To illustrate triggering cases, Kagan presents the following example:
FACTORY-FARMED CHICKEN: The butcher at the local supermarket will order an additional batch of 25 freshly slaughtered chickens from the local factory farm as soon as 25 chickens have been sold. If he places the order, 25 chickens will be hatched, raised and slaughtered.
Suppose I am considering buying a chicken. Although my purchase has a 24 out of 25 chance of making no difference to the suffering of chickens at all, it has a 1 out
of 25 chance of triggering the suffering of another 25 chickens. Provided that the pleasure I get from eating one chicken does not outweigh the suffering of a chicken raised, hatched and slaughtered under current factory farm conditions, the expected utility of my purchase is negative.
Kagan admits that this example is simplified (and my presentation is even more simplified). Still, it helps us to see why the expected utility approach entails that each of us has a reason not to act in the problematic way in triggering cases. Each of us has such a reason since acting in this way risks bringing about a bad outcome.
It is a familiar case of a choice under uncertainty.
As presented, the argument may seem to be suggesting that I will make a difference to the suffering of another 25 chickens if and only if I buy the 25th chicken. As Kagan clarifies, this is a misinterpretation. For one thing, if 26 chickens are sold that day, my purchase of the 25th chicken will have made no difference to the harmful outcome. Another batch would have been ordered anyway, whether or not I had bought a chicken. For another, if my purchase was the last that day, I would not be the only person affecting the harmful outcome. For, each of those who bought one of the first 24 chickens will also have made a difference. It is true of each of them that, had they not bought a chicken, no additional batch of freshly slaughtered chickens would have been ordered. So, rather than making a difference to the harmful outcome if and only if you buy the 25th chicken, you make a difference if and only if you buy a chicken and exactly 25 chickens are sold that day (or any multiple of 25, such as 50, 75 etc.). Still, buying one chicken has 1 out of 25 chance of triggering the suffering of another 25 chickens.1
Unlike triggering cases, imperceptible difference cases arise where many acts together result in a harmful outcome, but where no individual act makes a perceptible difference to the harm. To illustrate such cases, Kagan uses a slightly modified version of Derek Parfit’s (1984) case of the harmless torturers.2
HARMLESS TORTURERS: A victim is wired to a machine with a thousand switches.
There are a thousand torturers, each flipping one of the switches. When no switches are flipped, the victim is in no pain. When all switches are flipped, a strong current runs through the body of the victim, who then is in extreme pain. Still, the flipping of any given switch increases the current only by a very small amount, well below the perceptibility threshold.
1 There are alternative ways of answering this challenge. We could for instance treat at least some triggering cases as examples of pre-emption rather than overdetermination. Lawford-Smith (2016) uses this strategy.
2 In Parfit’s version there are a thousand victims as well as a thousand torturers, and the victims are already in mild pain at the start of the day when no switches are flipped. Kagan’s version is presented here in abbreviated form.
Note that in Kagan’s version of the case, the victim is in no pain when no switches are flipped. In this respect, Kagan’s version differs from Parfit’s (and from the version I have discussed earlier in the thesis), where the victim is in mild pain before any switch is flipped. As will become evident, it is important for Kagan’s argument that the victim is in no pain at the start of the day. Still, with some ingenuity, his argument could be revised to apply also to Parfit’s version of the case.
Kagan suggests that overfishing might also seem to be an imperceptible difference case. If enough people fish, a certain fish stock will collapse, and those who depend on fishing from this fish stock for their livelihood will suffer. Still, no one fish taken makes a difference for whether the fish stock collapses, and so makes no difference for the livelihood of anyone.
As Kagan notes, it is not entirely correct to say that the potentially problematic acts in imperceptible difference cases make no difference at all. They make no perceptible difference to the harm done, but they do make a difference in some underlying dimension. A flipping of a switch increases the current running through the victim, one fish taken means one fish fewer left in the lake, etc. The problem posed by imperceptible difference cases is rather that none of these acts makes a morally relevant difference: they do not make any difference in perceived harm for anyone. Here, Kagan presupposes what we can call:
THE PERCEPTIBILITY PRINCIPLE: Only perceptible differences in harm are morally relevant.
This principle has considerable intuitive appeal. How could consequences that are not experienced by anyone – not now, not later – be morally relevant? Moreover, as Kagan points out,
the only harm that seems relevant [in HARMLESS TORTURERS]… is the pain the victim is in, and it is difficult to see why it should be bad to increase pain in an imperceptible way. Indeed, it isn’t even clear that it makes any sense to say that pain has been increased imperceptibly. On the contrary, it seems that the pain hasn’t increased at all.
(Kagan 2011: 116) Still, reflecting on examples like this, philosophers like Parfit (1984), Barnett (2018) and Broome (2019) have embraced the initially unappealing position that some harms are imperceptible. In this paper, I will assume with Kagan (2011) that THE PERCEPTIBILITY PRINCIPLE (or something like it)3 is correct.
3 Shrader-Frechette (1987) argues that THE PERCEPTIBILITY PRINCIPLE is incorrect: imperceptible but measurable differences do matter. As an alternative to THE PERCEPTIBILITY PRINCIPLE, we could
Given that THE PERCEPTIBILITY PRINCIPLE is correct, there is no risk that acting in the problematic way in imperceptible difference cases would make a morally relevant difference. Since no flipping of a switch in HARMLESS TORTURERS makes a morally relevant difference, for instance, you can safely flip a switch knowing that doing so has no risk of making such a difference. Therefore, the expected utility approach does not entail that you have a reason to refrain from acting in the problematic way in such cases.
Kagan’s Argument and Nefsky’s Refutation
So, the expected utility approach can explain why we should refrain from acting in the problematic way (buying chickens, etc.) in triggering cases, but it cannot explain why we have a reason to refrain from acting in imperceptible difference cases. It is at this point that Kagan’s main thesis enters the picture. He argues that it is a conceptual truth that there are no imperceptible difference cases. In his words, “the relevant kind of case is impossible, as a matter of conceptual necessity” (Kagan 2011: 139). If correct, this ensures that all collective harm cases are triggering cases.
His diagnosis is that cases that seemed to be imperceptible difference cases are actually triggering cases in disguise. To get the gist of this idea, return to the example of overfishing. Here, Kagan claims that at some point one fish taken does in fact make the fish stock unable to successfully reproduce and thereby cause those who depend on fishing from this fish stock for their livelihood to suffer.
[I]t is not as though my catching an extra fish makes an imperceptible difference to the decline of the fish population’s ability to replenish itself. Rather, up to a point, as each person takes one extra fish, this makes no difference at all – the fish will be fully capable of replenishing their population, despite the extra fish taken. But at a certain point – an unknown point – one too many fish is taken, the stock is no longer large enough, and the population crashes.
(Kagan 2011: 118) Similarly, Kagan argues, the flipping of a switch in HARMLESS TORTURERS makes a perceptible difference in pain for the victim.
Kagan has offered an argument for the view that all collective harm cases are triggering cases, using HARMLESS TORTURERS as an illustration. However, though
adopt a measurability principle saying that an action cannot be right or wrong as a result of its effects if those effects are immeasurable. Since infinitesimal changes are not measurable, there could be cases of immeasurable difference. See Nefsky (2012: sec. XII) and Broome (2019:
appendix) for discussion. Kagan does not consider a measurability principle.
the general idea behind the argument is clear, it is stated somewhat differently in different places in Kagan’s paper. I will therefore consider three variants of it.
I start with Nefsky’s (2012) interpretation. In summary, she understands Kagan’s argument as follows:
ARGUMENT #1(REPORT VERSION)
(1) When no switches are flipped the victim is in no pain (call this s0), and if asked whether he is in pain, he will answer “No”.4
(2) Suppose (for reductio) that, (a) for all n, the victim cannot perceive the difference between sn and sn+1.5 If this is true, (b) the victim (who always gives a correct report of what he feels) will give the same answer to the question “Are you in pain?” in sn+1 as in sn.
(3) Therefore, when in s1000, if asked whether he is in pain, the victim will answer
“No”.
This is absurd! By hypothesis, the victim is in extreme pain when in s1000 and will therefore answer “Yes” when asked whether he is in pain.
\ Supposition (2a) must be wrong. There must be some n such that the victim can perceive the difference between sn and sn+1.6
This argument, Kagan claims, can be repeated for any alleged imperceptible difference case.
As Nefsky (2012) points out, argument #1 (report version) is not compelling. It relies on the assumption that the victim always gives a correct report of what he feels (an assumption made explicit in (2b)). This assumption is however highly questionable. The requirement that the victim must answer with a simple “Yes” or
“No” makes it unlikely that his report will reflect his experiences. His pain increases gradually in a fine-grained manner, but he is forced to give coarse-grained answers.
4 Sn denotes pain state n, that is, the pain the victim feels when n switches are flipped.
5 Towards the end of his paper, Kagan argues that it would not be genuinely troublesome for the consequentialist that the victim cannot perceive the difference between two adjacent pain states.
What is genuinely troublesome, Kagan suggests, is “the suggestion that an act might leave someone worse off, even though it makes no difference to how they feel” (2011: 137). This seems correct. Arguably, it is not the victim’s ability to distinguish two adjacent states that is morally relevant, but rather differences in how the victim feels. If you wish, you are free to replace (2a) with the following alternative premise: for all n, the victim feels the same in sn+1 as in sn (and to apply this premise throughout the paper, including to all versions of Kagan’s argument). My arguments stand either way.
6 Norcross (1997: 142) suggests a similar argument in which the victim screams when he is in pain rather than reporting “Yes”.
To avoid this difficulty, Nefsky recasts Kagan’s argument without references to what the victim reports.
ARGUMENT #1
(1) When no switches are flipped the victim is not in pain (call this s0).
(2) Suppose (for reductio) that, (a) for all n, the victim cannot perceive the difference between sn and sn+1. Therefore, (b) for all n, if the victim is in no pain in sn, he is also in no pain in sn+1.
(3) Therefore, when in s1000, the victim is in no pain.
This is absurd! By hypothesis, the victim is in extreme pain when in s1000.
\ Supposition (2a) must be wrong. There must be some n such that the victim can perceive the difference between sn and sn+1.7
Nefsky points to a flaw also in this improved version of the argument. We are not compelled to conclude that (2a) is wrong. In fact, we are not compelled to locate the problem in (2) at all. Rather, we face a dilemma. We need to reject either at least one premise or the validity of the argument, but neither option seems attractive. In Nefsky’s words, this is an argument where “apparently true premises are shown to lead to contradiction through a series of seemingly valid steps” (Nefsky 2012: 385, footnote 48). If argument #1 can be used to show that the victim can perceive the difference between one pain state and the next, we can use an analogue of it to show that adding a grain of sand can turn a non-heap into a heap, or that plucking a single strand of hair from a hairy person can make this person bald. As Nefsky puts it, Kagan is basically “giving a sorites argument as though it were a simple reductio proof that there cannot be vague boundaries” (Nefsky 2012: 385).
To bring out this point clearly, we can compare argument #1 with a generic sorites argument:
THE SORITES ARGUMENT
(1) x1 is F (Base premise)
(2) For all n, if xn is F then xn+1 is F (Inductive premise)
(3) Therefore, xk is F (Conclusion)
Paradox! Even though both (1) and (2) appear to be true, and (3) appears to follow from (1) and (2), (3) seems false for sufficiently large k’s.
7 This is the argument that Nefsky (2012) calls “Version 2”. The argument is presented here in condensed form.
Comparing the two arguments, we see that the conclusion (\) in argument #1 lacks a counterpart in the sorites argument. On reflection, we see that (\) points to a solution to the paradox, because it suggests that the problem is located in the inductive premise (2). However, just as the sorites argument does not force us to accept, say, that adding a grain of sand can turn a non-heap into a heap, premises (1) to (3) do not force us to reject (2). There is a range of possible solutions to the paradox, all of which have their own problems. We could, for instance, accept conclusion (3). Peter Unger (1979) advocates this. He argues that since (1) and (2) are true, and since the argument is valid, we must draw the conclusion, however unintuitive it may seem, that (3) is true. Adding one grain of sand to a non-heap will never result in a heap. In fact, there are no heaps, hairy persons or extreme pains.
Hence the title of his paper: “There are no ordinary things”. If Unger is correct, there will be no sharp boundary in imperceptible difference cases, and Kagan’s argument will be unsound.
Another option is to deny the validity of the argument. Bertrand Russell (1923) claims that arguments containing vague predicates are not the kind of thing that can be valid or invalid. If he is correct, argument #1 is invalid since it contains a vague predicate. A third option is to follow Michael Dummett (1975) and accept (1), (2) and (3) and the validity of the argument, and conclude that the predicate in question is incoherent. If we follow Dummett’s advice, we will not conclude that (2) is wrong as Kagan urges us to do. We will conclude instead that the predicate represented by F (e.g. “not a heap” or “pain”) is incoherent. If any of these accounts turns out to be correct, argument #1 will lack cogency.
This brings us to what is essentially a crux of the debate. Nefsky argues that argument #1 is not compelling, and that we are not forced to reject (2). But she does not show that Kagan’s conclusion is mistaken. It might still be a conceptual truth that the victim can perceive the difference between some adjacent pain states in
HARMLESS TORTURERS – and, more generally, that imperceptible difference cases are impossible. Nefsky proposes a range of other objections to Kagan’s argument.
However, none of these shows that Kagan necessarily is wrong to reject (2). Nefsky does, however, say the following:
[W]e should begin our evaluation of Kagan’s arguments – as he begins his arguments – from the intuitive, pre-theoretic perspective in which nontriggering cases seem to be a real possibility.
(Nefsky 2012: 378, note 35) From a pre-theoretic perspective, cases like HARMLESS TORTURERS do at least seem to be non-triggering cases (of the imperceptible difference variety). Nefsky also appears to be correct in claiming that we should begin our evaluation from this perspective. But it seems that the natural next step would be to move on from a
pre-theoretic perspective to a pre-theoretical perspective. What do our best theories of vagueness tell us about these issues? Do they tilt the scale in favour of Kagan’s position or indicate that his conclusion is mistaken?