Emergence and Incremental Impact

In 'What’s Wrong with Joyguzzling?', Kingston and Sinnott-Armstrong claim that individual greenhouse gas emissions never make a difference.  I find this to be a deeply bizarre claim, since they don't dispute that large amounts of GHG emissions together make a difference, and that large amounts of GHG can be produced by adding together many smaller amounts.



Consider some harmful large collection of n GHG molecules.  We can ask: was there some minimum size, or molecular count, m, below which the collection would no longer have caused the harm that it did?  If so, then it seems that an individual increment that brings the collection from size m-1 to m is one that causes harm.  Alternatively, and perhaps more realistically, suppose that it is a probabilistic matter.  Smaller values of n yield a smaller chance of the harm eventuating, and larger values yield a larger chance of causing harm.  In that case too, individual increments are harmful, in the straightforward sense of increasing the risk of real harms eventuating.  (This remains true even if the probabilities do not increase in linear fashion.  Perhaps each increment is much less risky when n is small, and more risky when n is already large.  Given that we've no way of knowing the current value of n, this makes no difference whatsoever in expectation.  We should thus regard the marginal expected disvalue of emitting 1 additional GHG molecule as exactly equal to 1/nth of the marginal disvalue of emitting n GHG molecules.)

Kingston and Sinnott-Armstrong try to block this kind of argument by appeal to emergent properties:

[I]t is just as inaccurate and misleading to say that individual molecules of greenhouse gases increase climate harms as it is to say that individual molecules of oil are slimy or yellowish.

But the claim is not that individual GHG molecules in a vacuum increase climate harms.  The claim is instead that individual increments in the number of GHG molecules in the atmosphere, given that this number is already high, can further increase climate harms.  The is more like the (plainly correct) claim that adding an extra molecule of oil to a suitable existing collection may increase the extent to which the collection exhibits slimy behaviour (or yellowish appearance).*  Emergent properties of groups are not possessed by individual constituents in isolation, but it is simply fallacious to infer from this that individual increments to the group size never make a difference to whether (or how) the group exhibits the emergent property in question.

It is scientifically uncontroversial that individual increments affect emergence.  As Helen explains in footnote 15 of her 'Seeing' paper (p.2028):

A single molecule of H2O does not have the relevant functional profile to constitute a liquid, but once the relevant threshold is passed the molecules will constitute liquid water. To the best of my knowledge the precise number of molecules necessary for H2O to function as a liquid at room temperature has not been pinpointed. But the minimum number of molecules necessary to constitute ice has: a minimum of 275 H2O molecules are necessary to form the crystalline structure essential to water in its solid form. (Pradzynski et al. 2012)

Just as the single increment from 274 to 275 molecules can make the difference to the emergence of ice, so we should expect some increments in the number of GHG molecules to make a difference to emergent climate harms (though we obviously don't know exactly where those thresholds lie).  To continue to insist that individual emissions never make a difference is indefensible.

* E.g., on p.179 they write, "While adding oil to an engine reduces the probability of a moving part failing, it is implausible that adding a molecule of oil reduces that probability of failure by 1/10^25." But this is just to observe a non-linear probability distribution: the very first molecule added plausibly has a much smaller chance of making a difference, but that simply guarantees that some other, later increments, have correspondingly greater chances of making a difference, far in excess of 1/10^25.  So long as the current baseline quantity of engine oil is in the rough vicinity of a "threshold" for preventing engine failure, there is a (proportionately) decent chance that adding one more oil molecule really could make the difference.

Perhaps the easiest way to see that this simply must be so is to imagine a sequence of counterfactuals, where a measuring device deposits exactly n oil molecules onto the engine, for increasing values of n. Given that small enough values of n result in engine failure, whereas large enough values avoid this physical outcome, and we are talking here about physical states of the world (and not the applicability of a vague concept like 'bald'), clear thinking surely requires us to acknowledge that there will be some point in the increasing sequence which is the first counterfactual in which the physical outcome of engine failure is avoided.  That nth increment is then, straightforwardly, a difference-making increment.  (I assume counterfactual determinacy for simplicity, but it's trivial to re-run the argument using probabilistic measures and expected value.)

The opposing view here just strikes me as completely incoherent.  Yet respected philosophers keep saying these things in print. Am I missing something?