Hume's Theory of Causation and the Deductive Nomological Model of Explanation
Humes theory is the starting point for most modern treatments of causation, and it is tied to the metaphysical abyss opened by Descartes view of the physical world as devoid of action.
Hume argues that causation involves a regular association between cause and effect with the cause contiguous with its immediate effects and preceding them. The spatial-temporal contiguity requirement creates difficulties for Hume, because he believes that mental things stand in causal relations even though they are not located in space (Treatise, Book I, Part IV, §5). Hume omits the contiguity requirement in his later account of causation in the Inquiry. In the Treatise he attempts to argue for the temporal priority of cause to effect, but the argument does not recur in the Inquiry.
Hume also argues that the human psychological propensity to pass from an "impression" (perception) of a cause to an idea of its effects (or from an impression of an effect to an idea of its cause) leads people mistakenly to believe that there is a necessary connection between cause and effect. The notion of a necessary connection is one of the casualties of Descartes mechanistic program. Since effects follow causes according to the laws of nature decreed by God, there is a sense in which causes necessitate. But the necessitation is completely mysterious. Causes contain nothing within themselves that could enable them to act on anything else.
Hume speaks of a "constant conjunction" among "similar" objects. According to Hume, when a causes b, "objects similar to" a are invariably followed by objects similar to b. There are serious problems in this account. My waving my hand is similar to my striking a match, but my hand-waving is not usually followed by flames. Most contemporary philosophers would explicate the relevant notion of similarity in terms of the laws of nature in virtue of which a causes b. If there is a law of the form (x)(Ax -> Bx), then objects similar to a are events of with property A that is, other instantiations of A and objects similar to b are events with property B.
Even if one has identified the kinds, the relation between events is very rarely invariable. Turning a switch causes a bulb to light, but the bulb does not always light when the switch is turned. Bulbs burn out, wires break, and so forth. Hume maintains that when the relation is not invariable, then one has not fully specified the cause. Turning the switch is only a part of the cause of its lighting. The cause is turning the switch when the battery is charged, the bulb in good repair, and . . . .
This response to the fact that what we call causes are not invariably linked to their effects conflicts with ordinary usage and the scientific concern to identify "causal factors" that promote the occurrence of effects without by themselves requiring them. Furthermore, it is virtually impossible to specify explicitly a set of substantive conditions, the satisfaction of which will lead invariably to the effects occurrence. Rather than calling the complete set of sufficient conditions if there is one "the cause," one should call the separate causal factors "causes."
The fact that it is so difficult to specify a set of causes that is sufficient for an effect constitutes a reason to question whether the connection between cause and effect is deterministic. To say that smoking causes lung cancer seems to imply only that smoking increases the risk of lung cancer. Such considerations have led a number of philosophers to propose theories of probabilistic causation. But let us stick here with deterministic causation. To say that causes determine their effects is not, by the way, to say that everything is caused or that nothing happens by chance, and it does not commit me to determinism. Taking causation to be a deterministic relation implies only that if something is caused, its causes are sufficient in the circumstances.
The notion of a constant conjunction between cause and effect of a deterministic causal relation requires further clarification. Even if one has identified the relevant properties, one must still characterize the regularities that obtain among them. J. L. Mackie, drawing on ideas of John Stuart Mill, argues that a cause, such as striking a match, need not be a necessary nor a sufficient condition for an effect, such as the match lighting. A cause is rather "at least an INUS condition" that is, at least "an insufficient but nonredundant part of an unnecessary but sufficient condition" for the effect (1980, p. 62). Jonathan Bennett speaks more simply of "NS conditions" necessary parts of sufficient conditions (1988, p. 44). For example, matches light in many conditions. They may be struck in the presence of oxygen in the right conditions of temperature, wind, and humidity. They may be kindled by the presence of a flame in other conditions. A match lights if and only if one or more of these sets of sufficient conditions obtains. Each of the sets of sufficient conditions is minimal in the sense that none of its conjuncts is redundant. The conjuncts of these minimal sufficient conditions are INUS conditions.
According to Mackie, the general form of an INUS condition is: For some properties X and Y B if and only if (AX or Y), where A is a causal factor and B an effect. X is a conjunction of properties such that AX is a minimal sufficient condition for B, and Y is a disjunction of alternative minimal sufficient conditions.
One must also insist that the biconditional B if and only if (AX or Y) is "lawlike" or else the account would be obviously unsatisfactory. For example, tossing a coin that lands heads on its only flip before being melted down is (given gravitation) sufficient for its landing heads and would accordingly explain why it landed heads.
So Hume's theory of causation maintains (as a first approximation) that a is a deterministic cause of b in circumstances of kind C if and only if a and b have properties A and B and there are laws of nature L such that, given L, AC is a minimal sufficient condition for B, A&C are jointly instantiated by a and the circumstances at a time before B is instantiated by b, no other minimal sufficient condition for B is instantiated at the relevant time and place, and A&C is not sufficient for B without L.
Note that to speak of a regularity theory of causation as many contemporary philosophers do or to speak as Hume does of constant conjunction is misleading. The tokens are linked by laws, and if it were possible to recreate the circumstances repeatedly, then a regularity would certainly appear, but there is nothing in the notion of causal connections as instantiating lawful connections that rules out unique sequences of cause and effect.
Given Hume's theory of causation, if a causes b, then there must be a deductive-nomological explanation for the occurrence of b (though of course we might not be able to give it). Furthermore, if there is a deductive nomological explanation of some explanandum E which states the occurrence of an event f, then any non-law premise describing the existence of an earlier event will automatically cite a cause of f. The D-N model is more general, because it is not limited to the explanation of events. But when the explanandum concerns an event, the D-N model builds in all the conditions that a Humean would require of causation except the requirement that causes precede their events. So it is not at all surprising that Hempel regards the D-N model as an account of causal explanation, which (like Hume's theory) avoids mysterious metaphysical claims about causation.
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Hume is well aware that his account leaves out what most people think is central to causation -- the notion of a necessary connection between cause and effect. Hume believes nevertheless that he has taken the mystery out of causation, while retaining the all-important links between causation and regularities and explaining the mistaken belief in necessary connections.
Hume's account of causation -- like Hempel's account of explanation -- is constrained by a commitment to empiricism that is, in Hume's language, that all our ideas derive from preceding impressions of sense or reflection. He is saying that nonlogical terms have meaning only if one can tell by observation whether they apply to things and that the evidence for all claims concerning matters of fact derives from observation. Hume claims to clarify the content of our "ideas" (mental contents) and of the relations among them, and he does not clearly demarcate philosophy from introspective psychology. In Hume's view, the way to clarify ideas, including the idea of causation, is thus to determine what "impressions" they derive from. Hume maintains that within the complex idea of causation are the ideas of temporal priority, spatial and temporal contiguity, regularity, and necessary connection.
Although necessary connection is, Hume maintains, the most important part of the idea of causation, he also maintains that it is impossible to have any impression of necessity. All we can ever observe are successions of separate occurrences.
What is our idea of necessity, when we say that two objects are necessarily connected together? Upon this head I repeat what I have often had occasion to observe, that as we have no idea that is not derived from an impression, we must find some impression that gives rise to this idea of necessity, if we assert we have really such an idea. In order to [do] this, I consider in what objects necessity is commonly supposed to lie; and, finding that it is always ascribed to causes and effects, I turn my eye to two objects supposed to be placed in that relation, and examine them in all the situations of which they are susceptible. I immediately perceive that they are contiguous in time and place, and that the object we call cause precedes the other we call effect. In no one instance can I go any further, nor is it possible for me to discover any third relation betwixt these objects. I therefore enlarge my view to comprehend several instances, where I find like objects always existing in like relations of contiguity and succession. The reflection on several instances only repeats the same objects; and therefore can never give rise to a new idea. But upon further inquiry I find that the repetition is not in every particular the same, but produces a new impression, and by that means the idea which I at present examine. For, after a frequent repetition, I find that upon the appearance of one of the objects the mind is determined by custom to consider its usual attendant, and to consider it in a stronger light upon account of its relation to the first object. It is this impression, then, or determination, which affords me the idea of necessity. (1738, p. 154)
The idea of necessary connection is a mental (causal) consequence of regularities. The idea of necessity arises from the way in which human minds react to perceptions of regularities, not from any feature of the objects. All that causation consists of in the objects themselves is regularity, contiguity (perhaps), and temporal priority of the cause to the effect. That is all there is to causation, although if one also wants to explain how people think about causation, it is important to add that the regular connection between cause and effect leads human minds to turn from the impression of one to the idea of the other and that this tendency of human minds makes people feel a further necessary connection. Hume knows that his account will seem implausible, but having argued that power is unobservable and having given such a neat explanation for how regularities give rise to the idea of necessity, he thinks readers should find his arguments convincing.