We can now resist the sceptic’s conclusion. But one might worry, in light of Hájek’s argument, that we gave up something important to avoid scepticism. In particular, one might worry that our analysis of counterfactuals is less objective than is required, since, on our proposal, the content of counterfactual statements is tied to domains of inquiry.
Hájek argues that support from science is an important desideratum for an account of counterfactuals. The idea is well expressed by Kutach (2005): ‘What makes counterfactuals especially suitable for science is that the truth of counterfactuals depends largely on the general patterns that science aims to describe.’Footnote 8 Others go further in claiming that a defining feature of the general patterns that science aims to describe—what makes these patterns or regularities lawful—is precisely their stability across counterfactual situations (see, e.g., Lange 2000). In any case, there is plausibly a tight connection between counterfactual dependence and the regularities science aims to describe.Footnote 9 So far we agree with Hájek.
We part ways concerning the implications of this general approach. According to Hájek, the ‘widespread falsehood [of would-counterfactual claims] is what one gets in a chancy world, as science teaches us that ours is’. But we contend that science does not teach us that all lawful regularities are chancy, once it is recognised that there are multiple autonomous domains of inquiry that differ in level or scope. In what follows we support this position by appeal to views (more and less widely held) within the philosophy of science literature. Our denial of the ‘widespread falsehood’ of would-counterfactual claims admittedly rests on an extension of this picture of science to include domains that are not typically recognised as scientific. We will not directly argue for the extension. Our strategy in this section is to outline the most compelling accounts of multiple autonomous domains of science, or special sciences, such that the reader sees the extension to the more homely domains, or extra-special sciences, as natural, or at least plausible.
At a superficial level, no-one disputes there being multiple domains of science. We recognise differences in the level of scientific inquiry. For example, the organisms studied in biology are clearly coarser-grained than the molecules studied in chemistry. We also recognise differences in the scope of scientific inquiry. For instance, it is not clear which of island biogeography and rainforest ecology is the more fine-grained inquiry, but the scope or subject matter of these two scientific domains differ. That said, no-one supposes that one could delineate and enumerate all the various scientific domains. Philosophers of science and scientists alike freely talk of domains of inquiry even if these domains have somewhat vague boundaries.
What is controversial is the status of ‘laws’ at domains other than fundamental physics. It is important for our account of counterfactuals that the higher domains, or special sciences, at least concern lawful regularities, i.e., non-accidental regularities that have some autonomy (whatever other conditions they may need to satisfy to count as full-blown laws). Some philosophers of science have indeed defended this position, typically by appealing to ceteris paribus laws (cp laws), so-named because they have an implicit scope restriction to circumstances in which the regularity in question holds. Positive accounts of cp laws are many and varied, however (for a summary, see Reutlinger et al. 2017), so the burden falls on us to articulate and motivate an account of cp laws that supports our proposal. In what follows we take up this challenge. We identify a general way of conceiving cp laws, (as well as some possible ways to fill in the details) that is independently attractive (3.1) and supports our proposed response to counterfactual scepticism (3.2).
The content of ceteris paribus clauses
Consider some paradigmatic examples of cp laws:
Mendel’s Law of Segregation: ‘In a parent, the alleles for each character separate in the production of gametes, so that only one is transmitted to each individual in the next generation’ (Rosenberg and McShea 2008, p. 36).
The Law of Demand: ‘Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supply of the commodity remains constant’ (Roberts 2004, p. 159; Kincaid 2004, p. 177)Footnote 10
The Character of Shield Volcanoes: ‘Shield volcanoes erupt effusively’ (Strevens 2014, p. 1819)
The hidden ceteris paribus clause in each case restricts the circumstances at issue. The possibility of other circumstances in which the regularity is not manifest does not necessarily threaten the truth of the law. Mendel’s law of segregation does not apply, for instance, when chromosomes fail to properly separate. The law of demand does not apply in cases where consumers are irrational. Shield volcanoes with pyroclastic shields erupt explosively rather than effusively.Footnote 11 Nonetheless, these cp laws arguably say something substantive and interesting about how the world is.
But what exactly is the content of a cp clause? If the regularities that are picked out by cp laws are to play a role in determining the truth of counterfactuals, their content had better stand up to scrutiny, such that they indeed amount to non-accidental regularities. A basic worry along these lines turns on whether the cp clause should be read as definite or non-definite. A definite cp clause enumerates circumstances (typically, those excluded) in a concrete way while a non-definite cp clause merely describes the (excluded) circumstances in vague, open-ended terms. Either way, it is assumed that the cp clause describes a set of circumstances that amount to necessary and sufficient conditions for when the stated regularity does (not) hold. The supposed dilemma is as follows: there are no true definite cp laws, because some conditions in which the relationship does not hold will inevitably be overlooked, while non-definite cp laws are trivial, because they effectively have the form ‘X holds unless it doesn’t’. So cp ‘laws’ are either trivial or false—either way they are not genuinely lawful.
There have been different responses to this supposed dilemma, informed by subtly different accounts of cp laws (Reutlinger et al. 2017). Here we describe what we take to be the most promising general response, common to leading accounts of cp laws. The response involves reconceiving the ceteris paribus clause as implicitly referring to a fitting set of circumstances in which the purported regularity does in fact hold. So the cp clause identifies merely sufficient, as opposed to necessary and sufficient conditions, for the regularity to hold. This reconception of the cp clause, being less ambitious, is not subject to the dilemma described above.
But what would make a set of circumstances special or fitting, such that, if a regularity were to hold across this set, it may be considered lawful? This is a significant challenge. Fodor (1991) exploits the fact that cp laws pertain to ‘higher-levels’ of inquiry than fundamental physics, and as such, involve more or less coarse-grained entities that are multiply-realised at the finer grains of analysis. He claims that, for the relationship ‘whenever A then B’ to count as a ceteris paribus law, it must be the case that, for all possible instantiations or realisers of A, namely, A(Ri), there exists circumstances Ci (a ‘completer for A(Ri)’) such that A(Ri) & Ci entails B. Admittedly this account of the cp clause is rather eccentric. The set of circumstances given by A(Ri) & Ci certainly has a special character, and ‘whenever A then B’ comes out true under these circumstances. But the cp laws on this account will not always correspond to what are ordinarily considered lawlike regularities.
We regard the dispositional account as more promising, not least in better according with what are ordinarily considered lawlike regularities (Mill 1836/2008; Cartwright 1989). On this account, the cp clause specifies circumstances under which the disposition or force underpinning the regularity is the only one that is manifested; there are no interfering factors that might otherwise compromise the regularity. For instance, ‘cp, the velocity of a falling object after elapsed number of seconds t is (approximately) 9.8 metres per second per second multiplied by t seconds’ says that in the special circumstances whereby gravity acts in isolation (for starters, when air resistance is nil), objects at the specified time have the stated falling velocity. The cp clause can in this way be understood as a statement of merely sufficient conditions in which the regularity in question holds. Moreover, as per Fodor’s account, the fact that the regularity in question holds in these circumstances may be regarded as conferring lawful status on the regularity, due to the special representative status of the circumstances. (On the dispositional account, there is supposedly also a sense in which cp laws always hold for the entities involved—in the form of a potentiality—which further bolsters the case for their being genuine laws.)
The completer and dispositional accounts of cp laws are different in many ways, but they both get something right—the implicit cp clause featuring in cp laws identifies special sufficient conditions, or fitting circumstances, in which the purported relationship holds. These accounts offer alternative ways, distinct from high probability, that a set of circumstances may be fitting. That is not to say that we rule out other notions of fitting circumstances based either partly or wholly on high probability (as per, e.g., Spohn 2002). Having identified the important properties of fitting circumstances, we want to leave open how exactly the further details are best specified. That said, throughout the paper we sometimes assume the dispositional account of cp laws, both for its prima facie plausibility and for ease of exposition.
The role of ceteris paribus laws in supporting counterfactuals
Let us now show how cp laws, broadly interpreted as above, can underpin our proposal for understanding counterfactuals, or at least those for which the relevant domain is a special science. (Recall that our strategy is to convince the reader of our interpretation of these more obviously ‘scientific’ counterfactuals, such that the extension to more homely or ordinary counterfactuals is a natural move.) The good news is that many cp laws state deterministic relationships that may play a role in securing the truth of would-counterfactual claims. Moreover, the fact that cp laws restrict the circumstances to those supporting the regularity in question seems to fit well with our account of counterfactuals.
But now the challenge: one cannot simply take for granted that the antecedent of an ordinary counterfactual implies the very same circumstance restrictions that are implied by the pertinent cp law. Indeed, it is thought that the literal inexactness of cp law statements (the fact that, absent the implicit ceteris paribus clause, they are false) comes back to bite when it comes to counterfactuals.
After all, ‘shield volcanoes erupt effusively’ is only true because it does not apply to any old shield volcano; it applies to shield volcanos in fitting circumstances. But therein lies a worry: the antecedents of typical counterfactuals do not seem to be so carefully specified as to pick out the relevant fitting circumstances. Consider 5:
(5) Were Mt Pinatubo a shield volcano, it would have erupted effusively.Footnote 12
The relevant cp law—‘shield volcanoes erupt effusively’—does not apparently make this counterfactual true, either because the antecedent is, in Hájek’s terms, unspecific, in encompassing all types of shield volcanos, or the connection between shield volcanos and effusive eruptions is really indeterministic. In short, it appears as if the antecedent of 5 does not restrict to cases where shield volcanos erupt effusively.
We get around this problem in that we understand counterfactuals similarly to the statements of cp laws, as having an implicit ‘fitting circumstances’ clause in the antecedent, whose meaning varies with the salient domain of inquiry. Here we part ways with some proponents of the lawfulness of cp laws who do not rule out the line of reasoning expressed above regarding 5. Lange (2002), Woodward (2003) and Hitchcock and Woodward (2003), for instance, all maintain a close connection between cp laws and the truth of counterfactuals, but they claim that a counterfactual invoking a cp law is true only if the antecedent refers to the specific circumstances implicitly required by the cp law. It is not clear whether the specific circumstances should be taken to hold if this is not stated explicitly. Lipton’s (1999, p. 157) position is clearer; when it comes to counterfactuals, or indeed any manifestation of the disposition expressed by a cp law, it is not assured that there will be no interfering factors, which complicates the usual relationship between lawful regularities and the way things are or would be:
‘‘All Fs are Gs, cp’ may be a law yet not entail that if something had been an F it would have been a G, nor will observed Fs that are G always provide reason to believe that the next F will be a G as well, since we may have no reason to believe that all things will be equal, the next time.’
According to this view, cp laws do not, after all, secure the truth of would-counterfactuals. Statements like 5 are false, since, on closer analysis, Mt Pinatubo might be a pyroclastic shield volcano.
Despite the presumption in favour of the inexact reading of would-counterfactuals, we maintain that this asymmetry—between carefully circumscribed cp law statements and uncircumscribed counterfactuals which invoke them—should be resisted. The asymmetry is puzzling in light of what seems to be common ground for all defenders of cp laws—that cp laws are regularities pertaining to particular domains of inquiry involving particular sorts of entities under fitting circumstances. Plausibly then, if cp laws are supposed to play a role in determining whether at least some counterfactuals are true, then the counterfactuals in question must already be understood as concerning the relevant domain of inquiry. In that case, one would expect the antecedent of the counterfactual to be understood as involving the parallel qualifications tied to that domain.
We regard it an attractive feature of our proposal that it allows counterfactuals to serve as tools for making claims whose truth values are tied to the many and varied regularities in the actual world. Some comments on this point are in order, although we save a more detailed analysis for future work. On our proposal, counterfactuals are true in virtue of facts about classes of circumstances that include more or fewer kinds of interferences, depending on the domain of inquiry. To be sure, sometimes the class of circumstances may include all the many and varied interferences that are physically compatible with the antecedent as stated (the trivial case where the domain is the most fundamental one; recall footnote 4). For instance, 5 may be read in this way if the conversation is one where a committee is pondering the extent to which a public official is responsible for the devastating effects of Mt Pinatubo’s eruption, there having been reasonable uncertainty about the type of volcano it was. On this reading, 5 is false: Mt Pinatubo may have been an unusual shield volcano that did not erupt effusively.
We suggest, however, that it is less common than one might suppose that counterfactuals need be interpreted such that all possible interferences are under consideration. Often, we maintain, the counterfactuals pertinent to a conversation simply express interesting, constrained regularities in the actual world. Take 5 above. On an alternative and very natural reading, the counterfactual conveys what the eruption would have looked like, were Mt Pinatubo an ordinary shield volcano, that is, under the circumstances fitting to ordinary volcano science. In this case, 5 is true: circumstances in which Mt Pinatubo is an unusual shield volcano that erupts explosively count as interferences and are thus excluded.
In other cases, counterfactuals are used to indirectly explain actual events by stating what would have happened if things had been different. But any such (complete or partial) explanation of an actual happening relies on the lawful regularities that hold across a pertinent class of cases. For instance, consider 5*:
(5*) Were Mt Pinatubo a shield volcano, it would have erupted effusively and had a less dramatic aftermath for the inhabitants of the area.
This counterfactual plausibly conveys information about Mt Pinatubo, specifically the impact of its eruption on the local inhabitants. The counterfactual provides a partial explanation of the volcano’s impact by suggesting conditions under which the impact would have been different. We are effectively told that shield volcanoes under fitting conditions erupt less violently, and from this claim regarding basic volcano science are presumably supposed to infer that Mt Pinatubo is not a shield volcano, and that is why its eruption had the dramatic impact it did.
Spelling out a precise taxonomy of the scientific claims that may be expressed by counterfactuals is beyond the scope of this paper. The point is simply that our appeal to domains of inquiry and the inclusion of an implicit ‘fitting circumstances’ proviso in the antecedent of counterfactuals is well-motivated, based on the relationship between counterfactuals and the diverse and domain-specific nature of scientific claims.