Causation: Metaphysical Issues
Causation: Metaphysical Issues
CAUSATION: METAPHYSICAL ISSUES
Causal concepts have surely been present from the time that language began, since the vast majority of action verbs involve the idea of causally affecting something. Thus, in the case of transitive verbs of action, there is the idea of causally affecting something external to one—one finds food, builds a shelter, sows seed, catches fish, and so on—while in the case of intransitive verbs, or at least those describing physical actions, it is very plausible that they involve the idea of causally affecting one's own body—as one walks, runs, jumps, hunts, and so on.
It was not long after the very beginning of philosophy in ancient Greece that serious reflection concerning the nature of causation arose, with Aristotle's famous discussion of causation in Book 2 of his Physics. The result was Aristotle's doctrine of four types (or, perhaps, aspects) of causes—material, formal, efficient, and final—an account that was immensely influential for about two thousand years.
What was not realized at any point during this time, however—perhaps because of the sense of familiarity with the idea of causation occasioned by the almost ubiquitous presence of causal concepts in even the most rudimentary parts of language—is that the concept of causation gives rise to very serious, puzzling, and difficult philosophical questions. Thus it was only many centuries after Aristotle, with David Hume and his famous discussions of the relation of cause and effect (1739–1740 and 1748), that philosophers realized that the idea of causation was by no means simple and straightforward.
Why did Hume see what so many thoughtful philosophers before him had not? The reason, it would seem, was that Hume held—as did the other British empiricists, John Locke and Bishop (George) Berkeley—that while some concepts can be analyzed in terms of other concepts, in the end analysis must terminate in ideas that apply to things in virtue of objects' having properties and standing in relations that can be immediately given in experience. Hume therefore asked whether the relation of causation was one that could be given in immediate experience. His conclusion was that it could not. The question for Hume, accordingly, was how the concept of causation could be analyzed in terms of ideas that do pick out properties and relations that are given in experience, and once this question was in view, Hume was able to show that arriving at a satisfactory answer was a very difficult matter.
Fundamental Issues and Alternative Views
One of the central issues in the philosophy of causation concerns, then, this Humean problem: Is the concept of causation basic and unanalyzable, or, on the contrary, does it stand in need of analysis? If it does need to be analyzed, how can this be done?
Many different answers have been offered to these questions. But the various approaches can be divided up into four general types: direct realism, Humean reductionism, non-Humean reductionism, and indirect, or theoretical-term, realism.
This fourfold division, in turn, rests upon the following three distinctions: first, that between reductionism and realism; second, that between Humean and non-Humean states of affairs; and, third, that between states that are immediately observable and those that are not. Let us, then, consider each of these distinctions in turn, starting with that between reductionism and realism.
realism versus reductionism
The realism-versus-reductionism distinction in this area arises in connection with both causal laws, and causal relations between states of affairs, and gives rise to a number of related theses. In the case of causal relations between states of affairs, a thesis that is essential to reductionism is this:
Basic Reductionism with respect to causal relations
Any two worlds that agree both with respect to all of the non-causal properties of, and relations between, particulars, and with respect to all causal laws, must also agree with respect to all of the causal relations between states of affairs. Causal relations are, then, logically supervenient upon the totality of instances of non-causal properties and relations, together with causal laws.
But while this thesis is an essential part of a reductionist view of causation, it is not sufficient. The reason is that this thesis can be combined with a view of causal laws according to which they obtain in virtue of atomic, and therefore irreducible, facts. What is needed, then, is a reductionist thesis concerning causal laws, and here there are two important possibilities:
Strong Reductionism with respect to causal laws
Any two worlds that agree with respect to all of the non-causal properties of, and relations between, particulars, must also agree with respect to causal laws. Causal laws are, then, logically supervenient upon the totality of instances of non-causal properties and relations.
Moderate Reductionism with respect to causal laws
Any two worlds that agree both with respect to all of the non-causal properties of, and relations between, particulars, and with respect to all laws of nature, must also agree with respect to causal laws. Causal laws are, then, logically supervenient upon the totality of instances of non-causal properties and relations, together with laws of nature.
What lies behind this strong reductionism versus moderate reductionism distinction? The answer is that while most philosophers who are reductionists with regard to causation tend to identify laws of nature with certain cosmic regularities, it is possible to be a reductionist with regard to causation while holding that laws are more than certain cosmic regularities: One might hold, for example, that laws of nature are second-order relations between universals. Such a reductionist would reject Strong Reductionism with regard to causal laws, while accepting Moderate Reductionism.
Each of these two reductionist theses concerning causal laws then entails, in conjunction with the Basic Reductionist thesis concerning causal relations, a corresponding thesis concerning causal relations between states of affairs:
Strong Reductionism with respect to causal relations
Any two worlds that agree with respect to all of the non-causal properties of, and relations between, particulars, must also agree with respect to all of the causal relations between states of affairs. Causal relations are, in short, logically supervenient upon the totality of instances of non-causal properties and relations.
Moderate Reductionism with respect to causal relations
Any two worlds that agree both with respect to all of the non-causal properties of, and relations between, particulars, and with respect to all laws of nature, must also agree with respect to all of the causal relations between states of affairs. Causal relations are, then, logically supervenient upon the totality of instances of non-causal properties and relations, together with laws of nature.
To be a reductionist with regard to causation, then, is to accept the Basic Reductionist thesis with respect to causal relations, and either the Strong or the Moderate Reductionist thesis with respect to causal laws. This then commits one either to the Strong Reductionist thesis or the Moderate Reductionist thesis with respect to causal relations.
A realist with regard to causation, correspondingly, is one who rejects either the Basic Reductionist thesis concerning causal relations, or else both the Strong and the Moderate Reductionist theses with regard to causal laws, or all of these.
humean versus non-humean reductionism
In addition to the gulf between reductionism and realism, there are also very important divides within both reductionism and realism. In the case of reductionism, the crucial division involves a distinction between what may be called Humean and non-Humean states of affairs. So let us now turn to that distinction.
Different authors offer different characterizations of what a Humean state of affairs is. The basic idea, however, is that Humean states of affairs are ones that consist of particulars having properties and standing in relations, where the properties and relations in question are, in some sense, immediately observable. The idea of being immediately observable can then be interpreted in different ways. A very restrictive interpretation would be one where immediate observation is equated with direct acquaintance, so that only properties and relations that are the objects of Hume's simple ideas—that is, properties and relations that can be immediately given in experience—are classified as immediately observable. Alternatively, one could construe the idea of immediate observation more broadly, so that any properties and relations that can be directly or noninferentially perceived would count as immediately observable.
What would be an example of a non-Humean state of affairs? One type would be any state of affairs that involves a dispositional property or power, since even if, for example, one sees something in the process of dissolving in water, an inference is involved if one is to arrive at the conclusion that the object is such that it is disposed to dissolve when it is in water, since its dissolving on the occasion in question could be a pure accident, or could be caused entirely by some external force, rather than being due to an intrinsic property of the object itself. So an inference is involved, and therefore the water-solubility of an object cannot be an object of direct perception.
Some twentieth-century approaches to causation attempt to analyze causation in terms of powers and propensities. Such approaches are reductionist, but not of a Humean sort.
direct versus indirect realism with regard to causation
Realists with regard to causation either reject the Basic Reductionist thesis concerning causal relations, or else both the Strong and the Moderate Reductionist theses concerning causal laws. But there is a crucial divide within realist approaches, and it concerns the question of whether causal states of affairs are immediately observable. According to direct realism, some causal states of affairs are immediately observable; according to indirect, or theoretical-term realism, no causal states of affairs are immediately observable.
What causal states of affairs are directly observable, according to a direct realist approach to causation? Since it is not at all plausible that one can be directly acquainted with causal laws, the relevant states of affairs must consist of causal relations between states of affairs. Thus direct realism can be defined as a version of realism that claims that the relation of causation is immediately given in experience.
Indirect, or theoretical-term realism rejects this claim, maintaining either that the relation of causation is itself an irreducible, theoretical relation, or, alternatively, that causal laws are irreducible, theoretical states of affairs, or both. Either way, then, the relation of causation is not directly observable.
We can now turn to a consideration of the four general types of approaches to causation, beginning with direct realism. This view of causation involves four main theses: first, that the relation of causation is directly observable; second, that that relation is not reducible to non-causal properties and/or relations; third, that the relation of causation is also not reducible to non-causal properties and/or relations together with causal laws—since such a reduction would entail that one could not be directly acquainted with the relation of causation; fourth, that the concept of the relation of causation is analytically basic.
A number of philosophers have claimed that the relation of causation is observable, including David Armstrong (1997), Elizabeth Anscombe (1971), and Evan Fales (1990). Thus Anscombe argues that one acquires observational knowledge of causal states of affairs when one sees, for example, a stone break a window, or a knife cut through butter, while Fales, who offers the most detailed argument in support of the view that causation is observable, appeals especially to the impression of pressure upon one's body, and to one's introspective awareness of willing, together with the accompanying perception of the event whose occurrence one willed.
Suppose that it is granted that in such cases one does, in some straightforward sense, observe that one event causes another. Does this provide one with a reason for thinking that direct realism is true? For it to do so, one would have to be able to move from the claim that the relation of causation is thus observable to the conclusion that it is not necessary to offer any analysis of the concept of causation, that the latter can be taken as analytically basic. But observational knowledge, in this broad, everyday sense, would not seem to provide adequate grounds for concluding that the relevant concepts are analytically basic. One can, for example, quite properly speak of physicists as seeing electrons when they look into cloud chambers, even though the concept of an electron is certainly not analytically basic. Similarly, the fact, for example, that sodium chloride is observable, and that one can tell by simply looking and tasting that a substance is sodium chloride does not mean that the expression 'sodium chloride' does not stand in need of analysis.
But might it not be argued in response, first, that, one can observe that two events are causally related in precisely the same sense in which one can observe that something is red; second, that the concept of being red is analytically basic, in virtue of the observability of redness; and therefore, third, that the concept of causation must, for parallel reasons, also be analytically basic?
This response is open, however, to the following reply. If a concept is analytically basic, then one can acquire the concept in question only by being in perceptual or introspective contact with an instance of the property or relation in question that is picked out by the concept. One could, however, acquire the concept of a physical object's being red in a world where there were no red physical objects: It would suffice if things sometimes looked red, or if one had hallucinations of seeing red things, or experienced red after-images. The concept of a physical object's being red must, therefore, be definable, and cannot be analytically basic.
What is required if a concept is to be analytically basic? The answer that is suggested by the case of the concept of redness is that for a concept to be analytically basic, the property or relation in virtue of which the concept applies to a given thing must be such that that property or relation is immediately given in experience, where a property or relation is immediately given in experience only if, for any two qualitatively indistinguishable experiences, the property must either be given in both or given in neither.
Is the relation of causation immediately given in experience? The answer is that it is not. For given any experience E whatever—be it a perception of external events, an awareness of pressure upon one's body, or an introspective awareness of some mental occurrence, such as an act of willing, or a process of thinking—it is logically possible that appropriate, direct stimulation of the brain might produce an experience, E*, that was qualitatively indistinguishable from E, but which did not involve any causally related elements. So, for example, it might seem to one that one was engaging in a process of deductive reasoning, when, in fact, there was not really any direct connection at all between the thoughts themselves—since all of them were in fact being caused instead by something outside of oneself. Causal relations cannot, therefore, be immediately given in experience in the sense that is required if the concept of causation is to be unanalyzable.
Let us now turn to objections to direct realism. The first has, in effect, just been set out. For if, for any experience in which one is in perceptual or introspective contact with the relation of causation, there could be a qualitatively indistinguishable, hallucinatory experience in which one was not in contact with the relation of causation, it would be possible to acquire the concept of causation without ever being in contact with an instance of that relation. But such experiences are logically possible. So the concept of causation must be analyzable, rather than being analytically basic.
Second, it seems plausible that there is a basic relation of causation that is necessarily irreflexive and asymmetric, even if this is not true of the ancestral of that relation. If either reductionism or theoretical-term realism is correct, one may very well be able to explain the necessary truths in question, since the fact that causal concepts are, on either of those views, analyzable means that those necessary truths may turn out to be analytic. Direct realism, by contrast, in holding that the concept of causation is analytically basic, is barred from offering such an explanation of the asymmetry and irreflexivity of the basic relation of causation. It therefore has to treat these as a matter of synthetic a priori truths.
Third, direct realism encounters epistemological problems. Thus, features such as the direction of increase in entropy, or the direction of the transmission of order in non-entropic, irreversible processes, or the direction of open forks, often provide evidence concerning how events are causally connected. In addition, causal beliefs are often established on the basis of statistical information—using methods that, especially within the social sciences, are often very sophisticated. Given an appropriate analysis of the relation of causation, one can show why such features are epistemologically relevant, and why the statistical methods in question can serve to establish causal hypotheses, whereas if causation is a basic, irreducible relation, it is not at all clear how either of these things can be the case.
Humean reductionist approaches to causation are of three main types: first, accounts that analyze causation in terms of conditions that in the circumstances are nomologically necessary, sufficient, or both; second, accounts in which counterfactual conditionals play the crucial role; and third, accounts based upon probabilistic relations of a Humean sort.
causes and nomological conditions
This first Humean reductionist approach comes in different forms. According to perhaps the most common version, a cause is a condition that is necessary in the circumstances for its effect. To say that event c is necessary in the circumstances for event e is roughly to say that there is some law, l, and some circumstance, s, such that the nonoccurrence of c, in circumstance s, together with law l, logically entails the nonoccurrence of e.
It may be held instead that a cause is a condition that is sufficient in the circumstances for its effect. To say that event c is sufficient in the circumstances for event e is to say that there is some law, l, and some circumstance, s, such that the occurrence of c, in circumstance s, together with law l, logically entails the occurrence of e. Finally, it has also been suggested that for one event to cause another is for its occurrence to be both necessary and sufficient in the circumstances for the occurrence of the other event.
What problems do such approaches encounter? Perhaps the most serious difficulty concerns the direction of causation. Suppose, for example, that our world were a Newtonian one, and thus one where the basic laws were time-symmetric. Then the total state of the universe in 1950 would have been both necessary and sufficient not only for the total state in 2050 but also for the total state in 1850. It would therefore follow that events in 1950 had caused both events in 2050 and events in 1850.
Less general objections are also important. First, if a cause is necessary in the circumstances for its effect, this precludes cases of causal preemption, in which event d would have caused event e were it not for the presence of event c, which both caused e and prevented d from doing so. In such a case c is not necessary for e since, if c had not occurred, e would have been caused by d. Second, cases of causal overdetermination are also ruled out. For if both c and d are causally sufficient to bring about e, and both do so, then neither c nor d was necessary in the circumstances for the occurrence of e.
These objections can be avoided if one holds instead that a cause is sufficient in the circumstances for its effect. But then other objections emerge. In particular, it follows that there can be no causal relations if all the laws of nature are probabilistic. This is a serious difficulty, especially given the indeterministic nature of quantum mechanics.
counterfactual conditional approaches
A second important reductionist approach attempts to analyze causation using subjunctive conditionals. One way of arriving at this approach is by analyzing causation in terms of necessary or sufficient conditions (or both) but then interpreting the latter, not as nomological connections, as above, but as subjunctive conditionals. Thus one can say that c is necessary in the circumstances for e if, and only if, had c not occurred e would not have occurred, and that c is sufficient in the circumstances for e if, and only if, had e not occurred c would not have occurred.
John L. Mackie (1965/1993, 1974) took this tack in developing a more sophisticated analysis of causation in terms of necessary and sufficient conditions. Thus, after defining an INUS condition of an event as an insufficient but necessary part of a condition which is itself unnecessary but exclusively sufficient for the event, and then arguing that c 's being a cause of e can then be analyzed as c 's being at least an INUS condition of e, Mackie asked how necessary and sufficient conditions should be understood. For general causal statements, Mackie favored a nomological account, but for singular causal statements he argued for an analysis in terms of subjunctive conditionals.
The most fully worked-out subjunctive conditional, or counterfactual approach, however, is that of David Lewis (1973/1986, 1979/1986, 2000). His basic strategy involves analyzing causation using a narrower notion of causal dependence and then analyzing causal dependence counterfactually: (1) an event c causes an event e if, and only if, there is a chain of causally dependent events linking e with c ; (2) an event g is causally dependent upon an event f if, and only if, had f not occurred g would not have occurred.
Causes, so construed, need not be necessary for their effects because counterfactual dependence, and hence causal dependence, are not necessarily transitive. Nevertheless, Lewis's approach is closely related to necessary-condition analyses of causation since the more basic relation of causal dependence is a matter of one event's being counterfactually necessary in the circumstances for another event.
What problems arise for such approaches? One objection involves overdetermination, where two events, c and d, are followed by an event e, and where each of c and d would have been causally sufficient, on its own, to produce e. If it is true, in at least some actual or possible cases of this sort, both that c causes e and that d causes e, then one has a counterexample to Lewis's counterfactual analysis.
A second objection involves cases of preemption; that is, cases where there is some event c that causes e, but where there is also some event d that did not cause e, but that failed to do so only because the presence of c prevented it from doing so.
Until the late twentieth century, the discussion of preemption had focused on cases where one causal process preempts another by blocking the occurrence of some state of affairs in the other process, and a variety of closely related ways of attempting to handle this type of preemption have been advanced, involving such notions as fragility of events, quasi-dependence, continuous processes, minimal-counterfactual sufficiency, andminimal-dependence sets (Lewis 1986, Menzies 1989, McDermott 1995, Ramachandran 1997). But none of these approaches can handle the case of trumping preemption, advanced by Jonathan Schaffer (2000), where one causal process preempts another without preventing the occurrence of any of the states of affairs involved in the other causal process.
Third, there is once again the problem of explaining the direction of causation. One possibility is to define the direction of causation as the direction of time, but neither Mackie nor Lewis favors that approach: both think that backward causation is logically possible. Mackie's main proposal appeals to the direction of irreversible processes involving the transmission of order—such as with outgoing concentric waves produced by a stone hitting a pond—and Lewis advances a somewhat related proposal, in which the direction of counterfactual dependence, and hence causal dependence, is based upon the idea that events in this world have many more effects than they have causes. But the problem with both of these suggestions is that the relevant features are at best contingent ones, and it would seem that, even if the world had neither of these features, it could still contain causally related events.
A final objection, and the most fundamental of all, is concerned with the truth conditions of the counterfactuals that enter into the analysis. One familiar approach to counterfactuals maintains that the truthmakers for counterfactuals concerning events in time involve causal facts (Jackson 1977). Such analyses cannot of course be used in an analysis of causation, on pain of circularity. Accordingly, Lewis formulated his analysis of causation in terms of counterfactuals whose truth conditions are a matter of similarity relations across possible worlds (Stalnaker 1968, Lewis 1973). It can be shown, however, by a variant on an objection advanced by Bennett (1974) and Fine (1975), that this account of counterfactuals does not yield the correct truth-values in all cases (Tooley 2003). Moreover, the same type of counterexample also shows an analysis of causation based on such conditionals will generate the wrong truth-values in the cases in question.
Among the more significant developments in the philosophy of causation since the time of Hume is the idea, motivated in part by quantum mechanics, that causation is not restricted to deterministic processes. This has led several philosophers to propose that causation itself should be analyzed in probabilistic terms.
The central idea is that causes must make their effects more likely. This idea can, however, be expressed in two rather different ways. The traditional approach, developed by Hans Reichenbach (1956), I. J. Good (1961/1962), and Patrick Suppes (1970), focuses upon types of events and involves the notion of positive statistical relevance. According to this notion, an event of type C is positively relevant to an event of type E if and only if the conditional probability of an event of type E, given an event of type C, is greater than the unconditional probability of an event of type E. The basic idea, then, is that for events of type C to be direct causes of events of type E, a necessary condition is that the former be positively relevant to the latter.
But do causes necessarily make their effects more likely? Consider two types of diseases, A and B, governed by the following laws. First, disease A causes death with probability 0.1, while disease B causes death with probability 0.8. Second, contracting either disease produces complete immunity to the other. Third, in condition C, an individual must contract either disease A or disease B. (Condition C might be a weakening of the immune system.) Finally, assume that individual m is in condition C and contracts disease A, which causes his death. Given these conditions, what if m, though in condition C, had not contracted disease A ? Then m would have contracted disease B. But if so, then m 's probability of dying had he not contracted disease A would have been 0.8—higher than his probability of dying given that he had contracted disease A. So the claim that lies at the heart of probabilistic approaches—that causes necessarily make their effects more likely—cannot be true.
Traditional probabilistic approaches, in analyzing causation in terms of statistical relations, offered a Humean reductionist account of causation. In the late twentieth century, however, an alternative type of probabilistic approach to causation was suggested, one that involves analyzing causation in terms of propensities, or objective chances. Objective chances, however, do not logically supervene upon the totality of Humean states of affairs, as is shown by the fact, for example, that if atoms of a given type take a certain average time t to undergo radioactive decay, that fact is logically compatible with different objective chances of such atoms' undergoing decay within a given period of time. An analysis of causation that involves objective chances is therefore a reductionist account of a non-Humean sort.
objective chance approaches to causation
A number of philosophers—such as Edward Madden and Rom Harré (1975), Nancy Cartwright (1989), and C. B. Martin (1993)—have both advocated an ontology in which irreducible dispositional properties, powers, propensities, chances, and the like, occupy a central place, and maintained that such an ontology is relevant to causation. Often, however, the details have been rather sparse. But a clear account of the basic idea of analyzing causation in terms of objective chances was set out in 1986 both by D. H. Mellor and by David Lewis and then, in the 1990s, Mellor offered a very detailed statement and defense of this general approach in his book The Facts of Causation (1995).
Mellor's approach, in brief, is roughly as follows. First, Mellor embraces an ontology involving objective chances, where the latter are ultimate properties of states of affairs, rather than being logically supervenient upon causal laws together with non-dispositional properties, plus relations. Second, Mellor proposes that chances can be defined as properties that satisfy three conditions: (1) The Necessity Condition: if the chance of P 's obtaining is equal to one, then P is the case; (2) The Evidence Condition: if one's total evidence concerning P is that the chance of P is equal to k, then one's subjective probability that P is the case should be equal to k ; (3) The Frequency Condition: the chance that P is the case is related to the corresponding relative frequency in the limit. Third, chances enter into basic laws of nature. Fourth, Mellor holds that even basic laws of nature need not have instances, thereby rejecting reductionist accounts in favor of a realist view. Fifth, any chance that P is the case must be a property of a state of affairs that temporally precedes the time at which P exists, or would exist. Finally, and as a very rough approximation, a state of affairs c causes a state of affairs e if and only if there are numbers x and y such that (1) the total state of affairs that exists at the time of c —including laws of nature—entails that the chance of e is x, (2) the total state of affairs that would exist at the time of c, if c did not exist, entails that the chance of e is y, and (3) x is greater than y.
This approach to causation is open to three main types of objections. First, this account necessarily involves the Stalnaker-Lewis style of counterfactuals, and, as was noted earlier, such a closest-worlds account of counterfactuals is unsound.
Second, there are a number of objections that can be directed against the view that objective chances are ontologically ultimate properties, one of which is as follows. Imagine that the world is deterministic, that every temporal interval is divisible, and that all causation involves continuous processes. Suppose that x at time t has an objective chance equal to 1 of being C at time (t + Δt ). Then there are an infinite number of moments between t and (t + Δt ), and for every such moment, t, it must be the case either that x at time t has an objective chance equal to 1 of being C at time t, or that x at time t has an objective chance equal to 1 of not being C at time t. But then, if objective chances are ontologically ultimate, intrinsic properties of things at a time, it follows that x at time t must have an infinite number of intrinsic properties—indeed, a non-denumerably infinite number of properties.
This view of the nature of objective chances involves, accordingly, a very expansive ontology indeed. By contrast, if objective chances, rather than being ontologically basic, supervene on categorical properties plus causal laws, this infinite set of intrinsic properties of x, at time t disappears, and all that one may have is a single, intrinsic, categorical property—or a small number of such properties—together with relevant laws of nature.
Third, there are objections to the effect that, even given this view of objective chances, the resulting account of causation is unsound. Here one of the most important is that, just as in the case of attempts to analyze causation in terms of relative frequencies, it can be shown that the crucial claim that a cause raises the probability of its effect remains unsound when one shifts from relative frequencies to objective chances.
Indirect, or Theoretical-Term, Realism
Direct realism with regard to causation is, as we saw earlier, deeply problematic. There is, however, a very different form of causal realism, according to which causation is a theoretical relation between events. On this view, all knowledge of causal states of affairs is inferential knowledge, and the concept of causation stands in need of analysis. But unlike reductionist accounts, the relevant analysis does not imply that causal states of affairs are logically supervenient upon non-causal states of affairs.
a theoretical-term realist account of causation
This approach to causation involves finding postulates that serve to define implicitly the relation of causation. One suggestion here (Tooley 1990), for example, starts out with postulates for causal laws that say, very roughly, that the a posteriori probabilities of effects are a function of the a priori probabilities of their causes, whereas, by contrast, the a posteriori probabilities of causes are not a function of the a priori probabilities of their effects. Then, when one adds the further postulate that causal laws involve the relation of causation, the result is an implicit definition of the relation of causation. That implicit definition can then be converted into an explicit one by using one's preferred approach to the definition of theoretical terms. So, for example, if one adopts a Ramsey/Lewis approach, the relation of causation can be defined as that unique relation between states of affairs that satisfies the relevant open sentences corresponding to the postulates in question.
Realism or Reductionism?
Reductionist approaches to causation are, as we have seen, exposed to a variety of objections. In addition, however, there are general objections that appear to tell against any reductionist approach. Two especially important ones are, first, that the Basic Reductionist Thesis is unsound, and, second, that reductionism cannot provide a satisfactory account of the direction of causation.
singularism and causal laws
According to the Basic Reductionist Thesis, causal relations are logically supervenient upon the totality of instances of non-causal properties and relations, together with causal laws. But this thesis is exposed to a number of objections, such as the following. Assume that indeterministic laws are logically possible and that, in particular, it is a basic law both that an object's acquiring property P causes it to acquire either property Q or property R, but not both, and that an object's acquiring property S also causes it to acquire either property Q or property R, but not both. Suppose now that some object simultaneously acquires both property P and property S and then immediately acquires both property Q and property R. The problem now is that, given that the relevant laws are basic, there cannot be any non-causal facts that will determine which causal relations obtain. Did the acquisition of P cause the acquisition of Q, or did it cause the acquisition of R ? On a reductionist approach, no answer is possible. Accordingly, causal relations between events cannot be logically supervenient upon causal laws plus non-causal states of affairs.
reductionism and the direction of causation
What determines the direction of causation? Reductionists have advanced various suggestions, but some arguments seem to show that no reductionist account can work. One such argument appeals to the idea of a very simple world—consisting, say, of a single particle, or of two particles rotating endlessly about one another. Such simple worlds would still involve causation since the identity over time of the particles, for example, requires causal relations between their temporal parts. But since such worlds are time-symmetric, the events in them will not exhibit any non-causal patterns that could provide the basis for a reductionist account of the direction of causation. Accordingly, no reductionist account of the direction of causation can generate the correct answer for all possible worlds. It would seem, then, that only a realist account of causation will do.
See also Anscombe, Gertrude Elizabeth Margaret; A Priori and A Posteriori; Aristotle; Armstrong, David M.; Bennett, Jonathan; Berkeley, George; Cartwright, Nancy; Hume, David; Lewis, David; Locke, John; Mackie, John Leslie; Philosophy of Statistical Mechanics; Reductionism in the Philosophy of Mind; Realism; Reichenbach, Hans; Suppes, Patrick.
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Michael Tooley (1996, 2005)