Abstract
Norman Campbell rightly set the task. It is the business of science not only to discover laws, but to explain them. And he added his voice to a philosophical tradition going back to Aristotle, of taking on the task of explaining what laws are, and explaining as well what explanations of laws are. Ever since the renewed interest spurred by seminal paper of Hempel and Oppenheim on scientific explanation, philosophers have been inspired to do better on scientific explanation. But it became painfully clear, from the counter-example offered in their paper, that their account of scientific explanation could not cover the explanation of laws. It is clear that although this is the business of philosophers, it is still unfinished business.
Even if we were sure that all possible laws had been found and that all the external world of nature had been completely ordered, there would still remain much to be done. We should want to explain the laws
N. Campbell, What is Science, Methuen & Co. Ltd., London (1921), p.77.
This chapter is based upon Koslow, A., “The explanation of laws: some unfinished business”, The Journal of Philosophy, Special Issue: Aspects of Explanation, Theory, and Uncertainty: Essays in Honor off Ernest Nagel, 2012, pp. 479–502.
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Notes
- 1.
“Studies in the Logic of Explanation”, Philosophy of Science, 15 (1948), pp.135–178.
- 2.
Cambridge University Press, 1953. All page references for Braithwaite are to this book.
- 3.
We omit the other features Nagel mentioned since they concern analogy and evidential requirements that are not directly relevant to the issues under discussion.
- 4.
“A Budget Of Problems In The Philosophy of Science.”, Philosophical Review, 66(1957), 205–225.
- 5.
We have added the parenthetical condition to avoid the consequence that every generalization of an established deductive system would be a law. It still does not blunt the possible case where a deductively strongest generalization of a deductive system might not be a law of that system. This is a consequence which Braithwaite called to attention, and developed an answer. It should also be noted that although such a highest generalization might not count as a law of a system D, it might very well be a law of an established deductive system that was an extension of D. His additional requirement that a highest-order hypothesis in a deductive system that has an occurrence of a theoretical term is a law seems very ad hoc to me. Nevertheless there are several important plausible cases when this is so –in systems in which the highest order hypothesis are the three laws of Newtonian mechanics, Newton’s theory of gravitation, Schrödinger’s formulation of quantum mechanics, and the basic (three or four) laws of classical thermodynamics.
- 6.
I am not endorsing any of these accounts. In fact there are fairly convincing examples of accidental generalizations that also support their corresponding counterfactual conditionals. Even worse, we showed in Chap. 3, that if a law implies its corresponding counterfactual conditional, then it is equivalent to that counterfactual. In that case there are examples of laws which scientific practice regards as logically equivalent, while their corresponding counterfactuals are not.
- 7.
We believe that here Braithwaite would have used something close to Campbell’s notions of the hypothesis and the dictionary of a theory . Those notions will be discussed more fully below.
- 8.
I suspect that part of the reason is that “is more general than” was sometimes used interchangeably with “is more comprehensive than” and with “is more fundamental than”.
- 9.
J.S. Mill, A System of Logic, 1843, p.230
- 10.
F.P. Ramsey, Philosophical Papers, ed. D. H. Mellor, Cambridge University Press, 1990, p.150.
- 11.
D. Lewis, Counterfactuals, 1973, p.73. A more nuanced version can be found in his “Humean Supervenience Debugged.”, Mind, 1994 (473–490).
- 12.
One interesting difference between (MR) and (MRL) on the one hand, and (MRB) on the other, is that all the statements of the first two kinds of deductive systems are required to be true, but the statements of (MRB) only need to be well established.
- 13.
The more general result also holds: If L∗ is a generalization that follows from several laws of D, then it too is a law of D.
- 14.
All page references are to Ernest Nagel, The Structure of Science, Problems in the Logic of Scientific Explanation, Harcourt, Brace & World, Inc., 1961.
- 15.
His conclusion, after a review of typical examples, is that explanations of statistical laws are deductive, at least one premise is statistical, and at least one premise must have a greater degree of statistical dependence than that of the law to be explained.(520)
- 16.
Nagel was certainly aware of the various criticisms of such a distinction between theoretical and observational terms, but he has a very vigorous account of that distinction, admitting its vagueness, that should not be discounted.
- 17.
Consequently, (ii) should be listed as a rule, rather than as a premise. Whatever status it has, it is supposed to guarantee a deductive transition to the conclusion, since, for Nagel, Campbell and Braithwaite, as we indicated, all explanations are deductive.
- 18.
“The Formation of Modern Conceptions of Formal Logic in the Development of Geometry”, Osiris, vol.7, 1939,and reprinted in E. Nagel, Teleology Revisited and Other Essays in the Philosophy and History of Science, Columbia University Press, 1979, pp.237–8. The particular passage (translated by Nagel) is also reprinted in P. Suppes, Representation and Invariance of Scientific Structures, CSLI Publications, Stanford, 2002, p.46 where it is used to support a set-theoretical account of axiomatic theories.
- 19.
Nagel’s view is subtle. He does say in effect that if it is required that every premise in an explanation is either true or false, then it is almost unavoidable to require that they be true (42–43). Factivity for him is a conditional. So, for him one could say that factivity holds (vacuously) for those premises in explanations that are, like (1)’, without any truth-value.
- 20.
According to Nagel, “If the theory is to be used as an instrument of explanation and prediction, it must somehow be linked with observable materials.” (93).
- 21.
A discussion of theories-for, theories-of and their importance for understanding the non-deductive relation of them to their successes, and the kind of explanation that they provide, can be found in S. Morgenbesser and A.Koslow, “Theories and their Worth”, The Journal of Philosophy, CVII, 12, Dec. 2010, pp.615–647.
- 22.
In fact, Hilbert had a short proof showing that there are an infinite number of such applications, which was subsequently rediscovered by B. Russell, and D. Davidson. (“Any theory can always be applied to infinitely many systems of basic elements. For one only needs to apply a reversible one-one transformation and then lay it down that the axioms shall be correspondingly the same for the transformed things (as illustrated in the principle of duality and by my independence proofs.”) Gottlob Frege,Philosophical and Mathematical Correspondence (Eds. G.Gabriel, H.Hermes, F. Kambartel, C. Thiel, A.Verart, abridged from German edition by B. McGuinness and tr. By H. Kaal., p. 42.
- 23.
C.G. Hempel, Aspects of Scientific Explanation, The Free Press, New York, (1965).
- 24.
“Reduction … is the explanation of a theory or a set of experimental laws established in one area of inquiry, by a theory usually but not invariably formulated for some other domain.” Nagel (338)
- 25.
The topics of explanation and generality are addressed again in sections 12.3, and 12.4, where the notions of explanation using non-schematic theories, and explanation∗ using schematic theories are compared, and a mini theory of the relation of “is at least as general as” is applied to the question of whether theories that explain laws, are at least as general as the laws that are explained.
- 26.
Newton C. A. Da Costa and Steven French, Science and Partial Truth, A Unitary Approach to Models and Scientific Reasoning, p.34, Oxford University Press., 2003..
- 27.
Cf. H. Halvorson’s “The semantic view, if plausible, is syntactic (2013)”,“Scientific Theories” Oxford Handbook of Philosophy of Science (2015), “What Scientific Theories Could Not Be” Philosophy of Science, 79 (April 2012, pp.183–206), and Clark Glymour, “Theoretical Equivalence and the Semantic View of Theories”, Philosophy of Science, 80,(April 2013), pp.286–297., and J. Azzouni, “A new characterization of scientific theories”, published online: 16 May 2014., and Newton C. A. Da Costa and Steven French, Science and Partial Truth, Oxford University Press, 2003.
- 28.
119 The argument is due to Otavio Bueno, conveyed in conversation with Da Costa and French.
- 29.
- 30.
This is not a form of instrumentalism that takes theories to be rules, and therefore lacking in truth value. The items in the schematic theories are sentential.
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Koslow, A. (2019). The Explanation of Laws: Two Neglected and Radically Different Theories. One Inspired by D. Hilbert; the Other Inspired by F. Ramsey. In: Laws and Explanations; Theories and Modal Possibilities. Synthese Library, vol 410. Springer, Cham. https://doi.org/10.1007/978-3-030-18846-7_8
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