Deductive-nomological model

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 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).

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. 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.

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. 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. 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. 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, Derivation of statistical laws from other statistical laws goes to the deductive-statistical model (DS 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. 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. 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.

Natural laws, so called, are statements of humans' observations, thus are epistemological—concerning human knowledge—the epistemic. Causal mechanisms and structures existing putatively independently of minds exist, or would exist, in the natural world's structure itself, and thus are ontological, the ontic. Blurring epistemic with ontic—as by incautiously presuming a natural law to refer to a causal mechanism, or to trace structures realistically during unobserved transitions, or to be true regularities always unvarying—tends to generate a category mistake.

Discarding ontic commitments, including causality per se, DN model permits a theory's laws to be reduced to—that is, subsumed by—a more fundamental theory's laws. The higher theory's laws are explained in DN model by the lower theory's laws. is through a causal mechanism of a straightly attractive force instantly traversing absolute space despite absolute time.

Covering law model reflects neopositivism's vision of empirical science, a vision interpreting or presuming unity of science, whereby all empirical sciences are either fundamental science—that is, fundamental physics—or are special sciences, whether astrophysics, chemistry, biology, geology, psychology, economics, and so on. All special sciences would network via covering law model. And by stating boundary conditions while supplying bridge laws, any special law would reduce to a lower special law, ultimately reducing—theoretically although generally not practically—to fundamental science.

Weaknesses

By DN model, 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". 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 simple correlations, for instance Z always following Y, but not Z because of Y, instead Y and then Z as an effect of X. (Probability standardly ranges from 0 (0%) to 1 (100%).) Epidemiology, an applied science that uses statistics in search of associations between events, cannot show causality, but consistently found higher incidence of lung cancer in smokers versus otherwise similar nonsmokers, although the proportion of smokers who develop lung cancer is modest. Versus nonsmokers, however, smokers as a group showed over 20 times the risk of lung cancer, and in conjunction with basic research, consensus followed that smoking had been scientifically explained as a cause of lung cancer, responsible for some cases that without smoking would not have occurred,

Covering action

Through lawlike explanation, fundamental physics—often perceived as fundamental science—has proceeded through intertheory relation and theory reduction, thereby resolving experimental paradoxes to great historical success, resembling covering law model. In early 20th century, Ernst Mach as well as Wilhelm Ostwald had resisted Ludwig Boltzmann's reduction of thermodynamics—and thereby Boyle's law—to statistical mechanics partly because it rested on kinetic theory of gas, hinging on atomic/molecular theory of matter. as even Boltzmann thought possible.

In 1905, via statistical mechanics, Albert Einstein predicted the phenomenon Brownian motion—unexplained since reported in 1827 by botanist Robert Brown. Meanwhile, all known physical phenomena were gravitational or electromagnetic, whose two theories misaligned. Yet belief in aether as the source of all physical phenomena was virtually unanimous. At experimental paradoxes, physicists modified the aether's hypothetical properties.

Finding the luminiferous aether a useless hypothesis, Einstein in 1905 a priori unified all inertial reference frames to state special principle of relativity, which, by omitting aether, converted space and time into relative phenomena whose relativity aligned electrodynamics with the Newtonian principle Galilean relativity or invariance. Originally epistemic or instrumental, this was interpreted as ontic or realist—that is, a causal mechanical explanation—and the principle became a theory, refuting Newtonian gravitation. By predictive success in 1919, general relativity apparently overthrew Newton's theory, a revolution in science resisted by many yet fulfilled around 1930.

In 1925, Werner Heisenberg as well as Erwin Schrödinger independently formalized quantum mechanics (QM). Despite clashing explanations, the two theories made identical predictions. From it, Dirac interpreted and predicted the electron's antiparticle, soon discovered and termed positron, but the QED failed electrodynamics at high energies.

In 1941, Richard Feynman introduced QM's path integral formalism, which if taken toward interpretation as a causal mechanical model clashes with Heisenberg's matrix formalism and with Schrödinger's wave formalism, Next, working on QED, Feynman sought to model particles without fields and find the vacuum truly empty. is apparently an effect of a field, Feynman failed.

Meeting in 1947, Freeman Dyson, Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga soon introduced renormalization, a procedure converting QED to physics' most predictively precise theory, subsuming chemistry, optics, and statistical mechanics. QED thus won physicists' general acceptance. and called for an aether. In 1947, Willis Lamb had found unexpected motion of electron orbitals, shifted since the vacuum is not truly empty. Yet emptiness was catchy, abolishing aether conceptually, and physics proceeded ostensibly without it, renamed vacuum, which—as such—is nonexistent. General philosophers of science commonly believe that aether, rather, is fictitious, "relegated to the dustbin of scientific history ever since" 1905 brought special relativity. Einstein was noncommittal to aether's nonexistence, and to explain motion was led back to aether in general relativity. Yet resistance to relativity theory became associated with earlier theories of aether, whose word and concept became taboo. but Einstein aether, too, was opposed. by abstract geometric relations lacking ghostly or fluid medium.

By 1970, QED along with weak nuclear field was reduced to electroweak theory (EWT), and the strong nuclear field was modeled as quantum chromodynamics (QCD). not truly fundamental. As QCD's particles are considered nonexistent in the everyday world, Confirmation of the Higgs particle, modeled as a condensation within the Higgs field, corroborates aether, particles being variant forms of distributed energy, how particles colliding at vast speed experience that energy's transformation into mass, producing heavier particles, although physicists' talk promotes confusion. As "the contemporary locus of metaphysical research", QFTs pose particles not as existing individually, yet as excitation modes of fields, apparently unifying all physical phenomena as the more fundamental causal reality, as long ago foreseen. Nature's deeper aspects, still unknown, might elude any possible field theory. even more Newtonian than was Isaac Newton. By now, most theoretical physicists infer that the four, known fundamental interactions would reduce to superstring theory, whereby atoms and molecules, after all, are energy vibrations holding mathematical, geometric forms. some conclude that the concept causality raises comprehensibility of scientific explanation and thus is key folk science, but compromises precision of scientific explanation and is dropped as a science matures. Even epidemiology is maturing to heed the severe difficulties with presumptions about causality.

Notes

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