Are we free to work miracles? On Peter van Inwagen's concept of the miraculous

Abstract To bolster his consequence argument against David Lewis's rejoinder, Peter van Inwagen uses the concept of miracle. He claims that the Lewisian compatibilist must admit that under determinism, we possess the ability to work miracles par excellence, that is, not just in some purely technical sense of the term. The article argues that van Inwagen's definition of a ‘miracle’ is too broad even if it is interpreted merely as an explication of one component often thought to be inherent in the religious concept of miracle, namely the concept of an event that breaks the laws of nature. Nomological effects of miracles are not miracles themselves.

The relation between free will and nomological determinism is one of those perennial metaphysical problems whose solution is important to the religious world-view. Some aspects of this issue are also closely connected to the theoretical interests of philosophy of religion, especially to the question concerning God's foreknowledge and human freedom. Moreover, it appears that considerations belonging to philosophy of religion are directly relevant to the contemporary debate between incompatibilists and their opponents. In an attempt to strengthen his consequence argument for incompatibilism against Lewis's (1981) critique, van Inwagen (2004 takes advantage of the concept of miracle. According to him, the compatibilist who claims that determinism does not rule out the ability to do otherwise is committed to endowing us with the ability to perform miracles par excellence. In this article, I argue that van Inwagen's definition of the term 'miracle' is inadequate. It is too broad even if interpreted merely as an explication of one component often thought to inhere in the religious concept of miracle, namely the concept of an event that breaks the laws of nature.
In the first two sections of the article, I summarize Lewis's critique of van Inwagen's consequence argument and outline that part of van Inwagen's reply which employs the concept of miracle. Next, I analyse the concept of miracle and specify conditions to be satisfied by any adequate definition of that notion. I argue that van Inwagen's definition fails even under the most favourable assumptions. In the subsequent section, I ponder possible ways of defending van Inwagen's explication against my criticism, with an emphasis on the Humean account of the laws of nature. I provide reasons for believing that all these attempts are unsuccessful. I conclude that as far as the concept of miracle is concerned, van Inwagen's reply to Lewis's critique should be considered unsatisfactory.

The background
According to incompatibilism, the thesis of determinism is incompatible with the proposition that we have free will. One of the most influential arguments in favour of this stance is Peter van Inwagen's consequence argument (van Inwagen (1975), Idem (1983)), which aims to demonstrate that if determinism is true, then we could not have acted otherwise than we in fact did. 1 However, in van Inwagen's view, if we do not possess the ability to do otherwise, our will is not free.
The sixth premise of van Inwagen's argument reads as follows: (1) J could not have rendered L false, where 'J' refers to the judge who does not raise his hand at instant T and thereby does not prevent the execution of a capital sentence upon a criminal, and 'L' denotes the proposition expressing the conjunction of all the laws of nature. 2 Proposition expressed by (1) was attacked by Lewis in his reply to van Inwagen's argument. First, let us introduce Lewis's concept of falsification: (2) An event would falsify a proposition iff, necessarily, if that event occurs then that proposition is false. (Lewis (1981), 119) Using this concept, Lewis (ibid.,[119][120] discriminates between the weak and the strong sense of the 'can render a proposition false' idiom. Applying this distinction to the laws of nature L, he gets two different interpretations of the sentence 'J could have rendered L false': (3) J could have rendered L false in the weak sense iff J could have done x such that, if J had done x, L would have been falsified. (4) J could have rendered L false in the strong sense iff J could have done x such that, if J had done x, L would have been falsified by x or by some event caused by x.
Lewis believes that (1) is false on the weak interpretation, that is, the judge possessed the ability to render the laws of nature false in the weak sense. It is true that J could have done x (i.e. he could have raised his hand) such that, if J had done x, L would have been falsified. But L would not have been falsified by x or by any event caused by xthat is why (1) is true on the strong interpretation. Instead, L would have been falsified by some event that would have occurred a little while before J's actby a divergence miracle. Thus, van Inwagen's consequence argument for incompatibilism is unsound on the weak interpretation. 3 Lewis's rejoinder is rooted in his miraculous analysis of counterfactuals, which attributes a central role to events that break the laws of nature (Lewis (1973), Idem (1979). Following Lewis, let us consider the counterfactual 'If Nixon had pressed the button at instant t, there would have been a nuclear holocaust.' To establish its truth valueunder determinism and the standard resolution of vaguenesswe need to examine possible worlds satisfying the following conditions: (a) until instant t ′ , just prior to t, their past matches perfectly the past of the actual world, (b) a divergence miraclea tiny, local event breaking the laws of nature of the actual world, sufficient in the circumstances for Nixon's pressing the button at t, occurs at t ′ at them, (c) they develop in conformity with the actual laws of nature after t ′ (and hence after t). In Lewis's view, the worlds satisfying conditions (a)-(c) are more similar to the actual world than any possible world where Nixon presses the button at t, but where the laws of the actual world remain intact. Thus, by virtue of Lewis's miraculous analysis, it is true that if Nixon had pressed the button at t, then there would have occurred a law-breaking event just prior to t.

Compatibilism and the ability to work miracles
Commenting on Lewis's rejoinder, van Inwagen (2004) argues that rejecting (1) by the compatibilist is tantamount to denying the following: (5) J was not able to arrange things in any way such that his doing so, together with the whole truth about the past, strictly implies the falsity of L. (van Inwagen (2004), 348) It is so by virtue of the interpretation of the 'can render a proposition false' phrase that van Inwagen (1983) adopts, and which is different from both Lewis's interpretations mentioned above. According to van Inwagen, s can render p false if and only if It is within s's power to arrange or modify the concrete objects that constitute his environment in some way such that it is not possible in the broadly logical sense that he arrange or modify those objects in that way and the past have been exactly as it in fact was and p be true. (van Inwagen (1983), 68) To bolster his stance against compatibilism, van Inwagen (2004) uses the concept of miracle. He argues that defining a miracle as an event whose occurrence would be inconsistent with the laws of nature tout courtthat is, defining it as Lewis doesis a mistake. Elijah's being in Babylon 10 minutes from now would not be a miracle under that definition even if Elijah is currently in Jerusalem. Elijah's act would not by itself be inconsistent with the laws of nature, but his accomplishment would clearly be a miracle. As a result, van Inwagen (2004, 349) defines a miracle as 'an event or state of affairs whose occurrence would be inconsistent with the whole truth about the past and the laws of nature'. The ability to perform miracles is the ability to perform miracles thus understood. Consequently, in light of van Inwagen's definition of a miracle and his rendering of the expression 'can render a proposition false', denying (1) entails the negation of (6): (6) J was not able to perform a miracle.
Van Inwagen (ibid., 349) supports his definition with the following remark: 'If I had proposed these definitions in an essay that was not about free will but about, say, the concept of the miraculous, no one would have taken exception to them.' Thus, he intends to strengthen incompatibilism by arguing that once the Lewisian compatibilist denies (1), he endows us with the ability to perform miracles. This is a reductio of compatibilism. For this reason, van Inwagen considers the price of accepting compatibilism as 'unacceptably counterintuitive'.

Against van Inwagen's concept of miracle
The credence we have in the proposition that we possess no ability to work miracles is higher than our credence in the proposition expressed by (1), interpreted via (5), and certainly higher than in the proposition that in a deterministic world, we are not able to do otherwise. However, if van Inwagen's attempt at supporting incompatibilism is to be successful, the above-quoted remark about his concept of miracle must be trueit must be true that his definition of a miracle is not arbitrary, that it is not just a definition of another technical term. This seems not to be the case. Let us begin with an obvious observation. Let us consider a paradigmatic example of a miracle, which is the cornerstone of Christianity: the resurrection of Jesus. 4 That event possesses, among other things, three essential features: (i) it is a natural or at least observable event, (ii) it violates the laws of nature, or at least is an event which would not have occurred solely as the result of what seem to us to be the relevant laws of nature applied to the existing initial conditions, and (iii) it is an effect of an act performed by a (benevolent) supernatural being. In contemporary literature on the religious notion of miracle, properties (i) and (iii)in one version or anotherare widely accepted as definitional (Hume (2007), 127;Swinburne (1970), 1, 11;Mackie (1982), 22;Hughes (1992), 190, 200;Clarke (1999); Mumford (2001), 192;Luck (2016), 267-268;Basinger (2018), 2, 4). 5 The problem is that van Inwagen's definition does not mention any supernatural agents. This makes van Inwagen's notion of miracle significantly different from the deep-rooted and most popular one. In addition, compatibilism does not entail that agents in a deterministic world are supernatural beingscomparable to the Jesus of Christianity in this respecteven if it were to entail that they have the ability to break the laws of nature. 6 Neither does it entail that they are assisted by such godlike entities. 7 My obvious observation does not articulate a clinching argument by any means. First, one could argue that there is also another way of thinking about miraclesthe way encapsulated in the contingency concept of miracle (Holland (1965), 43-44; see also Earman (2000), 10-11). This is the concept of a significant, unlikely event resulting from some extraordinary, happy coincidencethe concept of an event that can be taken as a sign, regarded with awe or made the subject of the vow, but that is an effect of purely natural causes. However, this is not van Inwagen's concept. Moreover, compatibilism does not entail that agents possessing the ability to do otherwise in a deterministic world haveby virtue of this fact alonethe ability to work miracles of the contingency sort, nor is it true that if they had that ability, that consequence would make compatibilism 'unacceptably counterintuitive'. Let us also note that in order to distinguish between a significant but ordinary happy coincidence and a contingency miracle sensu stricto one can stipulate that the latter must involve a direct divine intervention (Basinger (2018), 9-10, 27-28). 8 In such a case, van Inwagen's definition of a miracle would be inadequate also for the reason given in the previous paragraphit does not contain any condition concerning supernatural causation.
Second, van Inwagen's concept of miracle might be just a broad conceptsuperordinate to the religious notion. As we have noted, paradigmatic instances of miracles described in holy books are instances of events that violate or seem to violate the laws of nature. That property is epistemologically basic, and the epistemological function of miracles is most fundamental. Miracles are to provide evidence in favour of religious beliefs. What better evidence is there for the supernatural than the occurrence of events that transgress the laws of nature? For these reasons, many classic definitions of the religious concept of miracle include the property of being a law-breaking event (Aquinas (1981), 1.105.8, 1.110.4;van Inwagen (2007), 83, 127;Swinburne (1970), 3, 11;Mackie (1982), 19). Lowe (1987, 270) describes this conception of a miracle as the 'mainstream view'. Thus, introducing the concept of miracle as identical to the concept of a law-breaking event does not seem entirely arbitrary. This broad concept is used by Lewis. Van Inwagen's definition of miracle should also be construed along these lines, namely, as a definition of a lawbreaking event. This broad concept applies to religious miracles as well as to those alleged acts violating the laws of nature that are ascribed to people who are believed to possess supernatural powers on their own (e.g. it is believed in Hinduism that some mystics are able to levitate).
It should be emphasized that there are many sources of opposition to recognizing the property of law-breaking as one of the defining properties of miracles. Consequently, numerous philosophers would deny that the broad concept of miracle is legitimate at all. I have already discussed one such viewthe concept of contingency miracle. Another is motivated by the Humean belief that it is conceptually incoherent to think of any event that it occurs and violates the laws of nature at the same time. An important source of opposition comes from considerations of miracles under the supposition of indeterminism (Hughes (1992), 193-196;van Inwagen (1995), 48; see also Luck (2016), 272;Vicens (2016)). However, if miracles are not properly construed as law-breaking events, so much the worse for van Inwagen's argument. For this reason, the purpose of the remaining part of my article is to show that van Inwagen's definition is inadequate even in the best-case scenario for van Inwagen, that is, even if the broad concept of miracle is admissible (as I think it is).
Even if the broad concept of miracle can be considered legitimate, it does not mean that every analysis of that conceptthat is, every definition of a law-breaking eventis adequate. For it to be adequate, it must place the broad concept as close to the religious notion of miracle as possible. Using the term 'miracle' to refer to events that break the laws of nature merely in some technical sense would not be justified. In my view, the necessary conditions of adequacy of any such analysis are the following: (7) Events that are treated as paradigmatic examples of miracles within religious discourse should be classified as miraculous in the broad sense. (8) Events that are not considered miraculous within religious discourse, even though they are recognized there as natural or observable effects of acts on the part of supernatural agents, should not be classified as miraculous in the broad sense.
The hypothesis behind (8) maintains that if an event which satisfies the previously discussed uncontroversial conditions (i) and (iii), inherent in the religious concept of miracle, is nonetheless not classified as miraculous, then this must be because it is not regarded as breaking the laws of nature. Fulfilling condition (7) provides reasons for claiming that a given definition of a law-breaking event is not too narrow, while the fulfilment of condition (8) constitutes evidence that the definition is not overly broad. It is easy to see that van Inwagen's definition does not satisfy condition (8). Let us consider the resurrection of Jesus again, let us assume that it actually took place, and for the sake of simplicity, let us suppose that no other miracle had occurred before it. If van Inwagen's definition is to meet condition (7), then it should classify the resurrection as a miracle. Suppose that it does. Consequently, there is no possible world w such that the resurrection occurs at w, L is true at w, and the past of w is the same as the past of our actual world until the instant of the resurrection. That implies that proposition L expressing the conjunction of all the laws of nature of the actual world is false at our world. So far, so good. However, Christians believe that there are many effects of the resurrection of Christ, for example, various Easter customs, including the decoration of Easter eggs. Again, suppose that Christians are right, and we would not have decorated Easter eggs if not for the resurrection of Jesus. Yet, Christians do not see our painting of Easter eggs as miraculous at all. But if there is no possible world w such that the resurrection takes place at w, L is true at w, and the past of w is the same as the past of our actual world until the resurrection, then a fortiori there is no possible world which satisfies the enumerated conditions and in addition contains other events which occur in our world after the resurrection, such as our acts of painting Easter eggs. Thus, we come to the conclusion that in the scenario under consideration, any event which occurs in our world later than the resurrectionregardless of whether it is an effect of the latter or is causally independent of itsatisfies van Inwagen's definition and hence gets classified as a miracle. It appears that van Inwagen's definition not only does not meet condition (8), but also leads to absurd consequences.

The Humean account of laws and other possible counters
One could convincingly argue that there is no possible world containing an event that violates the laws obtaining in that very world because the laws of nature are at least exceptionless regularities. However, this Humean view of laws, although accepted by Lewis (e.g. Lewis (1973), 72-77;Idem (1979), 468-469), is rejected by van Inwagen. Van Inwagen allows for the possibility of such events being brought about by supernatural agents (van Inwagen (1983), 14;Idem (1995); Idem (2006)). Therefore, in his account, there is no contradiction in saying that proposition L is a law of nature and false at the same time. 9 But would accepting the Humean account of laws and interpreting the concept of a law-breaking event as applying exclusively to a relation between different possible worlds protect van Inwagen's definition of a miracle from my criticism? I believe it would not. As we have seen, the possible worlds that are key to Lewis's defence of compatibilism are worlds where a miracle occursa divergence miracle in relation to our actual worldfollowed, in a manner conforming to L, by an alternative action of the agent. Van Inwagen's definition correctly classifies events that are Lewisian divergence miracles as miracles relative to the actual world. The problem arises when we apply his definition to the effects of divergence miracles occurring in the relevant possible worlds in conformity with the laws of nature of our actual world: in van Inwagen's account, they also get classified as miracles in relation to the actual world. I take this to be fairly arbitrary. Within religious discourse, miraculous events, such as resurrections or turning water into wine, are systematically distinguished from those which are further effects of supernatural interventions, such as the previously mentioned decoration of Easter eggsthe effects consistent with the laws of nature designed by God. Van Inwagen acknowledges this fact when he discusses miracles in the religious context, for instance: Now suppose that God occasionally (and only momentarily) supplied a few particles with causal powers different from their normal powers. Such an action would cause a certain part of the natural world to diverge from the course that part of the world would have taken if He had continued to supply the particles in that part of the world with the usual complement of causal powers. Such a divergence would, presumably, spreadwith decreasing amplitudetill it encompassed the entire universe. The early stages of such a divergence [emphasis added] we shall call a miracle [van Inwagen's emphasis]. (van Inwagen (1995), 45) 10 More distant effects of supernatural interventions are not classified as miracles because they are not perceived as law-breaking. The fact that there might be no event that, while occurring at world w, breaks the laws of nature at w is not pertinent to the question of adequacy of van Inwagen's definition. 11 Clarke (1999) argues that even further effects of supernatural interventions in naturethe effects occurring by virtue of Lcan be correctly classified as miracles in the religious sense if they are intended by supernatural agents. 12 For example, if Jesus' intention in turning water into wine had been the subsequent, gradual, and nomological transformation of that portion of wine into vinegar, then the appearance of vinegar should be labelled a miracle. Van Inwagen's definition would allow us to classify such events as miracles, which might be perceived as weakening my argument. However, let us note that it would classify them as miracles for the wrong reason. Even if the nomological transformation of wine into vinegar had been miraculous, it would have been such due to having been intended by a supernatural being, not because it would have been a lawbreaking event.
The above remark suggests another possible way of deflecting my criticism. One could believe that decorating Easter eggs is not thought to be a religious miracle because it is not the direct effect of a supernatural interventionit is indirect only. The direct restriction could be held as an additional defining property of miracles in the religious sense. 13 Therefore, it would be a mistake to infer from the fact that indirect effects of supernatural interventions are not considered miracles that counting them as law-breaking events is inconsistent with the understanding of what it takes to break a law that is connected with the religious concept of miracle. This objection would undermine condition (8) as a necessary condition for adequate analysis of the broad concept of miracle.
In my opinion, this defence of van Inwagen's definition is ineffective. First, it is farfetched to suggest that the decoration of Easter eggs and similarly distant effects of alleged miracles are or should be regarded as law-breaking within the religious discourse. Second, the only reason why the direct restriction may appear justified is because actual reports of alleged miracles describe sequences of effects in which only the direct effect of a supernatural intervention is considered to be a law-breaking event. Only direct effects are miracles because contingently only direct effects of supernatural interventions (seem to) break the laws. Let us imagine that by virtue of a supernatural law designed and communicated to the people by God, each act of resurrection causes another event of rising from the dead to occur. The first act of resurrection is performed by Jesus and the following are further supernatural effects of his deedeffects deprived of any naturalistic explanation. Would we describe the subsequent resurrections as miracles, even though they would be only indirect effects of a supernatural intervention in nature? I think so. We would do this because those further effects of God's act would be thought to be violations of the laws of nature.

Conclusion
As far as van Inwagen's answer to Lewis's critique of the consequence argument relies on the former's concept of miracle, it cannot be regarded as convincing. Van Inwagen's definition of a miracle is arbitrary. Events which occur, in a manner conforming to the actual laws of nature, as effects of miracles are not miracles themselves. This is so independently of whether any law-breaking event occurs in a possible world whose laws it violates, that is, independently of whether the Humean view of laws is true. However, van Inwagen's definition does not allow for the discrimination between miracles and their nonmiraculous nomological effects, and, as a result, is too broad. It does not mean, of course, that Lewis's approach cannot be undermined in a different way. In particular, Lewis's account of a law-breaking event in terms of an event that falsifies the laws of nature in his sense of 'falsification' seems to be too narrow. In my opinion, van Inwagen's observation that Lewis's interpretation of a miracle is inadequate is correct, but his remedy for this problem does not work. Notes 1. Van Inwagen's (1983, 65) definition of determinism is uncontroversial: 'For every instant of time, there is a proposition that expresses the state of the world at that instant. If p and q are any propositions that express the state of the world at some instants, then the conjunction of p with the laws of nature entails q.' 2. According to van Inwagen (ibid., 6), ontologically speaking, laws of nature are propositions or 'whatever it is that are the bearers of truth-value'. Of course, only some propositions exhibit the property of being a law of nature. David Lewis's ontology of laws of nature is similar. Following Frank Ramsey, Lewis (1973, 73) defines a law of nature as a contingent generalization that 'appears as a theorem (or axiom) in each of the true deductive systems that achieves a best combination of simplicity and strength'. In line with this, laws of nature are taken throughout this article to be propositions. 3. Lewis also claims that if the strong interpretation is adopted, then the fifth premise of the consequence argument turns out to be false. This part of Lewis's critique is irrelevant to the purpose of this article and therefore will not be discussed here. 4. As Earman (2000, 12) remarks, 'for all the participants in the eighteenth-century debate on miracles, Hume included, a resurrection is the paradigm example of a miracle'. 5. Mumford (2001, 192) actually formulates a broader version of (iii), that is, he uses the concept of a supernatural cause. On property (i) specifically, see, for example, Mumford (2001), 192-193, andLuck (2016), 267-268. 6. I assume that the possession of the ability to cause law-breaking events is not sufficient for the status of a supernatural being. However, this assumption plays no role in my further arguments against van Inwagen. 7. As far as the religious concept of miracle is concerned, it is perhaps not analytically false to say that natural beings are able to work miracles. Perhaps there is a good sense in which Moses (a human agent) performed a miracle when he brought it about that his staff turned into a serpent. Even if it is true, the concept entails that the transformation of the staff was also an effect of an act performed by a supernatural being. The latter's involvement in this type of miracle is best conceptualized in terms of assistance given to a natural agent. See Stone (1998). Van Inwagen (personal communication, 2022) claims that 'a miracle performed by a natural being (without any assistance from a supernatural entity)' denotes a metaphysical impossibility, but it is not a contradiction in terms. 8. Contingency miracles could then be interpreted as events overdetermined by natural causes and supernatural influence. 9. Lowe (1987) also believes that miracles which violate the laws of nature of the actual world could conceivably occur in our world. However, unlike van Inwagen, Lowe holds that if such a miracle took place, the statements of the violated laws would nonetheless be expressed by true sentences. 10. See also van Inwagen (1995), 46, n. 3. Van Inwagen implicitly draws this distinction in his other works on philosophy of religion, in which he writes about miracles without referring to his discussion with see, for example, van Inwagen (2006), 114-115, 131, 148-149. According to van Inwagen (personal communication, 2022, any use of the word 'intervention' in connection with his attempt to define 'miracle' in van Inwagen (1995) is unacceptable: if God continuously supplies every creature with its existence and its causal powers, supplying a creature with different powers for a few seconds cannot be described as 'intervening in the world'. However that may be, the purpose of the quotation is to illustrate that in his other writings, van Inwagen regards only 'the early stages of a divergence' as a miracle. 11. Tognazzini (2016) claims that the whole rhetorical force of claiming that we are not able to perform miracles comes from the obvious truth that no-one is able to cause an event to occur in a world whose past and laws rule out its occurrence. He writes: 'That an event is inconsistent with the past and the laws of my world doesn't make that event a miracle in any interesting sense of the term unless that event also occurs in my world ' (ibid., 237). However, this is not the case. Let us assume that Jesus possessed the ability he is credited withfor example, the power to resurrect the deadbut he never exercised it. The fact that the closest possible worlds where Jesus exercises his power are worlds at which his deeds are consistent with the conjunction of the past and the laws of these worlds does not make it arbitrary to describe the ability Jesus has in the actual world in terms of the ability to perform miracles relative to the actual world. Certainly, he can break the actual laws of nature, and this is an incredible ability indeed. Van Inwagen's definition is overly broad, but not to the extent suggested by Tognazzini. 12. Although see Clarke (2003), where he offers a different definition of a miracle that does not have the consequence discussed above. 13. This view is shared by Mumford (2001, 200) and Hughes (1992, 201-202), among others; on the direct restriction, see also Luck (2016).