Shelly Kagan (2011, "Do I Make a Difference?"):

a single molecule of the toxin makes no difference to anyone's health. To be sure, if enough molecules are taken in, the result is sickness or death; but one molecule, more or less, simply doesn't make any difference at all to anyone's health.

Imagine, next, that there are thousands, or tens of thousands, of similarly polluting factories around the nation (or the world). Each scatters its toxins so widely that no single individual ever takes in more than a single molecule from any single plant. But because there are indeed thousands of such factories, many people do take in enough of the toxin to become ill. ... But for all that, it seems as though each factory owner can truthfully say to himself that it makes no difference whether or not he pollutes, for his decision puts at most one extra molecule of toxin in any given individual, and by hypothesis a single molecule, more or less, simply doesn't make a difference to anyone's health. When I think about my own decision whether or not to pollute, then, I have to admit that my polluting doesn't actually harm anyone, since it doesn't make a difference to anyone's health.

Is the above reasoning correct? If not, is there a name for the error or fallacy committed here?

  • @user3451767: Is that the policy here?
    – user46819
    Jun 2, 2020 at 5:47
  • 1
    But this is not homework. I'm just reading for my own pleasure/education. (I thought the above reasoning was obviously fallacious, but it coming from a Yale professor of philosophy in a good journal, I feared I might be mistaken. I am thus seeking the expert opinion of others.)
    – user46819
    Jun 2, 2020 at 5:54
  • 2
    The question is related to the paradoxes that can be produced by sorites
    – user37859
    Jun 2, 2020 at 11:55
  • Can you say why you think the reasoning here might not be correct?
    – E...
    Jun 2, 2020 at 20:20
  • It is absolutely a case of Tragedy of the common: en.wikipedia.org/wiki/Tragedy_of_the_commons
    – polcott
    Jun 3, 2020 at 1:15

4 Answers 4


This is a variation on the Tragedy of the Commons, in which minor misuses of a shared but limited resource result in the destruction of the resource entirely. The resource in this case is 'air', which is used for both breathing and waste disposal.

The Tragedy of the Commons is really a matter of solipsism. From the perspective of an individual, the common resource seems vast and inexhaustible; no individual can imagine personally overusing a common resource — certainly not a common resource as immense as an atmosphere — and thus sees no harm in taking a few selfish liberties. But the cumulative effect of many individuals taking small, selfish liberties can eventually overwhelm any limited resource.

I can't imagine Kagan presenting this as a serious argument, so he must be using it as an entry point for a more sophisticate philosophical or political argument. I'd read further and see where he goes with it.

  • You have misunderstood the Tragedy of the Commons, which is not at all a fallacy or "a matter of solipsism". Instead it is a very well studied and understood phenomenon in economics. You should be able to find simple numerical examples illustrating it in many economics textbooks. The reasoning in the Tragedy of the Commons is different from the reasoning given by Kagan (who's male by the way).
    – user46819
    Jun 3, 2020 at 0:45
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    I've never met Kagan, so apologies to him for the misunderstanding. I'll correct. With respect to misunderstanding the ToC... No, I'm sorry; you either don't know what you're talking about at all, or haven't put in the effort to think about what I wrote. Please take the time and reflect on it; if you still disagree with my assessment I will go through it step by step to make it clear. Jun 3, 2020 at 1:08
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    Please see for example Varian (2014, Intermediate Microeconomics), Ch. 35.6 The Tragedy of the Commons to try to understand it. The Tragedy of the Commons is similar to the Prisoners' Dilemma, in that what is rational for each individual ends up being collectively harmful. Importantly, it works even in the case where there are just two individuals. It has nothing to do with each individual being "too small" to "make any difference". (This is a popular misconception among non-economists who have merely heard the term abused usually by journalists.)
    – user46819
    Jun 3, 2020 at 1:30
  • @user135187: You'd do better to get your nose out of intermediate textbooks and use your brain to look at the case. No one (excuse me, no one except economists) uses rational actor theory seriously anymore. Jun 3, 2020 at 1:50

This is the Sorites Paradox (as pointed out by Ray LittleRock):

  1. One additional straw on a camel's back always makes no difference.
  2. Hence, for any positive integer 𝑛, if there are already 𝑛 straws on the camel's back and the camel's back is still not broken, then the camel's back will also not be broken by 𝑛 + 1 straws.
  3. Yet we do know that one billion straws will break a camel's back. This is a "paradox" because our observed real-world outcome contradicts #1 and #2.

One can come up with many variants of this "paradox", e.g.

  • One additional hair on a bald man's head makes no difference to whether he is regarded as bald;
  • One additional candy for someone on a diet makes no difference to the success of her diet;
  • One additional puff of a cigarette makes no difference to whether one will get lung cancer;
  • Kelly's reasoning.

There are apparently many solutions to the paradox (see e.g. the SEP entry).

But in my opinion, the error is the simple one of assuming that the effect of a very small but positive additional quantity is always equal to zero.

In particular, the error is in premise #1: that one additional straw/hair/candy/puff of a cigarette/factory/whatever always makes no difference.


The major sources of pollution are power plants and cars. Both of these require major changes to the economy. The first to move over to renewable sources of energy and in the second, to move over to using electric cars. This is one reason why both in the US and Europe the notion of a Green New Deal is being discussed. This would be a Keynesian transformation of the economy by investing in both infrastructure and people. There is more than enough scientific and technological expertise to make this happen. However, this would require visionary leadership, which unfortunately neither Johnsons or Trumps administration is capable of delivering.

The fallacy here is to mistake the individual choices that one can make with the collective choices that a community makes which shapes the individual choice.

Another apposite example here is the pollution of environment by plastics, to the point where plastics have been found in the deep ocean. The solution here is obvious - biodegradable plastics. This is nature's solution and humans would do as well to follow her lead here. Instead, we are encouraged to 'solve' the problem by individually using less plastics. This, however, doesn't get at the systemic roots of the problem.

Obviously large fossil fuel corporations have a vested interest in hoodwinking people into thinking that the problem is individual. That one can solve the systemic problem of plastic pollution if only fewer plastic bags were sold.

The fallacy here is again the one pointed out above, to avoid thinking about collective solutions as opposed to individual ones and to mistake one for the other.


Yes, the reasoning is correct, although it's important to keep in mind what the actual conclusion is. Here is Kagan's argument:

  1. A single toxin molecule makes no difference to anyone's health. (Premise)
  2. In the imagined scenario, each factory pollutes in such a way that no single person ever takes in more than a single molecule from any given factory. (Premise)
  3. For each factory, it makes no difference to anyone's health whether that single factory pollutes. (Conclusion)

This is a valid argument; if premises 1 and 2 are true, the conclusion must be true as well. It's important to keep in mind, however, before accusing Kagan of fallacies, that the following is not his conclusion:

It's morally permissible for each factory owner to pollute.

Rather, as you can see if you read the paper, Kagan holds that the factory owners in this scenario should not be polluting, because the overall pollution is bad. He presents the above argument as an objection to a version of consequentialism, according to which it's okay for the factory owners to pollute because their individual (rather than collective) actions make no difference to anyone's health.

  • Why the downvotes?
    – E...
    Jun 2, 2020 at 21:34
  • I don't think the inference is valid because it is missing the premise that the collective factories do cause sickness. If I absorbed n toxic particles and became sick, of which 1 came from factory A. Then clearly factory A contributed to my illness. If the threshold for sickness was n-1 then maybe I wouldn' t have gotten sick of factory A wasn' t around.
    – Cell
    Jun 3, 2020 at 0:11
  • @Cell I take the first premise to mean that a single cell never makes any difference, such that there is no threshold above which you are sick and below which you are not. Now, that premises may be incorrect, but that doesn't mean the argument is invalid.
    – E...
    Jun 3, 2020 at 0:27
  • Ok I thought the premise was that going from 0 to 1 toxin makes no difference. Ill change my vote. Scratch that I can't reverse my vote.
    – Cell
    Jun 3, 2020 at 1:50

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