NECESSITY IN SINGULAR CAUSATION

M.J. GARCÍA-ENCINAS

I want to make sense of the view that singular causation involves a metaphysical necessary connection. By this I understand, where A and B are particulars, that if A causes B then in every possible world in which A (or an A-indiscernible) or B (or a B-indiscernible) occurs, A (or an A-indiscernible) and B (or a B-indiscernible) occur. In the singularist approach that I will favour causal facts do not supervene on laws, causal relata are best understood as tropes, causation is founded on the nature of its terms, and the necessity thus involved does not entail essentialism, determinism, and other usual problems.

The structure of the discussion

I. First part introduces Davidson's criterion for the identity of events, and makes three considerations:

I.1. There is a dilemma concerning a possible interworld reading of the criterion. While an interworld reading leads to a fragile event ontology for causation, (just) an intraworld reading implies that the same effect could have different causes. Fragile events are counterintuitive, and, I will argue, an effect cannot have different causes. 
	Two conclusions are drawn from these ideas. First, that (NC) if either of the terms of a given causal fact were different, the other would not be. Second, that events do not constitute the proper ontology of causation. Yet we can ask whether an interworld reading of Davidson's criterion should be accepted for the identity of the elements that constitute the ontology of causation:

(D1) x is y iff necessarily ((z) (z causes x ↔ z causes y) & (z) (x causes z ↔ y causes z))

I.2. The principle of causation could be false, and it does not follow from (NC), so there is no reason to accept (D1) on causal grounds. Still, we could accept that:

(D2) Iff x or y are causal relata, then x is y iff necessarily ((z) (z causes x ↔ z causes y) and/or (z) (x causes z ↔ y causes z))

I.3. The principle of identity of indiscernibles could be false, and it does not follow from (NC) so there is no reason to accept (D2) on a causal bias. Yet, given (NC) it does follow that:

(D3) Iff x or y are causal relata, then x is indistinguishable from y iff necessarily x and y have indiscernible causes and/or effects.

If (D3) is true, then causation involves a necessary connection between its terms in the following sense:

If A causes B, then in every possible world in which A (or any A-indiscernible) or B (or any B-indiscernible) occurs, A (or any A-indiscernible) and B (or any B-indiscernible) occur.

II. The second part of the paper argues that (NC) is satisfied by an ontology of tropes. This kind of ontology does not imply that the principle of identity of indiscernibles is true and avoids the fragility problem —so it precludes essentialism. Tropes also allow the principle of causation to be possibly false —so (NC) does not entail determinism. Finally, a causal ontology of tropes combined with (NC) allows a non-supervenient view of singular causation.

I. Davidson's identity criterion for events

Taking the case of a vase that breaks because of the blow of a hammer, the singularist philosopher of causality J. C. Ducasse wrote:

If our assertion aims to include the whole of the occurrence which took place, namely not merely the fact that the vase broke then, but also that it broke in these particular pieces, disposed in this particular manner, and so forth, taking in all the inexhaustible concrete detail of the occurrence and of its circumstances, then it can be shown that what was sufficient to it was also necessary to it.

This primary intuition on causality, or something close to it, could be read in these words of Davidson:

The fuller we make the description of the cause, the better our chances of demonstrating that it was sufficient (as described) to produce the effect, and the worse our chances of demonstrating that it was necessary; the fuller we make the description of the effect, the better our chances of demonstrating that the cause (as described) was necessary, and the worse our chances of demonstrating that it was sufficient.

A difference in either of the terms of the causal relation asks for a difference in the other. Cause and effect seem to imply each other. This line of reasoning could be underlying the identity criterion for events originally proposed by Davidson. Let causes and effects be events. The cause considered in all its full detail does not involve a different effect. The effect considered in all its full detail does not involve a different cause. So it seems that two events are in fact the same one iff their causes and effects are also the same. That is, if x and y are events, 

x is y iff (z) (z causes x ↔ z causes y) &
         (z) (x causes z ↔ y causes z)

Davidson’s criterion is in fact problematic. But I want to show that, in spite of this, the metaphysical intuitions behind it are correct. 

I.1. A dilemma concerning an interworld reading of Davidson's criterion

The criterion is a formula for the identity of events. But there is a question about its domain: does the criterion allow an interworld reading, i.e. does it apply across different worlds, or is its reading intraworld and it applies only within worlds? An interworld reading would say that in any possible situation the same event has the same cause and effect. An exclusive intraworld reading would imply that events have their causes and effects contingently. This choice, I believe, faces us with the following dilemma.
	First horn. An interworld reading of the criterion leads to a fragile event ontology for causation. For consider two distinct but only slightly different events which could be causes. They would make, we may suppose, a tiny difference in the effect. Following an interworld reading of the criterion, one of the causes would have another and slightly different effect from the effect the other cause would have had, had this second cause occurred instead. 
	Suppose that two slaves could give Socrates two different amounts of hemlock. One of the amounts is slightly more concentrated than the other. If Socrates drinks the first one, he is going to have a little bit more painful and slower death than if he drinks the other. In fact, say, Socrates is forces to drink the first amount of poison and, with it, he gains a few minutes for giving his last speech on how to overcome fear of dying. Given an interworld reading of Davidson's criterion it is true that, had Socrates drunk the other and slightly different amount of poison, his death would have been other. So any of the actual properties of Socrates' death belongs essentially to it. For if any of them had been different (because of the action of another different cause), Socrates' death would have been another death. Socrates' death is, then, a fragile event, an event with a very rich essence.
	Lewis has argued that fragile events are counterintuitive. We want to say that Socrates' death would have been different, had it been a little more slower, not that another death would have occurred instead. We do not want every actual property of Socrates' death to be essential. Fragile events seem undesirable. But then, an interworld reading of Davidson's criterion should be precluded.
	However, and this is the second horn of the dilemma, an exclusively intraworld reading of the criterion, implies that the identity of an event remains despite its causal relations. So any event —an effect in fact— could have had a different cause, and any event —a cause in fact— could have had a different effect. 
	But a given effect cannot have a different cause. For if it had, it would be another effect, which is contradictory. And a given cause cannot have a different effect. For if it had, it would be another cause, which is contradictory. This is what the following argument shows:

(1) Iff x in w1 and y in w2 have different properties then x in and y are different.

(2) If the cause of x in w1 and the cause of y in w2 are different, then x and y are different effects.

(3) If x in w1 and y in w2 are different effects, then x and y are distinct effects. 

Consequently,

(4) If x in w1 and y in w2 have different causes, then x and y are distinct effects.

Note that this reasoning does not rest on this other:

(1) Iff x in w1 and y in w2 have different properties (in w1 and w2), then x and y are different (in w1 and w2).

(2*) If x in w1 and y in w2 have different properties (in w1 and w2), then x and y are distinct.

It could be argued that (2*) is not true: x in w1 and y in w2 may have different properties and be the same entity. Supposedly, Socrates could have had green eyes instead of brown. There is a world in which Socrates has green eyes and a different world in which Socrates has brown eyes. Socrates has different properties in different worlds but, it can be argued, it is the same entity, Socrates, the one which has different properties in different worlds. The same seems true of events —if fragile events are unacceptable: x and y could have different properties and still be the same event. Socrates' death could have been faster or more painful. But it would have been Socrates’ death. So an event or an individual may be different in different worlds without loss of identity. Consequently, (2*) seems false: not everything that is different in different worlds is distinct.
	But these reflections are independent of (1)-(4). (1) is trivially true. It is an interworld application of the truism of indiscernibility of indiscernibles: discernibles, in different worlds, have different properties in those worlds, and vice versa.
	(2) follows from (1). For a property of a given effect is to be caused by “what” causes it —I’ll be back on this "what" in sec. II.2. Change the cause, make the cause different, and you change the property of the effect. The effect would, then, be different. So, if x is caused by z1 in w1, and y is caused by z2 in w2, and z1 in w1 is different from z2 in w2, then x in w1 is different from y in w2.
	And (3). An effect is whatever is caused. So, if an effect were made different, whatever would be so differently caused would be another effect. For if it were different and effect, it would be a caused difference, and then another effect. To make a different change is to make another change. To be a different effect is to be another effect.
	Maybe you are thinking that, by changing an effect, a new effect is made besides the effect that changes "in the first place", and not that the changed effect is another effect. Consider a situation in which, say, Socrates is (causally) dying painfully but that, because of an intervening different cause, his pain is relieved. This is a situation with two effects. And the first does not "change into" the second in any metaphysical sense. But this is not the kind of situation under consideration. Better, think of a situation in which Socrates (causally) dies painfully. Now compare this situation with a different posssible one in which Socrates (causally) dies without pain. I am defending that the effect in the first situation and the effect in the second are distinct effects. They are distinct because they are different effects. Socrates is the same person in both situations. Socrates' death is the same death —there is only a tiny difference in the way it happens. But the effect is other. Whatever would have been caused, if the second situation had happened instead of the first, it would have been a distinct effect.
	Or maybe you are first individuating the occurrences in the situation (say, Socrates' death, or Socrates, or whatever), taking any of them as the effect, and then considering the possible changes in the individuated entity. This way, if the changes are not essential to the entity that changes (causally), it could seem that the effect is preserved in the different situation. But there is no a priori reason for which the effect should be any entity. An effect is the result of the action of a cause. The effect is a provoked change, and if it had been a different provoked change, "it" would have been another change. Different effects are other effects.
	From (2) and (3) it follows that (4) had the cause been different, the effect would have been other. So the very same effect cannot have a different cause.
	By a parallel reasoning: (3') if x and y are different causes in different worlds, then x and y are distinct causes. And, as (2') if x and y have different effects in different worlds, they are different causes at different worlds, then (4') had an effect been different, the cause would have been other.
	An exclusively intraworld reading of Davidson's criterion allows that the identity of causes and effects remains despite their causal relations. So, if the previous argument is correct, this exclusive reading is unacceptable. But an extraworld reading seems equally unaceptable for it conveys a counterintuitive fragile event ontology for causation. Is there any solution to the dilemma?
	the consideration of the dilemma has delivered two lessons The reason why an exclusively intrawold reading is unacceptable is that the same effect (or cause) cannot have different causes (or effects). So the first lesson is that causation involves a metaphysically necessary connection between its relata. Causal facts are grounded on the nature of the related terms: 

(NC) If either of the terms of a causal fact were different, the other would not be.

(NC), like the interworld reading of Davidson's criterion, would imply a fragile event ontology for causation. So the second lesson, I contend, is that neither events nor, by the same token, individuals or things are causally related. For any event, or individual, or thing, could keep its identity and be different —how different it can be while being the same nobody can say; but it can be different. The difficulty, then, is to find the kind of elements that satisfies (NC) without problems of fragility. But this will be the object of the second part of the paper because another question remains to be answered: should we accept an interworld reading of Davidson's criterion for the kind of elements, whatever it can be, that are causally related? 
	(NC) is incompatible with just an intraworld reading of the criterion. But should it be accepted, on causal grounds, that if x and y belong to the kind of elements that constitute the ontology of causation,

(D1) x is y iff necessarily ((z) (z causes x ↔ z causes y) & (z) (x causes z ↔ y causes z))?

I.2. (NC) does not imply that everything is determined

It has been argued that if causation involves a necessary connection then every occurrence must be caused. Consider this reasoning by Ducasse:

The supposition that the identical vase could have broken as it did when it did in the absence of the identical hammer blow, involves a contradiction, and we may therefore conclude that that hammer blow, such as it was in all its concreteness, if it was sufficient to the full concrete effect, was also necessary to it.

It is worth while to stress the point which the above argument incidentally brings out, namely that the universality of causation, namely, the assertion, ‘Every change or state has a cause’ or ‘No change occurs and no state persists without a cause’ is known to be true merely as a corollary of the law of identity when the word cause is once properly defined, provided only that anything occurs at all.

There are two errors in this reasoning. I consider the first one, a wrong inference, in this section. The second one, a controversial assumption, is examined in the following section. 
	A hammer blow causes the breaking of a vase. Ducasse starts from the idea that the identical vase could not have broken as it did when it did in the absence of the identical hammer. This, he says, involves a contradiction. If the breaking of the vase (the occurrence that is the effect in the situation) had been different it would have not been the same occurrence, i.e. the same breaking of the vase. This is (NC) applied to the effect: 

(I) The same effect cannot have a different cause (for then it would not be the same occurrence —and this is a contradiction).

From (I) Ducasse concludes that the same breaking of the vase cannot but be caused by the identical hammer blow, i.e.,

(II) A given effect cannot be caused by another cause.

This is what the first quoted paragraph asserts. Now, from (II) he concludes, at the second paragraph, that,

(III) A given occurrence cannot but be caused.

But (III) does not follow from (II). From the idea, if true, that a given effect cannot be caused by another cause, it does follow that any other effect should be caused by another cause; but it does not follow that any occurrence should be caused. If an occurrence is an effect, by (II), it must have the cause it actually has —otherwise it would be another occurrence. But it does not follow, from (II), that any given occurrence must have a cause. For this to be inferred we need to suppose that the considered occurrence is also an effect.
	But there is nothing in the idea of occurrence that leads to the thesis that it is an effect. Such as Thomas Aquinas put it, 

Since to be caused is not essential to the meaning of being as such we can meet with a being that is uncaused.

A necessary connection in causation, in the terms (II) prescribes, does not imply that anything that happens is caused. It does not imply that the principle of causation is true. For similar reasons, (NC) does not imply the principle of causation either. No effect can be caused by a different cause that its actual cause. But this does not make everything to be caused. No cause can cause a different effect than its actual effect. Again this does not make everything caused.
	This result has two important consequences. The first one is, of course, that the necessity involved in causation does not imply that everything is determined to happen. So even causal determinism is more than causal necessity. More to the point, the second consequence is the impediment of an identity criterion, in causal terms, for every element of the kind to which related occurrences belong. For not every element of this kind needs to be involved in causal relations. So nothing compels, on causal grounds, the acceptance of (D1). 
	Yet (II) implies that, necessarily, same effects have same causes and same causes have same effects. (II) does not gives us an identity criterion for every element of the kind to which causally related occurrences belong. But it gives us an identity criterion for the causally related occurrences themselves:

(D2) Iff x and y are causal relata, then x is y iff necessarily ((z) (z causes x ↔ z causes y) and/or (z) (x causes z ↔ y causes z))

The question remains whether (D2) should be accepted on causal grounds.

I.3. (NC) without the identity of indiscernibles

The second error of Ducasse is the use of an ungrounded assumption. He presupposes a principle that could be false: the principle of identity of indiscernibles, i.e. the principle that distinct occurrences are different. But the possible falsity of this principle precludes the inference from (I), i.e., (NC), to (II). 
	Or course, (NC) does not imply the principle of identity of indiscernibles by itself. (NC) says that the same effect cannot have a different cause, and that the same cause cannot have a different effect. So it is consistent with the negation of the principle. 
	But if (NC) does not imply the principle of identity of indiscernibles, there seems to be no reason why (D2) should be accepted on causal grounds. The very same cause could have indiscernible effects, and the very same effect could have indiscernible causes. So it would be false that x and y are the same effect iff "they" have the same cause. And it would be false that x and y are the same cause iff "they" have the same effect.
	(NC) leaves open the possibility that indiscernible effects occur. But if they do occur, (NC) forbids them to be caused by different causes. And (NC) leaves open the possibility that indiscernible causes occur. But if they occur, (NC) forbids them to cause different effects. That is, from (NC) it follows that, necessarily, indiscernible causes have indiscernible effects, and the other way round:

(D3) Iff x and y are causal relata, then x is indistinguishable from y iff necessarily x and y have indiscernible causes and/or effects.

Causation is grounded on the nature of its terms. A given effect cannot have a different cause (for otherwise it would be another effect), and a given cause cannot have a different effect (for otherwise it would be another cause). So, necessarily, indiscernible effects have indiscernible causes, and vice versa.:

If A causes B, then in every possible world in which A (or any A-indiscernible) or B (or any B-indiscernible) occurs, A (or any A-indiscernible) and B (or any B-indiscernible) occur.

This resumes the necessary connection between the terms involved in a causal relation; a necessary connection that is directly implied by (NC). This necessary connection can do without the aid of the questionable principles of causation —thus, avoiding determinism— and of the identity of indiscernibles —avoiding greater problems than determinism. Without them, it is true, no criterion of identity can be drawn from the nature of causation. 
	Some pages ago, (NC) left us with the following difficulty. The same effect cannot have different causes, and the same cause cannot have different effects. But then, events, individuals, and objects cannot be causally related; otherwise they would have very fragile essences. And fragile essences are undesirable. The difficulty, then, is to find the kind of elements that satisfy (NC) without problems of fragility. 

II. The ontology of causation

Given (NC), if events, such as Socrates’ death or the breaking of a vase, or individuals, such as Socrates or a vase, were causes and effects, a tiny difference in their effects or causes, would make them other individuals or events. This is an unwelcome consequence. Suppose that there is a causal relation between the event that is the burning of squirrel Martha’s tail and the event that is her flying over a fire. Given (NC), had the fire been stronger, the burning of her tail would have been another event. This runs against our intuitions. The burning of Martha’s tail could still be the same event, only some of its properties would have been different. The tail would have lost some more hair, but the burning could be the very same event it is. 

II.1. Tropes

Maybe the burning of Martha's tail is not the effect and the fire is not the cause in the example. Maybe the effect in the situation is the bundle of properties that the burning has. Maybe the cause is (at least, or among others) some of the properties of the fire.
	If causes and effects are properties —bundles of properties—, (NC) holds without problems. There is no difficulty in the idea that, necessarily, different properties in the fire cause different properties in the burning. And different properties in the burning are other properties of the burning! So, necessarily, different properties cause distinct properties. If properties constitut the ontology of causation, (NC) holds without fragility problems. At least, this is true of determinate, and undeterminable, properties.
	Fragility is not a problem for elements that would lose their identity if they were different. Determinate properties are of this kind. Different determinate properties are distinct properties. Suppose that the length of this table is exactly two meters and two cms. This is a determinate property. Cut the table. Its new length is, say, one meter. The second length is a different and other property (of the table). You cannot make determinate properties different without getting other properties. 
	(NC) holds naturally if determinate properties are causally related. Now, as we have seen, (NC) is neutral with respect to the status of the principle of identity of indiscernbiles and to the status of the principle of causation. We want to keep these advantages. So we need an account of specific properties that is consistent with the possible falsity of these two principles. There is nothing in the concept or notion of property that makes every property an effect. And there is nothing in the being, or occurrence of properties that makes every property an effect. So the denial of the principle of causation should be consistent with any account of properties. I leave the discussion of this point for the next section. Now, I want to show another two fundamental advantages of determinate properties.
	First. Let´s accept that laws are nomological relations between determinable universals. Determinate properties would solve preemption situations in the same way that fragile events would. Remember that in situations of preemption two, or more, causes compete without solution for the same effect, under a given account of causation. An ontology for causation in terms of determinate properties preempts preemption. Consider the sum of determinates that is the effect. It cannot be caused by a different sum of determinates, i.e. it cannot be cause by a different cause. For a different cause would cause a different sum of determinates. Different determinates are other determinates. So a different cause would have caused another effect. A paradigmatic case of preemption is the following one of Lewis (1986):

You shot a man who is being stalked by seven other gunmen. As it actually happens, the man dies on Tuesday morning, face down on the ground, his heart pierced by your bullet, with an entry wound in his back and exit wound in his chest. Without your act he would have died on Wednesday evening, slumped in his chair, his heart pierced by someone else’s bullet, with an entry wound in his chest and an exit wound in his back. (195)

Suppose that the causally related terms in the situation are events. Your act has preempted the death of the man to be different and caused by another shot. The laws governing your shot and the laws governing the impeded shots are the same laws. So the nomological relations in the situation are of no help for distinguishing the actual cause from the preempted one. A possible solution is to adopt a fragile event ontology. We know that if another shot had occurred instead of yours, the death of the man would have been slightly different (the heart of the victim being pierced in a different way, etc.). Let's allow the death of the man to have an essence rich enough to include these differences, no matter how small. Then no different cause can cause this death. The actual effect that is the actual death would not have occurred if another gunman had shot.
	Suppose now that the causally related elements in the situation are not events, but their actual determinate properties. Then preemption does not arise either. The determinate properties of the actual death are caused by the actual properties of your shooting. If the determinate properties of the shooting had been different, the determinate properties of the death would have been different. So the effect would have been another effect.
	Second. An ontology of determinate properties for causation avoids implications on the essence and fragility of the elements that possess them. Even if the whole sum of properties that constitutes an effect belongs to the same event or individual, this does not make them have fragile essences. The properties of given event could change causally while the event remains the same one. Socrates’ death could be the same death, even if a bit more painful, had he drunk another and slightly different amount of hemlock. This is so, at least, as far as we do not decide that to be the painful it was, is a defining characteristic of his death. But even if it is essential, it is not so because it is (necessarily) caused. The death of the shot victim would have been the same death, even if its determinate properties had been different and other. Or so its seems. If the ontology of causation is in terms of determinate properties, we escape the fragility problem, and consequently, any kind of causal essentialism. 
	In short, determinate properties fit (NC) and, at the same time, avoid problems of preemption and fragility, and do not affect the essences of the elements that possess them. These are good news. But something remains unsolved. Determinate properties can be either universals or tropes. The next section argues that tropes have an important advantage over universals: they are cheaper when dealing with indiscernible possibilities. 

II.2. Necessity in non-supervenient singular causation

The singular approach to causation (or non-supervenient view on singular causation) is the view that singulars may be causally related independently of whether they fall under laws, being the laws causal or not. A usual argument for this view is the following possible situation. Suppose there is a law that relates universal properties P and Q. (You may suppose that P and Q are determinate universals). Suppose also that the state of affairs a1 being P causes the state of affairs b1 being Q, and that a duplicate state of affairs, a2 being P, causes b2 being Q. Two distinct causal relations are then established in the situation. But the law is unable to determinate them Given the law, a1 being P may be the cause of b2 being Q; and a2 being P may be the cause of b1 being Q. So laws are not enough for giving an account of the causation: some singularist component is lost in the meanwhile. To this extent, I think, everybody agrees. But disagreement rapidly emerges while providing an account of this singularist component. I will consider two main accounts and, in fact, two opposite views on the nature of causation itself.
	On the one hand, there is what could be called the causal hyperrealist view. This view has been defended by singularist philosophers such as Tooley, Woodward, and Carroll. They argue that the possibility of indiscernible causal states of affairs shows that causal relations hold independently of the laws that, supposedly, govern them. The situation in the previous paragraph presents two distinct causal states of affairs that are indiscernible. Causes, on the one hand, and effects, on the other, share their nature: they instatiate the very same universals. But they stand in distinct causal relations. So causal relations hold independently of the nature of their relata involved. That there are two causal states of affairs means, then, that the causal relation itself instantiates twice.
	Causal hyperrealism implies that the instantiation of the causal relation occurs despite the nature of the related elements. So there is a possible situation in which states of affairs A and B are causally related, and another situation in which a replica of A and a replica of B are not causally related. Causal hyperrealism makes causation something magical and mysterious. So it is counterintuitive. Yet more, if (NC) is right, causal hyperrealism is false. Causal relations are grounded on the nature of their elements.
	The other account I am quickly considering is that of Armstrong or Fales. This is usually the neohumean causal supervenience view. It would read, I think, the exact duplicate situation in the following way. It is true that the law does not distinguish the two causal states of affairs that in fact happen to occur. But this does not mean that their occurrence is independent of the law. Following the law, states of affairs constituted by individuals instantiating P are causally related with states of affairs constituted by individuals instantiating Q  —but not with different states of affairs. It is nomologically true that everything that is P is causally related with anything that is Q. It is also true that there are two distinct causal states of affairs. But this can be explained taking into account that two distinct individuals, a1 and a2, instantiate P and two distinct individuals, b1 and b2, instantiate Q. The singularist element is provided by the individuals that instantiate the universals. The causal character of the states of affairs, on the contrary, supervenes on the nomological relation that holds between the universals themselves.
	The neohumean causal supervenience view is expensive where, maybe, there is no reason to pay so much. As we have just seen, it needs individuals for offering a plausible account of exact causal replicas. It implies that there is not actual causation without individuals. Nomological relations between universals govern causal relations. But without individuals instantiating the appropriate universals there are no singular causal states of affairs. (Note that this is so independently of whether you hold, as Armstrong, that there are not universals ante rem). 
	If properties are universals, the possible falsity of the principle of indiscernibles, then, shows that the ontology of causation is not in terms of universals, but in terms of individuals instantiating universals. Consider the following argument. The theses:

(i) Causes (and effects) are sums of properties

(ii)Two causes (and effects) can resemble exactly 

(iii) Causes (and effects) are sums of universals,

form an inconsistent triad. If (i) and (ii) are true, (iii) must be rejected. If causes (or effects) are nothing but sums of properties, and if properties are universals, then there cannot be two (or more) indiscernible causes (or effects). For universals are ubiquitous: the same universal is in any of its instantiations. So in order that there can be two or more indiscernible causes (or effects), causes (or effects) are not sums of universal properties.
	Of course, one can maintain (iii) and reject (i). ((ii) is a denial of the principle of identity of indiscernibles.) This is Armstrong's position. Causes and effects are not just sums of properties. Causes and effects are properties instantiated by individuals, i.e., states of affairs. Individuals, to be sure, have their own particularity. They are not just sums of properties either. 
	The possible falsity of the principle of identity of indiscernibles shows that, if properties are universals, the ontology of causation of causation is not in terms of properties alone. Rather, states of affairs are causally related. Individuals, with their own particularity, are necessary for the occurrence of causal facts. But this is against intuition.
	Maybe individuals are not just sums of properties but also a particularity. Maybe properties always belong to some individual —so every property in the cause (or effect) belongs to some individual. But neither of these possibilities implies that individuals, or their particularities, have any part in the holding of causal relations. Nor there is anything in causation itself by which individuals should play an active role for its occurrence. Yet more, the properties that constitute a cause (or an effect) could belong to distinct individuals. Which individual, with its particularity, would be the particularity of the cause (or effect) in that situation? There seems to be no reason to suppose that causes and effects are sums of properties plus a particularity in which the properties inhere.
	Kepa smokes marijuana, takes a drink of whiskey and falls asleep. It is some properties of the marijuana he smokes, some properties of the whiskey he drinks, and some properties of Kepa's body and brain, the cause of the actual properties of his sleep. The properties in the cause belong to different individuals: Kepa, the marijuana, the whiskey ... But the cause is not an individual. Nor any individual is part of a cause just because the properties that cause happen to belong to it. The cause is not a sum of properties and a particularity, even if every property in the cause is "attached to" a particularity. 
	If properties are universals, causes and effects are not only bundles of properties but also some individuality. The cause in the situation in which Kepa falls asleep, would be an entity on its own. The causal properties of Kepa’s body, and the causal properties of the marijuana, and the causal properties of the whiskey, and whatever may be the properties that are conforming the cause of the sleep in the situation, would belong to some particularity. But which entity could it be? 
	Tropes easily avoid these problems. Maybe they, like universals, need some supporting particularity —though this must be argued. But this does not involve the particularity in the causal relations. If properties are tropes, causes (and effects) can be mere sums of properties. No particularity is needed for allowing the possibility of indiscernible causes (or effects). Tropes are not ubiquitous. So indiscernible causes (or effects) are, necessarily, distinct sums of tropes.
	Tropes also allow a new view on singular causation. In the case of two duplicate causal facts, the hyperrealist and the neohumean supervenience views on causation, assume that causal duplicates are exactly alike because they are instances of the same universal properties. The distinctness of the singular causal states of affairs in the situation is then elucidated, either by defending distinct instantiations of the causal relation itself —thus, losing the grounding of causation; or by resorting to the particularity of the individuals that instantiate the nomologically related universals —thus, losing the singularity of causation. A trope causal ontology provides an in between and, I believe, straightforward account of the singularist component in the exact replica situation, and of causation itself. On this account we do not have to pay singularity in exchange for grounding, nor grounding in return for singularity.
	If (some) tropes are causally related, singular causation does not supervene on laws, so singularity is safeguarded. It is the particularity of tropes that accounts for the particularity of every distinct causal fact. In the duplicate case, there is a trope causal relation holding between P1 and Q1 (or between the fact that a1 is P1, and the fact that b1 is Q1). And there is a distinct but indiscernible trope causal relation holding between P2 and Q2 (or between the fact that a2 is P2, and the fact that b2 is Q2). Causal relations do not hold because P and Q are instantiated in particular individuals. The only role, if any, that particular individuals play is that the causally related tropes happen to be "attached to" them.
	But also, the necessary connection is safeguarded and causality is founded on the natures of the related elements. P1 is causally related with Q1, but not with any other different property. P2 is causally related with Q2 and not with any other different property. It is true that P1 could have been causally related with Q2 and that P2 could have been causally related with Q1. But this does not mean that causation holds independently of the natures of its relata. For this to be true it is necessary to show that P1 could be causally related, not with any indiscernible of Q1, but with a different property.
	It follows from (NC) that there is a necessity in causation. This necessity is happily grounded on the elements of causation if these are tropes. If P1 causes Q1, necessarily, if P1 (or any indiscernible from P1) occurs then Q1 (or any indiscernible from Q1) occurs. If P1 causes Q1, necessarily, if Q1 (or any indiscernible from Q1) occurs then P1 (or and any indiscernible from P1) occurs. This is so, not because P1 and P2 on the one hand, and Q1 and Q2 on the other, share their nature, but because their natures resemble exactly. That similar causes have similar effects is then a consequence of the necessity in singular causation: causal relations are founded on the particular natures of their relata.
	(I should make a stop right here. Q1 may be caused by P1 or by any indiscernible from P1. Some pages before (section 1.1., argument for (NC), step (2)) I said that "a property of a given caused occurrence is to be caused by "what" causes it. Make the cause different and then you change the property of the effect: the effect would, then, be different". And also (3), if x and y are different effects, then x and y are distinct effects. 
	It seems, then, that if the cause of Q1 were P2 instead of P1, Q1 would be different. So Q1 would not be Q1. It seems, consequently, that Q1 cannot be caused, not only by a different cause, but by a distinct cause either. In other words, it seems that Q1 must be caused by P1.
	Not so. P1 and P2 are indiscernible properties. So if Q1 is related to P1, the trope relation that holds between them is indiscernible, not different, from the trope relation that would hold between Q1 and P2. Q1 would have had a distinct property, had it been related with P2, not a different property.. (2) and (3), then, do not apply.) 
	That indiscernible causes have indiscernible effects is a consequence of the particular nature of particular properties causally related. That similar causes have similar effects is not, then, the root and reason of causation. Contrary to the idea that has guided the antisingularist tradition that succeeds Hume, similarity is not the foundation of causation, but its most straightforward consequence.

Conclusions

Causation involves a necessary connection between its relata in the following sense:

If A causes B, then in every possible world in which A (or any A-indiscernible) or B (or any B-indiscernible) occurs, A (or any A-indiscernible) and B (or any B-indiscernible) occur.

This necessary connection trivially follows from a deeper metaphysical thesis, namely,

(NC) If either of the terms of a given causal fact were different, the other would not be (the same one).

This thesis, in an important sense, conforms to our intuitions on causation. Necessarily, different causes make another effects, and different effects entail another causes. But, in an equally important sense, the thesis seems counterintuitive. When we say that this house is destroyed by a bomb, implying a causal relation somewhere, we do not mean that if the bomb had been thrown differently, the destruction of the house would have not occurred. This would imply that events are too fragile. Tiny differences would make them other events.
	I have argued that (NC) gets its proper place if tropes are causes and effects. Tropes avoid the fragility problem. The bombing could have been different and the destruction could have been the same. For it is their properties, not the events, that are causally related. And it seems unproblematic that if the particular properties of the bombing had been different, (at least some of) the particular properties of the destruction would have been different too. Different particular properties are other particular properties. So fragility is not a problem.
	The combination (NC) plus tropes has many other advantages. Necessarily, different tropes cause different tropes. And different tropes are distinct tropes. So, different tropes —it does not matter how tiny the difference betweem them is— cannot cause the same effect. Preemption dissolves. 
	(NC) does not affect the essence of the elements that possess the properties involved in causation. The particular properties of any event (or individual) could change causally without affecting the essence of the event. Of course, essential particular properties could be caused or disappear, but they are not essential because they are involved in causal relations. So the necessity involved in causation avoids problems concerning essentialism. 
	"Being a trope" does not entail "being caused". And (NC) is equally consistent with the denial of the principle of causation. The necessary occurrence of the sum of properties that is the effect (given its cause, or any indiscernible cause), does not make every other sum of properties an effect. So the necessity involved in causation does not imply that determinism rules the world. 
	(NC) is also consistent with the denial of the principle of identity of indiscernibles. Besides, in situations of causal duplicates tropes nicely allow the distinction of the duplicates. And they do so without involving elements, like the individuals that possess the properties, that seem foreign to causality.
	Moreover, the metaphysical necessity in causation that follows from (NC), combined with an ontology of tropes, assures the founding of the relation in the nature of its terms without the aid of natural laws. The relation between laws and causation, if any, could well be one of laws supervening upon causation. At least, contrary to the dominating Humean tradition, singular causation seems an excellent supporting basis for regularities.
	In general, (NC) and the ontology of tropes constitute the pillars of the non-supervenient view of singular causation.

RUTGERS UNIVERSITY
NEW BRUNSWICK, NJ 08903
USA

NOTES