It is something of a platitude that science does or ought to provide us humans more than mere empirical data. Rather the ideal, it is so said, is for science to provide us with knowledge. There are—of course—complications of nuance with any such bromide, but nevertheless philosophers also like to ask, ensuingly, what scientific knowledge consists in. Scientific knowledge: what is the real thing? One candidate is that science explains rather than merely reports. That is, explanation animates scientific knowledge. But, then, what is explanation?

Explanation is itself hard to explain. Many theorists have maintained that explanation is a matter of giving answers to why-questions. These differ from answers to other interrogations like what-questions, which are largely the domain of reporting and description and how-questions, which are the domain of engineering and artistry. But there are still complications. For example, think about Jimmy McNulty, the homicide detective in David Simon’s anti-hero in his series, The Wire, standing over the corpse of man killed in a vacant apartment building while next to a Baltimore coroner. They might question here

Why did this man die?

Both, in their own way, are scientists. But they seek different questions. And the answers which will satisfy them, therefore, will naturally be different. Probably the coroner is asking whether the man died of apoxia, whereas Jimmy asks who murdered him.

In a coming work, The Foundations of Microeconomic Analysis, I characterize what I claim is the fundamental explanatory methodology of neoclassical microeconomics and, in particular, general equilibrium theory. I call the methodology analogical-projective explanation. The explanatory regime is based on a more general epistemological phenomenon which I call a deprojection. I focus here on what the actual mode of explanation rather than its applications.

Both of these are terms of art, but there is really nothing new about them other than the terminology. Analogical-projective explanation belongs to a family of theories of explanation known collectively (and perhaps misleadingly) as deductivist theories. The term is misleading because they are meant to cover explanatory methods like deduction and induction.

What do they have in common? All such regimes of explanation require that when someone is explaining to you, say, what is so-and-so, that someone makes an inference where so-and-so is the conclusion. Why is the sky blue, you ask me? Here is a deduction which explains it: every time light passes through a scattering medium, light is scattered in an inversely proportional way to its wavelength. Every wavelength of light becomes more visible the more it is scattered. For all visible wavelengths of the spectrum (i.e. those not including x-rays and television waves, etc), the family of blue-violet has the shortest wavelength. The preceding three claims are what the philosopher C.G. Hempel called universally-quantified natural laws (or laws of nature). When we add the following plain assertion, that the sky is a scattering medium, along with the rules of the predicate calculus, should yield the conclusion the sky is blue. In this case, the portion of the deduction not including the conclusion serves as a explanation for the conclusion.

Such explanatory inferences can be carried out in other inferential systems. Outside of predicate logic, Hempel spent much time focused on regimes of statistical inference for the purposes of induction.

Figure 1. Some deprojectionists, surely. (Royalty-free. Vault Editions.)

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