b. Reified absences
The second option, reifying absences, also comes at a theoretical cost. Indeed, the cost might seem prohibitively high. If we reify all of the absences in the world, we will end up with Truthmaker Maximalism (2.1T.1). First, this involves a potentially very heavy cost in terms of ontological baggage. One must add one or more entirely new categories of things (absences, non-beings, privations, etc.), and one must populate the world with an infinity (at a very high level of cardinality) of such things. Absences of many kinds are potentially nearly ubiquitous. Think how many absences of hippopotamuses there are, to take just one example, not just in many stretches of river in Africa, but throughout the center of the earth, in every teaspoon of sugar, and throughout the vast stretches of outer space. In addition to the absence of hippopotamuses in general, we would have to consider the absences of this or that particular hippopotamus. We might have to recognize the existence of absences of merely possible hippopotamuses, to say nothing of all of the absences of impossible entities, like round squares.
Not only does Truthmaker Maximalism's addition of an infinite number of negative facts weigh against the theory by way of inflating its ontology, but also it requires (as we saw in Chapter 2) a huge number of mysterious necessary connections between positive and negative facts (PMeth 1.2). It must be impossible, for example, for the presence of water and the complete absence of water to coexist in the same place and time, and it must also be impossible for both the presence and the absence to be absent! There must be some necessary connection between the existence of a hippopotamus in some specific location and the non-existence of a hippo-absence in that same place, and a converse necessary connection between the existence of an absence of a hippopotamus somewhere and the non-existence of a hippopotamus there and then. This makes it impossible to change the world simply by deleting things. Each deletion necessarily involves a simultaneous creation. Deleting hippopotamuses necessarily increases the population of hippo-absences.
These objections can be at least partially met by introducing totality facts as the fundamental connections between universals and particulars. A negative atomic truth like ‘b is not F’ is made true by some totality fact that includes the universal F-NESS but not the particular b. Such totality facts could serve as the relata of negative causation.
Alternatively, we could make use of the absences that we discussed in Section 17.4, especially the view according to which absences were identified with bundles of bare particulars and spatial-location qualities, with no associated corporeal qualities like mass or charge. A complete absence of matter from a spatial region, that is, a vacuum, could be identified with a plurality of such absence-bundles, one for each bare particular, and each bundling that particular with the spatial region but with no corporeal qualities. We might need to add to this plurality the totality fact for the corporeal universals, like mass and charge, to ensure that our vacuum-fact hasn't left out any possible bodies.
In addition, this ontological inflation can be contained to some extent if we can limit, perhaps severely, the class of absences that are needed in a full account of negative causation. In addition, if we can limit the class of negative entities to a small enough range, we might be able to find positive entities with which the absences can be identified, entirely eliminating the ontological cost of absences.
A promising strategy for limiting the range of absences to a manageable size is John Haldane's (2007) proposal of privative causality, which builds on a long Aristotelian tradition. On this view, absences are causally efficacious only by connection to some causal power or disposition of a positive substance or process. In some cases, a thing's nature makes use of certain absences, as in the case of the firing of a nerve synapse by means of the absence of certain blocking chemicals normally present in the synapse. In other cases, a thing's nature requires the presence of some feature, either within the thing itself or in its environment. The absence of this normal condition causes deformity or failure on the part of the positive thing whose nature is thereby thwarted. We can postulate that in these cases, the absence corresponds to the position of a real, negative property, either by the thing itself or by something in its environment. Thus, the absence of water is a real property of the immediate environment of the drought-stricken plant, and the absence of blocking chemicals a real feature of the nerve synapse during firing. We can deny, however, that there are any absences except in such a relation to power-bearing individuals. The absences come into being by virtue of the coming to be present of some appropriate bearer of causal powers.
On this view, a real absence of hippopotamuses can occur only in relation to something that requires the presence of hippopotamuses as part of its normal operation. There could be an absence of male hippopotamuses in the immediate environment of some female hippopotamus, but no such absence occurs in the remoteness of outer space.
Since absences always involve the presence of some appropriate entity, we could take the further step of supposing that the absence is actually a feature of the entity itself. The absence of water in the environment of the plant could be taken to be a property of the plant itself. This would involve understanding the plant to extend somewhat into its immediate environment.
We would still need to expand our ontology to the extent of adding fundamentally negative properties, and we will still need to postulate some necessary connections between negative properties and their positive counterparts. These additions could be limited, however, to just those cases in which the dynamic natures of the things involved licenses the attribution of causality to the negative properties.
It is interesting to note that all of Schaffer's examples fit the privative model. In each case of negative causation, we have either a living thing or an artifact whose normal condition involves the absence in question. In each case, the absence has an effect either by being incorporated into a special kind of operation, like firing a bullet or activating a nerve synapse, or by depriving some operation of one of its necessary conditions, like depriving cells of the oxygen they need for respiration.
Notes
1. There are interpretations of quantum mechanics according to which all change is determined by prior conditions, including some versions of the Everett many-worlds interpretation and of the Bohm-de Broglie pilot-wave interpretation. However, all of these deterministic interpretations face serious objections. The many-worlds account has the problem of explaining the meaning of the probabilities associated with quantum predictions (since on that account all of the possible results occur with probability 1). The most promising solution, the Albert-Loewer many-minds interpretation (Albert and Loewer, 1988), re-introduces indeterministic causation into the picture, since individual minds are caused to travel along one branch of the evolving ensemble of branches in a probabilistic fashion. The Bohmian account has to introduce probability at the very beginning of the universe's history, suggesting a probabilistic cause of that initial state.
2. Parenthetically, trumping raises an interesting meta-philosophical or methodological question. In its original form (in Schaffer 2000), trumping involved two spells belonging to two different orders of magic, one higher and one lower. Such an example seems very remote from our view of how the actual world works. If the task of the theory of causation were simply conceptual analysis, then this remoteness from actuality wouldn't seem to matter, so long as our intuitions about the case are clear. If, in contrast, we are after the best theory about causation as a real feature of the world, then only examples that are clear examples of causation and non-causation in the actual world (or at least, in worlds we have reason to believe are genuinely, metaphysically possible) should count.
However, as Lewis (2000) points out, it's quite possible that something like trumping occurs in the actual world. For example, if Pauli's exclusion principle absolutely prevents an electron from going into a particular state because that state is already occupied by a different electron, we might want to say that the exclusion
principle preempts by trumping any other process that might also, in the absence of the exclusion principle, have prevented the electron from entering that state.
28
Discrete and Continuous Causation
Causal Connectionists need to provide an account of causal linkage and of causal direction. However, before we can turn to the details of such an account, we must distinguish between two kinds of causal connection, namely, discrete and continuous. A causal connection is discrete when there is either a direct causal link between the cause and the effect, or there is at most a finite number of such links between the two. Whenever we find an infinite number of intermediaries between cause and effect, we have a case of continuous causation.
Def D28.1 Causal Betweenness. Event z is causally between events x and y if and only if x causes z and z causes y, or y causes z and z causes x.1
Def D28.2 Linear causal order. A set of events S is a causal linear order just in case for any three distinct events x, y, and z in S, one of the events is causally between the other two.
Def D28.3 Discrete Causation. The causal connection between x and y is discrete if and only if x and y are causally connected, and the linear casual order consisting entirely of events between x and y is finite. (Compare Def D19.1 Immediate Causation.)
Def D28.4 Continuous Causation. The causal connection between x and y is continuous if and only if x and y are causally connected, and there is an infinte linear causal order consisting entirely of events between x and y.2
28.1 Is All Causation Discrete?
There seems to be good reason to think that there cannot be causation across a temporal gap. That is, if C causes E, then there cannot be a time gap between the end of C's existence and the beginning of E's existence. After all, to talk of causation as involving a causal connection between two entities seems to imply that the two entities both exist at the time at which they are connected.
Partial Simultaneity of Discrete Causes. If x is a cause of y, and x and y do not belong to any one process, then x's time of occurrence includes the time at which y begins.
In fact, it seems that we can go further than this and insist that when a cause and effect are connected discretely, they must be fully simultaneous, beginning and ending at exactly the same time. If a cause pre-exists its discrete effect, then it seems that we can divide the supposed cause into two entities, one that exists entirely before the effect and the other that begins to exist at the same time as the effect. It is only the latter that is, strictly speaking, causally connected to the effect. Similarly, if an effect endures after the end of its cause, we can make a similar distinction between the effect's earlier and later parts.
Full Simultaneity of Discrete Causes. If x is a discrete cause of y, then x and y begin and end at the same time.
It also seems plausible that some causes are earlier than their effects, especially if causation is transitive. If this were not the case, then we could never explain anything by reference to things existing at earlier times, which is obviously not the case.
Causation by Earlier Events. Some events are caused by earlier events.
The principle of Full Simultaneity and Causation by Earlier Events jointly entail that at least some causation is continuous. If all causation were discrete, and all discrete causation were fully simultaneous, then it would be impossible for earlier events to cause later ones.
28.2 The Nature of Discrete Causation
Causal Connectionists have a number of options for explaining the linkage between causes and effects in the case of discrete causation. Here are four popular options:
Causation as a primitive relation (like instantiation or distinctness) holding between pairs of truthmakers.
A causal link as an entity in its own right, consisting of one or more relational tropes (or nexuses or states of affairs). This tie could either be a single relational modifier trope or a pair of modular tropes.
If there were something to the causal connection above and beyond the effect, then that additional entity would be a truthmaker of the causal connection. Is the addition of such a truthmaker a plus or a minus? If there is a correspondence between the class of truthmakers and the class of causal relata, then the introduction of causal truthmakers threatens to generate a new infinite regress. Suppose, for example, that event A causes event B and that C is the truthmaker linking A to B. If B is contingent, so will C be. Hence, we should expect a cause of C. This cause is either identical to A or it is a new entity, D. In either case, there will have to be a truthmaker for the A-to-C or D-to-C causal connection. This truthmaker, E, will require a further cause, and so on.
A causal link as the transfer of a conserved quantity (mass, energy, charge or information) or the transfer of a trope.
This is a theory that has been defended by Fair (2003), Dowe (1995), and Ehring (1997). We will consider a version of this account in more detail when considering continuous causation. The transfer theory provides a clear account of the linkage between causes and effects, since the linkage consists in the identity of some trope or quantity attached to both the cause and the effect. However, it is not at all clear how the transfer theory explains the grounding of the causal direction. What constitutes a quantity's being transferred from one thing to another, especially when the cause and effect are simultaneous? An answer to this question would seem to require a prior explanation of the nature of causal direction.
A causal link as the exercise of one or more causal powers.
If we adopt Powerism (4.4A.3), then it would be natural to identify instances of causation with exercises of causal powers. The problem of grounding the linkage between cause and effect would then become the problem of linking a causal power to the result of its exercise. Let's consider this picture in more detail. On the one hand, we have some substance or process with an appropriate causal power, such as a fire with the power to heat bodies in its vicinity. On the other hand, we have the result of the exercise of the power, such as the heating of some body of water. What about the exercise of the power? Is it some third thing, linking the power to its result? As we've seen above, introducing a third entity here runs the risk of starting an infinite causal regress. A traditional answer, going back to Aristotle's Physics, is to identify the exercise of the power with the result. The exercise of the fire's power to heat is simply the heating of this water.
How then is an exercise (or result) tied to its originating power? There seem to be two options. First, we could take this relation to be a primitive relational fact, like instantiation. Alternatively, we could identify it with a relation of asymmetric token necessitation. That is, what ties this effect E to that causal power P is the fact that this very effect E could not have existed were P not to have existed and were not to have been in circumstances appropriate to the exercise of P. That is, it is of the very essence of the kind of power P that it be capable of being exercised in circumstances of the kind of actual circumstances C, and it is of the very essence of this very truthmaker E that it could not possibly have existed except in worlds in which this very power P and circumstances C exist. The existence of E as a particular necessitates the existence of P and C, as particulars, and the nature of P is such as to permit the production of something like E in circumstances like C. (For more details about asymmetric token necessitation, see Koons 2000.)
This necessitation has to be asymmetric, in order to ground the directedness of causation. That is, the existence of E necessitates the existence of P, but not vice versa. It must be possible for P and C to exist without E's existing, but impossible for E to exist without C's and P's existence. Such asymmetric necessitation fits very nicely in a world with indeterministic causal laws, since such laws never entail, in conjunction with the existence of the cause, the existence of the effect. However, it is possible to affirm both deterministic laws and asymmetric token necessitation, so long as it is metaphysically possible for each of the deterministic laws to be violated.
28.3 Is All Causation Continuou
s?
Let us now turn our attention to continuous causation. We have seen that there is some reason to think that some causation must be continuous, in order to explain the transmission of causal influence from earlier times to later times. Could all causation be continuous?
How are we to think about continuous causation? How can there be an infinite number of intermediaries between a cause and its effect? Wouldn't such an infinity of intermediaries involve the existence of infinite causal regresses? It seems, after all, that if E1 causes E3, and there is an intermediate cause E2 such that E1 causes E2 and E2 causes E3, then the causal link between E1 and E3 should depend upon the links between E1 and E2 and E2 and E3. If there were further intermediate links between E1 and E2, and between E2 and E3, then those two links would depend on those further intermediate links, and so on ad infinitum. We seem to have an infinite regress of causal dependency relations.
The error in this way of thinking about continuous causation is that it tries to understand continuous causation in terms of discrete causation, as though continuous causation simply consists in an infinite number of discrete causal connections. We should instead take seriously the idea that continuous causation involves a continuum of events. In the basic case, two events are connected by continuous causation when they are both parts of a single process. A real process is a temporally extended whole that is more metaphysically fundamental than any of its unextended, instantaneous parts. Later parts of the process are dependent on earlier parts because both are parts of the same process, not because there is some discrete connection or chain of discrete connections between the two.
The Atlas of Reality Page 99
