David Hume, oil painting by Allan Ramsay, 1766; in the Scottish National Portrait Gallery, Edinburgh.Courtesy of the Scottish National Portrait Gallery
Scruples about necessary connections also generated a third class of difficulties for Hempel’s project. There are examples of arguments that fit the patterns approved by Hempel and yet fail to count as explanatory, at least by ordinary lights. Imagine a flagpole that casts a shadow on the ground. One can explain the length of the shadow by deducing it (using trigonometry) from the height of the pole, the angle of elevation of the Sun, and the law of light propagation (i.e., the law that light travels in straight lines). So far this is unproblematic, for the little argument just outlined accords with Hempel’s model of explanation. Notice, however, that there is a simple way to switch one of the premises with the conclusion: if one starts with the length of the shadow, the angle of elevation of the Sun, and the law of light propagation, one can deduce (using trigonometry) the height of the pole. The new derivation also accords with Hempel’s model. But this is perturbing, because, while one thinks of the height of a pole as explaining the length of a shadow, one does not think of the length of a shadow as explaining the height of a pole. Intuitively, the amended derivation gets things backward, reversing the proper order of dependence. Given the commitments of logical empiricism, however, these diagnoses make no sense, and the two arguments are on a par with respect to explanatory power.
Although Hempel was sometimes inclined to “bite the bullet” and defend the explanatory worth of both arguments, most philosophers concluded that something was lacking. Furthermore, it seemed obvious what the missing ingredient was: shadows are causally dependent on poles in a way in which poles are not causally dependent on shadows. Since explanation must respect dependencies, the amended derivation is explanatorily worthless. Like the concept of natural necessity, however, the notion of causal dependence was anathema to logical empiricists—both had been targets of Hume’s famous critique. To develop a satisfactory account of explanatory asymmetry, therefore, the logical empiricists needed to capture the idea of causal dependence by formulating conditions on genuine explanation in an acceptable idiom. Here too Hempel’s program proved unsuccessful.
The fourth and last area in which trouble surfaced was in the treatment of probabilistic explanation. As discussed in the preceding section (Discovery, justification, and falsification), the probability ascribed to an outcome may vary, even quite dramatically, when new information is added. Hempel appreciated the point, recognizing that some statistical arguments that satisfy his conditions on explanation have the property that, even though all the premises are true, the support they lend to the conclusion would be radically undermined by adding extra premises. He attempted to solve the problem by adding further requirements. It was shown, however, that the new conditions were either ineffective or else trivialized the activity of probabilistic explanation.
Nor is it obvious that the fundamental idea of explaining through making the phenomena expectable can be sustained. To cite a famous example, one can explain the fact that the mayor contracted paresis by pointing out that he had previously had untreated syphilis, even though only 8 to 10 percent of people with untreated syphilis go on to develop paresis. In this instance, there is no statistical argument that confers high probability on the conclusion that the mayor contracted paresis—that conclusion remains improbable in light of the information advanced (85 percent of those with untreated syphilis do not get paresis). What seems crucial is the increase in probability, the fact that the probability of the conclusion rose from truly minute (paresis is extremely rare in the general population) to significant. Other approaches to explanation
By the early 1970s, Hempel’s approach to explanation (known as the covering-law model) seemed to be in trouble on a number of fronts, leading philosophers to canvass alternative treatments. An influential early proposal elaborated on the diagnosis of the last paragraph. Wesley Salmon (1925–2001) argued that probabilistic explanation should be taken as primary and that probabilistic explanations proceed by advancing information that raises the probability of the event (or fact) to be explained. Building on insights of Reichenbach, Salmon noted that there are cases in which giving information that raises probability is not explanatory: the probability that there is a storm goes up when one is told that the barometer is falling, but the fall of the barometer does not explain the occurrence of the storm. Reichenbach had analyzed such examples by seeing both the barometer’s fall and the storm as effects of a common cause and offering a statistical condition to encompass situations in which common causes are present. Salmon extended Reichenbach’s approach, effectively thinking of explanation as identifying the causes of phenomena and, consonant with empiricist scruples, attempting to provide an analysis of causation in terms of statistical relations. Unfortunately, it proved very difficult to reconstruct causal notions in statistical terms, and by the 1980s most philosophers had abandoned the attempt as hopeless.
Many, however—including Salmon—remained convinced that the notion of causation is central to the understanding of explanation and that scientific explanation is a matter of tracing causes. They were divided (and continue to be divided) into two groups: those who believed that Humean worries about causation are important and that, in consequence, a prior analysis of causation is needed, and those who think that Hume and his successors adopted a faulty picture of human knowledge, failing to recognize that people are capable of detecting causal relations perceptually. Salmon was the most prominent member of the first group, offering an intricate account of causal processes, causal propagation, and causal interaction by appealing (in later work) to the conservation of physical quantities. He also argued, against his earlier view, that causal explanation can sometimes proceed by making the event explained appear less probable than it formerly seemed. (Imagine a golfer whose ball strikes a tree and is deflected into the hole; a description of the initial trajectory of the ball would decrease the probability that the result will be a hole in one.)
Although regarding explanation as a matter of tracing causes responds in a very direct way to several of the problems encountered by Hempel’s approach, it was not the only program in the recent theory of explanation. Some philosophers attempted to remain closer to Hempel’s project by thinking of explanation in terms of unification. Especially concerned with examples of theoretical explanation in the sciences, they proposed that the hallmark of explanation is the ability to treat from a single perspective phenomena previously seen as highly disparate. They elaborate on the remark of the English biologist T.H. Huxley (1825–95) that “in the end, all phenomena are incomprehensible and that the task of science is to reduce the fundamental incomprehensibilities to the smallest possible number.” This view, however, faced considerable technical difficulties in addressing some of the problems that arose for Hempel’s approach. Its principal merits lay in the avoidance of any reliance on causal concepts and in the ability to give an account of explanation in areas of theoretical science in which talk of causation seems strained.