Hempel on Explanation

Hempel—Laws and Their Role in Scientific Explanation
Scientific Explanation (SE) must meet 2 requirements:
1.     Explanatory relevance
2.     Testability
Re 1: the explanandum (the thing being explained) is expected given the theory.  Hence, the theory is explanatorily relevant to the explanandum
“the explanatory information adduced affords good grounds for believing that the phenomenon to be explained did, or does, indeed occur” (73).
This is a necessary but not sufficient condition for SE: e.g. from red-shift in distant galaxies infer that those galaxies are receding, but the red-shift does not explain why the galaxies are receding
Re 2: “the statements constituting a SE must be capable of empirical test” (73).
Deductive Nomological Account:
  1. Laws of nature
  2. Particular facts (circumstances, etc)
  3. Explanandum Sentence
1 and 2 are the explanans sentences—they are what explain the explanandum sentence.
“The basic idea of the DN model is that explanations have the structure of sound deductive arguments in which a law of nature occurs as an essential premise” (37, Woodward, The Blackwell Guide to the Philosophy of Science)
DN-Laws: laws are regularities—Humean conception. 
Laws are
a.     To be exceptionless generalizations
b.     To support counterfactuals
Problems: 
With (a): most laws are not (a); e.g. Mendel’s law of segregation (M) has a number of exceptions such as meiotic drive (39, Woodward).
With (b): even Hempel’s example that all the rocks in the box contain iron supports the following counterfactual: if I were to pull out of the box a rock, then it would contain iron. So, we need a much more fine-grained account of the type of counterfactual relevant.
DN is committed to the relevance of laws and yet we do not have a satisfactory account of laws.  
Problems for DN: 
First: DN fails to respect the asymmetrical nature of explanation.  The height of the flagpole, the angle with the sun and so forth explain the length of the shadow.  But from the length of the shadow, the angle of the sun and so forth one can deduce the height of the flagpole.  According to DN the shadow (with the other stuff) explains the height of the flagpole.  This is false.   (Bromberger, 1966)
                        In general, if x explains y, then y does not explain x.  There are no circular explanations.
            Second: All males who take birth control pills regularly fail to get pregnant.
                        JJ is a male who has been taking birth control pills regularly.
                        JJ fails to get pregnant.
This conforms to the DN model.  We have a law, a particular fact and an outcome or some event that needs explaining.  The idea that one can explain an outcome solely on the basis of a law and circumstance looks to be in trouble. 
Third:some explanations that don’t cite laws seem perfectly adequate: the knee bumping the desk caused the water to spill



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