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Reply to Ellis and to Handfieldon essentialism, laws, andcounterfactualsMarc Lange aa University of North Carolina , Chapel HillPublished online: 19 Aug 2006.

To cite this article: Marc Lange (2005) Reply to Ellis and to Handfield on essentialism,laws, and counterfactuals, Australasian Journal of Philosophy, 83:4, 581-588, DOI:10.1080/00048400500338971

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REPLY TO ELLIS AND TO HANDFIELDON ESSENTIALISM, LAWS,AND COUNTERFACTUALS

Marc Lange

In Lange [2004a], I argued that ‘scientific essentialism’ [Ellis 2001] cannot

account for the characteristic relation between laws and counterfactualswithout undergoing considerable ad hoc tinkering. In recent papers, Brian Ellis[2005] and Toby Handfield [2005] have defended essentialism against mycharge. Here I argue that Ellis’s and Handfield’s replies fail. Even in ordinary

counterfactual reasoning, the ‘closest possible world’ where the electron’selectric charge is 5% greater may have less overlap with the actual world in itsfundamental natural kinds than a ‘more distant possible world’ where the

electron’s charge is 5% greater. But more importantly, essentialism’s flexibilityin being able to accommodate virtually any relation between laws andcounterfactuals is a symptom of essentialism’s explanatory impotence as far as

that relation is concerned.

It has long been widely believed that one important difference betweennatural laws and accidental facts involves their relations to counterfactualconditionals. Accordingly, an adequate metaphysical account of what anatural law is should explain why laws and only laws stand in a certainspecial relation to counterfactuals. One argument that has sometimes beengiven for ‘scientific essentialism’ (according to which, roughly speaking, lawsare metaphysical necessities that specify the properties essentially bound upwith membership in various natural kinds) is that essentialism accounts wellfor the laws’ distinctive relation to counterfactuals. I have argued recentlythat this is not so [Lange 2004a]. In particular, I do not see how essentialismcan explain the laws’ special relation to counterfactuals without undergoingconsiderable ad hoc tinkering.

What is the explanatory target here—the laws’ distinctive relation tocounterfactuals? A myriad of prima facie attractive candidates can beconcocted. Just for starters (hold on now!):

If it is a law that m, then for any p that is logically consistent with m, it is true

(in all conversational contexts) that if p had been the case, then m would stillhave been a law—i.e., it is true that p ¤! (m is a law). But if it is an accidentthat m, then it is not the case that for any p that is logically consistent with m,

it is true (in all contexts) that p ¤! (m is an accident).

Australasian Journal of Philosophy

Vol. 83, No. 4, pp. 581 – 588; December 2005

Australasian Journal of Philosophy

ISSN 0004-8402 print/ISSN 1470-6828 online � 2005 Australasian Association of Philosophy

http://www.tandf.co.uk/journals DOI: 10.1080/00048400500338971

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If it is a law that m, then for any p that is logically consistent with every nwhere it is a law that n, it is true (in all contexts) that p ¤! (m is a law). But if

it is an accident that m, then it is not the case that for any p that is logicallyconsistent with every n where it is a law that n, it is true (in all contexts) thatp ¤! (m is an accident).

If it is a law that m, then there is a logically closed, proper subset S of thetruths where for any p that is logically consistent with every element n of S, it

is true (in all contexts) that p ¤! (m is a law). But if it is an accident that m,then there is no logically closed, proper subset S of the truths where for anyp that is logically consistent with every element n of S, it is true (in all contexts)that p ¤! (m is an accident).

If it is a law that m, then for any p that is logically consistent with every truth

of the form ‘It is a law that n’, it is true (in all contexts) that p¤! (m is a law).But if it is an accident that m, then it is not the case that for any p that islogically consistent with every truth of the form ‘It is a law that n’, it is true (inall contexts) that p ¤! (m is an accident).

If it is a law that m, then for any p, q, r . . . where each of these is logicallyconsistent with every logical consequence of truths of the form ‘It is a law that

n’ and truths of the form ‘It is not a law that n’, it is true (in all contexts) thatp ¤! (m is a law), q ¤! (p ¤! (m is a law)), r ¤! (q ¤! (p ¤! (m is alaw))), and so forth. But if it is an accident that m, then it is not the case that

for any p, q, r . . . where each of these is logically consistent with every logicalconsequence of truths of the form ‘It is a law that n’ and truths of the form ‘Itis not a law that n’, it is true (in all contexts) that p ¤! (m is an accident),

q ¤! (p ¤! (m is an accident)), r ¤! (q ¤! (p ¤! (m is an accident))),and so forth.

Any one of the above relations (or several at once), and any one of the manyrelations that can be constructed along similar lines, could apparently beaccommodated by the essentialist’s view that laws differ from accidents byexpressing the natural-kind structure. But this flexibility is a sign ofexplanatory weakness, not strength. If essentialism could equally wellexplain the laws’ distinctive relation to counterfactuals whichever of theabove candidates genuinely captures that relation, then essentialism can dolittle to explain the particular relation in which laws stand to counter-factuals; that the laws express the natural-kind structure would fail toexplain why the laws stand in one relation to counterfactuals rather than inanother. Essentialism should tell us what it is about essences that makes thetruths that they secure (and only those truths) behave in a certain mannerunder counterfactual suppositions. It is difficult to see how essentialism’sgeneral metaphysical picture could discriminate finely among options likethose in the above list, explaining why the truths secured by essences behavein one of these fashions rather than in another.

In other words: various accidents display some degree of resilience undercounterfactual perturbations. For example, the relation between my car’sspeed on a dry, flat road and the distance of my car’s accelerator pedal from

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the floor, despite being an accidental relation, exhibits ‘invariance withrespect to certain hypothetical changes’ [Haavelmo 1944: 29], such as mydepressing the accelerator pedal farther toward the floor or my wearing adifferent shirt. Likewise, a law of nature is apparently not preserved underall counterfactual suppositions; some suppositions are counterlegals. It isnot evident why the laws’ specific behaviour under counterfactualsuppositions is a symptom of metaphysical necessity.

Of course, an essentialist could first identify the laws’ specific distinctiverelation to counterfactuals without consulting essentialism (e.g., by examin-ing scientific practice) and could then stipulate that essences are such that bymaking m true, they compel m to stand in precisely the relation tocounterfactuals in which the laws were found to stand. But this approachbrings to mind the famous quip from Russell [1919: 71]: ‘The methodof ‘‘postulating’’ what we want has many advantages; they are the same as theadvantages of theft over honest toil.’ An essentialism burdened by this sort ofad hoc fine-tuning has merely had the right answer inserted into it by hand.

This was the general spirit behind my more elaborate arguments in anearlier paper [Lange 2004a], to which Ellis [2005] and Handfield [2005] havenow responded. Here I wish briefly to comment upon their responses.

Ellis [2005: 76] considers one of the questions that I raised in my earlierpaper: How does essentialism account for the fact that had there been anelectron at spatiotemporal location L, then there would still have beenprotons in atomic nuclei rather than particles that lack some of the proton’sessential properties (such as having a mass of 1.6736 10724 grams)?Ellis writes:

I do not see how this is supposed to be a problem, except perhaps for aninductive sceptic (i.e., one who is likely to be concerned that emeralds will turn

out to be grue, rather than green). . . . Lange is apparently worried about howan essentialist can give a satisfactory account of the truth conditions forpropositions of the form: ‘If A were the case, then B would still be the case’,

where ‘B’ is an undoubted truth that is obviously compatible with theantecedent supposition. My reply is that this proposition:

will be true . . . if and only if in any world of the same natural kind as oursin which ‘A’ is true, in circumstances as near as possible to those thatactually obtain, ‘B’ must [still] be true.

[Ellis 2001: 278]

Lange thinks that this inductively non-sceptical reply is ‘ultimately ad hoc’ and‘unprincipled’ [2004a: 228]. How so? I would freely grant it to anyone. For theantecedent supposition that there is an electron at L simply does not challengethe consequent claim that protons will continue to be a principal constituent of

atomic nuclei.

[Ellis 2005: 76]

Of course, the issue has nothing to do with inductive scepticism; the issue ismetaphysical, not epistemological. I see how the facts about essences aresupposed to underwrite the fact that if there had been an electron at L, then

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all protons would still have been positively electrically charged (since havinga positive charge is supposed to be essential to being a proton). But how dothe facts about essences underwrite the fact that had there been an electronat L, there would still have been protons? Ellis’s reply seems to be that thesupposition that there is an electron at L ‘does not challenge’ the existence ofprotons. I agree that it doesn’t. But why doesn’t it? What does it take for acounterfactual supposition ‘to challenge’ the proton’s continuing to be oneof the natural kinds?

It is plainly not enough that the supposition be ‘obviously compatible’with protons continuing to exist, if this is understood as logicalcompatibility. For there are plenty of counterfactual suppositions thatare logically compatible with the continued existence of protons, butunder which the proton would not still have existed. (For example, hadthe electromagnetic force been much stronger, then the proton would notstill have existed; the ‘strong’ nuclear force among quarks would not thenhave been strong enough to hold a proton together.) The listedcandidates above are just some of the ways in which one might try tocash out what it takes to have a counterfactual supposition that ‘simplydoes not challenge’ a natural law. But however an essentialist chooses tocash out the range of counterfactual suppositions under which thenatural kinds would have been no different, he still faces the sameproblem. He must explain why the fact that the laws express the natural-kind structure would make the laws invariant under precisely that rangeof counterfactual suppositions.

Ellis believes that a possible world with different natural kinds wouldinevitably be very dissimilar to the actual world:

A world with non-physical content would have to be very different from thisworld, as would one with a different natural kinds structure. But if the theory

of laws of nature proposed in [Ellis 2001] is accepted, then sameness of naturalkinds structure implies sameness of laws.

[Ellis 2005: 78]

This seems perfectly reasonable. Handfield makes a similar suggestion:

It seems to be an intuitively plausible fact about our judgements of similaritythat they are highly sensitive to sameness of natural kinds. We need not insistthat counterfactuals always be evaluated in worlds with precisely the same

kinds as our own. That would be too restrictive, and would rule out allcounterlegal conditionals. But we may reasonably require that worlds withgreater overlap of natural kinds be closer than those with less overlap of

natural kinds.

[Handfield 2005: 83]

I am prepared to grant that the fact that laws express the natural-kindstructure would explain why laws have some special weight in determininghow ‘similar’ (for the purposes of counterfactual reasoning) a given possibleworld is to the actual world. Nevertheless, this does not suffice to explain thelaws’ special relation to counterfactuals—whatever that precise relation is.

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All of the candidates listed above give laws some special weight in deter-mining a possible world’s similarity to the actual world. The same may besaid even of a drastically different account of counterfactuals like Lewis’s,according to which (if the actual universe is deterministic) had I failed tobrush my teeth this morning, the laws of nature would have been different.1

Lewis regards the ‘miracles’ (i.e., violations of the actual laws) occurring in apossible world as having a special role in determining that world’s ‘closeness’to the actual world. Whichever of the listed candidates above turns out tocapture the laws’ special relation to counterfactuals, or even if (contrary to allof those candidates) Lewis is correct and the laws are not ‘sacred’,essentialism would be correct in holding that similarity in laws does a greatdeal to make two worlds alike. But once again, this ‘flexibility’ just goes toshow that the explanatory riches proffered by essentialism are illusory.

In short, to explain the laws’ relation to counterfactuals, essentialismmust show that the particular weight that laws carry in fixing a possibleworld’s closeness follows from the laws’ expressing the natural-kindstructure. Even if a possible world’s having the same laws as ours carriesconsiderable weight in determining that world’s similarity to ours, someother factor could still outweigh that similarity. Can similarity in the laws beoutweighed? If so, then that fact needs to be explained. If not, then that factneeds to be explained. It is difficult to see how essentialism could supplythese explanations, short of essentialism’s having the right answer built intoit in an ad hoc fashion.

Consider Handfield’s remark that ‘we may reasonably require that worldswith greater overlap of natural kinds be closer than those with less overlapof natural kinds’. This does sound reasonable, considering the importanceof natural kinds. But if we take this idea as following from scientificessentialism, then we might be able to show by counterexample thatscientific essentialism is mistaken. Counterfactuals like the following areasserted in physics:

Had the electron’s charge been 5% greater, then the energy levels of theelectrons within a silicon atom would have been 8% closer together, and so anelectron would have needed to acquire less energy to ascend to a higher-energyorbital.

Now what is the closest possible world where the electron’s charge is 5%greater? In that world, obviously, not all of the actual world’s fundamentalphysical laws are laws. But except for the law specifying the electron’scharge, all of the other fundamental physical laws could still be laws in thatworld, and so the principle in Handfield’s remark apparently demands thatthey all be laws in that world. However, they are not all laws in that world.In particular, the law specifying the proton’s electric charge is not, since thetruth of the above counterfactual requires that the silicon atom remainelectrically neutral, and so that the proton’s charge keep pace with the

1Lewis, then, denies Ellis’s innocuous-sounding claim that we should look to a world ‘of the same naturalkind’ as the actual world.

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electron’s. So arguably, the closest possible world where the electron’scharge is 5% greater has less overlap of fundamental natural kinds than amore distant possible world where the electron’s charge is 5% greater.

Admittedly, this example may not strike everyone as sufficientlycompelling to refute the principle in Handfield’s remark. But my mainpoint is that if examples like this do indeed turn out to undermine thatprinciple, the essentialist will presumably not regard this result asdemonstrating that essentialism is incorrect. Rather, the essentialist willsimply deny that the failed principle captures the relation in which laws muststand to counterfactuals if laws express the natural-kind structure. That isjust the kind of ‘flexibility’ that I believe demonstrates how little essentialismcan really do to explain the laws’ relation to counterfactuals.2

Likewise, Handfield suggests at the close of his paper that essentialismcould be happily wedded to the following account of the laws’ distinctiverelation to counterfactuals3:

It is a natural law that p if and only if p is not a logical truth and p belongs to a

logically closed set S of truths that non-trivially possesses non-nomic super-stability, where S is non-nomically super-stable if and only if for any memberm of S and any q, r, . . . such that each is logically consistent with every

member of S, q ¤! (m is non-vacuously true), r ¤! (q ¤! (m isnonvacuously true)), and so forth for multiply nested counterfactuals.

[Handfield 2005: 84 – 5]

But this proposal seems to be incorrect. Suppose that unobtainium-346 is avery rare radioactive isotope; only a few dozen atoms of this isotope everhappen to exist in the entire history of the universe.4 Suppose that m is somelaw about the properties of unobtanium-346. Let q be the supposition thatthere never exist any atoms of unobtainium-346. Although q is logicallyconsistent with every member of S where S contains exactly the laws(and their logical consequences), the counterfactual (q ¤! m is non-vacuously true) is false, contrary to Handfield’s suggestion, since if therewere no atoms of unobtainium-346, the laws concerning that isotope wouldbe vacuous.

My main point is not to show that that Handfield’s tentative proposal isincorrect. Rather, I wish to point out how easy Handfield believes it would beto couple essentialism with this (or, presumably, with virtually any otherprima facie attractive) proposal regarding the laws’ relation to counter-factuals. Handfield is correct; it is easy. But this ‘flexibility’ is a symptom ofessentialism’s explanatory impotence as far as the laws’ relation to counter-factuals is concerned.

2Of course, there may be other arguments for essentialism; I am concerned only with essentialism’s capacityto account for one aspect of the difference between laws and accidents.3This suggestion is a modified version of the account that I offered in the paper to which Handfield isresponding [Lange 2004a] and elsewhere [Lange 2000; 2002; 2004b; 2005a; 2005b; forthcoming a]. I’ll nowargue that by modifying it, Handfield made it vulnerable to a kind of counterexample to which my ownproposal does not succumb.4‘Unobtainium’ is a joke from Lewis [1999: 229].

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At the close of my earlier paper, I tentatively offered a positive proposalregarding what laws are: rather than being understood in terms of essences(or, for that matter, in terms of universals), laws simply are—roughlyspeaking—the truths that would still have been true under a certain range ofcounterfactual suppositions (a range that I specify without using the conceptof natural law). I have argued elsewhere [Lange 2000; 2002; 2004b; 2005a;2005b; forthcoming a] that this analysis can save many phenomena, such asthat the laws possess a distinctive variety of necessity, that the laws playspecial roles in induction and scientific explanation, that the laws form asystem (i.e., lawhood is a collective affair rather than an individualachievement), and that the laws would still have been laws—not merelytruths—under various counterfactual suppositions. On this picture, laws arenot the truthmakers of counterfactuals; rather, counterfactuals lie at thebottom of the world and are partly responsible for the laws.

Handfield notes that ‘there is something rather bewildering aboutprimitive counterfactual facts’ [2005: 84] and that essentialism, whateverits drawbacks may be, at least identifies truthmakers for the counter-factuals that I am tentatively prepared to regard as primitive. Granted.(This is not the place to address the difficult questions raised by ‘barecounterfactual truths’.5) On the other hand, my proposal avoids aproblem faced by essentialism and, for that matter, by analyses of laws ascontingent relations among universals. Any analysis of laws as truthshaving some particular weighty metaphysical character ought to explainwhy a truth, by virtue of possessing that character, is rendered invariantunder exactly the range of counterfactual suppositions under which thelaws are characteristically invariant. As we have just seen, such anexplanation threatens to fail in one of two ways. One way is for theexplanation to be unable to reach its specific explanatory target; theexplanation may tell us why the truths possessing the requisitemetaphysical character are influential in determining ‘similarity’ amongworlds (for the purposes of counterfactual reasoning), but not why thosetruths have precisely the influence characteristic of laws, no more and noless. The other way that the explanation threatens to fail is by beingad hoc: the laws’ precise degree of influence is artificially built into it. Incontrast, if the laws just are the truths having the requisite invarianceunder counterfactual perturbations, then there is no independentmetaphysical analysis of lawhood that must be forced somehow toaccount for the specific role in counterfactual reasoning that distinguisheslaws from accidents. That’s an advantage, I think.6

University of North Carolina, Chapel Hill Received: June 2005

5In Lange [forthcoming b], I argue that truths about instantaneous rates of change (such as instantaneousvelocity in classical physics), despite being venerable components of a system’s physical state, are baresubjunctive truths.6Thanks to Toby Handfield for useful discussion.

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Ellis, Brian 2001. Scientific Essentialism, Cambridge: Cambridge University Press.Ellis, Brian 2005. Marc Lange on Essentialism, Australasian Journal of Philosophy 83: 75 – 9.Haavelmo, Trygve 1944. The Probability Approach to Econometrics, Econometrica 12 (Suppl.): 1 – 117.Handfield, Toby 2005. Lange on Essentialism, Counterfactuals, and Explanation, Australasian Journal of

Philosophy 83: 81 – 5.Lange, Marc 2000. Natural Laws in Scientific Practice, New York: Oxford University Press.Lange, Marc 2002. Who’s Afraid of Ceteris-Paribus Laws? Or: How I Learned to Stop Worrying and Love

Them, Erkenntnis 57: 407 – 23.Lange, Marc 2004a. A Note on Scientific Essentialism, Laws of Nature, and Counterfactual Conditionals,

Australasian Journal of Philosophy 82: 227 – 41.Lange, Marc 2004b. The Autonomy of Functional Biology: A Reply to Rosenberg, Biology & Philosophy 19:

93 – 101.Lange, Marc 2005a. Laws and Their Stability, Synthese 144: 415 – 32.Lange, Marc 2005b. Ecological Laws: What Would They Be and Why Would They Matter?, Oikos [The

Journal of the Nordic Ecological Society] 110: 395 – 403.Lange, Marc forthcoming a. A Counterfactual Analysis of the Concepts of Logical Truth and Necessity,

Philosophical Studies.Lange, Marc forthcoming b. How Can Instantaneous Velocity Fulfill Its Causal Role?, Philosophical Review.Lewis, David 1999. Humean Supervenience Debugged, in Papers in Metaphysics and Epistemology,

Cambridge: Cambridge University Press: 224 – 47.Russell, Bertrand 1919. Introduction to Mathematical Philosophy, New York and London: George Allen &

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