The deductive-nomological model (DN model) of scientific explanation, also known as Hempel's model, the Hempel–Oppenheim model, the Popper–Hempel model, or the covering law model, is a formal view of scientifically answering questions asking, "Why...?". The DN model poses scientific explanation as a deductive structure, one where truth of its premises entails truth of its conclusion, hinged on accurate prediction or postdiction of the phenomenon to be explained.
Because of problems concerning humans' ability to define, discover, and know causality, this was omitted in initial formulations of the DN model. Causality was thought to be incidentally approximated by realistic selection of premises that derive the phenomenon of interest from observed starting conditions plus general laws. Still, the DN model formally permitted causally irrelevant factors. Also, derivability from observations and laws sometimes yielded absurd answers.
When logical empiricism fell out of favor in the 1960s, the DN model was widely seen as a flawed or greatly incomplete model of scientific explanation. Nonetheless, it remained an idealized version of scientific explanation, and one that was rather accurate when applied to modern physics. In the early 1980s, a revision to the DN model emphasized maximal specificity for relevance of the conditions and axioms stated. Together with Hempel's inductive-statistical model, the DN model forms scientific explanation's covering law model, which is also termed, from critical angle, subsumption theory.
Form The term deductive distinguishes the DN model's intended determinism from the probabilism of inductive inferences. The term nomological is derived from the Greek word νόμος or nomos, meaning "law".Woodward, "Scientific explanation", §2 "The DN model", in SEP, 2011. The DN model holds to a view of scientific explanation whose conditions of adequacy (CA)—semiformal but stated classically—are derivability (CA1), lawlikeness (CA2), empirical content (CA3), and truth (CA4).James Fetzer, ch 3 "The paradoxes of Hempelian explanation", in Fetzer, ed, Science, Explanation, and Rationality (Oxford U P, 2000), p. 113.
In the DN model, a law axiomatizes an unrestricted generalization from antecedent A to consequent B by conditional proposition—If A, then B—and has empirical content testable.Montuschi, Objects in Social Science (Continuum, 2003), pp. 61–62. A law differs from mere true regularity—for instance, George always carries only $1 bills in his wallet—by supporting counterfactual claims and thus suggesting what must be true,Bechtel, Philosophy of Science (Lawrence Erlbaum, 1988), ch 2, subch "DN model of explanation and HD model of theory development", pp. 25–26. while following from a scientific theory's axiomatic structure.Bechtel, Philosophy of Science (Lawrence Erlbaum, 1988), ch 2, subch "Axiomatic account of theories", pp. 27–29.
The phenomenon to be explained is the explanandum—an event, law, or theory—whereas the premises to explain it are explanans, true or highly confirmed, containing at least one universal law, and entailing the explanandum.Suppe, "Afterword—1977", "Introduction", §1 "Swan song for positivism", §1A "Explanation and intertheoretical reduction", pp. 619–24, in Suppe, ed, Structure of Scientific Theories, 2nd edn (U Illinois P, 1977). Thus, given the explanans as initial, specific conditions C1, C2, ... Cn plus general laws L1, L2, ... Ln, the phenomenon E as explanandum is a deductive consequence, thereby scientifically explained.
Roots
Aristotle's scientific explanation in Physics resembles the DN model, an idealized form of scientific explanation.Kenneth F Schaffner, "Explanation and causation in biomedical sciences", pp. 79–125, in Laudan, ed, Mind and Medicine (U California P, 1983), p. 81. The framework of Aristotelian physics—Aristotelian metaphysics—reflected the perspective of this principally biologist, who, amid living entities' undeniable purposiveness, formalized vitalism and teleology, an intrinsic morality in nature.G Montalenti, ch 2 "From Aristotle to Democritus via Darwin", in Ayala & Dobzhansky, eds, Studies in the Philosophy of Biology (U California P, 1974). With emergence of Copernicanism, however, Descartes introduced mechanical philosophy, then Newton rigorously posed lawlike explanation, both Descartes and especially Newton shunning teleology within natural philosophy.In the 17th century, Descartes as well as Isaac Newton firmly believed in God as nature's designer and thereby firmly believed in natural purposiveness, yet found teleology to be outside science's inquiry (Bolotin, Approach to Aristotle's Physics, pp. 31–33). By 1650, formalizing heliocentrism and launching mechanical philosophy, Cartesian physics overthrew geocentrism as well as Aristotelian physics. In the 1660s, Robert Boyle sought to lift chemistry as a new discipline from alchemy. Newton more especially sought the laws of nature—simply the regularities of phenomena—whereby Newtonian physics, reducing celestial science to terrestrial science, ejected from physics the vestige of Aristotelian metaphysics, thus disconnecting physics and alchemy/chemistry, which then followed its own course, yielding chemistry around 1800. At 1740, David HumeNicknames for principles attributed to Hume—Hume's fork, problem of induction, Hume's law—were not created by Hume but by later philosophers labeling them for ease of reference. staked Hume's fork,By Hume's fork, the truths of mathematics and logic as formal sciences are universal through "relations of ideas"—simply abstract truths—thus knowable without experience. On the other hand, the claimed truths of empirical sciences are contingent on "fact and real existence", knowable only upon experience. By Hume's fork, the two categories never cross. Any treatises containing neither can contain only "sophistry and illusion". (Flew, Dictionary, "Hume's fork", p. 156). highlighted the problem of induction,Not privy to the world's either necessities or impossibilities, but by force of habit or mental nature, humans experience sequence of sensory events, find seeming constant conjunction, make the unrestricted generalization of an enumerative induction, and justify it by presuming uniformity of nature. Humans thus attempt to justify a minor induction by adding a major induction, both logically invalid and unverified by experience—the problem of induction—how humans irrationally presume discovery of causality. (Chakraborti, Logic, p. 381; Flew, Dictionary, "Hume", p. 156. and found humans ignorant of either necessary or sufficient causality.For more discursive discussions of types of causality—necessary, sufficient, necessary and sufficient, component, sufficient component, counterfactual—see Rothman & Greenland, Parascandola & Weed, as well as Kundi. Following is more direct elucidation:
A necessary cause is a causal condition required for an event to occur. A sufficient cause is a causal condition complete to produce an event. Necessary is not always sufficient, however, since other casual factors—that is, other component causes—might be required to produce the event. Conversely, a sufficient cause is not always a necessary cause, since differing sufficient causes might likewise produce the event. Strictly speaking, a sufficient cause cannot be a single factor, as any causal factor must act casually through many other factors. And although a necessary cause might exist, humans cannot verify one, since humans cannot check every possible state of affairs. (Language can state necessary causality as a tautology—a statement whose terms' arrangement and meanings render it is logically true by mere definition—which, as an analytic statement, is uninformative about the actual world. A statement referring to and contingent on the world's actualities is a synthetic statement, rather.)
Sufficient causality is more actually sufficient component causality—a complete set of component causes interacting within a causal constellation—which, however, is beyond humans' capacity to fully discover. Yet humans tend intuitively to conceive of causality as necessary and sufficient—a single factor both required and complete—the one and only cause, the cause. One may so view flipping a light switch. The switch's flip was not sufficient cause, however, but contingent on countless factors—intact bulb, intact wiring, circuit box, bill payment, utility company, neighborhood infrastructure, engineering of technology by Thomas Edison and Nikola Tesla, explanation of electricity by James Clerk Maxwell, harnessing of electricity by Benjamin Franklin, metal refining, metal mining, and on and on—while, whatever the tally of events, nature's causal mechanical structure remains a mystery.
From a Humean perspective, the light's putative inability to come on without the switch's flip is neither a logical necessity nor an empirical finding, since no experience ever reveals that the world either is or will remain universally uniform as to the aspects appearing to bind the switch's flip as the necessary event for the light's coming on. If the light comes on without switch flip, surprise will affect one's mind, but one's mind cannot know that the event violated nature. As just a mundane possibility, an activity within the wall could have connected the wires and completed the circuit without the switch's flip.
Though apparently enjoying the scandals that trailed his own explanations, Hume was very practical and his skepticism was quite uneven (Flew p. 156). Although Hume rejected orthodox theism and sought to reject metaphysics, Hume supposedly extended Newtonian method to the human mind, which Hume, in a sort of antiCopernican move, placed as the pivot of human knowledge (Flew p. 154). Hume thus placed his own theory of knowledge on par with Newton's theory of motion (Buckle pp. 70–71, Redman pp. 182–83, Schliesser § abstract). Hume found enumerative induction an unavoidable custom required for one to live (Gattei pp. 28–29). Hume found constant conjunction to reveal a modest causality type: counterfactual causality. Silent as to causal role—whether necessity, sufficiency, component strength, or mechanism—counterfactual causality is simply that alteration of a factor prevents or produces the event of interest. Hume also highlighted the fact/value gap, as what is does not itself reveal what ought.Hume noted that authors ubiquitously continue for some time stating facts and then suddenly switch to stating norms—supposedly what should be—with barely explanation. Yet such values, as in ethics or aesthetics or political philosophy, are not found true merely by stating facts: is does not itself reveal ought. Hume's law is the principle that the fact/value gap is unbridgeable—that no statements of facts can ever justify norms—although Hume himself did not state that. Rather, some later philosophers found Hume to merely stop short of stating it, but to have communicated it. Anyway, Hume found that humans acquired morality through experience by communal reinforcement. (Flew, Dictionary, "Hume's law", p. 157 & "Naturalistic fallacy", pp. 240–41; Wootton, Modern Political Thought, p. 306.)