Deductive-nomological model

The deductive-nomological 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". The DN model holds to a view of scientific explanation whose conditions of adequacy —semiformal but stated classically—are derivability, lawlikeness, empirical content, and truth.
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. 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, while following from a scientific theory's axiomatic structure.
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. Thus, given the explanans as initial, specific conditions C₁, C₂,... C_n plus general laws L₁, L₂,... L_n, the phenomenon E as explanandum is a deductive consequence, thereby scientifically explained.

Roots

's scientific explanation in Physics resembles the DN model, an idealized form of scientific explanation. 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. 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. At 1740, David Hume staked Hume's fork, highlighted the problem of induction, and found humans ignorant of either necessary or sufficient causality. Hume also highlighted the fact/value gap, as what is does not itself reveal what ought.
Near 1780, countering Hume's ostensibly radical empiricism, Immanuel Kant highlighted extreme rationalism—as by Descartes or Spinoza—and sought middle ground. Inferring the mind to arrange experience of the world into substance, space, and time, Kant placed the mind as part of the causal constellation of experience and thereby found Newton's theory of motion universally true, yet knowledge of things in themselves impossible. Safeguarding science, then, Kant paradoxically stripped it of scientific realism. Aborting Francis Bacon's inductivist mission to dissolve the veil of appearance to uncover the noumena—metaphysical view of nature's ultimate truths—Kant's transcendental idealism tasked science with simply modeling patterns of phenomena. Safeguarding metaphysics, too, it found the mind's constants holding also universal moral truths, and launched German idealism.
Auguste Comte found the problem of induction rather irrelevant since enumerative induction is grounded on the empiricism available, while science's point is not metaphysical truth. Comte found human knowledge had evolved from theological to metaphysical to scientific—the ultimate stage—rejecting both theology and metaphysics as asking questions unanswerable and posing answers unverifiable. Comte in the 1830s expounded positivism—the first modern philosophy of science and simultaneously a political philosophy—rejecting conjectures about unobservables, thus rejecting search for causes. Positivism predicts observations, confirms the predictions, and states a law, thereupon applied to benefit human society. From late 19th century into the early 20th century, the influence of positivism spanned the globe. Meanwhile, evolutionary theory's natural selection brought the Copernican Revolution into biology and eventuated in the first conceptual alternative to vitalism and teleology.

Growth

Whereas Comtean positivism posed science as description, logical positivism emerged in the late 1920s and posed science as explanation, perhaps to better unify empirical sciences by covering not only fundamental science—that is, fundamental physics—but special sciences, too, such as biology, psychology, economics, and anthropology. After defeat of National Socialism with World War II's close in 1945, logical positivism shifted to a milder variant, logical empiricism. All variants of the movement, which lasted until 1965, are neopositivism, sharing the quest of verificationism.
Neopositivists led emergence of the philosophy subdiscipline philosophy of science, researching such questions and aspects of scientific theory and knowledge. Scientific realism takes scientific theory's statements at face value, thus accorded either falsity or truth—probable or approximate or actual. Neopositivists held scientific antirealism as instrumentalism, holding scientific theory as simply a device to predict observations and their course, while statements on nature's unobservable aspects are elliptical at or metaphorical of its observable aspects, rather.
DN model received its most detailed, influential statement by Carl G Hempel, 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". Leading logical empiricist, Hempel embraced the Humean empiricist view that humans observe sequence of sensory events, not cause and effect, as causal relations and casual mechanisms are unobservables. DN model bypasses causality beyond mere constant conjunction: first an event like A, then always an event like B.
Hempel held natural laws—empirically confirmed regularities—as satisfactory, and if included realistically to approximate causality. In later articles, Hempel defended DN model and proposed probabilistic explanation by inductive-statistical model. DN model and IS model—whereby the probability must be high, such as at least 50%—together form covering law model, as named by a critic, William Dray. Derivation of statistical laws from other statistical laws goes to the deductive-statistical model. Georg Henrik von Wright, another critic, named the totality subsumption theory.

Decline

Amid failure of neopositivism's fundamental tenets, Hempel in 1965 abandoned verificationism, signaling neopositivism's demise. From 1930 onward, Karl Popper attacked positivism, although, paradoxically, Popper was commonly mistaken for a positivist. Even Popper's 1934 book embraces DN model, widely accepted as the model of scientific explanation for as long as physics remained the model of science examined by philosophers of science.
In the 1940s, filling the vast observational gap between cytology and biochemistry, cell biology arose and established existence of cell organelles besides the nucleus. Launched in the late 1930s, the molecular biology research program cracked a genetic code in the early 1960s and then converged with cell biology as cell and molecular biology, its breakthroughs and discoveries defying DN model by arriving in quest not of lawlike explanation but of causal mechanisms. Biology became a new model of science, while special sciences were no longer thought defective by lacking universal laws, as borne by physics.
In 1948, when explicating DN model and stating scientific explanation's semiformal conditions of adequacy, Hempel and Oppenheim acknowledged redundancy of the third, empirical content, implied by the other three—derivability, lawlikeness, and truth. In the early 1980s, upon widespread view that causality ensures the explanans' relevance, Wesley Salmon called for returning cause to because, and along with James Fetzer helped replace CA3 empirical content with CA3' strict maximal specificity.
Salmon introduced causal mechanical explanation, never clarifying how it proceeds, yet reviving philosophers' interest in such. Via shortcomings of Hempel's inductive-statistical model, Salmon introduced statistical-relevance model. Although DN model remained an idealized form of scientific explanation, especially in applied sciences, most philosophers of science consider DN model flawed by excluding many types of explanations generally accepted as scientific.