# The is-ought gap

In another thread, A.N. Prior’s attempted refutation of the is/ought gap came up. Here’s one of Prior’s examples:

a. Tea-drinking is common in England.
b. Therefore, tea-drinking is common in England, or all New Zealanders ought to be shot.

(a) entails (b), (a) is descriptive, and allegedly, (b) is evaluative.

There’s an unjustly neglected article by Toomas Karmo ("Some Valid (but no Sound) Arguments Trivially Span the Is-Ought Gap", Mind [1988]: 252-7) that responds to this sort of example and provides a general proof of a version of the is-ought gap. Karmo’s argument goes roughly like this:

First, notice that it is really not intuitively clear whether (b) should be called evaluative or descriptive. Karmo provides a way of classifying statements like this. Assume that there is a class of uncontroversially evaluative statements (like "all New Zealanders ought to be shot") and a class of uncontroversially descriptive statements (like "tea-drinking is common in England"). There are also unclear statements, like (b) above. But I assume that the truth-values of the unclear statements supervene on the truth-values of the clearly descriptive and the clearly evaluative statements. Now, for these unclear statements, Karmo suggests that whether they are evaluative or not depends on whether, given the actual descriptive facts, their truth depends on which value system is correct.

For instance, if tea-drinking is in fact common in England, then (b) is non-evaluative, because its truth does not depend on the advisability of shooting New Zealanders, the truth-value of (b) having already been settled by the descriptive facts. On the other hand, if tea-drinking is not common in England, then (b) is evaluative, since in that case the truth of (b) depends on whether all New Zealanders ought to be shot. So a statement can be evaluative in some possible worlds and descriptive in others (without changing its meaning).

Here’s another example:

c. Everything Alfie says is true.

Whether this is evaluative depends on what Alfie has said. If Alfie has made at least one evaluative statement and no false descriptive statements, then the truth of (c) turns on whether Alfie’s evaluative statements were true, so (c) is evaluative. But if Alfie has made no evaluative statements, or if he’s made at least one false descriptive statement, then the truth of (c) does not depend on which value system is correct, so (c) is descriptive.

Given this understanding of "evaluative" and "descriptive", Karmo shows that it is not possible to have a sound argument from descriptive premises to a non-trivial evaluative conclusion. I won’t do the formal proof here, but instead I’ll illustrate the point with four attempted is/ought-spanning arguments:

(I)

a. Tea-drinking is common in England.
b. Therefore, tea-drinking is common in England, or all New Zealanders ought to be shot.

This fails because (b) is non-evaluative in the actual world, since the first disjunct is true. And if you go to a possible world in which the first disjunct of (b) is false, then the argument is unsound.

(II)

c. Everything Alfie says is true.
d. Alfie says lying is wrong.
e. So lying is wrong.

If Alfie has in fact said that lying is wrong, and he has made no false descriptive statements, then (c) is evaluative in the actual world (as explained above). On the other hand, if Alfie hasn’t said that lying is wrong, then premise (d) is false; and if Alfie has made at least one false descriptive statement, then premise (c) is false. So either the argument is unsound, or premise (c) is evaluative.

(III)

b. Tea-drinking is common in England, or all New Zealanders ought to be shot.
f. Tea-drinking is not common in England.
g. Therefore, all New Zealanders ought to be shot.

This fails because (f) is false. And if you go to a possible world in which (f) is true, (b) is evaluative in that world. So again, either the argument is unsound, or it has an evaluative premise.

(IV)

h. The sky is blue.
i. Therefore, murder is wrong or murder is not wrong.

This fails because the conclusion is trivial.

One can show that this sort of thing holds in general: Any valid argument is either going to have a false premise, an evaluative premise, a non-evaluative conclusion, or a merely trivial evaluative conclusion (one that is true according to every coherent value system). So, I think Karmo saved the is-ought gap from the likes of Prior.

## 63 Replies to “The is-ought gap”

1. Jamie says:

I have a paper in which I rehearse Karmo’s point. Philosophical Issues 12 (2002).
There’s something unsatisfying about Karmo’s solution. I’ll try to put my finger on it later.

2. robert Johnson says:

Thanks for the reference, Michael, and the fantastic summary. You’ve now made me want actually to know what I’m talking about. The last I looked at this topic was that exchange between Hare and Geach in *Philosophy* (1970’s I think…god I’m so lazy I don’t even look it up), the one with great examples (sodomy and murder, I think).

3. Here’s a different sort of example.
1. Necessarily, an action A is right iff. A has some set of descriptive properties P.
2. Whatever the relevant descriptive properties P happen to be, some action or other A has properties P.
______________________
3. :. Some action A is right.
(1) depends on nothing more than the moral supervening on the descriptive in every world. That is not a moral or evaluative claim, it is a metaethical platitude. (2) makes the descriptive claim that some action has the relevant descriptive properties, whatever they happen to be. It does not assume that any moral theory is true. It assumes only that moral claims depend on the possession of some set of descriptive properties. The conclusion is clearly evaluative.

4. Jamie says:

Uh.
Mike, that is not very clear to me.
Could you say which of the letters is a variable and which a constant? And for the constants, can you please say what their values are, and for the variables say just where and what the quantifiers are?

5. asg says:

Would a Moorean deny Mike A.’s (1)?

6. Michael H,
This is interesting. Thanks. I am curious about the Alfie challenge
c. Everything Alfie says is true.
d. Alfie says lying is wrong.
e. So lying is wrong.
By (d), Alfie made an evaluative statement. Further let us suppose he’s an ideal observer, who has never made a false descriptive statement. The argument now seems sound but something still seems amiss.
Our (at least, my) resistance to this argument might lie in the fairly obvious quesiton. In virtue of what is the evaluative statement made true? It seems real odd that Alfie’s assertion is the truth-maker. Couldn’t Prior respond by saying the truth-conditions for (c), where Alfie’s statements are evaluative, are moral facts rather than Alfie’s assertions?

7. Regarding the Alfie example, it seems like cheating to me. Suppose I say, “Lying is wrong is true.” And suppose I conclude from this that Lying is wrong. Have I constructed a valid argument that bridges the is/ought gap? Do things change if I let Alfie say “Lying is wrong” and then go on to say, “What Alfie said is true”?
I’m inclined to say that my utterance of “Lying is wrong is true” ought itself to count as a moral utterance if ‘Lying is wrong’ is. Whatever the faults or virtues of minimalist theories of truth, the theories highlight that we can use the notion of truth to affirm and deny things we do not ourselves say or even know the contents of. And that seems to me to indicate that if Alfie utters a moral statement and I endorse what he says using ‘true’, I’m saying something with moral content too.
Of course I have no expertise about theories of truth, and I have no line about the is/ought gap in general.

8. Sorry Jamie. Let me be less sloppy about it.
1. [](x)(EP)(x has relevant descriptive properties P only if x is right)
2. (Ex)(EP)(x has relevant descriptive properties P)
3. :. (Ex)(x is right)

Instead of putting this in a different post, I’ll just put it here. Here’s a reductio on the claim that a proposition p is evaluative if an evaluative fact makes it true. Let A = the sky is blue and let B = murder is wrong. Consider the true proposition in (1),
1. A & B
(1) is clearly evaluative on the account we have been given, since an evaluative fact is needed to make it true. The evaluative claim in (1) makes the disjunction in (2) true.
2. (A & B) v (A & ~B)
So (2) is an evaluative claim for the same reason that (1) is. But the disjunction in (2) expresses the same proposition as (3) (as we all know, they’re logically equivalent),
3. A
But then the proposition A is an evaluative claim. But recall that A states that the sky is blue. So we arrive at the false conclusion that the sky is blue is evaluative. I suppose it might be argued that logically equivalent propositions might not both be evaluative or both descriptive under the very same truth-making conditions. But, off hand, that’s not easy to believe.

9. Jussi Suikkanen says:

I really find something quite unintuitive in the way in which whether the conclusion b is evaluative or not depends on the actual, non-evaluative facts. If the Brits are tea-drinkers at the moment, it would be a non-evaluative statement that they are tea-drinkers or all New-Zealanders ought to be shot. Now, if all people unknowingly to themselvels as a group stopped drinking tea in Britain, then the statement would become an evaluative one. Presumably we wouldn’t even detect this. But that sounds odd. It just feels to me that whether a statement is evaluative or not ought to depend just on the terms used and their meanings rather than the contingent facts of the world that may change.
When it comes to the is/ought gap, I thought Searle and Jackson do pretty good job in bridging it put that is probably another story.

10. Mike A,
1. [](x)(EP)(x has relevant descriptive properties P only if x is right)
2. (Ex)(EP)(x has relevant descriptive properties P)
3. :. (Ex)(x is right)
–I think Karmo would allow that (1) is non-evaluative but say that (2) is evaluative. (1) is non-evaluative because it’s true according to every value system. But I think he’d say (2) is evaluative because I think “relevant descriptive properties P” in (2) means “the descriptive properties that would make something right”, and, after we fix all the descriptive facts, whether it’s true that there’s an action that has the descriptive properties that make an action right depends on what the correct value system is. (E.g., consider the bizarre value system on which the only thing it’s right to do is to fly to Mars.)
Also, in your other example (changing the numbers to avoid confusion)–
4. A & B
5. (A & B) v (A & ~B)
6. A
(where A is a true, clearly descriptive claim, and B is a clearly evaluative claim)–I think he’d say (4) is evaluative but (5) is descriptive. (4) is evaluative, as you say, because whether it is true depends on whether B holds (given that A already holds). (5) is non-evaluative, because whether it is true does not depend on which value system is correct; given the actual descriptive facts, (5) is true no matter whether B holds or not.
This might all seem vague. To really answer objections like yours, I have to be more precise about the criterion of evaluativeness. So:
Let’s say that a “value system” is a maximal consistent conjunction of clearly evaluative statements. A “possible world” is a maximal consistent conjunction of clearly descriptive statements. Let’s assume that for any unclear statements (statements like (4) and (5) where it’s not initially obvious whether they’re evaluative or descriptive), their truth value is fixed by a possible world together with a value system (i.e., a given combination of a PW and a VS is consistent with at most one assignment of truth values for all the unclear statements).
Now, let w be some possible world. For any unclear statement, u, we’ll say it is evaluative in w iff there exist value systems v1 and v2 such that (w & v1) entails u but (w & v2) entails ~u.
To illustrate, take your example “The sky is blue & murder is wrong.” This is evaluative in the actual world. Consider a value system v1 that opposes murder, and another value system v2 that endorses murder. In the actual world, the sky is blue. So the actual world conjoined to v1 entails “the sky is blue & murder is wrong”, but the actual world conjoined to v2 entails “It is not the case that (the sky is blue & murder is wrong)”.
Now take the case of “(A & B) v (A & ~B)”. This is non-evaluative in the actual world. Again, in the actual world, A holds. A entails “(A & B) v (A & ~B)”. So A conjoined to any value system still entails “(A & B) v (A & ~B)” (and also fails to entail “~[(A & B) v (A & ~B)]”).
A couple more illustrations. “A or B” is non-evaluative in the actual world, because (since A is actually true), the truth of “A or B” is independent of whether B holds.
“Some action or other has the relevant descriptive properties to make it right” is evaluative in every possible world. To see this, suppose that in world w, {F1,…,Fn} are the descriptive features had by actions that are performed. (I.e., for each member of {F1…Fn}, there’s an action performed in w that has it; and there are no other descriptive properties that any of the actions performed in w have.) Now consider a value system v1 on which each of {F1…Fn} are right-making features (let’s say they’re indefeasibly right-making). Also, consider another value system v2 on which each of {F1…Fn} are (indefeasibly) wrong-making. Then (w & v1) entails “Some action or other has the relevant descriptive properties to make it right”, but (w & v2) entails “It is not the case that Some action or other has the relevant descriptive properties to make it right”. Thus, “Some action or other has the relevant descriptive properties to make it right” is evaluative in w. (Note: not sure if I correctly interpreted your example statement here.)
Note that on Karmo’s interpretation, a statement doesn’t get to be evaluative just because some evaluative statement suffices to make it true. Rather, there has to be a value system on which the statement is true (given the descriptive facts), and another value system on which the statement is false.

11. Jussi,
Maybe Karmo’s characterization fails to capture our pre-theoretic understanding of “evaluative” and “descriptive” statements. (It also may well be that no precise characterization captures that.)
But his result is still of interest, because Karmo’s “evaluative statements” include all the statements that are uncontroversially evaluative, and his “descriptive statements” include all the statements that are uncontroversially descriptive. So he still shows that you can’t get from uncontroversially descriptive to uncontroversially evaluative statements.
We might phrase things differently. Karmo says certain statements are evaluative in some possible worlds but descriptive in others. But it doesn’t actually matter whether you think it’s proper to call these statements “evaluative” or “descriptive”. The point is that you can’t get from (statements whose truth doesn’t depend, given the actual facts, on a value system) to (statements whose truth, given the actual facts, depends on a value system).

12. Jamie says:

Mike A., what does ‘relevant’ mean in the argument?
Mike H. thinks it means ‘right-making’. If that’s what it means, then the argument pretty plainly has an evaluative premise. But I have my doubts that that’s the right interpretation, since if it were the first premise of the argument would presumably be unnecessary. We could just argue, “There is something with a right-making property. So, something is right.” If that argument is not valid, adding the first premise will not make it valid.
My first thought was that ‘relevant’ was just a helpful signpost for the reader. But if I leave it out of the argument, the argument is patently invalid. (Replace ‘right’ with ‘psychic’ to get an argument with true premises and a false conclusion.)

13. Jamie says:

Mike H., how do we know that there are any maximal consistent conjunctions of clearly evaluative statements?
For present purposes, a value system could just be an assignment of truth values to atomic evaluative sentences. Admittedly there would then be more work to do if some of the atomics are logically related to others, but to escape Prior we don’t need to worry about those relations.
Here’s one thing that is unsatisfying about Karmo’s solution. According to Karmo, somebody could have a perfectly consistent and reasonable collection of purely descriptive beliefs, and from them she could deduce a moral conclusion. This seems to violate even the spirit of Hume’s Law.
Here’s one thing that is very satisfying about Karmo’s solution: Karmo is a New Zealander.

14. Here’s a simple-minded response to Prior’s argument. (It’s fairly obvious; so I doubt it’s both original and good.)
Prior’s argument has the form of a dilemma, roughly as follows. Consider two sentences:
A. Tea-drinking is common in England.
B. All New Zealanders ought to be shot.
A is descriptive, and B evaluative. Their conjunction, (AvB), is either evaluative or descriptive. If it is evaluative, then the valid inference from A to (AvB) is a counterexample to Hume’s law. If it is descriptive, then the valid inference from ~B and (AvB) to A is a counterexample to Hume’s Law. So there is a counterexample to HL.
Now, here’s the response. Say that a sentence is purely descriptive if it is descriptive but not evaluative, and purely evaluative if it is evaluative but not descriptive. And define Hume’s law as follows:
(HL) There is no valid inference from purely descriptive premisses to a purely evaluative conclusion.
Prior’s argument is then valid only if we assume that (AvB) must be either purely descriptive or purely evaluative. But we might plausibly reject that assumption, saying either that (AvB) is both evaluative and descriptive, or that it is neither. In which case, Hume’s law is safe from Prior’s counterexamples.

15. Oops. I said ‘conjunction’ when I meant to say ‘disjunction’. Silly me.

16. Damn! Another mistake: I put ‘~B’ where I should have put ‘~A’, and ‘A’ where I should have put ‘B’.

17. David Sobel says:

After the fixes, Campbell’s thought seems good to me–the new motto would be “no pure ought from pure is”–but now perhaps I had better go back up and read about Prior.

18. A revision,
1.[](x)(EP)((P subvenes some moral property or other & x has P) only if x has some moral property)
2. (Ex)(EP)(P subvenes some moral property or other & x has P)
3. :. (Ex)(x has some moral property or other)
(1) now states more broadly that in every world, moral properties of actions depend on the subvening descriptive properties of actions. (1) is true in every world no matter what moral standards hold there.
Premise (2) simply says that in the actual world some action has some set of descriptive properties that subvene a moral property. Those subvening properties need not be what makes the action right; but any actions that has those properties is right. (2) does not depend on any particular moral theory or standard being true. Whatever evaluative standard holds, some action has some set of descriptive properties that subvene some moral property.

19. Jussi Suikkanen says:

How safe do you all think that Hume’s law is in the end even in the Campbell’s new and defined formulation? I mean if there were valid reductive analyses for evaluative terms wouldn’t they be enough to bridge the gap.
For instance couldn’t we get from the premise:
1. That act maximises happiness
to the conclusion:
2. Therefore, that act is right,
with a valid substitution of synonymous terms in the case that ‘right’ meant ‘maximizing happiness’?
Would that kind of a meaning claim count as a hidden evaluative bridge-premise in which case the Hume’s law would be safe? Or would the conclusion in that case count as a non-evaluative claim?
Of course the prospects of acceptable, simple definitions like that for evalutive terms are next to nothing. But, I take it that this is where Jackson’s network analyses are supposed to kick in by giving us logical equivalents for moral terms in terms of possible world sets from only supervenience and truth-apness.

20. Jussi,
Good question. Here’s a thought. Suppose the sentence
(1) That act maximises happiness
is synonymous with
(2) That act is right.
Plausibly, if two sentences are synonymous, then one cannot be evaluative unless the other is, and one cannot be descritptive unless the other is. From this it follows that if (1) is purely descriptive (in the sense I suggested above), then (2) is not purely evaluative. So the any inference from (1) to (2) would not violate Hume’s law, as I defined it.

21. Jussi Suikkanen says:

Campbell,
You are probably right. That shouldn’t be put in terms of synonymity. You could claim, as many do, that for instance ‘maximising happiness’ and ‘right’ have different senses but the same extension. This would give you substitutibility and still possibly an non-evaluative premise and an evaluatiave conclusion from it. I guess the question then would be, does the implicit premise ‘”right” refers to maximising happiness’ count as an evaluative claim or not? To me it doesn’t appear to be – no evaluative terms are being used, only mentioned. In this case, the Hume’s law is under a potential threat. Of course the reference claim is false, but that’s only for the illustrative purposes.

22. Robert Johnson says:

I too like Campbell’s reply. Also, apropos of Jamie’s appeal to the spirit of Hume’s law, I think it’s worth remembering amid the discussion of interesting formal questions that the sorts of arguments that Hume himself, and those who follow him, was exercised about are the patently invalid arguments from ‘is’ to ‘ought’ that are often made by moralists. It gives moral discussion the veneer of rational compulsion,when what’s doing the work to get to the conclusion is something else. Hume was surely right about these sorts of “arguments”. The crux of the ethical issue isn’t so much the ‘law’ against getting ought from is, that you can’t do it. It’s that (as Hume et. al. see it) moral judgments are reactions to facts, rather than inferences reason makes from those facts.

23. “. . . the sorts of arguments that Hume himself, and those who follow him, was exercised about are the patently invalid arguments from ‘is’ to ‘ought’ that are often made by moralists.”
But why get exercised about patently invalid inferences? I’m tempted to say that there had to have been more there for Hume to bother mentioning it. There is something on the face of inferences from ‘is’ to ‘ought’ that cries invalidity. It is not surpising at all that some simple inferences from ‘is’ to ‘ought’ fail miserably. It’s very surprising how hard it is to show that some invalid inferences from ‘is’ to ‘ought’ are more subtle and interesting: ones with broader implications for moral reasoning. I take it that this larger claim is what Karmo claimed to have established. Seems worth playing on Karmo’s field a bit and looking into what he did show.

24. Jamie says:

Campbell, I’m not sure what “evaluative and not descriptive” means. Are you thinking that the atomic sentences all have a clear classification and then the composite ones are purely descriptive iff all their atoms are?
That will block the Prior examples given so far, but I don’t think it’s going to solve the general problem.

25. Robert Johnson says:

Mike, I didn’t deny that the project isn’t quite interesting and important. Just pointing out something that might get lost, that a central reason to defend an is/ought gap is to respond to those who present themselves as establishing moral conclusions by reasoning from bare facts. You’re right that it’s not surprising that their arguments should be shown invalid so easily. What would be surprising is if turned out to be reason that was leading so many to give and accept these arguments — despite what their proponents might say. It doesn’t seem it could be reasoning that is leading them to their conclusions (given they are patently invalid). It seems instead a testament to the strength of their attitudes.

26. Miscellaneous replies:
asg–
An intuitionist would accept the supervenience principle–there’s a set of descriptive properties such that necessarily, an action is right iff it has them–although there need not be any single descriptive property that is right-making, and the set of right-making properties need not have anything in common other than that they make actions right.
Alan–
I didn’t understand your question, “Couldn’t Prior respond by saying the truth-conditions for (c), where Alfie’s statements are evaluative, are moral facts rather than Alfie’s assertions?” If the truth-maker for (c) contains some moral facts, then that seems to imply that (c) is evaluative. But Prior wants (c) to be descriptive so he can span the is-ought gap. In fact, I’m in agreement with you.
Mark–
Yes, I think what you say helps motivate Karmo’s approach to examples like that.
Jussi–
I don’t know the Jackson thing, but I have a reply to Searle (besides appealing to Karmo’s general proof). I think “A promised to do B” entails “A undertook an obligation to do B” only when “undertook” means something like “purported to place himself under”, not when it means “actually placed himself under”. For people to make promises, roughly speaking, there needn’t be any real obligations, only purported ones.
Jamie–
Provided any clearly evaluative statements are consistent, there must be maximal consistent conjunctions of them. By a “maximal consistent conjunction of clearly evaluative statements”, I mean a conjunction of clearly eval. statements such that (a) it is consistent, and (b) if you added another clearly eval. statement to it, the result would be inconsistent. There must be such a conjunction, since whenever (b) is not satisfied, you can just keep adding those clearly evaluative statements on (keeping (a) satisfied), until (b) is satisfied.
About what you say is unsatisfying: So here’s an example of what you say is possible. Suppose Jon rationally but mistakenly believes “Every cow has one stomach.” (Cows actually have four stomachs. This is my favorite example of a descriptive fact.) Jon validly deduces, “Every cow has one stomach, or murder is wrong.” According to Karmo, that conclusion is evaluative; it follows from the premise; the premise is descriptive; and Jon is perfectly reasonable in believing the premise and inferring the conclusion from it. However, of course Jon’s argument is unsound.
I don’t really think Karmo violates the spirit of Hume’s Law. I think what’s interesting about Hume’s Law (maybe even what Hume intended for it) is that it shows that there’s a problem in accounting for moral knowledge. It’s a piece in an argument for the conclusion that to account for moral knowledge, you need moral intuition (or for the conclusion that one can’t account for moral knowledge!). If Jon’s argument is unsound–and if there’s a general reason why it would have to be unsound given that it also satisfies the other conditions of interest (it spans the is-ought gap, is valid, and is non-trivial)–then that suffices to generate the problem of moral knowledge. Also note that it wouldn’t be rational for Jon in the example to believe that he’d spanned the is-ought gap–Jon would think his conclusion was descriptive.
Campbell–
I think what you say is right and consistent with Karmo. It’s consistent with what you’ve said to say that some statements (which are not purely evaluative or descriptive) can change their status as eval. or desc. in different possible worlds. The Karmo response to the dilemma you posed is that, when A is true, the “A; therefore (A v B)” inference has a descriptive conclusion; while the “~A; (A v B); therefore B” inference is unsound.
Mike A–
2. (Ex)(EP)(P subvenes some moral property or other & x has P)
I’m not clear whether this is evaluative, because I’m not sure what you’ll count as a moral property. E.g., some things are neither good nor bad, neither right nor wrong. Would you still say they have “moral properties” (e.g., the “moral property” of being evaluatively neutral?) If no, then (2) is evaluative, since some value system makes it false (a value system on which everything is evaluatively neutral). If yes, then I think (2) is non-evaluative, but then
3. :. (Ex)(x has some moral property or other)
–is also non-evaluative in Karmo’s sense because it’s true on all value systems (everything has to be either good, bad, or neutral, so everything has to have some moral property). Or we might just say that (3) is trivially true, so the argument doesn’t satisfy the desideratum of deriving a non-trivial evaluative conclusion from descriptive premises.
Jussi again–
I think meaning claims are non-evaluative, even if they’re about evaluative terms. E.g., “‘Right’ means ‘ought to be done'” is a non-evaluative fact. But I think any meaning claim of the form “‘E’ means ‘D'” where “E” is an evaluative term and “D” is descriptive is obviously false. And I think that if “x is right” really meant “x maximizes happiness”, then “x is right” would not be evaluative.
Also, more excitingly, I think the required disquotational principle would be evaluative. E.g., in the argument,
1. Act A maximizes happiness.
2. “x is right” means that x maximizes happiness.
3. If (“x is right” means that p, and p), then x is right.
4. So act A is right.
I think (3) is evaluative. (Note that we generally consider statements of the form “If D then E” to be evaluative when E is clearly evaluative. E.g., “If you promised to return the book, then you should return the book” is evaluative.)
Whew, I’m tired now.

27. Jamie says:

MikeH:
—-
By a “maximal consistent conjunction of clearly
evaluative statements”, I mean a conjunction of clearly eval. statements such that (a) it is consistent, and (b) if you added another clearly eval. statement to it, the result would be inconsistent. There must be such a conjunction, since whenever (b) is not satisfied, you can just keep adding those clearly evaluative statements on (keeping (a) satisfied), until (b) is satisfied.

I don’t get it. How do you know that (b) will ever be satisfied? That was what I was doubting. Not exactly doubting, but I’m completely agnostic about it. Maybe for every consistent conjunction there is some new conjunct that could be added consistently.
As to the point about knowledge: I agree that seems significant. But suppose we could manage to be *as justified* in some ethical belief as we are in our non-ethical beliefs. This would be a sense in which moral epistemology was no worse off than non-moral epistemology. But when we can deduce a statement, that’s a sense in which we are as justified in believing that statement as we are in believing the premises. (Actually I don’t really believe that, though I think it’s true in special cases.)

28. Jamie,
Yes, that’s just what I had in mind. Here’s a better way to put it. Say that a sentence if purely descriptive iff all of its atomic parts are descriptive and none is evaluative. (Mutatis mutandis for purely evaluative.) I think it would be straightforward to prove, in a suitable logic, that for any assignment of the propoerties “evaluative” and “descriptive” to atomic sentences, there are no valid, non-trivial inferences from purely descriptive to purely evaluative. The reason is that, in a valid, non-trivial inference, pereferences and conclusion must have at least one atomic part in common. If that shared atomic sentence is evaluative, then the premises are not purely descriptive, and if it is descriptive, then the conclusion is not purely evaluative.

29. Mike H,
Yes, it occurred to me moral nihilism world would falsify (2). You say,
“Would you still say they have “moral properties” (e.g., the “moral property” of being evaluatively neutral?) If no, then (2) is evaluative, since some value system makes it false (a value system on which everything is evaluatively neutral).”
This interestingly depends on whether morally nihilistic worlds are possible. For lots of reasons, some having to do with imaginative resistance, I’m not sure there are any. It is inconceivable, for instance, that gratuitous harm is morally neutral.
And if there are no worlds in which gratuitous harm is morally neutral, then no worlds/evaluative standards falsify (2).

30. I claim that the sentence,
(1) Either tea-drinking is common in England or all New Zealanders ought to be shot,
is both descriptive and evaluative. Here’s my argument.
The content of a sentence is given by a division between possibilities (I think this is one of Frank Jackson’s slogans). To grasp or understand a sentence is know which possibilities it rules out and which it rules in. In the case of (1), if a possibility is ruled out, this is because of both its descriptive and its evaluative features; neither its descriptive features nor its evaluative features alone would be sufficient to rule it out. (Or to put it differently, some possibilities are ruled in because of their descriptive features, and others because of their evaluative features). So (1) has both descriptive and evaluative content.
Karmo points out that one can know that the actual world is ruled in by (1) without consulting the evaluative features of the actual world. But to know merely whether the actual world is ruled in or out is not yet to fully understand the sentence. One must also know whether those possible worlds in which tea-drinking is not common in England are ruled in or out. The latter is an evaluative matter.

31. Jamie says:

Campbell, what does “non-trivial” mean here?

32. Campbell, you say (a few notes back),
“Say that a sentence if purely descriptive iff all of its atomic parts are descriptive and none is evaluative”.
Now this seems fine for truth-functional connectives. It looks a little like the beginning of an evaluative-functional definition. The impurely descriptive would presumably include some atomic evals and some atomic descrips. So this sentence (from just above),
(1) Either tea-drinking is common in England or all New Zealanders ought to be shot,
would be, more accurately, impurely descriptive and impurely evaluative, if I’m tracking this. But what do you do with non-truth-functional connectives? Consider (2)-(4) for instance.
2. Steve believes murder is wrong.
3. It is a well-known law that murder is prohibited.
4. It is possible that murder is not wrong.
(2) does not look evaluative to me, though it’s sole atomic sentence is evaluative. Neither does (3) or (4). These seem neither truth-functional nor (if you will) evaluative-functional.

33. Heath White says:

Here’s an is-ought inference that MacIntyre uses somewhere:
Joe is a sailor,
So, Joe ought to do whatever a sailor ought to do.
How does that fare on the proposed semantics?

34. Heath,
That conclusion is trivially true, and I think it’s agreed (on any proposal above) that trivial truths follow from anything.

35. Whoa! Scratch that, Heath. I mean the conclusion doesn’t follow.

36. Jamie,
‘Non-trivial’ means that the premises are not a logical contradiction and the conclusion is not a logical tautology.
Mike,
That’s right. I was thinking only of truth-functional connectives. So, I guess, my argument shows at most only that Hume’s law holds for arguments composed out of atomic sentences and truth-functional compounds. That’s enough to defeat Prior’s tea-drinking counterexample. But it won’t do for others, such as the one suggested by Heath.

37. On Heath’s example, it might be said that the conclusion implies that there is something that a sailor ought to do (I imagine this is so on a Russellian analysis). But the premise does not imply this. So the argument is invalid. Perhaps that’s what Mike had in mind.

38. I see, Campbell. Heath’s doesn’t present a worry either.
1. Joe is a sailor.
2. :. Joe ought to do whatever sailors ought to do.
(2) does not follow from (1). Suppose Joe is also a dancer and doing what a dancer ought to do overrides doing what a sailor ought to do. In that case, Joe ought to do whatever dancers ought to do. Presumably, on that occasion, Joe ought to dance, not sail.

39. Heath White says:

I think the objections so far can be dodged. Consider
Joe is a sailor.
Therefore, For any action A, if A is an overriding obligation for any sailor, then Joe ought to perform A.
The conclusion does not entail that sailors have any overriding obligations, and the obligations it does mention cannot be overridden by the obligations of dancers. But it still looks evaluative.

40. Heath,
Still doesn’t follow. Suppose Joe is landlocked…

41. Heath,
Just to be clear, if Joe is landlocked, then what sailors overridingly ought to do is not something that Joe can do. So it is not true that Joe ought to do it. There are obviously many other conditions that would have to be met: e.g. that Joe is not a disabled sailor, or a demented sailor, or a moribund sailor and so on and on.
The argument is also an enthymeme. That is there is a suppressed premise in the argument,
1′. If Joe is a sailor, then Joe ought to do what a sailor (all things considered) ought to do.
And (1′) is as much a candidate for an evaluative sentence as the conclusion.

42. Heath White says:

Over lunch, I figured out the nub of the problem. I think everyone agrees that there are lots of 2-premise arguments to evaluative conclusions of the form
[Descriptive Premise]
[Evaluative Premise]
So, [Evaluative Conclusion]
For example (they’re easy to generate),
I am a rational being
Rational beings should treat other rational beings as ends in themselves.
So, I should treat other rational beings as ends in themselves.
But for any such 2-premise argument, there will be a 1-premise argument of the form
[Descriptive Premise]
So, [if EP then EC]
e.g.
I am a rational being.
So, if rational beings should treat others as ends in themselves, then I should treat others as ends in themselves.
I think it’s obvious that in the 1-premise argument, the premise is descriptive. And it’s pretty clear that the conclusion is evaluative and non-trivially so. I’d be interested to hear arguments to the contrary.

43. Heath, that’s pretty clever,
As far as I can tell, the argument has this form,
1. Ra
(a is a rational being)
2. (x)(y)((Rx -> xTy) -> aTy)
(if all rat. being should treat everyone as an end, then a should treat everyone as an end).
Looks to me like (2) does follow from (1). But it doesn’t follow that (2) is not trivially true. For all we can tell from this argument, the antecedent in the conclusion is false (i.e., for all I know from this argument, no rational beings have such an obligation). That’s one cost of tucking premises into antecedents.

44. Heath,
I may be able to extend the strategy I proposed above to handle your example too. You suggest two arguments. Here’s the first:
A1. Ra
A2. (x)(Rx -> Tx)
So,
A3. Ta
I say any instance of a universal generalisation is a part of it. So (Ra -> Ta) is a part of (x)(Rx -> Tx). And any consequent of a conditional is a part of it. So Ta is part of (Ra -> Ta). And parthood is transitive. So Ta is part of (x)(Rx -> Tx). And a purely descriptive sentence cannot have an evaluative part. So, if the conclusion A3 is evaluative, then the premise A2 is not purely descriptive.
Here’s the second argument:
B1. Ra
So,
B2. (x)(Rx -> Tx) -> Ta
By parallel reasoning, I say B1 is part of B2. So, if B1 is descriptive, B2 is not purely evaluative.
So either way, you don’t get a purely evaluative conclusion from purely descriptive premises.

45. Jamie says:

Campbell, there aren’t many purely ethical statements now. Indeed, the statement that was supposed to be the *paradigm* of an ethical statement (“All New Zealanders ought to be shot”) now turns out to be partly descriptive.

46. Jamie,
The objection from those insisting on a sound is-ought argument with a conclusion that is non-trivially evaluative will be pretty clear. Consider this argument,
1. Ra
2.(x)(y)((Rx -> xTy)
3. :. aTx
This will meet the requirements only if
(2) is true and non-evaluative. But, if true, then (2) is clearly non-trivial and evaluative.
Now suppose it is suggested that the solution to this problem is that you just move premise (2) into the antecendent of a conditional conclusion.
1′. Ra
2′.:. (x)(y)((Rx -> xTy) -> aTy)
Can you imagine for a moment that their worries would be assuaged? Obviously, they will now say that we have no assurance that the conclusion is not trivially true: i.e. they have no assurance that the consequent of the antecedent is not false for every rational agent. And indeed there is no such assurance.

47. Jamie says:

Hm.
I was pointing out that Campbell’s suggestion, which is distinct from Karmo’s, has as a consequence that what was supposed to be the paradigm of an evaluative sentence turns out to be mixed.

48. I’m worried about the sort of implication that is at issue in these debates. For all I know different parties to this debate have different ideas in mind and maybe even legitimately so given what they take Hume’s Law to show. In particular, do the rules for constructing valid arguments allow replacement of synonyms with synonyms? Co-referential expressions with co-referential expressions? Necessarily co-referential expressions with necessarily co-referential expressions? Some of the examples above seem to be even looser than that, for example the sailor example.
For example is this a valid inference according to the rules?
(B) My bucket has a hole in it.
Therefore, (P)there is a pail with a hole in it.
It seems that different theorists will regard the arguments question-begging on most of the standards for valid inferences. If the standard allows substitution of synonyms analytic reductive naturalists will think they have examples of valid is/ought arguments. If the standard allows substitution of co-referential expressions (and the analogue for property terms) synthetic reductive naturalists may well claim they have examples which cross the divide as well.
If the standard allows any inference where necessarily the conclusion must be true whenever the premises are, and someone has robust views about what metaphysically necessitates what, all sorts of inferences will count as valid.
My antecedent impulse is to think that there is something to Hume’s Law, but I’m no longer sure that my sense that there is depends on other controversial metaethical assumptions.

49. Jamie–
(a)
About the maximal consistent conjunctions of purely evaluative claims: Are you questioning whether infinite conjunctions exist? You seem to be imagining a case in which there is an infinite series of evaluative claims, (E1, E2, …), such that when you conjoin each successive claim to the earlier ones, the result is still consistent. And you never get to the end, so you never get the maximal consistent conjunction. But, provided you allow infinite conjunctions, I would just ask you to consider the conjunction of all the members of that series.
Maybe then you would say: but there could then be yet another evaluative claim, E1a, which could be consistently conjoined to that infinite conjunction. And then an E2a, and so on. And then I’d say: “Okay, just throw in all of those.” In fact, just throw in all the claims that are going to appear anywhere in any sort of series of this kind that you’re going to claim exists. (This move might be problematic if you have some sort of Russell-style paradox coming. But that sort of thing probably won’t ultimately be relevant to the is-ought gap.)
(b)
I think Campbell’s approach is still of interest, even though it makes “All New Zealanders ought to be shot” not purely evaluative. This is because statements that are directly action-guiding, like “I should do A now”, are still purely evaluative. Also, our basic empirical evidence is purely descriptive. So Campbell gets us to the point that you won’t be able to figure out what you ought to do at some time on the basis of empirical evidence. (Again harking back to the problem of moral knowledge.)
Mark–
I think we should allow substitutions of synonyms, but not allow substitutions of necessarily coextensive terms. We shouldn’t allow the latter, because in that case, anyone who thinks (a) there is a true comprehensive moral theory, and (b) moral truths are necessary, would reject Hume’s Law — and Hume’s law would seem really uncompelling. Also, if you allow substitutions of necessarily coextensive expressions, then the fact that I have a glass of water “entails” that I have a glass full of H2O molecules. But that “entailment” goes no distance toward explaining how I know about H2O molecules. And I think the is-ought gap is mostly interesting for its implications for moral epistemology.
Heath–
So to simplify slightly, we could have:
D.
:. [(D -> E) -> E].
where D is some descriptive proposition and E is evaluative. (D; therefore, if (if D then E) then E.) The conclusion is nontrivial, and it looks evaluative, since usually statements of the form p -> E, with E evaluative, are evaluative.
Karmo would say–and this seems plausible to me:
Either D is true or it’s false. In worlds in which D is true, the conclusion [(D -> E) -> E] is non-evaluative. This is because every value system will agree on that conclusion. For example, I agree that if (if the sky is blue then you should torture babies), then you should torture babies. Of course, this has nothing to do with how I feel about baby torture (since the antecedent of the whole statement is false, it doesn’t matter what the consequent says).
On the other hand, in worlds in which D is false, the conclusion [(D -> E) -> E] is evaluative. For instance, “[If (if 2=3, then you should torture babies) then you should torture babies]” is evaluative: its truth depends on whether you should torture babies. (The antecedent of the whole statement is true, so the truth of the whole statement depends on the truth of the consequent.) However, the argument is unsound since D is false, so it doesn’t help us gain any moral knowledge.

50. Mike A–
I think I agree with you: nihilism is false in all possible worlds. However, all we need is that there exists a consistent nihilistic “value system” (if you want to call it a value system). We can see intuitively that nihilism is false, but it still isn’t inconsistent.
Also, now I’m unsure how you intended your (2). Consider a possible world in which all that exists is hydrogen. In that world, is nihilism true? One might say “yes, because nothing in that world is good, bad, right, or wrong.” Or you might say “no, because it’s still true that ‘pleasure is good’, even though there are no instances of pleasure.”

51. Jamie says:

I agree with Mike H. about which kind of ‘validity’ or ‘entailment’ matters. Think of Hume:
“…what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.”
Mike, as a purely technical matter we can’t assume that there is any series the infinite conjunction of which is a maximally consistent (evaluative) conjunction. I wasn’t expressing doubt about the existence of infinite conjunctions. I suppose if there are large cardinal conjunctions I can (maybe) see why there must be maximal consistent ones (some analog of transfinite union), but I don’t know just what kinds of things those conjunctions would be. They wouldn’t be sentences, that’s for sure!
As a less technical and more philosophical matter, it just seems to me to be a substantial issue, a substantial question, and not one answered by trivial considerations, whether there are any maximally consistent conjunctions in one domain or another. It’s not that I have some idea of what prevents it; rather, I can’t see any good reason to think it’s one way or the other.
This doesn’t seem crucial to the very idea of a ‘value system’, in any case.

52. Mike H.,
How do you know that the proposition,
(x)(y)((Rx -> xTy) -> aTy)
is not trivially true? For all I can tell, the antecedent is necessarily false. I wonder how you know it isn’t?
—————
Jamie,
The consistency claim is very interesting. It might be true that any maximally consistent set S includes a maximally evaluatively consistent set S’. Roughly, suppose S is max. consistent. Let E be some purely evaluative proposition. It is impossible to add E to S without contradiction (by def. of maximal consistency). But E is not inconsistent with any descriptive claim in S (no purely evaluative proposition is inconsistent with a descriptive proposition). So E is inconsistent with some subset of evaluative claims S’ in S. But we chose E arbitrarily. So any such E is inconsistent with S’. But then S’ is maximally evaluatively consistent. No?

53. Jamie,
I think the sentence “All New Zealanders ought to be shot” is both evaluative (ethical) and descriptive. I don’t see a reason to say that it’s evaluative for which there’s not a parallel reason to say it’s descriptive. For example, you might say it ascribes the evaluative property of being a thing which ought to be shot to all New Zealanders; so it’s evaluative. But, I say, it also ascribes the descriptive property of not being a New Zealander to everything that is not a thing which ought to be shot; so it’s also descriptive.

54. Jamie says:

Mike A.,
Not sure about that — I guess it depends partly on what kind of consistency is meant. (Consistent set = there is a world in which all are true, or do we mean logical consistency?) But in any case, I say the same thing about maximally consistent sets of propositions as I say about maximally consistent evaluative conjunctions.
Campbell,
Fine, but this is apparently a different sense of being evaluative than the one Prior, at least, had in mind.
This topic may have run its course, but here’s another way of thinking about what seems unsatisfactory to me about both Campbell’s and Karmo’s way of recapturing the kernel of Hume’s Law. Hume’s point seems to me to be a close relative of Moore’s point in advancing the Open Question Arg. (I think Mike H. agrees.) But that point doesn’t have to do with logic-in-the-strictest-sense. It has to do as much with analyticity. And the Karmo-type protection from the Prior-ish counterexamples has nothing to do with analyticity. This is why I think Frank Jackson’s approach, though much less discussed even than Karmo’s, is more to the point. (1974: ‘Defining the Autonomy of Ethics’. Philosophical Review 83.)
(By the way, both Campbell and Toomas ought to be shot. Unless, of course, tea drinking is common in England. I’ll have to look into that possibility.)

55. (By the way, both Campbell and Toomas ought to be shot. Unless, of course, tea drinking is common in England. I’ll have to look into that possibility.)

Prior, too. But I guess it’s too late for that now.

56. Jamie says:

I am ashamed to admit that I did not know that about Prior. I knew he spent a large part of his career in NZ, but not that he was… one of you.

57. Heath White says:

Well, one last set of questions, regarding the attributive use of ‘good’ and ‘bad’. The following seem to me to be something close to conceptual truths:
Farmers who regularly grow lots of healthy crops are good farmers.
Guns which have a tendency to blow up when fired are bad guns.
Arguments which affirm the consequent are bad arguments.
Watches which tell time accurately are good watches.
If these are conceptual (thus necessary) truths, then the following seem to be valid arguments:
Joe is a farmer who grows lots of healthy crops. / Joe is a good farmer.
This is a gun with a tendency to blow up when fired. / This is a bad gun.
My Seiko tells time accurately. / My Seiko is a good watch.
Do we say (a) That attributive uses of ‘good’ and ‘bad’ are not reallly evaluative? (b) That premises with functional terms in them (‘farmer’ ‘gun’ ‘argument’ ‘watch’) are not really descriptive premises? (c) The arguments are enthymematic, and must include the (evaluative) conceptual truths I began with? This last option entails that some evaluative truths are conceptually true, which at least runs counter to the spirit of Hume, and also allows us to make this argument:
x is a watch / x is a good watch iff it tells time accurately.

58. I think some instances of “x is a good A” are non-evaluative. For instance, I may acknowledge that Joe is a good assassin, but I’m not endorsing Joe, what he does, etc. Another, more common case is that of judgements as to what is a good way to get oneself killed. Driving while drunk is a good way to get yourself killed. I’m not endorsing drunk driving in any respect.
But some instances of “x is a good A” are evaluative, like “Joe is a good man.”

59. Heath White says:

Mike,
That was more or less the response I anticipated. I wanted to bring up the issue because there is an approach to ethics (virtue) on which “good watch” and “good man” are the same kind of claim. On that view, the fact that we have conceptual truths about good watches but none about good men says more about the state of our concepts than any metaphysical (or psychological or linguistic; whatever) divide between descriptive and evaluative claims. (In simpler societies, and even in our society in most cases, there is no more mystery about what makes someone a ‘good man’ than about what makes something a good watch.)
There are a number of things one could say at this point: that Hume’s claim is contingent on, or reflective of, a non-virtue approach to ethics; that Hume proved the virtue approach bankrupt; or no doubt something else. But we should probably let this thread die….

60. This is a hugely interesting thread. Thanks, Mike, for drawing Karmo’s paper to our attention!
I’m inclined to think that for the absolute “state of the art” on the “Is-Ought gap”, one has to read Gerhard Schurz’s book, The Is-Ought Problem: An Investigation in Philosophical Logic (Kluwer, 1997). It’s a ferociously technical essay on deontic logic, but I think he succeeds in capturing the intuition behind Hume’s Law better than anyone else. His idea, roughly, is that the most defensible version of Hume’s Law is that no deontic conclusion follows non-trivially from any set of wholly non-deontic premisses. For a deontic conclusion to follow “trivially” from a set of premisses is (very very very roughly) for it to be the case that a corresponding statement with any other deontic component whatsoever would also follow from the same set of premisses in the same way.
Prior’s inference doesn’t count as a counterexample to this version of Hume’s Law, because you could substitute any other atomic deontic sentence (like ‘All New Zealanders ought to become Professors of Philosophy in the UK’) for the atomic sentence that features as a component of Prior’s conclusion (‘All New Zealanders ought to be shot’), and you would still have a valid inference.
However, we would still have a counterexample to the Is-Ought gap if “‘Ought’ implies ‘Can'” is a logical or analytic truth, because then ‘A cannot F’ implies ‘It is not the case that A ought to F’. If the ‘may’ of permissibility is the dual of ‘ought’, then ‘A cannot F’ implies ‘It is permissible for A not to F’. Moreover, if (as I’m inclined to believe) the ‘may’ itself implies at least a weak sort of ‘can’, then the appropriate sort of ‘cannot’ implies ‘may not’ (i.e., if you can’t do it, it’s not permissible for you to do it); and if ‘may’ is the dual of ‘ought’, it follows that ‘It’s impossible for A not to F’ entails ‘A ought to F’.

61. Jamie says:

That was Frank Jackson’s idea, the ‘non-trivially’ formulation. (For the record.)
And as you say, Ralph, it’s actually a lot harder to formulate than one might think.

62. Thanks, Jamie, for this! Could you remind us where Jackson suggests formulating the idea in terms of “non-trivial” implication?
Even though (as you say) this idea is so hard to formulate precisely, I believe that Schurz has succeeded both in giving a precise formulation of the idea, and in proving that it is in fact a theorem of the metalogic of absolutely all normal deontic logics. So even if it was Jackson had the original idea, it was Schurz who worked out the idea in full detail.

63. Jamie says:

‘Defining the Autonomy of Ethics’, Philosophical Review 83 (1974).