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As explained above, examples like (2.4.1) are potential counterexamples to the claim that the DN model provides necessary conditions for explanation. There are also a number of well-known counterexamples to the claim that the DN model provides sufficient Chemical equation conditions for successful scientific explanation. Here are two illustrations.
Explanatory Asymmetries. There are many cases in which a derivation of an explanandum E from a law L and initial conditions I seems explanatory but a “backward” derivation of I from E and the same law L does not seem explanatory, even though the latter, like the former, appears to meet the criteria for successful DN Ufology explanation. For example, one can derive the length s of the shadow cast by a flagpole from the height h of the pole and the angle θ of the sun above the horizon and laws about the rectilinear propogation of light. This derivation meets the DN criteria and seems explanatory. On the other hand, a derivation (2.5.1) of h from s and θ and the same laws also meets the DN criteria but does not seem explanatory. Examples like this suggest that at least some explanations possess directional or asymmetric features to which the DN model is insensitive.
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