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.

Comments

[Jamie]

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.

[Mike Almeida]

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?

[Campbell]

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.

[Jamie]

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.)

[Campbell]

(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.

[Jamie]

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.

[Heath White]

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.
Your argument affirms the consequent. / Your argument is bad.
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.

[Michael Huemer]

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."

[Heath White]

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....

[Ralph Wedgwood]

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'.

[Jamie]

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.

[Ralph Wedgwood]

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.

[Jamie]

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