion of one such incompatibility, see Garrett 1981.) Discussion of these issues lies beyond the scope of this paper; for the present, I will adopt the expository policy of treating items given non-standard or skeptical analyses in one argument as, nonetheless, meant to be thought of in an ordinary, unanalyzed way in others, unless appeal to those analyses is made specifically. (See note 6, below.) [back]

5. To see that these are distinct conditions, notice that Hume states that "[s]econdary, or reflective impressions are such as proceed from [i.e., are caused by] ... original ones" (T 275:16f, my emphasis). Here we have impressions caused by others they do not resemble, and whose content they do not assume. [back]

6. Notice that if, contrary to the policy adopted in note 4, one were to attempt to combine the causal resemblance theory with Hume's account of external objects (roughly, there are no external objects, and if there were, impressions could not resemble them), one would have to adopt a view on which impressions of sensation had no representational content; on such a view, representational content could be had only by ideas. (One would then have to choose between saying that impressions have no contents at all, or saying that there is a thinner, non-representational notion of content exhausted by the merely intrinsic qualities of impressions. One would also have to assume the exegetical task of reading away references to objects in passages like the one just quoted (T 37:29-31).) Since I wish for the purposes of this paper to remain agnostic on this point, I will for simplicity of exposition continue to speak of external objects as the possible sources of contents of ideas and impressions; but I intend my discussion to be compatible, mutatis mutandis, with a reading of Hume of this more exotic variety. (I'm grateful to Cora Diamond for pressing me on this point.) [back]

7. Mackie 1980, 58, is unable to believe that Hume was willing to endorse this conclusion, and construes Hume "as intending to say that this is what you ought to mean, because that is all that, on reflection, you could maintain." Stroud also finds this unlikely (1977, 180f), as does Hudson 1968, 297; and Fogelin has his qualms as well (1985, 137). But see E 62:8-63:5, esp. 62:21-25, and, on a slightly different but related point, T 23:14-18; 33:9-18 (esp. 15-18). Hume also thinks that we can use names with no idea of what we are naming; this is a risky practice, and following the procedure for determining what the content of an idea is may actually establish that some our words are meaningless: E 74:14-20; 78:2-4; T 61:36-62:1; compare T 162:20-25; 168:7-29; 224:6-14.

Even if textual evidence seems to show that Hume held this view, isn't it too outlandish to be attributed to him charitably? Is it Hume's view that, for example, I could really be thinking about a can of cat food when I think I'm thinking about my Form 1040? (I'm grateful to Felicia Ackerman for the example, and for pressing the objection.) To see that Hume has ways of handling this kind of case, recall the role of resemblance in controlling reference. How are we to imagine such a case? Suppose we have a mental picture that (we would say) qualitatively resembles a Form 1040, but is causally connected to a can of cat food. In this case, the content of the picture cannot be the can of cat food because it fails to resemble the can of cat food. Suppose we substitute for this picture one that qualitatively resembles a can of cat food; now there is no trouble in seeing that it is a picture of the cat food, but it is implausible that I should mistake this picture for a picture of my Form 1040. (Dan Brock has suggested that the problem might be kept in play by considering a chain of partial resemblances. I'm not sure what the Humean response would be here, but I doubt that Hume considered this problem himself.) [back]

8. The closest contemporary rendering of "demonstration" is "deduction", and treating these as synonyms is a helpful reminder that they play analogous roles in their respective philosophical environments. However, it is important to remember that the fit is not precise. [back]

9. In this context, ignoring mental contents that are not visual images is not unreasonable. It can be at least at first glance sensible to imagine deductive thought as done with pictures; but it would be another matter entirely to conceive of deduction as performed with, say, olfactory sensations. [back]

10. Harrison 1976, viii. Harrison's view of the upshot (p. 34) is that "since [Hume] confuses propositions with ideas or mental images, he confuses entailment, which is a relation between propositions, with relations such as resemblance between mental images." This parochial and tendentious statement of an important point is worth rephrasing: Since Hume has a different understanding of thought than we do (one not necessarily more confused than our own), he has an appropriately different understanding of deductive inference. I have not yet come across an adequate treatment of this subject, which I can only touch on in this paper. [back]

11. I don't mean to suggest that one would choose this example if one wanted to explore Hume's views of demonstration in greater depth; while it illustrates the way in which demonstration must be pictorial, it may not be helpful when considering other features of demonstration. For instance, its very simplicity makes it at best a borderline case; since the relation of equality is "discoverable at first sight, [it] fall[s] more properly under the province of intuition than demonstration" (T 70:9f). [back]

12. It might be objected that Hume finds arithmetic and algebra more precise than geometry, and that we should consider them, rather than geometry, 'foremost' for Hume. Moreover, since Hume imputed the 'defects' of geometry to the fact that its "original and fundamental principles are deriv'd merely from appearances" (T 71:30-32), we might conclude that algebra and arithmetic owe their "perfect exactness and certainty" to their non-pictorial nature. I won't try for a judgment call on which of the mathematical sciences was Hume's favorite; note, however, the amount of discussion which geometry receives in the Treatise, as opposed to arithmetic or algebra. (Cf. also T 181f.) And as to whether Hume considered algebra to be at bottom non-pictorial: he reiterates, on the following page, "that principle so oft insisted on, that all our ideas are copy'd from our impressions"(72:32f); it follows that arithmetic and algebra are unlikely to be exceptions. [back]

13. Actually, the dilemma here is not entirely familiar, since Hume has substituted 'relations of objects' for 'relations of ideas'. I take it that he chose this way of putting the point partly in view of opponents' views that moral facts can be discerned in relations of objects (the locution being the opponents' rather than Hume's: cf. Mackie 1980, ch. 2). Since perceptions of objects will represent whatever relations are to be found among the represented objects, it does not much matter for Hume whether he is considering relations of objects or relations of ideas. (Cf. T 456: "All these systems concur in the opinion, that morality, like truth, is discern'd merely by ideas, and by their juxta-position and comparison." See also T 20:1f and T 29:3-6.) Nonetheless, as we'll see, the emphasis on relations of objects turns out to be a pointer to the way the argument actually works. [back]

14. See Mackie 1980, 53f, or Harrison 1976, 63, for something like this objection. Harrison says elsewhere that "[t]his is mere assertion, and Hume is guilty of appealing more to rhetoric than to argument" (p. 61). Stroud makes a related point as well (1977, 179f). [back]

15. T 34:6-9: "my senses convey to me only the impressions of colour'd points, disposed in a certain manner." Cf. also E 63:13-15 and T 56:23-27. In any case, as Steve Engstrom has reminded me, the realization that modal facts are not directly perceptible predates Hume. [back]

16. The claim should be distinguished from the separate point, that no proof can be given that two distinct objects are necessarily connected. That very different argument would be the structural analogue of arguments we will consider below. Cf. E 63:33-64:7. [back]

17. Cf. E 64:8-12. [back]

18. T 164f, emphasis Hume's. Cf. also E 75:19-24; 78:10-18. [back]

19. Or more generally, judgments that play the role in action that moral judgments play in moral action; the argument is more general than morality. [back]

20. This is of course not to say that vice is, on Hume's view, in the object but causally ineffective with respect to our sense organs. At this point in the argument, however, this possibility has not yet been ruled out. The claim that vice is not in the object is the conclusion of the argument. [back]

21. T 469:4-8, my italics. Notice that this is not a skeptical conclusion - that there is no such thing as, say, vice -- but the hard-won result of semantic analysis, which does not dispose of the concept of vice, but rather tells us just what it is a concept of. Hume's skepticism lies elsewhere. [back]

22. Thinking of the surplus content as repulsiveness may be too strong. Hume tends to describe the feeling as 'uneasiness' (e.g., T 499:25-28; 471:5-9); at one point he suggests that it can distinguished from other kinds of uneasiness, but does not say much about its "peculiar" qualities (T 472). [back]

23. For variations on this complaint, see Harrison 1976, 48, Fogelin 1985, 135, and Stroud 1977, 175f. [back]

24. It might be thought that this argument is morality-specific, and does not settle the question with respect to deontic facts more generally. But this would be to misconstrue the intent of the argument. Moral facts are a subset of deontic facts; from a moral argument one concludes that one ought to do such-and-such, just as one might conclude, from a prudential argument, that one ought to do something else. If moral facts cannot be specified in terms of available relations, this will suffice to show that not all deontic facts can be so specified. [back]

25. Notice that the circularity in these cases is only partial; there is more to being intelligent than thinking that one is, more to the object of justified pride than the pride itself, and, presumably, more to being a member of the club than knowing the rules. But vice has the same structure; there is more to being vicious than thinking that one is. [back]

26. It must of course involve other things, if only because the representation of the objects may present you with many more relations between them than the small number that now have your attention. But I cannot here discuss Hume's answer to the question: what picks out one represented relation as the object of my thought? [back]

27. The modal aspect of this fact raises difficulties which we shall touch upon later, but ignore for now. [back]

28. Annette Baier has pointed out to me that intention is liable to involve a similar circularity, and that this will be a problem for Hume. However, the feature of intention that makes it problematic is specifically its reflexivity: intending to do P is, in part, intending that that very intention be causally effective in bringing it about that one Ps. But as this feature of intention has come in for attention only recently, we may wonder whether Hume saw that there is a problem here. He defines the will as "the internal impression we feel and are conscious of, when we knowingly give rise to any new motion of our body, or new perception of our mind" (T 399, italics deleted). The knowingness is not part of the impression that is the will, but is only a surrounding circumstance; and whether it is a problem depends on what Hume takes it to be a knowingness of. The circularity problem only arises here if knowingness consists in having an idea of, among other things, having that very idea; an idea of, for instance, a passion causing an action would be innocuous. [back]

29. This brings out an interesting tension in the view I am attributing to Hume. On the one hand, I am suggesting, the availability of Euclidean geometry, then the paradigm of deductive reasoning, made plausible to Hume the thought that demonstrative inference could be reconstructed within the pictorialist constraints of his semantic theory. On the other hand, however, his semantic theory required him to insist that Euclidean geometry could not be understood in the standard way. [back]

30. Broad, for instance, ignores it, perhaps, one senses, out of embarrassment (1930/1951, 104-115). Raphael, normally a sympathetic and careful reader, quotes the argument in its entirety and then, in a short paragraph, dismisses it as "depend[ing] on an absurd identification" and "rest[ing] on a confusion" (1947, 60-62). Some commentators manage to do more than one of these. Harrison conflates this argument with the previous one. He also mangages to accuse Hume of begging the question, of tautological vacuity, and of vulnerability to the objection that men have a "passion for morality" -- even though Hume went to great lengths to defend this very view, making it hard to believe that this was an objection he had overlooked (Harrison 1976, 53ff). [back]

31. Mackie 1980 cites Harrison as raising this objection (1976, 53f), and defends Hume by "not[ing] how big a concession this [i.e., surrendering (1)] would be, and how reluctant Clarke, for instance, or Butler would be to make it" (p. 54; see also p. 57). Compare Fogelin 1985, 127. [back]

32. Harrison, for example, attributes to Hume the "premiss that if morality consists in relations apprehended by reason, morality must necessarily move us", and asks whether "there [is]... any reason why this... premiss should be true" (1976, 35). Mackie takes Hume to be concerned with "[t]he connection between the supposed moral relation and choice by any rational agent" (1980, 57, my emphasis). [back]

33. There is a potential ambiguity in this passage: 'action' might mean a product of human agency, or merely an event. (If the latter -- and this reading could be supported by the introductory phrase, "even in human nature" -- then an 'action' might be an instance of coming to have a motivation, after all.) Hume uses the word both ways, and the sense seems to be controlled by context: when he is discussing morals, he generally means human action; when he is discussing inert objects, he means (roughly) events. Because Hume is here discussing morals, I take it that here he means by 'action', human action. If this is right, it removes the ambiguity of the earlier phrase, "conform the will". 'Conforming the will' might be a matter of good intentions, or it might require actually doing something. But on the former construal, pointing out that actions do not necessarily follow would be irrelevant, since one can have the best of intentions, yet not act.

Now suppose I am wrong on this point. As we will see below, when we consider Hume's way of handling moral theories that require not actions but merely good intentions, it turns out not to matter. Once we see why 'effects' must be 'necessarily the same', we will see that even when Hume's opponent has a moral theory that does identify some (or even all) 'effects' with motivations, Hume's argument will work anyway. But we will also see another reason that it is unlikely that Hume has in mind only motivations and not actions. Hume's argument makes the 'effects' out to be what his opponent's moral theory requires of agents. Now moral theories that require only meaning well are rather rare: most moral theories require agents to actually act, at least in some circumstances. And in these cases, the 'effects' will be full-fledged actions, not mere events. [back]

34. T 415:18-20; " 'tis not the passion, properly speaking, which [can be] unreasonable, but the judgment" that it interacts with (416:25-28; compare 459:26-29). For further discussion of these passages, see Millgram 1995. [back]

35. A modern version of this response can be found in Locke 1982. [back]

36. There is yet another reason for resisting the identification of effects with motivations. The argument construed as turning on motivations would be unsatisfactory, because it would prove too much. The point of the argument is to establish a contrast between genuine deductive reasoning and moral or practical reasoning. On the conventional interpretation, this is done by showing that while the conclusions of deductive reasoning are necessarily adopted, the conclusions of moral or practical reasoning are not. But recall that the argument appeals to a very general fact about causation -- roughly, the fact that effects cannot be deductively inferred from their causes. If this fact establishes that the conclusions of practical reasoning -- understood as ideas of the reasoning's conclusion, or motivations -- do not necessarily ensue on the mental processes that would in normal circumstances produce them, it seems equally to establish that the conclusions of deductive reasoning -- similarly understood as mental entities -- do not necessarily follow either: if you believe p, and you believe if p then q, you may be hit over the head before you get around to concluding q. So the argument, construed in this way, would, if it worked in the case of practical reasoning, work in the case of deductive reasoning as well: it would have to establish that there really is no deductive reasoning either. Leaving to one side the intrinsic merits of such an argument (it looks pretty bad), we may note that since its purpose was to establish a contrast between deductive and moral or practical reasoning, the argument, so construed, would fail by virtue of overkill. [back]

37. T 26-65; esp. 45:4-7. It might be suggested that the arguments are not admittedly deductive, since Hume says that "with regard to such minute objects, they are not properly demonstrations" (45:1-3). This, however, is precisely the point: without ideas of such objects, you cannot have deductions that take them as their subject; this is the way in which the scope of deductive argument is constrained by Hume's semantic theories. [back]

38. Two points need mentioning here: First, lacking an adequate treatment of Hume's understanding of deduction, I wish to leave open the question of whether picture1 and picture2 need in fact be different pictures. (A geometrical demonstration may start and finish with the same picture.) Second, recall that the 'pictures' need not be entirely visual; my idea of a heavy object may involve simple ideas derived from tactile rather than visual impressions. But this complication does not affect the present point. [back]

39. For Hume's views on these matters, cf., e.g., T 18:22-28; 19:36-20:1; 29:11-14; 32:17-23; 36:17-22; 40:26-28; 43:5-13; and esp. 29:3-6. [back]

40. See note 13, above. [back]

41. Two points: First, if Hume's argument works even when the 'effects' are merely motivations, why the insistence that Hume takes the 'effects' to be actions? Recall that 'effects' are whatever is required by the moral theory being examined. Even if many moral theories impose motivational requirements, and even if some impose only motivational requirements, most moral theories require actions. (What you ought to do, it is often thought, is not merely to mean not to kill your father, but actually not to kill him.) So it is important that Hume's argument be effective against theories that require actions, and not merely motivations.

Second, now that we have seen the argument, it might be thought that there is a further reason that the effects cannot be motivations: motivations cannot be represented either. (This would make it difficult to understand Hume's subsequent insistence that motivations rather than actions are the appropriate object of moral judgment; cf., e.g., T 477:13-17.) But motivations can be represented. I can have impressions of reflection; and have ideas that are derived from them, resemble them, and consequently represent them. [back]

42. Understood in this way, Hume's argument evades the overkill objection discussed earlier (note 36). When one idea is demonstrable from another, the holding of the state of affairs depicted by the latter does entail the holding of the state of affairs depicted by the former. Whenever you have an idea of two spots together with another two spots, you have an idea of four spots; and whenever you have two spots together with another two spots, you have four spots. Showing that moral (or, more generally, action-guiding) reasoning is not like this establishes a contrast with genuine deductive reasoning that is sufficient to show action-guiding reasoning to be non-deductive. [back]

43. Cf. Harrison 1976, 30, 32f, Stroud 1977, 75. Stroud's point is quite general, and is closely related to the central themes of this paper. But he fails to exploit it to elucidate the large body of Humean doctrine it bears upon. [back]

44. This may be a difficulty for philosophers other than Hume who are committed to pictorial construals of content; perhaps the early Wittgenstein is an example of this. Cf. Hudson 1983, 107ff. [back]

45. It is worth remarking that the territories covered by modern theories of content and by Hume's are only identical to a first approximation. Modern accounts of necessity tend to be extensions of non-modal semantics, such as possible-world semantics. But Hume must rely on radically different tools (impressions of reflection) to reconstruct modal notions. So while we can think of a proposition with a modal operator in it as fully representational if we want to, Hume cannot.

If only representational items come under the aegis of deductive inference, it will follow from this that necessity cannot be established by a priori deductive inference. It is, I think, useful to read certain of Hume's arguments regarding induction and necessity with this in mind.

One worry that might be raised here is that Hume seems to be committed by this account to a view on which mathematical necessity will not be representable or expressible; but since he has been arguing that mathematical necessity will not account for obligation, it must be possible, somehow or other, to express the notion. An adequate treatment of this question would require a full-dress reconstruction of Hume's understanding of deduction; here it suffices to note that Hume's treatment of mathematical necessity can be expected to be continuous with his treatment of causal necessity and obligation: he writes that "the necessity, which makes two times two equal to four, or three angles of a triangle equal to two right ones, lies only in the act of the understanding, by which we consider and compare these ideas" (166:5-10); and he does so in the course of drawing a comparison between mathematical necessity and causal necessity, the account of which we sketched in section 2. [back]

46. As for example Mackie 1980, 61, is inclined to: "the passage about 'is' and 'ought'... is plainly an afterthought for Hume himself." Stroud 1977, 187, similarly states that "Hume apparently added it as something of an afterthought he hoped would be helpful." And the view echoes at Harrison 1976, 69, who refers to the passage as an "argument, inserted almost as an afterthought." On the other hand, Atkinson 1968, 274, regards it as a continuation of the previous argument, and Fogelin 1985, 138f, takes it to be a recapitulation of the argument at 463:17-468:20. [back]

47. Harrison 1976, 69-82, summarizes a number of (generally modern) responses of this kind. Moreover, even if Hume's opponent does not take himself to have such an account, he may not concede that he has to shoulder the burden of proof: it is, he may suggest, no more reasonable to demand such an account of him than it is to demand a independent justification of the transition from a proposition universally quantified throughout to one containing proper names . The building blocks of practical reasoning, he may claim, are not to be expected to be amenable to any more justification than are other building blocks of reason. [back]

48. I'm grateful to Jaegwon Kim and Martha Nussbaum for pressing me on this point. [back]


Atkinson, R. F. 1968. "Hume on 'is' and 'ought': A Reply." In V. C. Chappell, editor, Hume: A Collection of Critical Essays, pp. 265-77. Notre Dame, Ind.: University of Notre Dame Press.

Broad, C. D. 1930/1951. Five Types of Ethical Theory. New York: Humanities Press.

Fogelin, R. J. 1985. Hume's Skepticism in the Treatise of Human Nature. Boston: Routledge and Kegan Paul.

Garrett, D. 1981. "Hume's Self-Doubts about Personal Identity." Philosophical Review 90 (3): 337-58.

Hare, R. M. 1963. Freedom and Reason. Oxford: Oxford University Press.

Harrison, J. 1976. Hume's Moral Epistemology. Oxford: The Clarendon Press.

Hudson, W. D. 1968. "Hume on is and ought." In V. C. Chappell, editor, Hume: A Collection of Critical Essays, pp. 295-307. Notre Dame, Ind.: University of Notre Dame Press.

Hudson, W. D. 1983. Modern Moral Theory. Second edition. New York: St. Martin's Press.

Hume, D. 1777/1978. Enquiries Concerning Human Understanding and Concerning the Principles of Morals. Third edition. Edited by L. A. Selby-Bigge and P. H. Nidditch. Oxford: The Clarendon Press.

Hume, D. 1888/1978. A Treatise of Human Nature. Second edition. Edited by L. A. Selby-Bigge and P. H. Nidditch. Oxford: The Clarendon Press.

Locke, D. 1982. "Beliefs, Desires, and Reasons for Action." American Philosophical Quarterly 19 (3): 241-49.

Mackie, J. L. 1980. Hume's Moral Theory. Boston: Routledge and Kegan Paul.

Millgram, E. 1995. "Was Hume a Humean?" Hume Studies 21 (1): 75-93.

Raphael, D. D. 1947. The Moral Sense. London: Oxford University Press.

Stroud, B. 1977. Hume. Boston: Routledge and Kegan Paul.

Rendered into HTML on 10/22/01.

Elijah Millgram
Philosophy Department
University of Utah
Salt Lake City UT 84112

© 1997 Iyyun