, 12:213

Mind in a Humean World


    • Economics and PhilosophyWitten/Herdecke University

DOI: 10.1007/s12133-011-0086-2

Cite this article as:
Harbecke, J. Int Ontology Metaphysics (2011) 12: 213. doi:10.1007/s12133-011-0086-2


The paper defends Humean approaches to autonomous mental causation against recent attacks in the literature. One important criticism launched at Humean approaches says that the truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. This paper argues that special science causal laws and physical causal laws cannot be distinguished in terms of degrees of strictness. It follows that mental-to-physical counterfactuals are supported—or not supported—by laws in just the same way as are physical-to-physical counterfactuals.


Mental causationCounterfactual causationHumean metaphysicsCausal lawsCausal overdetermination

1 Introduction

Within the debate on mental causation of the last 20 years, there have been scattered but recurrent attempts to argue that a Humean metaphysics provides a plausible model of how an autonomous mind can have effects in a physical world. The contrast between different frameworks implicitly referred to by this contention is that between ‘thin’ Humean theories and certain ‘thick’ theories of causation, such as process or power theories. In particular, if causation is the transference of energy quanta, an autonomous mind can be causally efficacious only through the transference of non-physical energy quanta. However, the existence of non-physical energy quanta directly violates well-established physical conservation laws (cf. Papineau 2002, Appendix). Similarly, under a power theory of causation the power manifestations of an autonomous mind are always redundant with respect to the mind’s putative physical effects given that all physical effects have a sufficient physical cause. As a consequence, there is no genuine contribution that mental powers would ever make. But a power that never makes any contribution in any situation is no power at all (cf. Shoemaker 2003/1980 for the original theory of properties as powers).

Within a Humean framework, causation is essentially defined over either a counterfactual dependence of one event upon another (cf. Lewis 1973a) or a universal regularity connecting types of events (cf. Graßhoff and May 2001; Baumgartner 2008, 2009). Hence, from a Humean perspective the mind has physical effects either if at least some physical events depend counterfactually on mental events or if all instantiations of at least one mental type are succeeded by events belonging to a corresponding natural physical type. An incomplete list of authors that have transformed this fundamental idea into various arguments for mental causation includes: Baker (1993, 93), Bennett (2003, 486–89), Heil and Mele (1991, 68), Harbecke (2008, ch. 4), Horgan (1989, 61), Kallestrup (2006, 473), Kroedel (2008, 137f), LePore and Loewer (1987, 639), Loewer (2001, 322f; 2002, 660f; 2007b, 257), Mills (1996, 108f), Pietroski (1994, 358) and Raatikainen (2006, 7).

In a recent paper, Michael Esfeld (2010) argues that notably theories that infer the factuality of mental causation from the truth of certain counterfactuals are fundamentally flawed. Esfeld shares the belief of some of the above-mentioned authors that, if a counterfactual ¬p1□→ ¬ p2 referring to two non-overlapping physical events p1 and p2 is true, and if p1 is the supervenience base of a mental event m1, then the counterfactual ¬m1□→ ¬p2 is necessarily true as well, even if m1 and p1 are not identical. However, Esfeld diverges from these authors by denying that counterfactual dependence as stated by such a counterfactual conditional is sufficient for causation. In his view, the truth-makers of causally interpretable counterfactuals include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. Hence, counterfactuals such as ¬m1□→ ¬ p2 are not causally interpretable, and even a Humean must ‘…come to terms with a version of the identity theory…’ (Esfeld 2010, 5)

The present paper aims to show that Esfeld points to an important question concerning Humean theories of mental causation. Ultimately, however, his argument faces three serious problems. Firstly, sometimes true counterfactuals that are not supported by causal laws are causally interpretable nevertheless, contrary to what Esfeld assumes. Secondly, Esfeld’s proposal to opt for an identity theory is at tension with his claim that mental-to-physical counterfactuals are not supported by laws whilst (the appropriate) physical-to-physical counterfactuals are: If the mental event m1 is identical to the physical event p1 which has a physical effect p2, then both counterfactuals ¬m1□→ ¬ p2 and ¬p1□→ ¬ p2 should be supported by the laws because the terms ‘m1’ and ‘p1’ have exactly the same referent.

Thirdly, and most severely, when describing the laws of the special sciences as ‘less strict’ than physical laws (Esfeld 2010, 3), the author overlooks an important distinction between generic law schemata and causal laws. Once that distinction is made explicit, the putative difference between special science and physical causal laws identified by Esfeld vanishes. As a general result of our paper, the weaknesses of Esfeld’s argument indirectly provide reasons to think that a Humean metaphysics contains the resources for an adequate model of autonomous mental causation.

The structure of the paper is as follows. Section 2 makes precise the version of the problem of mental causation that figures in the background of the debate. Section 3 provides a brief overview over those Humean theories of mental causation that are directly or indirectly attacked by Esfeld. Section 4 reconstructs the main steps of Esfeld’s argument. Some potential inconsistencies and false assumptions found in Esfeld’s overall argument are analysed in Section 5. Section 6 summarizes the main points of the paper and makes some concluding remarks.

2 The Problem of Mental Causation

The problem of the causal efficacy of mental events is usually construed as consisting in the fact that the conjunction of the following four principles is inconsistent:
  1. 1.

    Distinction: mental events are not identical with physical events.

  2. 2.

    Causation: mental events cause physical events.

  3. 3.

    Completeness: any physical event has sufficient physical causes, insofar as it has causes at all.

  4. 4.

    No systematic overdetermination: events are not systematically overdetermined by mental and physical causes.


As we have shown elsewhere (cf. Harbecke 2010), only under some interpretations these principles are in fact inconsistent with another. For the present purposes, an interpretation implying an inconsistency shall be presupposed. The inconsistency is often illustrated by a hypothetical case of mental causation. In this hypothetical case, a particular mental event m1 is supposed to cause a physical event p2 in the sense of assumption (2). According to assumption (3), this p2 has a sufficient physical cause p1. Assumption (1) rules out that m1 is identical with p1. Altogether this implies that the situation described is a case of causal overdetermination. Finally, if the situation is considered prototypical for mental causes, it contradicts assumption (4). It follows from this that the set of assumptions (1)–(4) is inconsistent.

The cases usually discussed in Humean approaches to mental causation presuppose assumptions (1)–(4) as well. Additionally, a further assumption is made according to which every mental event strongly supervenes on a simultaneous physical cause of its physical effect.1 This turns the hypothetical situation described above into a case that is often illustrated by a graph resembling Fig. 1.
Fig. 1

The problem of mental downward causation. The vertical arrow indicates a supervenience relationship. The horizontal and the diagonal arrows indicate (potential) causal relationships

The arguments summarized in the next section are attempts to establish that, under the presupposition of a Humean theory of causation, a situation illustrated by Fig. 1 is a good model as to how mental events are sometimes causes of physical events.

3 Humean Approaches to Mental Causation

As already mentioned, Humean theories of causation fall into two broad categories, namely counterfactual theories (cf. Lewis 1973a; Ramachandran 1997; Sartorio 2005; and the contributions in Collins et al. 2004) and regularity theories (cf. Mackie 1974; Graßhoff and May 2001; Halpin 2003; Baumgartner and Graßhoff 2004; Baumgartner 2008, 2009). Up until today, there are only few attempts to apply regularity theories of causation for a model of mental causation (but cf. Rupert 2006; Bauer 2010). Most Humean approaches have used the counterfactual analysis in order to provide a satisfactory analysis of mental causation. In what follows, we will focus on these approaches, not the least because they are the main target of Esfeld’s criticism.

To highlight the main idea behind counterfactual approaches to mental causation, recall that the classical theory as developed by David Lewis (1973a) uses a counterfactual dependence between two non-overlapping events as a starting point. Lewis defines this notion as follows:

Counterfactual Dependence:

ψ counterfactually depends on φ if, and only if, φ □→ ψ and ¬φ □→ ¬ ψ (cf. Lewis 1973a, 561/62)

The symbol ‘□→’ is intended by Lewis as a counterfactual conditional operator roughly corresponding to the English subjunctive conditional schema ‘if … had been the case, then … had been the case’ (cf. Lewis 1973b, c). Lewis then explicates the semantics for such conditionals in terms of a possible worlds space. According to this idea, a counterfactual φ □→ ψ is non-vacuously true at a world w if, and only if…

‘…either (1) there are no possible φ-worlds (in which case φ □→ ψ is vacuous), or (2) some φ-world where ψ holds is closer (to w) than is any φ-world where ψ does not hold.’ (Lewis 1973a, 560; minor modifications)

In the final step of his proposal, Lewis argues that counterfactual dependence implies causal dependence, and that ‘[c]ausal dependence among actual events implies causation.’ (Lewis 1973a, 563). In short, he proposes the following sufficient condition for causation (for two non-overlapping events φ and ψ within a deterministic causal frame):

Counterfactual Causation:

If ψ counterfactually depends on φ, then φ causes ψ.

The approaches to mental causation presupposing a Humean framework have explored this fundamental idea in various ways. One approach reflected, for instance, by Lynne Rudder Baker (1993, 93) and Barry Loewer (2001, 322f; 2002, 660f) points out that, whilst our best science gives us reason to believe in the counterfactual ¬p1□→ ¬p2, our explanatory practices and common sense understanding strongly suggests the truth of the counterfactual ¬m1□→ ¬p2 as well. From the latter counterfactual it follows directly that mental events sometimes are causes of physical events.2,3

A second approach that is reflected, for instance, by Loewer (2007b), Ausonio Marras (2007), and Thomas Kroedel (2008) employs what can be called a ‘counterfactual transition inference’. It deduces a causal efficacy of mental events for those physical events that counterfactually depend on the mental events’ physical supervenience bases. The argument can be reconstructed as follows. Again it is first pointed out that our best science gives us reason to believe in the counterfactual ¬p1□→ ¬p2 (causation) and that broader philosophical arguments strongly support a modal claim of the form (¬m1 → ¬p1) (supervenience). From these two assumptions (and an implicit background condition4) it can be inferred that ¬m1□→ ¬p2 is true as well. With Lewis’ criterion for causation, m1 then clearly qualifies as a cause of p2.5

The two approaches mentioned so far are obviously closely related. The difference between the two consists in the fact that the former takes the counterfactual ¬m1□→ ¬p2 to be independently supported by common sense or by quotidian explanatory practice whilst the latter infers this counterfactual from ostensibly less problematic assumptions. However, both essentially take Lewis’ original counterfactual criteria as sufficient for causation, so that the truth of the counterfactual ¬m1□→¬p2 is sufficient for a causal relation between m1 and p2 if m1 and p2 are actual events. It is this inference from the truth of the counterfactual ¬m1□→ ¬p2 to a causal claim about m1 and p2 that Esfeld mainly attacks.6

4 Esfeld’s Objection

As mentioned above, Esfeld does believe that, if a counterfactual ¬p1□→ ¬p2 referring to two non-overlapping physical events p1 and p2 is true and if p1 is the supervenience base of a mental event m1, the counterfactual ¬m1□→ ¬p2 is necessarily true as well. In his own words:

‘Consequently, in the context of a counterfactual theory of causation, if p1 causes p2, the proposition ‘If p1 had not occurred, p2 would not have occurred either’ is a true counterfactual. Then, by strong supervenience, the proposition ‘If m1 had not occurred, p2 would not have occurred either’ is a true counterfactual as well.’ (Esfeld 2010, 3).

In short, he takes the inference ¬p1□→ ¬p2 and (¬m1 → ¬p1) to ¬ m1□→ ¬p2 to be valid. As it turns out, this inference is actually invalid (cf. footnote 4). Hence, it needs to be argued that, in the present case, validity is preserved because the special cases discussed by Lewis (1973b, 32) to illustrate the invalidity of the argument schema can be ruled out as potential interpretations of the conditionals.

Once this is done, Lewis’ original criterion, according to which counterfactual dependence implies causal dependence and ‘[c]ausal dependence among actual events implies causation…’ (Lewis 1973a, 563), establishes the claim about the causal relation between m1 and p2. Esfeld, however, rejects Lewis’ contention that counterfactual dependence is sufficient for causation. As he says:

‘…the mere fact of there being a true counterfactual that links the absence of p1 with the absence of p2 and there being a true counterfactual that links the absence of m1 with the absence of p2, while strong supervenience ensures that an event of the same type as p1 always goes together with an event of the same type as m1, is not sufficient to establish that there is a causal relation between m1 and p2, not even on Humean standards’ (Esfeld 2010, 3)

In other words, Esfeld argues that, contrary to the statements quoted above, as a good Humean not even Lewis himself could have potentially believed that causal dependence among actual events implies causation. Rather, even on Lewis’ own terms a further condition needs to be satisfied by, for instance, m1 and p2 in order for a counterfactual such as ¬m1□→ ¬p2 to be causally interpretable. In Esfeld’s view, this condition says that, for any two events φ and ψ, the counterfactual ¬φ □→ ¬ ψ is causally interpretable only if it is supported by strict laws or, at least, comparatively strict laws. Esfeld claims that this condition is satisfied by the counterfactual ¬p1□→ ¬p2 referring to the events in the situation illustrated by Fig. 1:

‘[T]he counterfactual ‘If p1 had not occurred, p2 would not have occurred either’ can, with reason, be taken to express a causal relation between p1 and p2 because it is supported by strict laws—at least, if one takes p1 and p2 to be placeholders for appropriate configurations of fundamental physical tokens, p1 standing for the fundamental physical supervenience base of m1. The laws in which types of physical properties figure are strict laws or, at least, comparatively strict laws.’ (Esfeld 2010, 3)

The point is, however, that the mentioned condition is typically not satisfied by counterfactuals referring to mental-to-physical counterfactuals such as ¬m1□→ ¬p2. As the author explains:

‘The laws of the special sciences, by contrast, are never strict—or, in any case, less strict than fundamental physical laws, if one wants to leave the question of there really being strict laws open. If there are laws in the special sciences at all, these are ceteris paribus laws that admit a lot of exceptions, which cannot be specified in the vocabulary of the special science in question. This observation applies, in particular, to psychophysical laws.’ (Esfeld 2010, 3)

In other words, a mental-to-physical counterfactual such as ¬m1□→ ¬p2 is typically supported by laws that are either essentially non-strict, or perhaps it is not supported by any laws whatsoever. This observation shows that Lewis’ original condition for causality between actual events cannot be right:

‘[I]n the case of the … counterfactual [¬m1□→ ¬p2], there are no laws available that support the link between m1 and p2, at least not in the same way as there are laws that support the link between p1 and p2. As things stand, given the truth-makers for the first counterfactual [¬p1□→ ¬p2], the counterfactual [¬m1□→ ¬p2] is true only in virtue of m1 strongly supervening on p1.’ (Esfeld 2010, 4)

Esfeld still does not dispute that the counterfactual ¬m1□→ ¬p2 is true. But it is not ‘made true in the right way’, so to speak. Only if a counterfactual is supported by strict, or at least comparatively strict, laws it is causally interpretable. However, this condition is not met by mental-to-physical counterfactuals. Hence, the true counterfactual ¬m1□→ ¬p2 referring to the hypothetical situation illustrated by Fig. 1 is not causally interpretable: m1 does not cause p2 even under a Humean theory of causation.

Esfeld’s own conclusion is that, if one wants to maintain a realism with respect to mental causation, ‘…one has to attack [assumption (1) of the problem of mental causation] and come to terms with a version of the identity theory, whatever the best physical theories of the real world are, and whatever is one’s preferred stance in the metaphysics of causation’ (Esfeld 2010, 6).

5 Some Problems of the Objection

Esfeld’s argument raises important questions about the various connections between counterfactuals, laws, and causal relations that are of general interest to the debate. For it is true that the debate on Humean metaphysics and mental causation has paid little attention to these issues so far.

Lewis did make clear that, within a Humean metaphysics, laws of nature have a central position in fixing the possible worlds metric, which in turn fixes the truth values of counterfactuals (cf. Lewis 1973a, 560; 1973b, 75; 1986, xii; and 2004, 279). Other authors have argued that laws of nature are the direct truth-makers of counterfactuals (cf. Jackson 1977; Kistler 2002, 650–652; Loewer 2007a, fn. 33).

However, to our knowledge no one has so far investigated systematically whether all, or only some, of the counterfactuals that are true at a particular world w stand in a systematic connection to the causal laws holding at w, and whether the causal laws that make true certain corresponding counterfactuals are all of the same kind. The answers to these questions may in fact have implications for the interpretation of counterfactuals with respect to the putative causal relations between the events referred to. Hence, Humeans should try to provide an answer to them. In this sense, Esfeld points to important questions whose clarification is overdue.

Nevertheless, Esfeld’s own argument is quite problematic, and its conclusion should be treated with caution, accordingly. The following subsections highlight the critical points in the author’s train of thoughts. The first two (Sections 5.1 and 5.2) are minor in the sense that they discuss certain tensions between some of the claims made by the author. However, the third remark (Section 5.3) presents substantial independent reasons to doubt that physical causal laws are stricter than are psychophysical laws, which is a crucial premise in Esfeld’s argument.

Before Esfeld’s argument is examined in more detail, note that the author takes the Humean approaches to mental causation attacked by him to drop assumption (4) of the problem of mental causation, which is the denial of systematic overdetermination of certain kinds of physical events (cf. Esfeld 2010, 2). This is probably true, for instance, for Loewer (2001, 2002), but it clearly does not apply to all authors referred to by Esfeld. In particular, Karen Bennett (2003), Harbecke (2008, ch. 4), and Kroedel (2008) out of independent reasons all offer interpretations of the situation illustrated by Fig. 1 to the end that the described case does not involve genuine causal overdetermination. Hence, these authors embrace an interpretation of assumptions (1)–(4) that renders the four assumptions consistent! The chosen interpretation is, of course, immediately motivated by the Humean framework presupposed by these authors.

Nevertheless, it is still the case all of these accounts put a special emphasis on a counterfactual dependence between the relevant events in Lewis’ sense. Therefore, the question still remains whether the putative difference identified by Esfeld between physical-to-physical counterfactuals and mental-to-physical counterfactuals is a problem for Humean approaches to mental causation.

5.1 True Counterfactuals and False Laws

In Esfeld’s view, mental-to-physical counterfactuals are supported by law-like generalizations. However, these law-like generalizations are invariably non-strict. As the author points out, the relevant mental-to-physical generalizations are essentially ‘…ceteris paribus laws that admit a lot of exceptions, which cannot be specified in the vocabulary of the special science in question’ (Esfeld 2010, 3). And yet, Esfeld has no doubt that the counterfactual ¬m1□→ ¬p2 has the same truth value as the counterfactual ¬p1□→ ¬p2. How is that possible?

The idea behind these contentions seems to be that p1 falls under a physical type, call it ‘P1’, whose instances are each followed by an instance of another physical type, call it ‘P2’, or in short: P1 → cP2.7 In the situation described by Fig. 1 the mentioned instance of P2 is p2, of course. In contrast, the type that subsumes m1, call it ‘M1’, does not secure an instance of P2.

The intuition driving this claim seems to be the following: The mental event m1 may be the event of Otto desiring to lift his left arm on a particular occasion. The type M1 then subsumes all desires of lifting the left arm. The physical event p1, being the supervenience base of m1, may be a very specific brain event, for example, a specific network activity pattern within the frontal lobe as well as the premotor and primary motor cortex of the right hemisphere. p2 may then be thought of as a very specific activation pattern of neural networks in the central grey nuclei, the cerebellum, the spinal cord and eventually the muscle fibres within the left arm.

For the case described, it seems fairly obvious that the law-like causal generalization M 1cP2 is false: not any instance of M1 is followed by an instance of P2, even if M1 may always be followed by an instance of a type A = {x | x is the lifting of a left arm}. The reason is that sometimes the supervenience base of an instance of M1 may be an instance of a different pattern involving slightly different neural networks. Call this pattern P1*, and assume that instances of P1* are always followed by instances of P2* (i.e. P1*cP2*), where P2* is a slightly different firing pattern of neural networks in the central grey nuclei, the cerebellum, the spinal cord and the muscle fibres within the left arm. Perhaps the firing rates of the neurons in these regions are different, or perhaps certain subsidiary neural pathways are being activated when P2* is instantiated.

Esfeld’s reasoning now seems to be that, because M 1cP2 is false, the counterfactual ¬m1□→ ¬p2 is not causally interpretable, even if it turns out true. One of the problems of this reasoning is that, if applied generally, it characterizes partial physical causes as non-causes.

Assume that p1 is only a part of the complex network firing mentioned above. For instance, let it be only the firing of neural networks in Otto’s primary motor cortex. Then there is any reason to suppose that the following counterfactual is true: ¬p1□→ ¬p2. The firing of neural networks in Otto’s primary motor cortex is a necessary part of the complex event that leads to the occurrence of p2. That is, p1 so-construed is a partial cause of p2. And since all partial causes are causes, p1 is a cause of p2. At the same time, there is any reason to suppose that the law-like causal generalization P 1cP2 is false! The firing of neural networks in someone’s primary motor cortex described above is not always followed by an instance of P2, because more things than just primary motor cortex firing are needed to secure an instance of P2.

These insights support the following conclusions: Counterfactuals are sometimes causally interpretable even if they are not supported by laws. Secondly, the interpretation more or less explicitly favoured by Esfeld of the situation illustrated by Fig. 1 is misleading. If from the start it would be assumed that m1 secured the occurrence of p2—perhaps because p2 was a much more abstract physical event rather than a complex brain event as proposed above—then there would be any reason to believe that the law-like causal generalization M1cP2 is true, and hence, that ¬m1□→ ¬p2 is not only true, but it is supported by causal laws. Only if p2 is construed in a way that precludes m1 from securing it, we reach the conclusion that ¬m1□→ ¬p2 is not supported by causal laws. Consequently, there is a feeling that Esfeld’s line of reasoning begs the question.

5.2 Identical Events and their Properties

As mentioned above, Esfeld claims that, given that the mental counterfactuals are not causally interpretable, the only option open for mental causation is to embrace an identity of mental and physical events (cf. Esfeld 2010, 6). This is an interesting statement out of the following reason.

One necessary, and potentially sufficient, condition for the identity between an event φ and an event ψ is that φ and ψ share all of their properties, including their contextual properties. In particular, if φ falls under a particular type, so does ψ, and if the counterfactual ¬φ □→ ¬μ is made true by a particular distribution of facts and laws, then also ¬ψ □→ ¬μ is made true in this way.

As it was just said, Esfeld does think that assumptions (1)–(4) should be taken to imply the negation of (1). With respect to the situation of Fig. 1, he therefore wants to say that the strong supervenience initially postulated between m1 and p1 turns out to be identity. But if so, the counterfactuals ¬m1□→ ¬p2 and ¬p1□→ ¬p2 should be true in just the same way. Consequently, it cannot be the case that one counterfactual is supported by the laws and the other is not. But this difference with respect to being supported by laws was precisely what the author claimed in order to demonstrate the impossibility of a Humean approach to mental causation. Or in other words, Esfeld’s conclusion that a Humean framework cannot provide a model for unreduced mental causation is essentially based on a premise that the author eventually rejects himself.

This is not to say that the identity theory is incoherent. In fact, it may well be true. But there remains a sense that Esfeld’s argument for the identity theory begs the question. For the event m1 referred to in the illustration of Fig. 1 cannot be the same event that is eventually referred to in the identity claim m1 = p1. Hence, this identity claim cannot be attained by inference from the initial assumptions, which is to say that it was simply postulated without argument.

5.3 Law Schemata and Causal Laws

Whatever else causal laws are, they certainly are regularities whose antecedent type and consequent type are always instantiated by non-overlapping spacetime points or regions. In other words, the causal relation is non-instantaneous. This fundamental assumption about causation emerges already in Hume’s characterization of effects as ‘following’ their causes (cf. Hume 2000/1748, Section 7). It also occurs in Lewis (1973a, 562), who declares his analysis to be adequate only for ‘distinct’ events. Modern regularity theories of causation explicitly require that the instances of the antecedent type(s) and the consequent type ‘differ’ but are ‘spatiotemporally proximate’ (cf. Baumgartner 2008, 330).

All this suggests that a causal regularity relating two types Φ and Ψ does not have the form of a simple universally quantified sentence such as ‘∀xx → Ψx)’. Rather, it has the following more complex general form: ‘∀xx → yy & Rxy))’.8 In words: ‘for all individuals x, if x instantiates the property Φ, then there is another individual y which instantiates property Ψ and to which x stands in the relation R.’ The individuals quantified over can be understood as objects occupying a particular space at a time, or simply as spacetime regions. The predicate ‘R’ is intended to capture the idea of ‘a non-overlap plus a spatiotemporal proximity’.9

The logical form of causal laws makes obvious why, for instance, the classical ideal gas law is not a causal law. Rather, the ideal gas law expresses strict general relationships between certain properties, namely, for some amount of gas (n; measured in moles), the absolute pressure (P), the volume (V) and the temperature of the gas (T). The conventional way of stating the ideal gas law is by an equation (here, R is the universal gas constant):
$$ PV = nRT $$

Equation 1 is a simple and compact way to summarize a whole set of strict laws describing various systems. In fact, part of what it means to understand the ideal gas law is to understand how Eq. 1 can be used to generate certain strict laws applying to particular systems. An example of such a law would be:

SL1: For all ideal gases of an amount of n moles in a container of volume V, if the gas acts with pressure P onto the walls of the container, then its temperature equals \( \frac{{PV}}{{nR}} \).

One way to bring out the logical structure of SL1 is the following: ‘∀x(Gnx & Vx & Px→Tx & (\( T = \frac{{PV}}{{nR}} \)))’, where ‘Gn(…)’ = ‘…is a gas of n moles’, ‘V(…)’ = ‘…has volume V’, ‘P(…)’ = ‘…exerts pressure P’ and ‘T(…)’ = ‘…has temperature T’. Note that this formula makes reference to single objects at a time, or spacetime regions. Hence, it specifies the relationship of certain properties a particular system has at an instant, in contrast to characterizing a regular succession of certain kinds of events. Hence, if the formula reconstructs SL1 adequately, SL1 is not a causal law. However, understanding the ideal gas law also means to understand how to use Eq. 1 in order to generate a range of causal laws. One example for such a generated causal law would be the following.

CL1: For all ideal gases of an amount of n moles that are coupled to an ideal heat bath10 of temperature T, if at a time t the gas is in a container of volume V and has pressure \( P = \frac{{nRT}}{V} \), then, if a particular force is applied to the container at time t altering its volume to V' in a reversible manner11 until time t', the pressure of the gas at time t' is given by \( P\prime = \frac{{nRT}}{{V\prime }} \).

Expressing this sentence in formal logic gets quite complex, so that we relegate the details to a footnote.12 But the transition from Eq. 1 to either SL1 or CL1 illustrates well that Eq. 1 itself does not conform to the logical structure demanded for causal laws. Only CL1 meets this formal requirement, which was derived on the basis of Eq. 1 and added information about the heat bath, the slow, reversible dynamics etc. Consequently, Eq. 1 is better understood as a law schema, from which strict laws and causal laws can be generated with the help of certain assumptions about particular systems.

The example generalizes. Take as a second case Newton’s second law and Newton’s law of gravitation, where F is the force, a is the acceleration, m, m1 and m2 are masses, G is the gravitational constant, and r is distance.
$$ a = \frac{F}{m} $$
$$ F = G\frac{{{m_1}{m_2}}}{{{r^2}}} $$

Again, Eqs. 2 and 3 are strict. However, they are not yet causal laws but only law schemata from which causal laws can be generated. Once more, understanding Eqs. 2 and 3 adequately means to be able to transform them into various causal laws. A fairly simple example of such a causal law would be:

CL2: For all spacetime regions s1 inhabited by only two masses m1 and m2 apart at distance r and with zero relative velocity, there is another spacetime region s2 occurring t seconds later than s1 in which the distance between m1 and m2 equals r − d (unless d > r), where d is the solution to the equation \( \int_1^{{\frac{{r - a}}{r}}} {\sqrt {{\frac{x}{{1 - x}}}} {\text{d}}x = t\sqrt {{2r\left( {{m_1} + {m_2}} \right)G}} } \).

As before, only with respect to a particular system—in this case the two-masses-in-space system—can Eqs. 2 and 3 be used to generate a causal law. Another example would be a container with two particles inside each of which is assigned an initial location and a velocity vector. Certain causal laws generated from classical mechanics allow to predict the locations and velocities of the particles at any future (and past) point of time as illustrated by Fig. 2 (call the corresponding causal law ‘CL3’). However, the Newtonian laws specifying the relationships of forces, masses, velocities etc. do not make any claims about particular container events involving actual forces, masses and velocities. They are merely law schemata on the basis of which causal laws about container systems can be generated.
Fig. 2

Two particles in a box

The main point of the distinction between generic law schemata and causal laws consists in the fact that causal laws, in contrast to (at least some) law schemata, are never strict. Causal laws essentially describe systems as they evolve through time, such as the two-particle box or the two-masses-in-space system, instead of strict relationships between properties at an instant. However, for any system evolving through time apart from the ideal total system—a system which would instantiate all actual and possible properties or their negation, respectively—confounders can occur.

For instance, if the gas container is taken out of the heat bath that thermodynamics assumes it to hover in, the ideal gas law would still apply to it at any point in time but CL1 would almost certainly be falsified. Secondly, the distance of the two masses at the time described by t will not be r − d as described by CL2 if a spacetime region nearby is inhabited by a larger third mass. Similarly, if a larger mass is located outside the container illustrated by Fig. 2, the prediction of the locations and velocities of the particles at a future (and past) point of time as delivered by CL3 will almost certainly fail. These observations suggest that there is no causal law characterizing systems apart from the ideal total system that are strict, including all physical-to-physical causal laws.

It can now be seen that Esfeld’s contention that ‘[t]he laws in which types of physical properties figure are strict laws…’ (Esfeld 2010, 3) suffers from an ambiguity. If it were intended as referring to law schemata, the claim would be correct. But since the claim is clearly intended as referring to physical causal laws, it is false. The causal physical laws relating complex neural types to other complex neural-and-muscle-fibre types are non-strict. Similarly, the laws relating the types describing the immensely complex microphysical states or ‘configurations’ (cf. Esfeld 2010, 3) that are correlated with mental types are non-strict. Since such relatively large microphysical configurations are inconceivably complex, it even seems plausible that their causal connection is much more confounder sensitive than cases of mental causation typically are.

To illustrate this point, suppose that MP1 and MP2 are the types subsuming the microphysical states mp1 and mp2 underlying m1/p1 and p2 respectively in the situation described by Fig. 1. Whereas X-raying Otto’s skull immediately after the occurrence of his mental event m1 may not jeopardize the occurrence of p2 (the neural-and-fibre event in Otto’s left arm), it will very likely produce a counterexample to the causal regularity ∀x(MP1x →y(MP2y & Rxy)) since the X-rays will probably have some influence, for instance, on the distribution of electrons and the relative position of atoms as specified by the extremely detailed state type MP2. At the same time, by supervenience, anything that is a confounder to the mental cause is necessarily also a confounder of the microphysical cause.

This insight casts doubts even on Esfeld’s weakened claims that ‘[t]he laws in which types of physical properties figure are strict laws or, at least, comparatively strict laws’ and that ‘[t]he laws of the special sciences…are…, in any case, less strict than fundamental physical laws.’ (Esfeld 2010, 3; emphasis added) On the contrary, fundamental physical-to-physical causal laws can be expected to have just as many exceptions as mental-to-physical causal laws. Since the quoted claims are central premises in Esfeld’s argument against the causal interpretability of mental-to-physical counterfactuals, the argument in its present form must be considered unsound. This is the main conclusion of our paper.

At this point, it should be mentioned that there is a well-known procedure to make causal laws strict. Once a ‘that’s all’—claim or a ‘ceteris paribus’—clause is attached to the antecedent condition of the regularity, an overall environmental condition is held fixed and potential confounders are ruled out. A supplementary argument hinted at by Esfeld makes reference to this idea.

As the author claims, psychophysical laws, just as all special sciences laws, ‘…are ceteris paribus laws that admit a lot of exceptions, which cannot be specified in the vocabulary of the special science in question.’ (Esfeld 2010, 3; quoted already above in Section 4) The idea is that, in contrast, all potential confounders of physical causal laws can be specified in the vocabulary of physics. Esfeld takes this to show that mental-to-physical counterfactuals are supported by the laws in a much weaker sense than physical-to-physical counterfactuals. In consequence, he believes that mental-to-physical counterfactuals are not causally interpretable.

One strategic problem of this argument is that it cannot be presupposed a priori that all potential confounders of physical causal laws are specifiable in the vocabulary of physics. However, to suppose so begs the question against the general argument, because it excludes all mental events as potential confounders to physical causes and, therefore, excludes autonomous mental causation. Moreover, it cannot be assumed a priori that the exceptions to a special science law cannot be specified in the vocabulary of the special science in question. For instance, a particular environment in which a biological law holds can perhaps be described wholly in an advanced biological vocabulary at a future state of science.

Finally, a general problem is that any physical causal law must contain a ‘ceteris paribus’—or ‘that’s all’—clause conjoined to its antecedent no matter how large the number of potential confounding environments that the antecedent explicitly excludes. The reason is that, for any causal laws no matter how detailed, the number of potential confounders is infinite, whilst the number of explicitly excluded confounding environments is necessarily finite. If so, it makes little sense to speak of physical causal laws as ‘stricter’ compared to special science laws. The ratio of confirming environments to the total number of potential environments is the same for both. This suggests that the supplementary argument is not sound either.

6 Conclusions

This paper argued that Esfeld’s attack on Humean approaches to mental causation has three weaknesses. Firstly, it overlooks that sometimes true counterfactuals that are not supported by causal laws are causally interpretable nevertheless. Secondly, Esfeld’s proposal to opt for an identity theory is at tension with his claim that mental-to-physical counterfactuals are not supported by laws whilst (the appropriate) physical-to-physical counterfactuals are. An identity requires that, if the mental event m1 is identical to the physical event p1 which has a physical effect p2, both counterfactuals ¬m1□→ ¬p2 and ¬p1□→ ¬p2 should be supported by the laws because the terms ‘m1’ and ‘p2’ have the same referent. But precisely this claim the author denied.

The most crucial problem of Esfeld’s argument, however, is grounded in an ambiguity about physical law schemata and causal physical laws. Law schemata are typically strict, but they do not meet certain formal requirements of causal laws. Causal laws, in contrast, are always non-strict generalizations unless they refer to states of the total system. Moreover, the more specific the types get that occur in causal laws, the more potential confounders there are for any of their instances, and the less strict they become. As a consequence, Esfeld cannot argue that the laws supporting mental-to-physical counterfactuals are less strict than are the laws supporting physical-to-physical counterfactuals. Consequently, he cannot argue that, from a Humean perspective, physical-to-physical counterfactuals are causally interpretable, whereas mental-to-physical counterfactuals are not.

Note that by identifying the problematic parts of Esfeld’s argument we have given indirect support to Humean approaches to mental causation, for we have provided reasons to believe that mental-to-physical counterfactuals sometimes are causally interpretable, even if mental events are not identical to physical events. Of course, whether or not such a non-reductionist Humean theory of mental causation fares better than an identity theory depends on a host of further questions that we could not discuss in detail in this paper. Nevertheless, our results suggest to take Humean approaches to mental causation seriously.


Describing the relation of mental and physical events in this way is actually problematic as all canonical formulations of the concept of supervenience are not about relations between events but rather between classes of properties (cf. McLaughlin and Bennett 2008). However, at least under a fine-grained event model (cf. Kim 1973) there is a simple and plausible interpretation of the claim that an event supervenes on another. According to this idea, an event e1 supervenes on another event e2 if, and only if, the individuals and times of e1 and e2 are identical, and the property E2 instantiated by e2 is sufficient for the property E1 instantiated by e1. This parlance refers to a strong supervenience (cf. Kim 1984) of the property class of E1 on the property class of E2.


Baker (1993) claims that satisfaction of the two Lewis counterfactuals is sufficient for causation (cf. op. cit., 93). As the author takes at least some mental events to satisfy these counterfactuals with respect to certain physical events ‘…the problem of mental causation just melts away’. (op. cit., 93). A similar view is expressed by Loewer (2001, 2002). As he says: ‘Suppose that ¬m1□→ ¬p2 so m1 is a putative cause of p2. … The non-reductive physicalist holds that there are mental events m1 that are putative causes that are not pre-empted by events that they themselves don’t pre-empt.’ (Loewer 2002, 660; minor modifications). In the author’s view, this insight proves that at least some mental events are causes.


A related line of argument claims that, from the standpoint of the interventionist theory of causation, there are defensible causal models indicating a causal relevance of the mind (Raatikainen 2006, 5–8; Shapiro and Sober 2007, 241; Weslake 2009, 15–18). Since the structural equations used in such causal models condense sets of counterfactuals (cf. Hitchcock 2007, 501), these approaches bear a certain correspondence to the argument mentioned in the text.


The point is that the inference from ¬p1□→ ¬ p2 and (¬m1 → ¬p1) to ¬m1□→ ¬p2 is actually invalid (Lewis 1973b, 32). Hence, in the present case the implicit assumption must be that validity is preserved because the special cases responsible for the invalidity of the corresponding argument schema can be ruled out on the basis of independent reasons.


This line of thought is explored by Loewer (2007b) when he claims that ‘…[non-reductive physicalism] holds that [due to supervenience] the connection between p1 and m1 is one of metaphysical not merely nomological necessitation. In the most similar world at which ¬m1, it is also ¬p1 since there is no question of ‘breaking’ the metaphysical connection. So in this situation ¬m1□→ ¬ p2 may well be true.’ (op. cit., 257; minor modifications) For slightly less explicit versions of the line of argument, cf. Heil and Mele (1991, 68), Horgan (1989, 61), Kallestrup (2006, 473), Marras (2007, 318–319), and Kroedel (2008, 137f).


It should be mentioned that Esfeld explicitly also attacks more sophisticated Humean accounts of mental causation that are more cautious about the inference from counterfactual dependence to causal claims. One of these is Harbecke (2008, ch. 4), which builds on some insights mentioned by Yablo (1992). This theory denies that counterfactual dependence is sufficient for causation and thereby rejects the inference that Esfeld attacks primarily. In contrast, Harbecke introduces certain further necessary conditions for causation between two actual events φ and ψ, among which is an iterative sufficiency counterfactual such as ¬φ □→ (φ→ ψ) (cf. Rasmussen 1982). But also in Harbecke’s and Yablo’s theories a counterfactual dependence between actual events as defined by Lewis place a central role. Hence, Esfeld’s claim that the relevant counterfactuals must not only be true, but be made true ‘in the right way’ (see below) for them to be causally interpretable is relevant to these theories as well.


The expression ‘P1cP2’ abbreviates a more complex conditional. For the exact logical form that law-like causal generalizations should be taken to have, see the comments below in Section 5.3.


Formulas such as ‘P1cP2’ used in Section 5.1 to express causal regularities should be read as short forms of formulas conforming to this more complex structure.


If one rejects deterministic causation, the conditional should perhaps take the form ‘∀xx[P(Ψ|Φ)]yy & Rxy)’, where P(Ψ|Φ) is the probability of y instantiating Ψ conditional upon x's instantiation of Φ. Of course, if one thinks of physical causal laws as irreducibly probabilistic, their non-strictness is immediately accepted. This is the reason why we restrict our discussion to the existence of deterministic and reducibly probabilistic physical causal laws.


A system that is coupled to a heat bath is a system that is in good thermal contact with a much larger system (the heat bath) with a given temperature. The system and the heat bath can exchange heat and energy freely and since the heat bath is (ideally, infinitely) larger than the system, the temperature of the heat bath stays constant at all times. If the system and the heat bath are both in equilibrium the temperature of the system equals the temperature of the heat bath.


A reversible change to the system is a slow change in time through which the system remains in equilibrium (or very close to it).


It would have to use a formula such as: ‘∀x(Gnx and Vx and Tx and FV'x → y(Gny & \( P\prime y \) & \( \left( {P\prime = \frac{{nRT}}{{V\prime }}} \right) \) & Rxy))’. In words, ‘for all spacetime regions x, if they host n moles of gas in a container of volume V, such that the gas acts onto the walls of the container with pressure P and such that a particular force FV' is applied to the container eventually altering it to volume V', then there is a second spacetime region y that is distinct from, but proximate to, x that hosts n moles of gas in a container such that the pressure of the gas equals \( \frac{{nRT}}{{V\prime }} \)’. The length of this expression makes clear why using the compact string of symbols of Eq. 1 is very useful to summarize certain causal laws.



We would like to thank Ran Rubin and Michael Esfeld for helpful comments and advice on earlier drafts of this paper. This work has been supported by a fellowship within the postdoctoral programme of the German Academic Exchange Service (DAAD).

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© Springer Science+Business Media B.V. 2011