Explanation DN, SN & more

Deductive-Nomological The standard example: To explain the length of its shadow, we appeal to the height of the flagpole and the angle of elevation of the sun. In this case, we deduce the length of the shadow from the height of the pole, the geometry of the situation and the law (nomos) that light travels in straight lines.

Statistical Often our explanations don’t look like deductive arguments– often they’re probabalistic… For example, to explain how someone contracted a contagious disease, we can describe how they came into contact with a carrier of the disease. But it’s rarely possible to say that there is a deterministic law linking exposure to illness.

Difficulties The argument-based view of explanation runs into serious trouble here, though. Often we think we have explanations, even though the claims involved in the explanans don’t make the explanandum probable. (Syphillis & motor ataxia) Sometimes the explanans of what seems to be a correct explanation even makes the explanandum less probable than it was relative to background information. (Polonium/U238) Even ‘statistical relevance’ (Salmon’s early view) fails when the explanans leaves the explanandum’s probability unchanged.

Asymmetry: A deeper puzzle Even straightforward DN cases (the flagpole) raise a very puzzling problem. We can deduce the length of the shadow from the height of the flagpole and the elevation of the sun, and this explains the shadow’s length. But we can equally well deduce the height of the flagpole from the length of the shadow and the sun’s elevation. And this clearly does not explain the height of the flagpole, right?

Why the asymmetry? The DN story about explanation offers no reasons for this asymmetry. One obvious suggestion, though, is to say that the height of the flagpole causes the shadow’s length, and not vice-versa. Is the asymmetry of causation the source of the asymmetry of explanation? Does an explanans have to give an account of the cause(s) of the explanandum?

From argument to ontology: A deeper change Shifting to talk of causes has the advantage of fitting some of our problem cases earlier. A cause can explain its effect even if it doesn’t make that effect more probable or affect its probability at all! But it also changes what we expect from an explanation– to cite a cause is very different from providing an argument (deductive or statistical/probabalistic) for the explanandum.

Causation? This is pretty tough– Hume’s empirical approach to causation invoked constant conjunction: Where two event-types are constantly conjoined, we take them to be causally related (and the prior is taken as a cause while the later is the effect). Either can be inferred from the other (we reason from effects to causes and from causes to their effects). But this view just captures the asymmetry of causation by appeal to the asymmetry of time. And not just any cause will answer a given request for explanation: different ‘interests’ focus our attention on different causes.

Unification Kitcher, Friedman and others proposed a ‘unification’ based account of explanation. On this view, what makes an explanation desirable is what it contributes to the unity of our body of knowledge. This unity seems to be inferential: we want to be able to link different events together by connecting them to shared processes and causes (as Newton’s gravity united ‘satellite motion’, planetary motion, falling bodies and tides…)

Pluralism Maybe there is no ‘core’ notion of explanation that will fit all the uses we make of it. When we seek explanations in different areas, we may be looking for something that really is different (though perhaps there is a family resemblance linking these different things). We even recognize explanations in mathematics (not every proof ‘explains’ its result…)– but here causation is out of the question; any asymmetry must be based on a different sense of the ‘order’ of things in mathematics…

Shifting standards One argument for this pluralism comes from changes in the standards for explanation. Does gravity really explain the motions of falling bodies etc.? Many thought not– after all, it’s action at a distance, and according to the mechanists/ corpuscularists, that is an utterly opaque, even occult notion. But pretty soon physicists accepted Newtonian explanations… Consider also Bohr on the hydrogen spectrum.

Looking for depths? GS resists looking for ‘depths’ here— A description of the process of DNA replication may be complete in itself. It doesn’t require ‘causes’ lurking behind or connecting the various elements and stages in the process, in order to be explanatory… But philosophers often look for more. Looking for more detail in different sciences is fine– but it needn’t point towards the same ideas or basic concepts.

What is a law? DN explanation makes laws a central notion. But what distinguishes a law from other true generalizations? Compare: – All iron bolts exposed to an environment with humidity levels of … and oxygen levels of… for a period of … rust. – All the iron bolts on my car are rusty. The first is explanatory; the second isn’t. But what makes the difference here?

Causation? Causation is equally difficult to sort out. One ‘idealist’ response is to locate these notions in our conceptual outlook: The inferential relations connecting our concepts (and certain asymmetries in how we use them) may account for a lot here— But many reject this turn, since it seems to leave out any special place for these notions in nature itself (something realist metaphysicians are not happy about)!