# A Degrees-of-Moral-Wrongness Argument that the Numbers Do Count

John Taurek (1977) argued that in conflict situations–situations in which we can save some people only by failing to save some others–the numbers don’t count–i.e., it is not morally wrong to save the smaller group instead of the larger group. His argument is controversial. Here I offer a degrees-of-moral-wrongness argument for the conclusion that, contra Taurek, the numbers do count.

Consider the following case:

DROWNING – Four people—W, X, Y, and Z—are all drowning. Bloggs has 4 options:

(a) save W, X, Y, and Z

(b) save W

(c) save W & X

(d) save Y & Z

Now here’s my argument:

1. In DROWNING, (b) is more morally wrong than is (c).
2. In DROWNING, (c) is just as morally wrong as is (d).
3. In DROWNING, (b) is more morally wrong than is (d). [from 1,2 arithmetic]
4. Therefore, the numbers matter.

Premise 1 is justified because even a numbers skeptic should agree that it is more wrong to save only W than it is to save only W & X. (Both (b) and (c) are wrong because Bloggs morally ought to do (a). But, all the same, (b) is more morally wrong than is (c), and any numbers skeptic should admit as much.)

Premise 2 is also justified; what by a numbers skeptic’s lights could make one of (c) and (d) more morally wrong than the other?

As 3 follows from 1 and 2 via arithmetic—if (b) > (c), and (c) = (d), then (b) > (d)—it seems that the numbers must count, for if saving only W is more morally wrong than is saving only Y & Z, how could that be except because the numbers count?

That’s my argument. Is it plausible?

(We could also run a similar argument with a five-option version of DROWNING:

DROWNING’ – Four people—W, X, Y, and Z—are all drowning. Bloggs has 4 options:

(a) save W, X, Y, and Z

(b) save W

(c) save W & X

(d) save Y & Z

(e) save Y

A similar style argument to the one given above should establish here that (b) = (e) > (c) = (d). One benefit of this version of the argument, perhaps, might be to forestall the following possible rejoinder to my original argument: the presence of (b) (somehow!) makes (c) either more or less wrong than (d) in DROWNING. Because in DROWNING’ there is option (e) in the mix, that should scotch any attempt to have it that (c) and (d) are somehow unequal in moral wrongness–the perfect symmetry of the options should be sufficient to render that objection a non-starter.)

## 14 Replies to “A Degrees-of-Moral-Wrongness Argument that the Numbers Do Count”

1. This looks like an interesting argument to me! But one question: Might the Taurekian deny that (c) and (d) are equally wrong? They might instead claim that these options are not comparable at all, rather than strictly equal. Compare the choice to Sophie’s choice, which is often cited as an example of incomparability, and which looks the same. With this revised claim, the conclusion that (b)<(d) would not follow.

2. Matt King says:

Hi Pete,
I wonder whether one who thinks the numbers don’t count might also think that wrongness is binary, and so not scalar. The quick defense of the claim would be that wrong actions are impermissible, but that means not permitted. An action cannot be less permitted than another; they either are or aren’t.
One might therefore agree that the options in DROWNING are more or less harmful or involved better or worse outcomes, but not think they vary in amount of wrongness.
(NB: I don’t endorse this view, but it strikes me as a natural partner of the numbers don’t count view — though certainly not necessitated by it.)

3. Peter Graham says:

Hi Alex,
Thanks! I agree that a Taurekian might deny that (c) and (d) are equally wrong. My only reply to that is: what motivates it other than a desire to resist the conclusion? I guess I’d want to see a principled motivation for that move. I’m not up on the comparability literature. The Sophie’s Choice case is complicated because it is also used sometimes to demonstrate the existence of moral dilemmas (moral tragedies). Presumably the Taurekian would want to say that in an entirely different case in which one must choose only between saving A or saving B that both options are permissible–both are wrong to 0 degree–and thus are deontically equal. Yet I don’t see how this case is any less Sophie’s Choice-ish than is the choice between (c) and (d) in my case. What’s more, it’s not as if (c) and (d) aren’t incomparable to other options in the case; and, in fact, we can set up the case in such a way that there is an option both are more wrong than and one which they are both less wrong than–so, each is such that its wrongness is determinately such that it lies within some range of degrees of wrongness. So, in the end, I guess, I can’t think off the top of my head how to refute the maneuver you suggest, but I do wonder how it is to be independently motivated. If it can’t be, then, I claim, it is ad hoc.
Hi Matt!
Thanks for this reply. Yeah, a numbers skeptic could resist the thought (in my view, the incredibly intuitive thought) that wrongness comes in degrees. But I’m not sure why you think that a numbers skepticism and deontic binariness are natural partners. I don’t see any direct connection between the two views. (True, one is a view about numbers “not counting” and the other is a view according to which we can’t assign numbers to a certain property. But in the former case the number is *of people* and in the latter it is the property of moral wrongness to which numbers can’t be assigned. As I say, I don’t see any reason to think that there is any natural affinity between these two views.) For my own part, I think it is highly intuitive that there are indeed degrees of moral wrongness and it is a serious cost to any moral theory which denies that there are such things. Suppose I have to choose between (a) doing nothing, (b) pinching my spouse very severely on the arm, (c) cheating on him behind his back, and (d) gruesomely murdering him. I think it is clear that (d) is more wrong than is (c), (c) is more wrong than is (b), and (b) is more wrong than is (a). What’s more, it’s not clear that this deontic ordering can be replaced by something else, whether merely axiological or otherwise. (Of course, one can fiddle with and make one’s axiology as complex as one wants in order to capture these orderings–but, then again, the more one complicates one’s axiology, the more implausible one’s theory might then become.)

4. Matt King says:

Hey Pete,
I guess my thought was that if one rejects counting the numbers, then one is less consequentialist (in some broad sense). Or if one prefers, is less likely to let one’s deontic notions be driven by axiological considerations. But while I agree that we often talk about actions being more wrong than others, it’s less clear to me exactly what this comes to.
But I suppose it would be too much to demand of your argument that it also give a full accounting of wrongness! I find ‘wrong’ too thin a term to have very strong intuitions about it.
In a different vein, however, doesn’t the argument just show that the numbers sometimes count? And isn’t that compatible with Taurek’s claim that the numbers sometimes don’t count?
Suppose one thought that the guiding principle should be something like ‘equal respect requires affording all we can save with an equal chance of being saved’. This is why it might follow that if the groups are discrete (i.e., no one is a member of two groups we can save), the numbers don’t decide what we should do. But in your case, since there are individuals who appear in multiple groups, we aren’t affording the others equal chances. (That is, if our choices are between saving W and saving W&X, W gets saved whatever we choose, whereas X only has a 1/2 shot — that’s unfair to X. Or so the thinking goes.)

5. Peter Graham says:

Hey Matt,
Thanks again for engaging with me on this.
I guess I just don’t see why being less consequentialist (or less inclined to let axiology (something which is most surely degree-theoretic (I know of no one who is binary-ist about goodness and badness)) drive the deontic) naturally makes one less inclined to admit of degrees of wrongness. I think there is nothing even slightly theoretically odd about being a consequentialist who denies that there are degrees of wrongness (it is certainly intuitively odd, in my view, in virtue of its denying that there are degrees of wrongness), nor is there anything even slightly theoretically odd about being a non-consequentialist who does admit of degrees of wrongness (in fact I think some such view is true!).
Whereas you find ‘wrong’ too thin a notion to have any strong intuitions about, I’m inclined to think that wrongness is THE fundamental moral notion. Currently, I incline toward the view that all moral notions are definable in terms of, and fundamentally reducible, degrees of wrongness. This is a much larger project though, of course.
(For what it is worth, the appeal to degrees of wrongness might be eliminable from the argument. That is, I might well be able to run the argument all in terms of conditional obligations. (This is no mere coincidence, of course: I think there is an intimate connection between the conditional obligations true of a moral situation and the wrongness facts in that situation.) The argument would proceed by showing that something like:
[Conditional on both your not doing (a) or (c), you morally ought to do (d) and you morally ought not to do (b).]
Now the conditional obligation version of the argument might well be a little bit messier than the degrees of wrongness argument, but I think it might be able, in the end, to do all the work the degrees of wrongness argument can do. Would you be more sympathetic to a conditional obligation version of the argument?)
You are right that my argument does only show that the numbers sometimes count. But, that’s supposed to be the thin end of the wedge. If the numbers can count with respect to the wrongness of certain of your choices in a conflict situation, then it’s kind of theoretically unstable, I’d maintain, to think that what one is morally obliged to do (i.e., that option which is least wrong) in that situation isn’t also dependent on the numbers. This is especially so if the degrees of wrongness facts are the fundamental facts.
With respect to the “equal respect requires affording all we can save with an equal chance of being saved” principle, I’m not sure whether it entails what you say it does, nor is it clear that that is what the Taurekian has in mind. Also, whether that principle, as you understand it, is true, I take it is what is in question; my argument can be seen as showing that that principle is false. So even were it the case that that is what the Taurekian has in mind, why isn’t my argument an argument to the effect that the Taurekian’s numbers skepticism is founded on a false principle? (For what it’s worth, I don’t think the structure of Taurek’s argument is such that it relies on any principle like the one you articulate. But that’s just a small point, of course. My aim is to refute numbers skepticism, not just Taurek.)

6. Matt King says:

Hi Pete,
I’ll give it another go (though I reiterate that I’m not really defending most of these claims – just trying to articulate them).
As to theoretical oddity, I think if what explains wrongness varies in degree, it’s more natural that wrongness itself would then vary in degree. So, since goodness (we agree) is definitely a degree notion, explaining wrongness in terms of goodness will more naturally produce a view in which wrongness, too, is a degree notion. The one doesn’t necessitate the other — it would just be more surprising if the degree variation didn’t carry over.
If what explains wrongness doesn’t itself vary in degree, then it would be more surprising for wrongness to vary in degree. Take forms of contractualism, where wrongness looks more like legality. Being illegal doesn’t seemingly come in degrees. Murder isn’t more illegal than stealing. Of course, we can still construct a view on which murder is more illegal than stealing, but I suspect that in order to do so, whatever explains the illegality would itself have to come in degrees. So, that’s the source of the oddness to me — to the extent that what explains wrongness comes in degrees or not would more naturally pair with remaining binary or not when it comes to wrongness. Or so it seems to me.
To bring things back to your argument, I take it that we should all agree that, of the options open to Bloggs, (a) is the best choice, and (b) and (c) and (d) are clearly sub-optimal. But since (a) only serves to establish that all other options are wrong, we can drop it for now.
Instead, we have to compare saving two pairs of persons with saving only one, present in one pair but not the other. Here we can bring the contrast out with Taurek’s conclusion. We should all agree, I take it, that between saving W and saving W&X, we should save W&X. And I take it the Taurekian can agree (or at least should). So, the remaining question is whether saving Y&Z over just W is the better choice (when they are the only choices).
The reason to think the numbers count here is that there is no difference between saving Y&Z and saving W&X, but since saving W&X is better than saving just W, saving Y&Z must be better, too. So, instead of showing that the numbers count, the challenge for the Taurekian (or whoever) is to explain why the no difference between W&X and Y&Z doesn’t translate to the comparison between W and Y&Z.
For someone who doesn’t take moral wrongness to be the basic fact, it is possible that arithmetic won’t work because what makes (b) worse than (c) and (c) equivalent to (d) won’t hold true of the comparison between (b) and (d).
For instance, shorn of details, it could be that choosing to save W over W&X disrespects X, but that no one is disrespected when we choose W&X over Y&Z (or vice versa). This would leave open the possibility that similarly no one is disrespected when we choose to save W over Y&Z (or vice versa). (The rough view might be that proper respect involves being given a fair shot at being saved. Such a view also predicts that (a) is the best choice, since every other choice will disrespect someone.)
Now, I’m not saying this is the right view, nor am I defending it. But I think it’s a sensible way to take the case, and it also might illustrate that there are ways to preserve conclusions about pairs of cases without committing ourselves to an underlying ‘measurement’ that would fund applying arithmetic.

7. Peter Graham says:

Hi Matt,
The whole purpose of the argument is to deal with degrees of wrongness and that’s why I included option (a). So I don’t think we can just drop (a). If we drop (a), then we can’t argue that the Taurekian must admit that W&X and Y&Z are equally wrong, because she needn’t say that they’re wrong at all. (Now, you could try to force her to say that because both are permissible they’re equally wrong–i.e., equally wrong to degree 0–but that’s an added element that I didn’t want to incorporate into the argument. (True, I do have to incorporate a step at the end whereby I assert that thinking that the numbers matter to wrongness facts but not to the obligation facts is theoretically unstable. And maybe, you might think, that added step is just as much of a weighty additional premise as the premise I think you need to add to your suggested revision of my argument where we just drop (a). I’m not sure about that.))
As regards the goodness-comes-in-degrees-so-wrongness-must-too point. I just don’t get it. We don’t ordinarily think that just because X facts are true in virtue of Y facts, where the Y facts happen to be degreed, that the X facts then must be degreed as well (or even that there is the slightest theoretical pressure to have it be the case that the X facts are degreed).
Case 1: Knowledge facts are often thought to be true in virtue of justification facts and justification facts are often taken to be degreed. But it doesn’t follow that there need be any theoretical pressure to admit that knowledge facts admit of degrees.
This seems fine: Sanchez and Chang have some justification for thinking Gotit owns a Ford but Sanchez has more justification for thinking so than does Chang.
This doesn’t seem fine: Sanchez and Chang both know that Gotit owns a Ford but Sanchez more knows that Gotit owns a Ford than does Chang.
This also doesn’t seem fine: Sanchez and Chang both don’t know that Nogot doesn’t own a Ford, but Sanchez more doesn’t know that Nogot doesn’t own a Ford than does Chang.
Case 2: Whether a number is non-prime is a function of the number of factors it has. The number of factors a number has is something that varies in degree. Twelve has 6 factors and eight has 4 factors, but there’s nothing whatsoever theoretically odd about our not taking non-prime-ness to be non-degreed. We surely don’t say that twelve and eight are both non-prime, but that twelve is MORE non-prime than eight is.
Case 3: Whether a substance is in gas phase or not depends (at least partly) on the average distance between the molecules of that substance. The average distance is a degreed notion, of course. But we don’t say that the one gas is more of a gas than the other is just because the average distance of the molecules of the one is greater than is the average distance of the molecules of the other.

8. Matt King says:

Hey Pete,
I think I agree with most of what you say here. We disagree about whether it is more natural for X facts explained by degreed Y facts to be degreed themselves. But I explicitly denied that this *must* be the case. It just seems a better fit to my theoretical intuitions.
I could respond to the suggested counterexamples. In short, I think there’s pressure to explain why, if there is a higher degree of the relevant explanatory consideration, why the explained feature isn’t similarly higher degreed. Why doesn’t Sanchez better know than Chang, if she is better justified in believing? That, to my mind, would be the default position given the explanatory relation, though it could certainly be explained away.
Similarly, one non-prime number could be “closer to prime” than another non-prime, even though they are both non-primes and English doesn’t allow the locution “more non-prime than another”. English also doesn’t allow ‘more taller than’. If A is 6 foot tall, B five foot tall, and C four foot tall, then A is taller than B and A is taller than C. But A is more taller than C than A is taller than B. I suppose that for any threshold term we could make it degreed by talking of “distance to the threshold”. A gas can be closer to non-gas the smaller it’s average distance between its molecules gets.
But theoretical considerations aside, I took the main force of my previous point to be that the inference to the third premise, which relies on arithmetic, assumes that what makes the options wrong, when they are wrong, is the same feature throughout the cases. But if that’s not the case, as the toy example involving respect and fairness was meant to illustrate, then the inference wouldn’t necessarily go through.
I hope our exchange has been at least mildly interesting to the rest of the PEA Soup community. I’ve enjoyed it.

9. Peter Graham says:

Hi Matt,
I’ve enjoyed it too, and thank you!
A couple final thoughts. A message or so back you wrote:
“The reason to think the numbers count here is that there is no difference between saving Y&Z and saving W&X, but since saving W&X is better than saving just W, saving Y&Z must be better, too. So, instead of showing that the numbers count, the challenge for the Taurekian (or whoever) is to explain why the no difference between W&X and Y&Z doesn’t translate to the comparison between W and Y&Z.”
Exactly. That’s just my argument. Your last sentence is basically taking the conclusion of my argument and saying the challenge for the Taurekian is to say what is wrong with the argument. I agree. That is the challenge for the Taurekian.
You then wrote:
“For someone who doesn’t take moral wrongness to be the basic fact, it is possible that arithmetic won’t work because what makes (b) worse than (c) and (c) equivalent to (d) won’t hold true of the comparison between (b) and (d).”
I don’t really understand what this position would be. In the scenario as described, Bloggs isn’t choosing between options (b) and (c), or between options (c) and (d), or between options (d) and (b). Bloggs faces one choice, that between all four options, (a), (b), (c), and (d). I took it that each of these options has some degree of wrongness and then I argued that the degree of wrongness that one of them has, (d), is less than that of another of the choices, (b), and I did this by appealing to two apparent moral data about the case: that (b) is clearly more wrong than (c) and that (c) can’t be more or less wrong than (d), and so must be as wrong as (d). Now of course, the last step could be questioned, but I’d want some independent rationale for why the last step doesn’t go through. I don’t see any rationale in the offing.
You also wrote, in your most recent post:
“But theoretical considerations aside, I took the main force of my previous point to be that the inference to the third premise, which relies on arithmetic, assumes that what makes the options wrong, when they are wrong, is the same feature throughout the cases. But if that’s not the case, as the toy example involving respect and fairness was meant to illustrate, then the inference wouldn’t necessarily go through.”
I don’t see why different things making different options wrong would undermine the arithmetic step in my argument. The arithmetic step simply assumes that each wrong option has some determinate degree of wrongness. The arithmetic should be kosher just in case each option does have a determinate degree of wrongness. The arithmetic works just at the level of those facts and thus does not depend on what makes each option have the wrongness degree it determinately has. (Compare: it may well be that (a) pinching my spouse is wrong to degree 5, (b) cheating on him behind his back is wrong to degree 45, and (c) killing him is wrong to degree 100. What makes each of these options wrong to the degree that it is wrong is different for each option (consequences for some of them, deontological stuff for another of them), but that doesn’t scotch the inference from (a)’s being less wrong than (b) and (b)’s being less wrong than (c) to the conclusion that (a) is less wrong than (c) is. Once we’ve got determinate degrees of wrongness for each option, then mathematical inferences should go through just fine irrespective of what makes each option have the particular determinate degree of wrongness that it has.
Presumably what grounds the relative wrongness facts–(b)’s being more wrong than (c)–are the determinate non-relative wrongness facts in the situation–(b)’s being wrong to degree 10 and (c)’s being wrong to degree 3. That is, presumably (b) is more wrong than (c) is BECAUSE (b) is wrong to degree 10 and (c) is wrong to degree 3 and not the other way around. So it’s not as if the ground of (b)’s greater wrongness than (c) is the conjunctive fact (i) that (c) is wrong and (ii) that (b) must be more wrong than it because (c) is pareto optimal with respect to (b). True, appeal to principles about pareto optimality play a role in my argument, but those facts aren’t what ground the relative wrongness facts in the situation. What ground those are the determinate degree of wrongness facts regarding each option and the degree of wrongness facts for each particular option are in turn grounded by facts about what is involved in that option and all of its relations to all of the other options in the entire (a)-(b)-(c)-(d) choice situation.

10. Thanks for the reply Peter! I don’t know if I have much to add on this, but here what springs to mind:
I suppose I was thinking that the Taurekian view is motivated by something like the Rawlsian point about the distinctness of persons, and that might do something to motivate the claim that gains for some are not commensurable with losses for others. (Where this is understood not to say that these always perfectly balance out, but that the comparison makes no sense.)
In the next part of your reply, I think you assume that if an option is permissible, then it is wrong to some particular degree, such that all permissible options are equally wrong (to degree 0?). But we might alternatively think either (a) that permissibility consists in having no degree of wrongness at all (not even 0 on the scale), or (b) that permissibility consists in having some degree of wrongness within certain bounds, where different points within those bounds might be incomparable with one another. Perhaps there is a literature on this, but in my state of ignorance, I’d want to hear more about why we should accept your assumption.
(I don’t have much to add on your final point: I agree that there is something fishy about denying that numbers matter but allowing other comparisons, such as between your options (b) and (c).)
Best,
Alex

11. Peter Graham says:

Hi Alex,
Thanks again for engaging with me on this.
I didn’t mean to commit myself to permissible options having 0 wrongness–for precisely the reasons/replies you suggested might then be available to the Taurekian. (That’s in fact why I wanted to run the argument with options W, W&X, and Y&Z when all three of those options are wrong, for while it might be plausible to maintain that a permissible option has no wrongness whatsoever, not even 0, it would be much harder to maintain, I believe, granting the existence of degrees of wrongness, that a wrong option might have no degree of wrongness.)
I should say though that my own view that degrees of wrongness are the fundamental moral notion is still a completely un-worked-out view. And I think you are right that there are few different ways of going in connecting wrongness (and then, derivatively, permissibility, obligation, etc.) to degrees of wrongness (two quick alternatives: (a) x is wrong iff x has some non-0 degree of wrongness and (b) x is wrong iff of all the options available to the agent there is an option with less wrongness than x). I think degrees of wrongness, though they’re, in my view, utterly quotidian, very under-theorized in the ethics literature. (Though Tom Hurka is doing some very interesting work on the topic.)

12. Suppose we recast DROWNING:

1. In DROWNING, (b) is worse than is (c).
2. In DROWNING, (c) is just as bad as (no better than?) (d).
3. In DROWNING, (b) is worse than is (d). [from 1,2 “arithmetic”]
4. Therefore, the numbers matter.

[sidebar: you claim that statement 3 in the DROWNING case follows by “arithmetic,” but that cannot be correct, as you have not mentioned any numbers. If it follows, it must be by the transitivity of wrongness, and now you’re committed not just to demonstrating degrees of wrongness but the also transitivity of the relation.]
This argument strikes me as compelling in a way that yours does not, and the difference seems to suggest a possible conflation of “wrongness” (the very term is awkward) with badness (a natural term).
Do we have degrees of “wrongness” locutions in ordinary speech? “That’s so wrong!” might be one, if it weren’t ironic. My sense of ‘wrong’ is that it means ‘impermissible’, which has as many degrees as ‘impossible’. That is to say, none.
I don’t see a straight line between badness and being wrong: we sometimes choose the lesser of two evils as the best (and permissible) option. The evils might be rather bad indeed: their badness is a reason not to choose them other things equal, but if all options are bad I might yet have reason to choose a bad option that is not therefore wrong. The worse options would be wrong, but none “more wrong” than others.
Being “in the wrong” is being over the line, and that does not seem to be a status that comes in degrees. Outcomes are better or worse (and sometimes on a par, or incommensurable, or incomparable). Some impermissible acts yield terrible outcomes, others yield mildly bad outcomes. Some might yield good outcomes, though perhaps not as good as permissible alternatives. Again, no straight line from badness to being wrong.
Your intuition seems to be that when two impermissible actions yield outcomes differentially bad, that one of the alternatives is therefore “more wrong.” Given the surface unnaturalness of your way of talking, the burden seems to be on you. What does this way of talking help explain that we cannot explain with the idea of impermissibility plus differentially bad outcomes?

13. Jamie says:

I think we do have degrees-of-wrong locutions in ordinary English. “That was very wrong of him” is quite common; “was very wrong” gets over 444,000 ghits, and “very wrong” gets 6 million.
But I think Michael has a good point anyway. It’s pretty plausible that “very wrong” means “gravely wrong” and “more wrong” means “a more serious wrong” — that is, the intensifiers are really modifying something other than the wrongness itself. Compare “double parking is illegal but tax evasion is much more illegal,” which doesn’t sound like nonsense but surely doesn’t literally mean that illegality comes in degrees. Which is more against the rules of chess: castling through check, or moving your opponent’s king when they aren’t looking?
I wonder whether Pete thinks his argument is just as good if the degrees attach to seriousness of various wrongs, rather than to their wrongness.
[[Sidebar to the sidebar: it’s not ‘wrong’ that is transitive. It’s ‘more’ and ‘just as’; more elegantly, it is the transitivity of their union that does the work in Pete’s argument. This is not just a quibble. The point is that once we admit degrees of wrong, we do not need another assumption about transitivity, since the stuff about ‘more’ and ‘just as’ is uncontroversial and a matter of the logic of comparatives and equivalence relations.]]

14. Peter Graham says:

Thanks Michael and Jamie,
First, as Jamie says, I’m not appealing to transitivity. At most I’m appealing to the, what seems to me to be, valid inference form
A is more X than B is
B is equally X as C is
to
A is more X than C is
That’s not transitivity and it seems plausibly valid to me.
I do prefer my argument to Michael’s. One of the whole points of the argument is to cast it in terms of wrongness, i.e., something deontic, as opposed to something axiological. (Though Michael talks in terms of badness of actions, I understand ‘bad act’ either as ‘wrong act’, or ‘act with some negative feature’, though I find badness has its most natural home in axiological contexts.) I take it that the interesting Taurekian view (or at least the view I find interesting) is the deontic view that in conflict cases it is not the case that we’re morally obliged to save the greater number. Though Taurek himself often casts the argument in terms of the axiological, I’m more interested in the deontic thesis. (As I’m a non-consequentialist I don’t think the way to approach the deontic thesis is by way of the axiological one. And because I’m a non-consequentialist, contra Michael, my intuitions are not tracking badness of outcomes–that’s precisely why I use the example of cheating on my spouse behind his back’s back being more wrong than pinching him.)
[A probably uninteresting Taurek interpretation sidebar: I think Taurek probably endorsed both an axiological numbers skepticism and a deontic numbers skepticism. And I think it’s plausible that Taurek’s deontic skepticism derived from his axiological skepticism–he probably thought that when it comes to the duty to aid, what you morally ought to do is bring about the better state of affairs, but he also thought–and here’s his axiological skepticism–that it is not the case that five people alive and one dead is a better state of affairs than one person alive and five dead is.]
My ear may just be way off, but to my ear “more wrong than” is perfectly fine, quotidian even. I think we say this kind of thing all the time both when making intra-case option comparisons (pinching him would be wrong, but it would be way more wrong to cheat on him behind his back) and inter-case option comparisons (it was wrong of you to pinch him yesterday, but it was much more wrong of you to cheat on him behind his back this morning). I think we often use ‘worse’ to mean ‘more wrong’ and so perhaps that makes more wrong sound off to some. (It’s a mistake, I believe to think that ‘worse’ ONLY means ‘more bad’. I think it’s plausible that it means BOTH ‘more bad’ and ‘more wrong’.)
I do of course believe that there is a binary meaning of ‘wrong’ according to which it does not admit of degrees. That’s most surely true. (That notion of ‘wrong’ is synonymous, in my view, with ‘impermissible’ (and I certainly agree that impermissibility does not admit of degrees).) But what’s at issue is whether there is a degreed notion of wrongness (by the way, I don’t see anything wrong with ‘wrongness’ (no more so, at least, than ‘badness’)), and as I’ve said above, I do believe that there is such a notion. I don’t think that ‘more wrong’ means just ‘more gravely wrong’ or ‘more seriously wrong’. (I think the view Jamie is suggesting is Tom Hurka’s view.) I do think that there is wrongness and it comes in different amounts. And, what’s more, I think the binary notion of wrongness is less fundamental than the degreed notion; that is, I think that whether something is wrong is made true by facts about how wrong it is. (There’s a theoretical choice here which I don’t know yet what to think about: is an action wrong iff it has a non-zero degree of wrongness or is an action wrong iff there is an option the agent has which has a lower degree of wrongness than it, or … ?)
The analogy I like to think in terms of is that with the property of being charged. There is a binary notion of being charged and a degreed notion of being charged. Plausibly, in my view, an electron’s being charged (binary) is true in virtue of the fact that it is charged (degreed) to the degree -1.6×10(-19) Coulombs. (I don’t go all-in with the analogy though. To do so would be to endorse the first of the two theoretical choices I mention above and as of right now I’m agnostic about that.)
All of this said, I think if my argument goes through at all, I can’t see why it wouldn’t go through if the degrees attached to the seriousness of the wrong as opposed to the wrongness itself. The last step would change slightly. Now the last step would involve saying that it is implausible to think that the numbers don’t matter to whether something is wrong, but to think that they do matter to how seriously wrong an option is. (Heck, that might even be a stronger final step than the step in my original argument.)