Abstract
I shall assume for the present that the basic features of Hempel’s Deductive Nomological Model of Explanation are familiar to the reader: a deductive explanation of some fact Ga about a particular object a, requires some other fact Fa, and since it was assumed that Fa would not by itself yield a deduction of Ga, that the deductive connection between the two facts was to be supplied by an additional premise L –a law. So, though the target of their paper was scientific explanation, we want to consider what it tells us about scientific laws.
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Notes
- 1.
Carl G. Hempel and Paul Oppenheim, “Studies in the Logic of Explanation,” Philosophy of Science, Vol. 15 (1948).
- 2.
C.G. Hempel and Paul Oppenheim, “Studies in the Logic of Explanation”, Philosophy of Science, Vol. 15, pp. 135–178.
- 3.
Cf. Chap. 7
- 4.
F. Dretske, “Laws of Nature”, Philosophy of Science, 44, 1977; M. Tooley, “The Nature of Laws”, Canadian Journal of Philosophy, 7, 1977; D. Armstrong, “What is a Law of Nature?”, Cambridge University Press, Cambridge, 1983.
- 5.
The emphasis of one universal generating another seems to be behind Armstrong’s requirement that laws are binary relations. The fact that fairly simple laws such as the gas law that pressure times volume equals a constant times the temperature (PV = nRT) involves three magnitudes, raises some technical issues that surely have to be addressed.
- 6.
D. Lewis, Counterfactuals, Harvard University Press, 1973, p. 132.
- 7.
“a contingent generalization is a law of nature if and only if it appears as a theorem (or axiom) in each of the true deductive systems that achieves a best combination of simplicity and strength)”, Counterfactuals, p. 132. We will return to this kind of systems account in Chap. 8.
- 8.
One further caveat: (VC) does not cover quantified sentences. We shall assume that for the quantificational cases above, the natural generalization will work. Therefore the quantified counterfactuals can piggy back on whatever the universal conditionals can do deductively. However, the formulation of a system for quantified counterfactuals has some technical difficulties, since it turns out to be a kind of quantified modal logic, and there is at present no one standard account of quantified modal logic.
- 9.
Since the quantified counterfactual about the expansion of the metal implies the indicative quantified material conditional in Lewis’ system (VC), it would seem to follow that the quantified counterfactual yields not only the expectation that the metal would expand upon heating, but that it also yields the expectation that the metal will expand upon heating. That strange result might lead to the belief that it is not a good idea to read off expectations from conditionals, counterfactual or indicative.
- 10.
This is not so if the logic used is intuitionistic.
- 11.
If a law is not expressed as a conditional, then of course all talk of its contrapositive makes no sense.
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Koslow, A. (2019). Hempel’s Deductive-Nomological Model: In the Beginning …. In: Laws and Explanations; Theories and Modal Possibilities. Synthese Library, vol 410. Springer, Cham. https://doi.org/10.1007/978-3-030-18846-7_2
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