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Chapter Two examines the question of ‘whether the numbers count’. Suppose that we can either save the life of one person, A, or the life of one other person, B. Let us assume for this and each other example that everything else of moral relevance is kept equal (they are all strangers, there is no pre-exisitng promise to save any of them etc.). Kamm holds that in such a case we should give each of them maximal equal chances of being saved: that is, we should flip a coin giving them each a 50% chance of being saved. Now suppose that the choice is between saving A or saving both B and C. Should we continue to decide by flipping a coin, or should we directly choose to save B and C? This is the question at the heart of Chapter Two.

Kamm holds that we should save B and C, and she spends the chapter examining many arguments for and against this conclusion. It is a very intuitive conclusion, but has historically drawn significant opposition from nonconsequentialists on the grounds that it requires some form of aggregation of B and C’s claims so that they together outweigh A’s claim. Nonconsequentialists are suspicious of aggregation because it seems to cross the boundaries of individuals and thus it doesn’t take seriously the ‘separateness of persons’. Kamm wants to preserve the intuition that the numbers (of people) do count, and thus goes to great pains to explore arguments that reach this conclusion without any explicit aggregation, thus respecting the separateness of persons.

The chapter is called Aggregation and Two Moral Methods and refers to the main methods that she uses: pairwise comparison and virtual divisibility. The first of these is common in nonconsequentialist work and involves reducing comparisons between groups to a set of comparisons between pairs of people, with one from each group. The second method, virtual divisibility, is less common. It involves analyzing the ethics of distributing non-divisible resources in terms of parallel situations which are identical in every respect, except that the resource is divisible. Most of the chapter is concerned with pairwise comparison and I found that the material on virtual divisibility was not required to reach Kamm’s main claims.


Kamm begins by presenting John Taurek’s argument that initiated the discussion on whether the numbers count. She distinguishes two key premises in his argument:

1) No one of the people in the larger group will suffer a greater loss than the one person would.
2) (a) It is not true that we produce a better outcome if the greater number survive as (b) there is no impartial perspective from which to judge the issue.

From these Taurek famously concluded that if the stakes for each individual are the same, we should always flip a coin to determine which group to save regardless of the numbers of people in the groups.

Kamm argues that (2)(b) should be abandoned, as it is too strong. It doesn’t stop at ignoring the numbers of people, but implies that even the stakes to each person can be ignored. Taurek himself states that from A’s perspective A’s losing his leg could be worse than B’s losing his life, but from this we could use (1) and (2) to argue that we should flip a coin to decide between these possibilities, instead of directly saving B’s life and letting A lose his leg. Kamm points out that this will be found to be unacceptable — even to most numbers skeptics. Instead numbers skeptics should only hold equal chances to be required when the stakes for each individual are at least roughly equal, and thus Taurek would need a premiss more subtle than (2)(b) to achieve this.

Taurek might be able to save his argument by keeping (1) and (2)(a), while dropping (2)(b), but Kamm thinks that he must abandon (2) altogether because there is reason to believe that saving the larger group is indeed a better outcome than saving A alone. We have her argument already in Chapter One, but it is a major focus of the chapter and is worth repeating. It is called the Argument for Best Outcomes. She first says that it is worse if B and C both die than if B alone dies (from a consideration of Pareto superiority). She writes this symbolically as:

(a) B + C < B

She then says that it is just as bad from an impartial point of view if A dies as if B dies:

(b) A = B

She then says that we can use (b) to substitute A for B on the right hand side:

(c) B + C < A

And thus the numbers count when it comes to determining badness from an impartial point of view. This would make Taurek’s premise (2)(a) false as well, removing much of the support for his conclusion. However, as Kamm admits, it would still be possible for his conclusion to be true as considerations of fairness may make it right to toss a coin even though it would be impartially better to directly save B and C.

This argument is Kamm’s primary example of her method of substitution, which she looks at in detail throughout the chapter. I think that this particular example works, but that the method is not generally valid. However, the problem I have detected seems to be fixable in a way that ends up strengthening Kamm’s overall position. I shall thus leave my (rather lengthy) discussion of this flaw until the end of this summary.


Kamm next considers an argument due to Elizabeth Anscombe that is skeptical about numbers in a slightly different way. Anscombe claims that A’s need provides a reason to save him and since there is a reason to do so, we can save A without wronging anyone. She admits that there is a greater reason to save both B and C, but says that when we have a reason to do X and a reason to do Y, we don’t need a further reason to do X rather than Y in order to be justified in doing X.

Kamm disagrees with this approach, pointing out that if it were a choice of saving A or saving A and C, we would have reasons to do either option, but it would be impermissible to save A alone. Kamm also points out that Anscombe’s position is compatible with directly choosing A in a choice of A or B, and does not require equal chances.


Having criticized two of the main arguments of the number skeptics, Kamm then turns to her arguments that we should save the greater number (both of which are mentioned in Chapter One).

Kamm has already presented an argument that it is better from an impartial point of view to save the greater number of people. So long as there are no deontological objections on the grounds of fairness, or justice or something of that ilk, it will not be wrong to do what is best and to save the greatest number. Kamm attempts to show this with the Consistency Argument:

…in saving the greater number we need not be overriding fairness or justice: In many other cases, nonconsequentialists who think that numbers count will not violate justice in order to save the greater number. For example, they will not ordinarily kill one person even in order to save a thousand. Why would such nonconseqeuntialists, who refuse to sacrifice justice or fairness in order to save more lives in these other cases, override justice or fairness in order to save merely two people rather than one? It is most reasonable to believe that they would choose to save the two rather than the one because fairness or justice is not being overridden in such a case.

I do not think that this is a particularly strong argument, as it merely states that many people who take justice and fairness seriously don’t see how they are applicable here. This is not a valid argument form (‘most people of a certain type think X, therefore X’), but it may appropriately shift the burden of proof onto those who claim that either justice or fairness is violated. After all, before sacrificing the greater good in the name of fairness or justice, it should be explained how one of these is relevant if many genuinely concerned people cannot see.

Her second argument is the Balancing Argument:

…in a conflict case involving unequal numbers each of whose life is at stake, justice demands that each person on one side should have her interests balanced against those of one person on the opposing side; those whose interests are not balanced out in the larger group help to determine that the larger group should be saved. Those who are balanced out in the larger group are saved instead of those in the smaller group.

Thus, according to Kamm, we should always save the greater number, as it is not only better to do so, but also demanded by justice. This would be a very strong conclusion and it is not clear to me that Kamm offers enough to fully support it. Her major argument appears to be that if we were to toss a coin between saving A and saving B, and would also toss a coin between saving A and saving B and C, then we would be wronging C by giving him no further weight.

However, it is not clear that this argument ultimately supports saving the greatest number. For suppose that we have two cases:

(1) A and B and C versus D

(2) A and B and C versus D and E

If we save A, B and C in (1) and save them in (2), then it would appear that we are doing in (2) just what we would have done were E not present. Despite saving the greatest number, we would still be committing the same sin that Kamm complains of above. If instead we were to always give chances to each side proportional to the number of people, then Kamm’s complaint will be inapplicable. It thus seems that if taken seriously, this argument really points towards proportional chances, or another system with this property (there are infinitely many). [I owe this point to Ben Saunders].


There is much more in the chapter, but I have perhaps said more than enough in terms of breaking open the chapter for further comment and analysis. By way of briefest summary, I offer the following:

In part IV, Kamm considers Thomas Scanlon’s view. His view on saving the greatest number is shaped by his Individualist Restriction. He uses this to formulate his Tiebreaker Argument which is quite similar to Kamm’s Balancing Argument. Both are forms of the moral method of pairwise comparison, as only pairs of individuals are ever directly compared: decisions between groups are broken into many comparisons of the groups’ individuals with each other.

In part V, Kamm looks at pairwise comparison more generally, dividing it into methods which use a Context Aware View, and those which use a Blinder View. These help to cast light on the Balancing and Tiebreaker arguments and on Michael Otsuka’s criticisms of them.

In part VI, Kamm considers choice situations where the stakes are different for the different people. For example, A’s life versus B’s life and C’s legs. She concludes that C’s legs are a sufficient benefit to warrant directly saving B’s life and C’s legs rather than A’s life. However, she argues that this would not be the case if the it had been C’s sore throat. In that case, tossing a coin would again become appropriate. I personally find this very hard to accept, but would love to see any comments on the issue.

In part VII, Kamm considers Scanlon’s view and an objection made by Derek Parfit, which she thinks can be resolved through insights offered by the method of Virtual Divisibility (the other moral method of the chapter).

In part VIII, she shows how Virtual Divisibility is also at play in an ingenious argument by Otsuka that tries to demonstrate that we should save the greatest number without requiring any balancing of equals.

I mentioned earlier that I had noticed a slight problem with Kamm’s method of substitution as used in her Argument for Best Outcomes. At risk of lengthening an already lengthy summary, here is my argument. I found this very interesting, but if you feel it is time to move onto the discussion, then do feel free to skip this part…


Recall that in her Argument for Best Outcomes, Kamm uses

(a) B + C < B


(b) A = B

to get:

(c) B + C < A

I think that this argument is a good one, but perhaps not in quite the way that Kamm intends. In particular, she goes on to say that we could also have substituted (b) into the left hand side of (a) to get:

(d) A + C < B

However, I don’t think this follows (at least not without further argument) and Kamm sets herself up for additional criticism by allowing it. She talks of ‘substituting’ people for other people and mentions that some philosophers might not accept this nonconsequentialist technique. However, she doesn’t really need to do any substituting of persons at all, for (c) follows from (a) and (b) by mere logic (and the rules of comparatives, like ‘worse than’). If one thing is worse than a second and this second thing is equally bad as a third, then the first thing is worse than the third. Thus she doesn’t need to do anything controversial to get (c) from (a) and (b): anyone who wants to deny (c) must deny at least one of (a) and (b).

However, we cannot get (d) from (a) and (b) in this way, as the left hand side (‘A + C’) is not already contained in (a) or (b). Thus she needs to use a somewhat contentious principle of substitution to turn ‘B + C’ into ‘A + C’. This may look fine in Kamm’s algebra-like notation, but it does not follow from (a) and (b) alone. The ‘+’ that Kamm uses is deceptive for it makes us think that the badness of A and C dying is just the badness of A dying plus the badness of B dying, but this is not always the case. For suppose that both A and C are the only people capable of ending world hunger and that so long as one of them is saved, world hunger will be ended. This is quite compatible with (a) and (b) as in each case one of A and C survives, but makes it extremely bad if both A and C were to die, such as in (d).

This shows that substitution is generally illegitimate and (d) is correct only because of additional information that Kamm provides about there being no other morally relevant facts in the example. This is crucial for her substitution to work and means that it may not work when taken to situations that are not so artificially constrained.

I should also note that we can reach (d) using just logic and comparatives if we used (b) in combination with

(e) A + C = A

which could be introduced using the Pareto method. Kamm would do better to explicitly use a premise like (e) to derive (d) rather than the somewhat murky method of substitution that she uses. This is particularly relevant if she wants to reach the conclusion that it is worse if three people die than if two others do:

(f) A + B + C < D + E

Kamm would presumably deduce this using pareto:

(g) A + B + C < B + C

two instance of equality:

(h) D = B
(i) C = E

and some substitutions. However, I don’t think that it can be legitimately done without going beyond pairwise equality and asserting something like:

(j) B + C = D + E

Which, in combination with (g), logically produces the desired outcome (f) and avoids the need for Kamm’s style of substitution.


  1. 1. Posted by Fiona Woollard | July 13, 2007 9:18 am

    Did anyone else think that Kamm’s first point against Anscombe – that her view implies that someone does nothing wrong when he saves just A, while he could save A and C – didn’t quite hit home.

    It strikes me that the most sympathetic reading of Anscombe restricts her principle to mutually exclusive acts: so if one has a reason to do X and a reason to do Y (and cannot do both X and Y) one need not have a reason to do X rather than Y to be justified in doing X.

    If we understand Anscombe in this way, I don’t think she is vulnerable to Kamm’s charge. It seems clear that we have a reason to save A and a reason to save B, and thus a reason to save A and B, but we do not have reason to ‘save A but not save B’. Thus there is no X that we have reason to do that is incompatible with Y, where Y = “save A and B”. So, with the caveat I added, Anscombe’s principle does not imply that it is permissible not to save A and B.

    I must admit that I’m not familiar with Anscombe’s original work, so would be happy to have someone point out a reason why we cannot understand her in this way.

  2. 2. Posted by Toby Ord | July 13, 2007 12:44 pm


    Yes this occurred to me as well. Kamm’s argument may work against this particular wording of Anscombe’s principle, but Anscombe would probably respond by restricting the principle to mutually exclusive acts (which was perhaps her intention all along).

  3. 3. Posted by S. Matthew Liao | July 13, 2007 3:07 pm

    Toby, thanks for the very helpful summary!

    Two comments on your points and two comments on Kamm.

    1. You say that Kamm holds that

    if we were to toss a coin between saving A and saving B, and would also toss a coin between saving A and saving B and C, then we would be wronging C by giving him no further weight.

    You argue that suppose we have two cases:

    (1) A and B and C versus D
    (2) A and B and C versus D and E
    If we save A, B and C in (1) and save them in (2), then it would appear that we are doing in (2) just what we would have done were E not present. Despite saving the greatest number, we would still be committing the same sin that Kamm complains of above.

    But I think Kamm would respond that the two cases are not analogous. In your case, E has been given further weight in the sense that E can make a claim. Indeed, E’s claim is balanced by B or C. In the case of tossing a coin though, C is not given the chance to make a claim at all.

    You go on to say that “if taken seriously, this argument really points towards proportional chances.” I think Kamm or someone might argue that a proportional chance approach gives the individual in the lesser group too much weight. Suppose there are one million people on one side and one individual on the other. And suppose a one-million-and-one sided dice has been cast in favor of the one individual. One would be required to save the one individual on this approach. But this seems counterintuitive. It might also be pointed out that the fact that the proportional chance approach makes it more likely than not – perhaps even overwhelmingly likely – that the greater number will be saved is insufficient to establish that this approach solves the problem at hand, given that the problem at hand is that of explaining why we should always save the greater number in these cases.

    2. You say that

    However, she doesn’t really need to do any substituting of persons at all, for (c) follows from (a) and (b) by mere logic (and the rules of comparatives, like ‘worse than’). If one thing is worse than a second and this second thing is equally bad as a third, then the first thing is worse than the third.

    The problem is that (b) is not true by ‘mere logic.’ The moral equivalence of persons is a substantive moral claim that has to be argued for, and a claim that someone who holds that persons are incommensurable might deny.

    Comments on Kamm:
    3. On p. 50: Kamm says that Taurek’s premise (i) (that no one of the people in the larger group will suffer a greater loss than the one person would) suggests that we are engaging in a pairwise comparison. But (rightly or wrongly), Taurek could deny that he is engaged in pairwise comparison; he could instead hold the view the persons are incommensurable. This interpretation would be consistent with Taurek’s holding 2) and in particular, 2 b) (that there is no impartial perspective from which to judge this issue.)

    4. Why isn’t Kamm’s Context-Aware View of pairwise comparison really just consequentialism in disguise? Indeed, why not call it the ‘Consequence-Aware’ view? Kamm might respond that unlike consequentialism, she is not aggregating. But as the Argument for Best Outcomes shows consequentialists do not necessarily have to aggregate either. Moreover, Kamm is already comparing, substituting, balancing, dividing persons. Why not also aggregate? Her stopping point seems arbitrary.

  4. 4. Posted by Toby Ord | July 13, 2007 4:43 pm


    In your case, E has been given further weight in the sense that E can make a claim. Indeed, E’s claim is balanced by B or C. In the case of tossing a coin though, C is not given the chance to make a claim at all.

    This is true, but I wonder how much merely being able to make a claim is worth, if it doesn’t correspond to any increased chance of being saved. I personally support saving the greatest number rather than any of the randomised methods, but don’t think that Kamm’s reasoning here really works.

    The problem is that (b) is not true by ‘mere logic.’ The moral equivalence of persons is a substantive moral claim that has to be argued for, and a claim that someone who holds that persons are incommensurable might deny.

    I agree. Kamm certainly needs moral principles to get claims (a) and (b) off the ground, though once she has them, she doesn’t need an additional principle of substitution of persons.

    But (rightly or wrongly), Taurek could deny that he is engaged in pairwise comparison; he could instead hold the view the persons are incommensurable.

    This is true, however he may then find himself in trouble if he wishes to say that we shouldn’t toss a coin between A’s life and B’s little finger.

  5. 5. Posted by S. Matthew Liao | July 13, 2007 5:09 pm


    This is true, however he may then find himself in trouble if he wishes to say that we shouldn’t toss a coin between A’s life and B’s little finger.

    That seems right to me, though maybe Taurek or someone could respond that there is a ‘sphere of incommensurability’ that includes lives, legs, arms, etc., but not fingers, hair, finger nails, etc.

  6. 6. Posted by S. Matthew Liao | July 13, 2007 6:53 pm

    By the way, for those who may not have Kamm’s book, Chapter 2 is based on her article “Aggregation and Two Moral Methods,” which can downloaded here if you have the appropriate access.

  7. 7. Posted by Jeff Huggins | July 13, 2007 7:57 pm

    Thanks for the great summary, Toby.

    As I read chapter 2, as much as I enjoyed it, it made me wonder whether I was ‘missing something’ that is unstated in the work (perhaps explained in Kamm’s earlier work?) or simply taken as a given, i.e., as a standard accepted assumption?

    That ‘something’ is, in my view, an understanding and acknowledgment of the basic ‘effective function’ of morality itself, i.e., its ‘reason for being.’ Although morality includes fairness (for example) as a very important means and as a subsidiary ‘end’, morality is not ultimately ‘about’ fairness. Put another way, the topic of human ‘morality’ itself, as well as our human social-moral faculties, exist by virtue of human survival (life), and they will continue to exist (hopefully) by virtue of continuing human survival. So, relatively speaking, morality itself is more ‘about’ survival (of humans), and continuing survival (of the human species), than it is about other very important means to this survival, including fairness, justice, and etc. This doesn’t mean that morality is solely ‘about’ survival, or continuing survival; it just means that morality is first-and-foremost about (continuing) survival, and that fairness and justice are means and subsidiary ‘ends’, and happiness is also a motivator, a subsidiary ‘end’, and (when we enjoy it) icing on the cake of survival. In my view, if this broader context were understood or made explicit, it would help support many of the arguments made, call for refinement of a few, and place the whole exercise in a more grounded context.

    Consider various benefits that were mentioned in the chapter: Life (avoidance of death), chances at life, resources that could help sustain life, a reasonable life span (or extensions to achieve such), enhanced intelligence, legs (the avoidance of losing them), arms (the avoidance of losing them), a cure for a sore throat, a cure for an earache, and etc. What differentiates whether some of these (or their associated losses) count (for example, in a tie-breaker situation) or whether they should be aggregated against each other? Why? And what tells us how real humans (even very intelligent and moral ones) assess such situations, relevance, probabilities, and direct and indirect consequences? And do/should the ‘example’ represented by (and proclaimed by) a choice, as well as the notions ‘what if everyone thought this way?’ or ‘what if someone made this decision that resulted in this consequence to me?’, play real roles in our human intuitions about these types of choices? I.e., are these aspects of the situation to be included in some sense among the ‘consequences’ of a given choice, rather than consequences being limited to the direct lives lost or gained in the immediate incident? In my view, there are answers to these questions that are grounded in a broad and science-informed view of morality itself.

    This leads me to two questions that, it seems to me, one should consider:

    Is it the goal (of the book or the broader enterprise) to discover or propose an ‘ideal’ morality that is justified and described in many situations based on intricate rules and logic that (probably) don’t capture how most people assess situations and make choices (even very responsible people making very moral choices)? OR,

    Is it the goal to discover or propose an ‘ideal’ morality that we should strive for that is justified by, and described using, an understanding of the effective function of morality itself, an understanding of people at their ‘reasonable best’, an understanding of how humans assess situations and how they ‘work’, and an understanding of human limits?

  8. 8. Posted by John Alexander | July 14, 2007 1:43 pm

    I want to make a comment on one the examples that Kamm uses in discussing’pairwise comparison’ and being ‘contect aware,’ and the ‘Blinder View.’ She is discussing how one ought to choose whom (what group) to benefit between 2 groups of unequal size. On page 58 she asks us to imagine two groups, one with 1000 people and the other with 900 people “who are in competition with each other for an education, where all are equally needy and capable of as good an outcome.” She then discusses ways to resolve the issue of which group to aid.

    It seems to me that this example is not a good one; there is no reason to presume that there are two groups. If people share the same characteristics and have an equal interest of securing a good and all are equally capable of as good an outcome as anyone else, then it seems to me that there is only one group, or set, namely those who want x, an education in her example. It seems to me that the only way we could break them into two groups is to use some criteria other then the equal desire for, and capability of, securing x. Relative to her example, the moral issue would be which criteria, that are not morally suspect, could one use to break people into groups? The ones I come up with, race, ethnicity, age, gender, etc. are all morally irrelevant and using any of these criteria is morally problematic. The key to resolve this issue is to treat the 1900 people as members of one set. If there are less then 1900 openings and everyone is equal in capacity to succeed and achieve the outcome, then the ‘coin toss’ (an impartial method) would be the morally preferable way to select those who will ‘get in.’

    The point I am getting at is that in some situations (trolley-like problems) numbers come into play, but in many others, the number of people does not matter if they are not in differentiated sets that can be establised using morally acceptable criteria. What matters is how many people with desire x (that which gives membership in a set)can be satisfied if everyone with desire x cannot be satisfied. Impartiality seems the only morally defensible way to solve who gets x in these situations.

  9. 9. Posted by Fiona Woollard | July 14, 2007 7:08 pm

    Dear John,

    I think you make a good point. Kamm’s discussion is only really applicable to cases in which we really do have two competing sets.

    However, I’m not sure that this makes Kamm’s example a bad one. We can certainly imagine a case in which the potential beneficiaries of an education are split into two groups. Suppose that we have two remote islands (perhaps in the Hebrides). 1000 children live on one island and 900 on another. We only have enough money to build one school. (Of course, we will do all we can in terms of remote learning for the other children.)

  10. 10. Posted by John Alexander | July 14, 2007 8:40 pm

    Deat Fiona
    I am not sure that your example works. Even if the groups are on two different islands it is still not clear that it is a choice of helping 1000 or 900. For example, how many children will be served by the school? If it is 901+ then build it on the island with 1000 and give the remaining students remote learning along with the 900 on the other island. If it is 900, then impartiality (coin toss) will still work here in chosing which island gets the school. If it is 500, impartiality will still work as to which island gets the school. Given your suggestion, the remaining children will still benefit in some way so it makes little difference who receives this (lesser) help as long as it is done as impartially as possible assuming everything else is equal, as it is in Kamm’s example. The question I would ask is how best to utilize the available funds so that as many, if not all, of the 1900 benefit. I still think this is one set’ 1900 desiring x; the question is how best to satisfy this desire.

  11. 11. Posted by Guy Kahane | July 16, 2007 4:35 pm

    Toby, you wrote you’d love comments on Kamm’s claims about ‘irrelevant goods’ in part VI. I’m happy to oblige.

    Kamm claims that a broken leg can break a tie, but not a sore throat. You find this claim incredible. There is of course a certain form of utilitarianism that would make such a claim extremely hard to defend. But do you think that this claim is incredible for a non-consequentialist who employs something like Kamm’s methodology? I’d say she’s making a commonsensical point.

    The claim does need grounding. It ties to some big questions. It is similar to the intuitive view that it would be wrong to allow one person to suffer just because this suffering is needed to produce a moment of pleasure in millions (as in an example of Scanlon’s).

    Such claims assume a normative threshold in facts about well-being. To defend them, one needs to (1) show that we really are committed to such a threshold in many different evaluative contexts (it needn’t be a sharp line of course), (2) that there is some principled grounding for this threshold. Only then could one hope to (3) show that this threshold can support such strong normative claims.

    I certainly don’t intend to mount such a defense. I’m not sure how to defend (3). (1) seems to me fairly easy to establish, though not much noticed in philosophical discussions of well-being. So just a remark on (2). A number of people have independently claimed that brief passing hedonic states that are not significantly connected to one’s ongoing projects and values can be discounted in assessments of lifelong well-being. One way of interpreting this claim would make sense even to a utilitarian. Such episodes don’t really make a life go better. But this would mean that they are not, in the relevant sense, irrelevant goods.

  12. 12. Posted by Fiona Woollard | July 16, 2007 8:56 pm

    Dear John,

    The capacity of the school is 15000. All of the children on the island that the school is built on can attend the school. However, the islands are far enough away from each other (and all other communities) that no one from the other island can attend the school. (Assume for the example that) attending school is much better for children than remote learning. In this case, we have a choice between providing an good education to 1000 children and providing a good education to 900 children, with the memembership of each group fixed.

  13. 13. Posted by John Alexander | July 16, 2007 10:17 pm

    Hi Fiona
    Thanks for responding.

    I do not see how your example counters mine. Given your assumption that inclass learning is better then remote learning then utilizing the principle of utility, we should provide the most good to the most people affected by our action. If we assign a value of 1 to inclass learning and a value of .8 to remote learning then it is clear that we should build the school on the island of 1000 and provide remote learning for the 900.

    However, why would one build a school with a capacity that so far exceeds the amount of children to be served? On consequentialist/utilitarian grounds it would seem morally preferable that if it were possible to build a school with that capacity then we should build two schools; one with a capacity of 1000 on that island and a smaller school on the other island. Given the values assigned to inclass versus remote learning above isn’t that what we should do?

  14. 14. Posted by Toby Ord | July 16, 2007 10:19 pm


    I agree that Kamm’s claim (lost legs break ties, but sore throats do not) is in line with common sense. I also agree that it is the type of claim that is fairly typical in nonconsequentialist reasoning. However, it is closely related to claims that have been shown to be very problematic. Kamm has previously claimed something like the following: sufficiently many sore throats outweigh one person losing their legs and sufficiently many people losing their legs outweigh one death, but no amount of sore throats outweigh one death. This is not explicitly contradictory as Kamm need not decide what we ought to do purely on the grounds of what is better and thus her theory can survive intransitivity, but Alastair Norcross has shown that the induced intransitivity is very counterintuitive (Gustaf Arrhenius has some similar troubling results for theories like Kamm’s).

    Suppose that the number of sore throats needed to outweigh loss of a pair of legs is 1,000 and the number of pairs of legs being lost needed to outweigh a death is also 1,000 (any other numbers also work). Now suppose you are faced with:

    (A) saving 1 life
    (B) saving 1,000 pairs of legs
    (C) curing 1,000,000 sore throats

    For each option there is a long windy road leading to the people in need. Faced with (A) and (B) you must choose (B), from (B) and (C) you must choose (C) and from (A) and (C) you must choose (A). If faced with all three options, there must be a permissible option. It doesn’t matter which it is, but let’s say that (A) is permissible and that you set off down the road to where the person can be saved. Now suppose that as you set off, a tree falls blocking the road to (C). You are now facing a choice between (A) and (B) and since the legs outweigh the life, (A) is no longer permissible and you must change to road (B). This is very odd, and the phenomenon occurs so long as any one of them is permissible. Indeed whenever a theory has intransitivity in its ought claims, you get this strange dependence on irrelevant alternatives. Thus, while deontological theories are not entirely destroyed by intransitivity (as consequentialism would be), the intransitivities still lead to very strange and unmotivated ethical constraints.

    I don’t think that Kamm says quite enough about lives, legs and throats in the chapter to pin her to a Norcross style argument like this one, but I think she is dangerously close, and would run into it if she made her position entirely explicit.

  15. 15. Posted by Jeff Huggins | July 16, 2007 11:56 pm

    Should a broken leg (or sore throat, or etc.) of a third person be used as a tie breaker when deciding whether to save person (A) who would otherwise die or person (B) who would otherwise die, if you have to choose between saving ‘A’ and curing the third person’s leg OR saving ‘B’?

    It seems to me that there are at least two central considerations having to do with the tie-breaking question in this type of situation, in my view: 1.) The likelihood and degree that the third person’s ailment will undermine her/his own survival or her/his own ability to have or raise children; and 2.) The ongoing role that the society’s concept of fairness plays in its sustainable survival and healthy stability, and the precedent set by (or lesson learned via) the way the pending choice is ultimately made. Of course, this assumes that the moral status and situation of persons ‘A’ and ‘B’ are equal and that all else of relevance is equal.

    Considering item ‘2’ first: In my view, coming from a scientific standpoint, there is probably not an absolute, precise, exacting principle of fairness written into the cosmos. When we consider (and weigh) the concept of fairness, we should probably do so in light of other aspects of being human, and in light of the question: Fairness to what end? In other words, we should see fairness as a very important subsidiary goal (after all, it’s nice and helpful to be treated fairly!) and, importantly, as a valuable means and dynamic in our human quest for survival as a species. So, what do (and would) humans consider fair, and why? Although (as has been pointed out) intuitions are not everything, intuitions that can be validly tied to sensible reasons that all serve some sensible function and that pass other tests are probably as good as it gets. This brings us to consider item ‘1’.

    If the ailment of the third person (or what he would suffer if not saved) only causes a temporary diminishment in his happiness (or temporary increase in suffering), and if it will not likely lead to his death, and if it will not prevent her/him from having children (if she/he chooses to do so), then such an ailment should probably not be considered a tie-breaker (in deciding which of two other people will have to die), because using such a temporary ailment as a tie-breaker would actually (likely) undermine the intuitive sense of fairness in a society and can’t be tied to the most foundational ‘effective’ function of human social-moral nature. Survival has a grounded value. The ability to have children has a grounded value. Without adherence to these values, at least on average, the human species would not continue to exist for very long (in evolutionary terms). Although we all like happiness, and we like to avoid suffering, temporary sadness and temporary suffering are common aspects of life (and most people intuitively understand this) and are thus not sufficient reasons to rob ‘B’ of a 50% chance to be saved and in so doing give everyone else in that society the idea that her/his own lot could be similar if ever in a situation similar to that of ‘B.’ (If living in such a society, it might be wise to always go around with someone chained to you who has at least a broken leg, or better yet a broken leg and a sore throat.)

    On the other hand, if the ailment of the third person could likely be life-threatening (even a year from the choice being considered) or if it would rob her/him of the ability to have children, then such an ailment could be reasonably considered a tie breaker for deciding whether to save ‘A’ or ‘B’, all else equal, without undermining the ongoing societal sense of fairness in a way not ground-able in a basic understanding of ongoing human survival.

    Look at it this way: Consider an isolated society that, for some odd environmental or behavioral reason, routinely faces such difficult choices. One of two equal persons, ‘A’ or ‘B’, will (unfortunately) die. A third person exists (with some ailment) as a possible tie-breaker. One side of the calculus involves the question/likelihood that the ailment, if not cured, will cause the third person to die or will cause her/him to be unable to have children. The other side of the calculus involves the role of ‘fairness’ in the society’s stability, health, and ongoing ability to survive and regenerate (reproduce). I think it’s accurate to say that, if members of the society face these choices often, and if they don’t do this calculus at least reasonably correctly, the society will likely decline and may even decline itself into non-existence, other things equal. Or, if it catches its miscalculation in time, it can change policy. On the other hand, if a society gets the calculation right, its choices will be consistent with its own ongoing survival and regeneration from one generation to the next.

    This is an oversimplification, of course, but (I believe) is directionally correct.

  16. 16. Posted by Rebecca Roache | July 17, 2007 11:26 am

    Toby, Guy,

    I think it’s important to recognise that the common sense intuition that lost legs but not sore throats break ties between decisions about whose life to save may depend upon another common sense intuition: that sore throats are irrelevant to decisions about whose life to save because we really ought to be looking for less trifling considerations to help us make such massive decisions. If this is right, the fact that Kamm has, in introducing dilemmas such as that between saving A’s life or saving B’s life and curing C’s sore throat, specified that there are no other morally relevant considerations to help us reach our decision means that she has artificially removed the possibility of satisfying the common sense desire to find a consideration less trifling than a sore throat. In this case, the common sense intuition that sore throats should not break ties in life-or-death decisions fails to apply, and so (like Toby) I find her denial of the relevance of such things as sore throats difficult to accept. It’s true that it’s difficult to accept that someone’s sore throat could be morally relevant to a decision about whose life to save, but it seems to me to be no more difficult to accept than the stipulation that there is no other factor more morally relevant than a sore throat that could help us reach a decision.

    I’m not sure, either, that Kamm’s methodology excuses her from ignoring C’s sore throat in the scenario that she has described. She does, after all, accept that an act’s consequences can be relevant to its rightness – she only denies that the act’s consequences are the only, or the most important, relevant factors (see the beginning of chapter 1). However, if the option of saving A’s life, and that of saving B’s life and curing C’s sore throat, are – C’s sore throat aside – matched in all morally relevant nonconsequentialist and consequentialst factors, then I don’t see how the addition of even a trifling consequentialist factor to one side can fail to be morally relevant.

  17. 17. Posted by Fiona Woollard | July 17, 2007 7:59 pm

    Dear John,

    I think we’re talking a little at cross purposes here. My example was only intended to defend Kamm against your comment:

    “It seems to me that this example is not a good one; there is no reason to presume that there are two groups.”

    I just wanted to show that we can easily imagine scenarios in which we do have to choose between providing a good education to 1000 people and providing a good education to 900 people, with two clear groups. It wasn’t intended to be a counterexample to any of your normative claims.

    However, I’m pretty sure that Kamm would not accept straightforward appeal to the principle of utility. As a non-consequentialist, she wouldn’t see this as settling the matter. Before we can just say that they ought to build the school where it will do most good, we must check that we are not treating unfairly those who do not get the benefit. Surely that’s the interest of this chapter?

  18. 18. Posted by Jeff Huggins | July 17, 2007 10:47 pm

    Dear Fiona,

    I find the last comment in your recent post, and similar types of comments by Kamm, to be very interesting, and they prompt me to ask the questions listed below. But first, your comment:

    “Before we can just say that they ought to build the school where it will do most good, we must check that we are not treating unfairly those who do not get the benefit. Surely that’s the interest of this chapter?”

    Your comment, and very similar ones by Kamm (I believe), cause me to wonder and ask: What do non-consequentialists think ‘fairness’ to be (beyond a concept, that is), what do they think the role of fairness is when it comes to societal stability and well-being, and what greater end do they see fairness serving, more or less, if any?

    To put this another way, do non-consequentialists consider ‘fairness’ to be an ultimate end in itself, to be considered equal to ‘the good’ in weight, and to sometimes trump ‘the good’? (If fairness trumps ‘the good’, is it because fairness can sometimes trump ‘the complete good’ (all things considered and accurately calculated), or is it because ‘the good’ that is trumped is only a partial and incorrectly calculated ‘good’?) Or, do non-consequentalists consider fairness to be a very important means to help, in concert with other considerations, achieve ‘the good’ as well as a subcomponent of the good and a subsidiary end?

    And, on this matter anyhow (i.e., ‘fairness’), is the main difference between consequentialists and non-consequentialists merely definitional or is it substantive? In other words, is the main difference between the two the fact that non-consequentialists consider fairness (and the impact on fairness of any given decision) to be a very important consideration in decision-making, but prefer not to call this impact a ‘consequence’, while the consequentialists prefer to call this impact a ‘consequence’? Or, do consequentialists exclude the impact on fairness from their calculus entirely, i.e., do they not consider it as a ‘consequence’ of any given moral choice? Or, do consequentialists and non-consequentialists both consider the impact on fairness (though one calls it a ‘consequence’ and one doesn’t) but hold very different views regarding what ‘fairness’ is, its role in society, and the larger end that it often serves?

    I apologize if these questions don’t make sense as written. I’m very interested in your thoughts, and I also wish that Kamm could answer these questions from her own perspective (though perhaps she has already done so in her earlier works that I, unfortunately, have not read).

  19. 19. Posted by Jeff Huggins | July 19, 2007 4:14 pm

    Given our focus here on the question of ‘whether the numbers count’, and given the important role of human ‘intuition’ in Kamm’s methodology, I thought I’d mention a very interesting radio program I heard recently on public radio in the U.S. The program segment, half-hour in total, called ‘Numbed by the Numbers’, included among other things a brief (five-minute) interview of an Ellen Peters, senior research scientist at Decision Research, talking about some recent research regarding the human perception of numbers in certain types of social situations. In the interview, she uses phrases such as ‘basic ways of processing information’ that are part of ‘human nature’, and the results she briefly discusses would be quite interesting for anyone interested in the general topic (i.e., the topic of this thread). I have not read the actual research, and I can’t vouch for it myself, nor do I know its full scope of applicability. But, the entire program segment, and in particular the part involving Ellen Peters (which begins about 12-and-half minutes into the segment and lasts for about five minutes), would probably be helpful and thought-provoking to anyone interested in (using the term as a shorthand) ‘human nature’ as it relates to our interpretation of numbers in certain social-moral situations. An on-line audio recording of the show can be heard (for free!) at the following link:

  20. 20. Posted by Guy Kahane | July 20, 2007 8:02 pm

    Toby, I suspected you had such transitivity issues in mind. But your remark that Kamm’s view here is incredible suggested something stronger. After all, the transitivity problem arises through this further claim of Kamm’s that you mention. But the ‘irrelevant goods’ claim doesn’t require that further claim. Even if 1000 sore throats did outweigh a life, it might still be true that one sore throat is an irrelevant good in the context of this kind of choice, despite making the overall outcome a better one.

    Rebecca, I’m not sure I fully understand your remarks on this. As you note, Kamm isn’t denying that betterness of outcome CAN matter. She is however denying that it always does, and that it matters through consequentialist aggregation.

  21. 21. Posted by Kamm’s Intricate Ethics: Chapter 9 : Ethics Etc | August 31, 2007 10:59 am

    […] (see, for example, Toby Ord’s discussion of a case from Alastair Norcross (comment number 14 on chapter 2) and Nir Eyal’s introduction of a Sidney Morgenbesser case (chapter 6 summary)), and Kamm has her […]

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