Can an OUGHT follow from no ISs?

Suppose murder just is wrongful killing. Then it seems that Sally ought not murder Bob follows from no premises, the empty set of premises. Trivially, the empty set of premises is a set containing only descriptive premises, in Hume’s sense. But then, Sally ought not murder Bob, a substantive normative claim, follows from a set of purely descriptive sentences. So, you can derive an ought from iss. Take that, is-ought gap.

I have some half-baked potential responses in mind, but let’s see what you think.


27 Responses to Can an OUGHT follow from no ISs?

  1. nate charlow says:

    Well, the standard claim is that you cannot derive a non-trivial “ought” (i.e., not a logical truth) from a premise-set containing no “ought”s (see, e.g., Prior’s “The Autonomy of Ethics”). Insofar as “Sally ought not to wrongfully kill” “follows” from an empty premise-set, it probably counts as a logical truth (in this case, a validity of some species of deontic logic with a “wrongness” predicate), and isn’t a counterexample to Hume’s Law.

  2. Marc Artiga-Galindo says:

    Could you please develop the idea that the empty set of premises is a set containing only descriptive premises? that does not seem obvious to me. If a set does not have members, how can you determine their properties?

  3. Dustin Locke says:

    Marc, a set contains only members with property if and only if it does not contain a member that does not have property P. Since the empty set contains no members, it thus contains only members with property P, for any property P, including the property of “being a descriptive premise”.

    In English, “only members with P” usually implies/implicates that there ARE SOME members, and that theses have P. In logician/philosopher speak, we ignore that implication/implicature.

    • Marc Artiga-Galindo says:

      But then, it is not true that ‘a subtantive normative claim follows from a set of PURELY descriptive sentences’. If, for any property P, the empty set only contains members with P, then this empty set also contains normative sentences.
      To say that the empty set ONLY contains members that are P is different from saying that it contains members that are ONLY P, isn’t it? If I understood you properly, from the claim that it is the empty set it follows the former, but you need the later in ordrer to get to the conclusion.
      (I apologize for the capital letters, but I don’t know how to write italics here)

    • Hey there Marc,

      Yeah, I was thinking what Dustin said. A set that contains no members trivially satisfies the claim that all of its members are P-members, for any P. You’re right to point out the ambiguity in the English between “contains only” and “only contains”, and I was imagining that the natural way to interpret “contains only” is the same as “only contains”. Maybe that’s wrong, and “contains only” requires non-emptiness whereas “only contains” doesn’t. For the argument to go through, I mean to use whatever language doesn’t implicate the existence of members.

  4. al says:

    Yeah, I think Nate and Professor Locke have got it right. Maybe one way to think of it is as a dilemma: either ‘x ought not murder y’ is trivially true, or it’s a substantive claim. If the former, what Nate and Dustin said. If the latter, then it looks like ‘murder just is wrongful killing’ is a substantive claim as well, in which case you actually are using a premise, and one that has normative content as well. But you might want to check out the prologue to Prinz’s ‘The Emotional Construction of Morals’ where he discusses this.

    • Hey Alex, Nate and Dustin,

      Thanks. I’m starting to think this is right. My immediate reaction was that it is a substantive normative claim, but that option is not as promising as I thought, as Alex points out.

  5. Dustin Locke says:

    I like the discussion of the ‘Is-ought fallacy’ in Richard Joyce’s “The Evolution of Morality”.

  6. Lewis Powell says:

    Gillian Russell has a good paper defending Hume’s law, I think it addresses examples like this one, but I could be mis-remembering:

  7. The most sophisticated discussion of the ‘Is’-‘Ought’ gap, in my view, is a ferociously technical treatise on deontic logic: Gerhard Schurz, *The Is–Ought Problem: An Investigation in Philosophical Logic* (Dordrecht: Kluwer, 1997). As Schurz convincingly argues, the claim that there is an ‘Is’-‘Ought’ gap must be the claim that there is no *non-trivial* ‘ought’ proposition that can be derived from non-normative premises. So the task is to define a notion of “non-triviality” on which this comes out true, on any reasonable deontic logic.

    Is ‘Sally ought not to wrongfully kill Bob’ a “trivial” truth in the relevant sense?

    It is surely not trivial that it is metaphysically possible for killings to be wrongful. And some philosophers might think that if it is *metaphysically impossible* for Sally to wrongfully kill Bob, then it would not be true that Sally ought not to wrongfully kill Bob. (Is it true that Sally ought not to simultaneously be a prime number and not a prime number?) So these philosophers would be committed to denying that ‘Sally ought not to wrongfully kill Bob’ is trivial (since in their view it entails that it is possible for some killings to be wrongful).

    However, I would strongly disagree with these philosophers. It follows from my semantics for ‘ought’ that if it is impossible for an agent x to be such that p, then x ought not to be such that p. (Moreover, in standard deontic logic, if p is *logically* impossible, then ‘It ought to be that not-p’ is a logical truth.) Still, I wonder how many other philosophers would share my view about this….

    • Hey there Ralph,

      Thanks for the comments. I plan to look into the non-triviality option some more, since it certainly seems that this sentence isn’t trivially normative in the sense that “Either you ought to \phi or it’s not the case that you ought to \phi.” is. But, as Alex pointed out above, the non-triviality option does look like it needs to claim that the premise that murder is wrongful killing is also substantive. I’ll think about whether one could get around this.

      Thanks again!

  8. Incidentally, ‘Sally ought not to murder Bob’ certainly doesn’t follow from the *empty* set of premises, because it would surely be false if Sally doesn’t exist. (It is surely *not* true that Santa Claus ought not to murder me!)

    Indeed, if this occurrence of ‘ought’ is what I call the “practical ‘ought'”, then it is implicitly indexed to a *time*, and so will not be true unless Sally exists and is an agent *at that time*.

    • Yes, that’s right. I was (willfully) ignoring that at the outset. These conditions can just be thrown into an antecedent of a conditional with my sentence as the consequent. I have the intuition that if the categorical statement is substantive, then so is the relevant hypothetical.

    • Jonathan Livengood says:

      Why are you so confident that the statement, “Santa Claus ought not to murder me,” is false? I would have thought it was vacuously true that non-actual agents shouldn’t actually do anything. Anyway, I’m especially surprised since you said earlier, “It follows from my semantics for ‘ought’ that if it is impossible for an agent x to be such that p, then x ought not to be such that p.” I’m not sure what sense of “impossible” you had in mind, and I know there are other fiddly details as well (like how to fix reference to Santa Claus). However, on a first reading, it looks natural to me to say that Santa Claus is the kind of agent such that it is impossible for Santa Claus to murder you (or me or any other actual person). And hence, on your own semantics, Santa Claus ought not to murder you. Could you fill in some details to clear this up for me?

    • Thanks, Jonathan!

      Actually, I didn’t say that ‘Santa Claus ought not to murder me’ was *false*: I said that it was *not true*. (On the “truth-value gap” view of non-referring names, the sentence would be neither true nor false.)

      I was assuming that Daniel’s example ‘Sally ought not to murder Bob’ involved the practical ‘ought’, which is always indexed to an agent (and a time). On this interpretation, the sentence ‘Santa Claus ought not to murder me’ is logically equivalent to one that ascribes the property of *being an agent x such that x ought not to murder me* to Santa Claus. Surely it is plausible that no such sentence is true!

      Admittedly, there is another possible interpretation of ‘Santa Claus ought not to murder me’ — an interpretation on which it involves, not the practical ‘ought’, but what I call “the ‘ought’ of general desirability”. On this interpretation, it is roughly equivalent to: ‘In all the relevantly desirable possible worlds, it is not the case that Santa Claus murders me.’ I agree that this sentence is vacuously true.

      Anyway, here is a more careful statement of what my semantics entails about the practical ‘ought’ (which in my view is always indexed to an agent and a time): If an agent x and time t are such that x is an agent at t, and it is impossible for x and t to be such that p, then at t, x ought not to be such that p.

    • Jonathan Livengood says:

      You’re right that you didn’t say that “Santa Claus ought not to murder me” is false. I should have read more carefully. However, you *did* say, “‘Sally ought not to murder Bob’ … would surely be false if Sally doesn’t exist.” Could you tell me what the relevant difference is between Sally and Santa, or was the remark about Sally a slip of the keys, or were you just playing with your appeal to truth-value gap theories of reference?

      I agree that it is *plausible* that the statement, “Santa Claus ought not to murder me,” is not true. But then, I think that the statement, “Santa Claus ought not to murder me,” is true is also plausible. What I was asking was what reasons inspired the confident statement you made that *surely* the target sentence is not true. (Or do you think that it is impossible for both p and ~p to seem plausible? — in which case, I’m not sure that either one is plausible.)

      On your revised version, does something have to be an *actual* agent at time t? I was reasoning that since Santa is a fictional agent at time t (for some t and maybe for all t), Santa is an agent simpliciter at time t. Moreover, Santa is such that at any time t, it is impossible for Santa to be such that Santa murders me. Hence, Santa (still) ought not to be such that he murders me.

    • Lewis Powell says:


      It seems to me that being a fictional agent at time t no more entails being an agent (simpliciter) at time t than being a fake policeman at time t entails being a policeman (simpliciter) at time t.

    • Jonathan Livengood says:

      If you mean by “fake policeman” somebody who impersonates a policeman in real life, then I think I agree with you. Being a fake policeman in that sense would not entail being a policeman. But I’m not sure the same is true for *fictional* policemen. I want to say that Lestrade is a policeman, not a fake policeman. Whereas, the T-1000 in the second terminator movie is not a policeman but sometimes pretends to be one (and in those cases is a fake policeman).

      Going further, there are a lot of at least apparently true things to be said about fictional characters, events, and objects. For example, Santa is a right jolly old elf who drives a sleigh pulled by flying reindeer. And Sherlock Holmes is a brilliant detective who lives at 221B Baker Street and wears a deerstalker hat (though maybe the deerstalker is only in movies and tv). All of these attributions are going to be a yes and no sort of thing. Does Santa fly a sleigh? Well, yes and no. Yes in that he is depicted as flying a sleigh. No in that he doesn’t *actually* fly a sleigh. Agency seems to work similarly. And if that is right, then I think it is fair to ask, “In what sense does something need to be an agent at time t for the semantics of practical oughts to apply?”

      Anyway, I don’t think it is at all clear that they don’t apply, since they seem to apply perfectly well within the context of fictions. I think it is perfectly sensible to say, “Sherlock ought not to use so much opium,” or “the T-1000 ought not to murder policemen.”

    • Lewis Powell says:

      I don’t think the inference from “x is depicted as F” to “x is F” is valid. In general, things that are not F can be depicted as being F without thereby becoming F.

      I think that, in some settings, we may have a background assumption that we are talking about what a particular fiction or myth or legend depicts as being the case, and so, utterances of “Santa flies a sleigh” in those settings would assert that the popular myth depicts Santa as flying a sleigh. It is even possible to take the question “Does Santa fly a sleigh?” as ambiguous between a question about what is depicted by the popular myth vs. what is the case in reality, and explain why sometimes it is correct to say “yes” in reply to the question. But this does not require thinking that there is a sense in which it is true that Santa flies a sleigh.

    • Lewis Powell says:

      In other words, I don’t think there is a sense in which Santa flies a sleigh; even though I think sometimes we might convey a true claim by saying the sentence “Santa flies a sleigh”. It is not that there are two ways of flying a sleigh: actually and fictionally; there is one way of flying a sleigh, and some fictions claim (falsely) that Santa flies a sleigh in that way.

    • Jonathan Livengood says:


      Your approach to fiction looks reasonable. Still, I’m not convinced that it is *obviously right* or that the position I’ve been staking out is *obviously wrong*. Recall that this all started with Ralph confidently asserting that sentences of the form “x ought not to y” are not true if x is non-actual, and then me asking why he was so confident. (I was assuming that for a philosopher to confidently endorse p, he or she needs to have good reasons for believing p, and I wanted to know what those reasons were.)

      I think you’re right to locate the issue with something like the inference from “x is depicted as F” to “x is F.” But notice that the validity of the inference depends on the sense that we give to the second phrase, “x is F.” If “x is F” means “x is F in the actual world,” then I agree that the inference is invalid. My follow-up question to Ralph was exactly about how he understands phrases of the form “x is F.” If he wants to stipulate that for “x is F” to be true, x has to be an actual something-or-other, then I’m happy. I’ll know how he’s using his terms. However, I think it is sometimes reasonable — maybe only for fictions and hypothetical constructs — to say that “x is F” means “x is an F in the (fictional) world in which it appears.” And now the inference doesn’t look straightforwardly invalid to me. One might maintain that x literally has the properties that make it an F (and so, it is an F simpliciter) even though it doesn’t have those properties in the actual world. In any event, I don’t think the problem here is easy; if it were, philosophers wouldn’t be so divided on the topics of existence and non-existent objects.

      That said, I’m not sure that your remark about what fictions assert is going to work. You say, “It is not that there are two ways of flying a sleigh: actually and fictionally; there is one way of flying a sleigh, and some fictions claim (falsely) that Santa flies a sleigh in that way.” That seems to imply that fictions are asserting things about the actual world, and that the declarative statements made in fictions could be checked by looking at the actual world. But that isn’t the impression that I get when reading fiction. Authors of fiction aren’t (or at least need not be) making assertions about the actual world at all. Hence, I still want to say that if I read, “Santa flies his sleigh all over the world,” it is at the same time true to say that Santa flies a sleigh (in the fiction) and also true to say that Santa does not even exist, let alone fly a sleigh (in the actual world).

  9. nate charlow says:

    You’re right, Dan, that it’s not trivial in the way that “Either you ought to \phi or it’s not the case that you ought to \phi” is trivial. That’s a validity of propositional logic, and your sentence is not. Rather, it’s a validity of some species of deontic logic (one which has to have been axiomatized by somebody). But it’s still a validity, if it follows from \emptyset.

    There are lots of sentences like this — deontic, but not classical, validities. O(Op -> p), Op -> Pp, Op -> F~p. (O = it’s obligatory that, P = it’s permitted that, F = it’s forbidden that)

  10. Steve C. says:

    Hey Dan, not sure if anyone has raised this point yet, but the move from wrongful to ought is also fairly controversial, at least if “wrongness” means moral wrongness. Many deny that moral wrongness claims entail ought claims; moral considerations have to compete with other kinds of considerations (etiquette-related, prudential, aesthetic) on the substantive battlefield.

  11. al says:

    Hm, I think Steve has a good point– in moral dilemmas, (say Williams’ case of Jim and the Indians, for example), it seems that to murder would be wrong, but not necessarily that we ought not murder. Or, if we ought not, it at least seems like an ought that can be overridden– not an ‘all things considered’ type of ought.

  12. Fabrizio Cariani says:

    I’m in agreement with most of the reactions here: there is a slightly different angle on a closely related point that occurred to me when you mentioned the “throwing stuff in the antecedent” strategy.

    If you are willing to consider sentences like “p–>O(q)” (sorry no corner quotes) as potential counterexamples to the thesis, the question you are looking at is not whether you can infer an ‘ought’ from an ‘is’, but more something like whether you can infer a normative claim from purely descriptive premises. So there are two distinctions to track here. One is substantive/non-substantive. The other is normative/non-normative.

    One of the early points in the discussion of is/ought arguments was to notice that, in regards to the second distinction, you really should distinguish three categories: normative, descriptive and mixed (the Russell and Restall paper that Lewis mentioned is really good on this point).

    The reason is that you don’t want “p v O(q)” to be descriptive, but it can’t be normative either because otherwise you get obvious counterexamples to the thesis (let “p” be descriptive…).

    So the thesis needs to be something like: you can’t infer purely normative claims from purely descriptive premises.

    Now comes the question of how you delimit normative/descriptive and mixed. One attractive assumption is to do that purely in terms of their contents.

    If you accept a simple intensional semantics for ‘ought’, then the game is over: if the claim really is a logical truth of your intensional deontic logic it gets the same modal profile as ordinary tautologies. On this view, perhaps we are mislead by its superficial form to think it’s a normative sentence but it isn’t.

    Something similar is true on many non-standard intensional semantic theories as well. So, if you buy into all of that, the challenge for someone who pushed your argument would be: come up with a deontic semantics and an account of normativity on which being a logical truth can naturally be separated from being descriptive.

    (Full disclosure: I’m inclined to say that the sentence is normative, but I’m inclined to deny that it’s a logical truth).

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