The deductive-nomological model (DN model) is a formal view of scientific explanation. The DN model poses scientific explanation as a deductive argument with at least one natural law among its premises. DN model goes by several names, including covering laws model, Hempel's model, Hempel–Oppenheim model, Popper–Hempel model, and subsumption theory (Niiniluoto 1995).
In the DN model, the statement of the phenomenon to be explained is the explanandum—which can be an event, law, or theory—whereas the premises stated to explain it are the explanans. The explanans must be true, contain at least one law, and entail the explanandum. Thus, given initial conditions C1, C2 . . . Cn plus general laws L1, L2 . . . Ln, event E is a deductive consequence, and has thereby been scientifically explained.
In the DN model, a law is a universal generalization that follows from a conditional proposition—If A, then B—and has empirical content testable.1 (A law differs from mere true regularity—for instance George always carries only $1 bills in his wallet—by a law's suggesting what must be true,2 and by being consequent of a scientific theory's axiomatic structure.3)
Auguste Comte's positivism, expounded in the 1830s, but suggested by Francis Bacon in 1620, was the first modern philosophy of science. The emergence of philosophy of science as a discipline within philosophy and distinct from science itself, however, occurred in the 20th century. Positivism had viewed science as description, whereas the logical positivists, who emerged in the 1920s under greater influence by David Hume and Ernst Mach than by Comte, accepted science as explanation, perhaps to better realize Comte's envisioned unity of all sciences by covering principles in the special sciences, too, for instance biology and anthropology.4
The question of proper scientific explanation is ancient, yet even Aristotle posed it as statement of initial conditions plus general laws, and the DN model resembles the aspiration of even primitive and folk explanations. The DN model received its most detailed and influential statement by Carl Hempel, however, first in his 1942 article "The function of general laws in history", and more explicitly with Paul Oppenheim in their 1948 article "Studies in the logic of explanation".5 The term deductive distinguishes the DN model's intended deterministic inferences from inductive inferences, probabilistic. The term nomological follows the Greek word νόμος or nomos, meaning "law".
A leading logical empiricist, Hempel embraced the Humean empiricist view that humans observe sequence of events, not cause and effect.4 Thus the DN model shuns addressing causality beyond mere constant conjunction—first event A and then always event B.4 Hempel's elucidation of DN model thus took natural laws—empirically confirmed regularities—to be satisfactory, and if formulated realistically to approximate causal explanation.6
In later articles, Hempel defended the DN model and proposed a probabilistic explanation as the inductive-statistical model (IS model).6 DN model and IS model together form the covering law model,6 as named by a critic, William Dray.7 (Derivation of statistical laws from other statistical laws goes to the deductive-statistical model (DS model).)8 Georg Hendrik von Wright, another critic, gave it the name subsumption theory.9
The logical empiricists' scientific epistemology verificationism and other variants of positivism were successfully refuted by Karl Popper's scientific epistemology falsificationism, offered in Popper's 1935 book Logik der Forschung, published in Austria, and translated by Popper into English for publication in 1959 as The Logic of Scientific Discovery. Yet even this work by Popper embraces the DN model,5 widely accepted as the model of scientific explanation for as long as physics remained the model of science examined by philosophers of science.
In philosophy of science, the epistemological is distinguished from the ontological.10 Ontology poses which categories of entities exist, and so although a scientific theory's ontological commitment can be modified in light of experience, an ontological commitment inevitably precedes scientific epistemology's empirical inquiry.11
Causal mechanisms, which exist as the natural world's structure itself, are ontological claims, the ontic. Natural laws, however, are statements made by humans as to knowledge of the natural world's states via human observations, and so are epistemological, the epistemic. Blurring the epistemic with the ontic—for instance incautiously presuming a natural law to refer to a causal mechanism—usually results in a category mistake.
Discarding ontic commitments, DN model permits a theory's laws to be reduced to—that is, subsumed under—a more fundamental theory's laws. The higher-level theory's laws are explained, in DN model, by the more fundamental theory, whose ontology subsumes the higher theory's ontology.10 Thus the epistemic success of Newton's theory of motion with its law of universal gravitation is reduced to—and thus explained by—Einstein's general theory of relativity, although Einstein discarded the ontic claim of Newton's theory that the law of universal gravitation's epistemic success predicting Kepler's laws of planetary motion was explained by Newton's hypothesized causal mechanism of a straightly attractive force instantly traversing supposedly empty space.
Thus, by omitting causal mechanism per se, DN model suits theory reduction, and coheres with the logical empiricist vision of eventually networking all scientific theories—even in special sciences like chemistry, biology, psychology, and economics—and then reducing all special sciences to a shared foundation of fundamental physics, fundamental science.12
By the DN model's problem of symmetry, if one asks, "Why is that shadow 20 feet long?", another can answer, "Because that flagpole is 15 feet tall, the Sun is at x angle, and laws of electromagnetism", but if one instead asked, "Why is that flagpole 15 feet tall?", another could answer, "Because that shadow is 20 feet long, the Sun is at x angle, and laws of electromagnetism", likewise a deduction from observed conditions and scientific laws, although this answer is clearly incorrect.6 By the problem of irrelevance, if one asks, "Why did that man not get pregnant?", one could in part answer, among the explanans, "Because he took birth control pills"—if indeed he took them—as DN model indicates nothing to forbid that observation among the explanans.
Thus many philosophers have concluded that causality is integral to scientific explanation.13 DN model offers a necessary condition of a causal explanation—successful prediction—but not sufficient conditions of causal explanation, as a universal regularity can include spurious relations or mere correlations, for instance z always following y, but not z because of y, instead y and then z as an effect of x.13 Indeed, by relating temperature, pressure, and volume of gas within a container, Boyle's law permits prediction of an unknown variable—volume, pressure, or temperature—but does not explain why to expect that unless one adds, perhaps, the kinetic theory of gases.13
Scientific explanations increasingly pose not determinism's universal generalization, but probabilism's chance. Smoking's causal contribution to lung cancer fails to meet the criteria even of the inductive-statistical model (IS model), which requires probability over 0.5 (50%).14 (Probability is standardly accepted to range from 0 (0%) to 1 (100%).) An applied science that applies statistics to discern probability of association between events, epidemiology cannot demonstrate causality, but consistently found higher incidence of lung cancer within smokers versus otherwise similar nonsmokers, although the overall proportion of smokers who develop lung cancer is modest.15 Versus nonsmokers, however, smokers as a group showed over 20 times the risk of lung cancer, and in conjunction with basic science and basic research, consensus followed that smoking had been scientifically explained as a cause of lung cancer.16
Most philosophers of science consider the DN model a flawed model of scientific explanation, since it fails to cover many types of explanations generally accepted as scientific.8 Still, fundamental physics has proceeded by theory reduction,17 approximating the covering laws model.
In fact, Ernst Mach had resisted Ludwig Boltzmann's reduction of thermodynamics—and thereby Boyle's law—to statistical mechanics because it rested on the kinetic theory of gas, which hinged on the atomic/molecular theory of matter. Interpreting matter as a variant of energy, Mach regarded molecules as "mathematical illusions".
In 1905, Einstein reduced statistical mechanics and Brownian motion—unexplained since reported in 1827 by botanist Robert Brown—to Newton's equations. By faith in Newton's theory, physicists at last began to widely accept that atoms and molecules exist. Yet later in 1905, Einstein's special theory of relativity refuted Newton's theory itself, and held the consequence of mass/energy equivalence, matter as a variant of energy. In 1919, the empirical success of Einstein's general theory of relativity was accepted as falsifying Newton's theory.
In the 1950s, Brownian motion and statistical mechanics were reduced instead to quantum electrodynamics (QED).17 By 1968, QED was reduced along with the weak nuclear field to the Standard Model's electroweak theory (EWT).17 Today, most theoretical physicists infer that the Standard Model reduces to superstring theory, explaining that atoms and molecules, after all, are vibrations of energy holding mathematical forms.17
Given the uncertainties of scientific realism, some conclude that as a science matures, it indeed discards causality, which concept is key in folk science since it raises comprehensibility of scientific explanation, but is dropped as a science matures since it lowers precision of scientific explanation.18 Even epidemiology is maturing to recognize the severe difficulties involved with the conception of causality.19
- Explanandum and explanans
- Hypothetico-deductive model
- Models of scientific inquiry
- Philosophy of science
- Scientific method
- Eleonora Montuschi, Objects in Social Science (London & New York: Continuum, 2003), pp 61–62
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), p 25
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), pp 27–28
- James Woodward, "Scientific explanation"—sec 1 "Background and introduction", in Zalta EN, ed,The Stanford Encyclopedia of Philosophy, Winter 2011 edn
- James Woodward, "Scientific explanation"—Article overview, Zalta EN, ed, The Stanford Encyclopedia of Philosophy, Winter 2011 edn
- Frederick Suppe, pp 619–621, in Suppe F, ed, The Structure of Scientific Theories, 2nd edn (Urbana IL: University of Illinois Press, 1977)
- Georg Hendrik von Wright, Explanation and Understanding (Ithaca NY: Cornell University Press, 1971), p 11
- Stuart Glennan, p 276, in Sarkar S & Pfeifer J, eds, The Philosophy of Science: An Encyclopedia, Volume 1: A–M (New York: Routledge, 2006)
- Manfred Riedel, pp 3–4, in Manninen J & Tuomela R, eds, Essays on Explanation and Understanding: Studies in the Foundation of Humanities and Social Sciences (Dordrecht: D Reidel Publishing, 1976)
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), p 11
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), p 9
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), p 29, 71
- John O'Shaughnessy, Explaining Buyer Behavior: Central Concepts and Philosophy of Science Issues (New York: Oxford University Press, 1992), pp 17–19
- William Bechtel, Philosophy of Science: An Overview for Cognitive Science (Hillsdale NJ: Lawrence Erlbaum Assoc, 1988), p 38–39
- Kenneth J Rothman & Sander Greenland, "Causation and causal inference in epidemiology", Am J Public Health, 2005;95 Suppl 1:S144–50
- Paolo Boffetta, "Causation in the presence of weak associations", Crit Rev Food Sci Nutr, 2010 Dec;50(s1):13–16
- John H Schwarz, "Recent developments in superstring theory", Proc Natl Acad Sci U S A, 1998 Mar 17;95(6):2750–7
- John D Norton, "Causation as folk science", Philosopher's Imprint, 2003;3(4)
- Lucien R Karhausen, "Causation: The elusive grail of epidemiology", Med Health Care Philos, 2000;3(1):59-67
- Hempel, Carl G.; Oppenheim, Paul (1948). "Studies in the Logic of Explanation". Philosophy of Science 1948 (15): 135–175. Reproduced in Hempel, Carl G. (1965). Aspects of Scientific Explanation. New York: Free Press.
- Mayes, Randolph G. (2006). "Theories of Explanation". In Fieser; Dowden. The Internet Encyclopedia of Philosophy.
- Niiniluoto, Ilkka (1995). "Covering Law Model". In Audi, Robert. The Cambridge Dictionary of Philosophy. New York: Cambridge University Press. ISBN 0-521-40224-7.
- Popper, Karl (1959). The Logic of Scientific Discovery. London: Hutchinson.
- Salmon, Wesley (1990). Four Decades of Scientific Explanation. Minneapolis: University of Minnesota Press. ISBN 0-8166-1825-9.
- Woodward, James (Jan 16, 2009). "Scientific Explanation". In Zalta, Edward N. The Stanford Encyclopedia of Philosophy. Stanford University. Retrieved Nov 29, 2012.
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