Supporting Causal Counterfactuals with Properties

In his classic Fact, Fiction and Forecast (1955), Nelson Goodman presents two problems of counterfactuals. One is the problem of determining what conditions are supposed to obtain under counterfactual antecedents. The other is the problem of providing an account of laws that is adequate for ensuring that the consequents of counterfactuals would be true had the relevant conditions held in conjunction with the counterfactual’s antecedent. What is explicitly given in the antecedents of counterfactual sentences typically do not entail their consequents. For instance, the antecedent of

does not guarantee the truth of its consequent. When we accept a counterfactual like (1) as true, we do so on the grounds that certain conditions obtain which, in conjunction with those explicitly stated in the antecedent, would provide for the truth of the consequent. For instance, in asserting (1) we suppose that were match m struck it would also be dry, there would be oxygen present, there would be no strong drafts, etc. The first of Goodman's problems of counterfactuals is that of identifying the relevant conditions supposed to obtain were the antecedent of the counterfactual true. But, even assuming that we have settled what relevant conditions are presumed to obtain under the antecedents of counterfactuals, the truth of the counterfactual’s consequent is only assured if we also have grounds for thinking the laws of nature would still obtain under the relevant counterfactual circumstances. Were the laws different, then match m's being struck might fail to issue in its lighting even if all of the relevant conditions pertaining to the first problem of counterfactuals obtained. Hence, Goodman's second problem of counterfactuals is that of giving an account of laws such that given the relevant conditions, the truth of the counterfactual’s antecedent would assure the truth of its consequent.

I will argue that a view of laws as metaphysical necessities provides the best answer to Goodman's second problem. Such views have been advanced by authors including Shoemaker (1980), Swoyer (1982), and Ellis and Leirse (1994). But advocates of necessary laws have yet to provide an account of counterfactuals that adequately treats both of Goodman's problems of counterfactuals. The aim of this paper is to advance that cause, if only by a few small steps. I propose a property theoretic account of counterfactuals. The leading idea of the proposed account is that counterfactual conditionals, when true, are made true in part by complexes of properties, the joint instantiation of which would metaphysically necessitate the truth of the counterfactual’s consequent. The account of counterfactuals to be developed here is motivated by consideration of the role of laws in supporting counterfactuals. I will start with a discussion of the problem of law for supporting counterfactuals. This will lead us to a view of laws as metaphysically necessary accounts of the essential and dispositional nature of properties. We will then employ this conception of essentially dispositional properties as the central component of an account of causal counterfactuals.

The Problem of Laws

It was regularity theories of laws that were initially subjected to criticism for failing to support counterfactuals[1]. On a simple regularity view of laws, to say that it's a law that copper expands when heated is say nothing more than

But (2) is consistent with the truth of either of the following counterfactual conditionals.

(3) If this piece of copper had been heated at time t, then it would have expanded at t'.

(4) If this piece of copper had been heated at time t, then it would have shrank at t'.

The mere truth of the generalization (2) gives us no grounds for favoring the truth of (3) over the truth of (4). But in asking that laws support counterfactuals, we expect an account of laws to play an important role in accounting for the truth of (3) and the falsity of (4).

The available alternatives to the regularity theories of laws propose to handle the problem of supporting counterfactuals by modally strengthening the laws in certain ways. Armstrong (1983), Dretske (1977) and Tooley (1977) offer an alternative to regularity theories of laws in their view that laws are nomic relations that hold among universals (henceforth, the ADT view). On the ADT view, laws are not general facts but second order singular facts about universals. On this view, "laws issue in regularities but are not exhausted by regularities" (Armstrong, 1983). With the exception of Swoyer (1982), adherents of this view of laws have taken nomic relations to hold between universals contingently. A nomic relation N (F,G) holds between the universals F and G contingently, but its holding between F and G necessitates that all Fs are Gs and, further, is alleged to support our claims that non-Fs would be Gs if they were F. The difficulty for this view is specifying just how we should understand the nomic relation N so that counterfactuals will be adequately supported. We might try to understand contingent nomic necessitation as holding no more than that universals standing in a nomic relation necessitates a general regularity. This much can be asserted as follows:

However, in terms of supporting counterfactuals, (5) offers no advance over the regularity theory on which it holds trivially that

Supporting counterfactuals requires that nomic relations have some "modal weight" not enjoyed by other contingent facts. That is, our account of nomic necessitation must give us good grounds to believe that the laws hold under the antecedent suppositions of counterfactual conditionals. If nomic relations hold contingently, their holding under counterfactual antecedents cannot be taken for granted.[2]

To appreciate the force of this point, we should consider more closely what truths hold and what truths fail to hold under the suppositions of counterfactual antecedents. To employ the metaphor of possible worlds, the closest possible world at which the antecedent of a counterfactual is true must differ from the actual world in more respects than those specifically cited in the antecedent. On a rainy day, I might correctly hold that if my cat were outside, she'd be wet. At the closest possible world where my cat is outside, the fact that my cat is sleeping by the fireplace presumably does not hold. But other truths must also fail to hold. The closest possible world where my cat is outside must be one where, contrary to fact, either I opened certain doors or windows this morning, or I neglected to let my cat in last night, or the laws of nature differ in ways that allow my cat to pass through walls or closed doors and windows. We are happy to allow that were my cat outside I would have opened or failed to open doors or windows at various times. But we do not allow that had my cat been outside, the laws of nature would have differed. The problem at hand for an account of laws is that of explaining why we should expect the actual laws to hold under counterfactual antecedents while other contingent truths do not. Armstrong, Tooley and Dretske each assert that laws are preserved under the antecedents of non-counterlegal counterfactuals. But none of these authors gives an account of nomic necessitation that would explain the privileged status of laws over other contingent truths.

The problem of law for supporting counterfactuals apparently has a limited number of possible solutions. We can attempt to identify some special modal status for nomic relations which is adequate for supporting counterfactuals but falls short of metaphysical necessity or we can accept laws as metaphysical necessities. Perhaps most philosophers who endorse realist accounts of laws would prefer the first of these options. But the matter of supporting counterfactuals has been a standing problem for the view that laws are contingent relations between universals for some while and little headway has been made. Nor do the prospects look good.

In recent literature, the view that laws are metaphysical necessities found early support in the work of Sydney Shoemaker (1980) and Chris Swoyer (1982) and has more recently found favor in Ellis and Lierse (1994). Following Ellis and Lierse, I will call the view of laws that has emerged in this literature “dispositional essentialism.” Dispositional essentialism is the view that laws are accounts of the dispositional nature of fundamental properties. Dispositional essentialism can be developed in a variety of ways depending on just what properties are taken to be fundamental and determine laws. Ellis proposes that dispositions are constitutive of natural kinds. So to be a proton, for instance, is just to be a thing that has certain mass, charge and spin dispositions. Since instantiation of a disposition entails a counterfactual, it is clear that dispositional essentialism about laws will adequately support at least some counterfactuals. Consider, for instance, (3) from above:

(3) If this piece of copper had been heated at time t, then it would have expanded at t'.

This counterfactual is adequately supported because the disposition to expand when heated is essential to the kind copper. But dispositional essentialism faces an obstacle in providing a general solution to the problem of law in the measures it must take to accommodate certain of our modal intuitions.

Dispositional essentialism makes the laws of nature metaphysically necessary. An obvious objection to dispositional essentialism is that it appears to violate a modal intuition that the laws are contingent. Intuitively, the speed of light might have been a bit faster or a bit slower, gravity might have been a bit stronger or weaker, and so forth. Accommodating these intuitions appears to require that the laws of nature might have been different. We might easily conclude that the laws must then be contingent.

In fact I think this objection is fairly easily dispatched. Dispositional essentialists take the laws to follow necessarily from the dispositional properties of things. This view allows that the world might have been different in a variety of respects. It might have differed with respect to the amount of matter/energy in the world, or the distribution of stuff in space-time, or with respect to the fundamental dispositions had by that stuff. What dispositional essentialists ought to say about the alleged intuition that the laws are contingent is that it is really just the intuition that things might have been differently disposed. If things had different dispositions, then events would have been governed by different necessary laws.

On the dispositional essentialist’s account, if it is a law that all Fs are Gs, it is so due to the causal powers essential to F-ness. The essential nature of F-ness makes it metaphysically necessary that all Fs are Gs. If laws are taken to be metaphysical necessities, then there is no question to be asked about whether they are true at this world or that. They are simply true at all worlds. But the actual Fs might not have been Fs. They might instead have been Hs where it is metaphysically necessary that Hs are Js but not Gs. Dispositional essentialism does not deny that things might have had different dispositions. So it looks like necessary laws can be reconciled with our modal intuitions. However, this raises a new issue of relevant conditions for supporting counterfactuals. Given that things could have been otherwise disposed, events might have been governed by other necessarily true laws that analyze the different dispositions things might have had. Given this, the problem of support for counterfactuals re-occurs in a different form. We must now ask what grounds we have for supposing that things are similarly disposed at the closest possible world where the antecedents of counterfactuals are true.

The underlying stuff of which our piece of copper is constituted might have constituted a thing of a different kind, having different dispositions. The antecedent of (3) specifies copper as the kind of thing that is heated. If the disposition to expand when heated is essential to things of the kind copper, then (3) is adequately supported. But the following counterfactual isn't:

The underlying stuff of which the thing at issue is constituted might have belonged to some kind other than copper, which lacks the disposition to expand when heated. Dispositional essentialism makes clear how laws as accounts of fundamental dispositions can support a range of counterfactuals whose antecedents invoke dispositional properties. But counterfactual antecedents don't always specify such law grounding properties, the essential nature of which can support the counterfactual.

At this point we should pause to notice that we are no longer concerned with Goodman's second problem of counterfactuals. Here we are raising a concern about the role of relevant accidental conditions in supporting counterfactuals. Dispositional essentialism resolves what Goodman took to be two problems of counterfactuals into one: the problem of relevant conditions. Possible worlds semantics provides one framework for addressing this issue. In the remainder of this paper I will suggest how the resources of dispositional essentialism can be developed into an alternative to possible worlds semantics for counterfactuals.

Towards a Property Theoretic Account of Counterfactuals

The dispositional essentialist’s ontology suggests a property theoretic account of counterfactuals as an alternative to Lewis’s possible worlds semantics for counterfactuals. On this account, what makes a counterfactual true, and what is expressed or conveyed by a counterfactual’s antecedent, is in part a complex of properties including a disposition whose manifestation entails the counterfactual’s consequent. That metaphysically necessary laws are entailed by the dispositional components in the property complexes we invoke with counterfactuals explains the widely held notion that laws have a special role to play in supporting counterfactuals. But ultimately it is properties that do the work of making true counterfactuals true.

The leading idea of the proposed account is that true counterfactuals are made true in part by relations of metaphysical necessitation holding between properties. That is, a counterfactual represents a relation of metaphysical necessitation holding between those properties expressed by its antecedent, and properties whose instantiation provides for the truth of the counterfactual's consequent.

On the proposed account, part of what is expressed by a counterfactual is a strict conditional of the form

The antecedent of this strict conditional is a proposition that represents the instantiation of a complex of properties. The consequent follows from the antecedent as a matter of metaphysical necessity. In the case of causal counterfactuals, the complex property given in P is an event type that includes dispositional components and involves the obtaining of their precipitating conditions. The consequent is a proposition entailed by the manifestation of those dispositional elements. So for instance, in

the antecedent represents an event type that involves match m being struck, flammable, dry, in the presence of oxygen, etc. and the consequent represents an event that is metaphysically necessitated by the event type (including its dispositional elements) that is represented by the antecedent. But (9) must express more than this strict conditional. For the strict conditional is true whether or not match m is dry or wet, in the presence or absence of oxygen, etc. In addition to expressing the strict conditional, (9) affirms the instantiation of those conditions relevant to a counterfactual’s support.

If it seems surprising that so much should be expressed by such a simple claim as (9), consider in detail the propositional content of a belief one might use (9) to express. It is not a belief merely about a match being struck; without regard to the presence or absence of gales, tidal waves or space suits. It is a belief about a flammable, well-made, dry match struck against an appropriately abrasive surface in the presence of oxygen and in the absence of strong breezes, etc. When we assemble all of these conditions presumed in the contents of our beliefs it is not implausible that the propositional content of our counterfactual beliefs include strict conditionals.

An Objection and a Reply:

I have proposed that, strict conditionals are part of what we express with counterfactuals. In Counterfactuals (1973), Lewis argues against the view that counterfactuals are strict, or necessary, conditionals. Among the challenges the proposed account of counterfactuals must meet is to answer Lewis' argument for taking counterfactuals to be "variably strict", rather than strict conditionals. Lewis' grounds for denying that counterfactuals are strict conditionals involve series of conditionals including the following:

(12) But if Waldo had come as well [as Otto and Anna], it would have been lively.

Given appropriate beliefs about Otto, Anna and Waldo, we would want to endorse (10), (11) and (12). In (11), the antecedent of (10) is strengthened and the consequent of (10) is denied. Likewise, in (12), the antecedent of (11) is strengthened and the consequent of (11) is denied. But since the strengthened antecedent in (11) entails the weaker antecedent in (10), (11) entails,

And (13) contradicts (10). A similar contradiction can be derived in the case of (11) and (12). Lewis concludes that (10) cannot be taken to assert the strict conditional,

I think the way to answer this argument is to accept counterfactual sentences as "variably strict" in the specific sense that they can be used to express (or perhaps we should say, "convey") different counterfactual propositions on different occasions. This strikes me as a natural and intuitive view to take of counterfactual sentences like (10) through (12). When we accept (10), we take it as expressing (or conveying) something more complex and specific than what is explicitly stated in (10). We accept it as expressing something about what would have been the case had Otto come to the party, without Anna, and Otto is in good spirits, and not in a coma, and Otto's friends still attended, and nobody called the police, etc. When we accept (11), with its negation of (10)'s consequent, we accept it as expressing or conveying a strict conditional antecedent which does not entail the antecedent of the counterfactual proposition expressed (or conveyed) by (10), but contradicts it specifically with regard to Anna's presence at the party.

Counterlegals

I have presented the property theoretic account of counterfactuals in terms of counterfactuals whose antecedents are consistent with the laws that hold (those that analyze the dispositions that in fact are had by things). Counterlegal counterfactuals (counterfactuals whose antecedents are not consistent with the laws that hold) present a challenge for the proposed view. We seem to have clear intuitions about counterfactuals such as the following:

(15) Had there been a negatively charged proton in the neighborhood of an electron these particles would experience a mutual repulsion in accordance with Coulomb's law.

But according to the dispositional essentialist, the antecedent of (15) is metaphysically impossible. One way to handle counterlegals on the proposed treatment of counterfactuals is to take terms like "proton" in counterlegal antecedents to have non-standard referents. There may be good reasons to deny that negatively charged but otherwise proton like particles are protons. We can take this essentialist view of protons and still make sense of counterfactual antecedents that use "negatively charged proton" as really concerning negatively charged but otherwise proton like entities. The account proposed can be extended to cover counterlegals by means of such re-interpretation of terms in counterlegal antecedents. There is the concern that in recognizing such non-standard usage in counterlegals, we undermine the essentialist semantics we employ elsewhere. But I find nothing implausible in the view that counterlegal antecedents are just semantically peculiar. If I object to someone's use of "negatively charged proton" in a counterfactual antecedent on the grounds that a negatively charged particle would not really be a proton, I think it likely that I will be accused of taking the speaker too literally and that what they are really concerned with is not a proton but a negatively charged and otherwise proton like particle. The likelihood of hearing a defense of the possibility of negatively charged protons is remote.

Bird, Alexander. “The Dispositionalist Conception of Laws,” in Foundations of Science (forthcoming 2003).

Ellis, Brian and Caroline Lierse. “Dispositional Essentialism,” Australasian Journal of Philosophy. 72 (March 1994) 27-45.

Lange, Marc. Natural Laws in Scientific Practice. New York: Oxford University Press, 2000.

Lewis, David. Counterfactuals. Cambridge: Harvard University Press, 1973.

Lewis, David. “Forget about ‘the Correspondence Theory of Truth,” Analysis 61 ( October 2001).

Mackie, J. L. Truth Probability and Paradox. Oxford: Oxford University Press, 1973.

Prior, Elizabeth, Robert Pargetter and Frank Jackson, “Three Theses about Dispositions,” American Philosophical Quarterly (1981) 251-56.

Pargetter, Robert and Elizabeth Prior. “The Dispositional and the Categorical,” Pacific Philosophical Quarterly, 63 (1982) 366-370.

Shoemaker, Sydney. "Causality and Properties," in Time and Cause, ed. Peter van Inwagen, 109-135. Dordrecht: Reidel, 1980.

Swoyer, Chris. "The Nature of Causal Laws." Australasian Journal of Philosophy 60 (1982): 203-23.

Tooley, Michael. "The Nature of Laws." Canadian Journal of Philosophy 7 (1977): 667-98.

[1] Among those who have raised this objection is Armstrong (1983)

[2] Among those who raise this objection is Marc Lange in Natural Laws in Scientific Practice, 90.