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 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. 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.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 ''C''₁, ''C''₂, ... ''C''_''n'' plus general laws ''L''₁, ''L''₂, ... ''L''_''n'', 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. 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 philosophyBourdeau, "Auguste Comte", §§ "Abstract"
"Introduction"
in Zalta, ed, ''SEP'', 2013.—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.Woodward
"Scientific explanation"
§1 "Background and introduction", in '' SEP'', 2011. After defeat of National Socialism with World War II's close in 1945, logical positivism shifted to a milder variant, ''logical empiricism''.Friedman, ''Reconsidering Logical Positivism'' (Cambridge U P, 1999)
p. xii
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.Chakravartty
"Scientific realism"
§1.2 "The three dimensions of realist commitment", in ''SEP'', 2013: "Semantically, realism is committed to a literal interpretation of scientific claims about the world. In common parlance, realists take theoretical statements at 'face value'. According to realism, claims about scientific entities, processes, properties, and relations, whether they be observable or unobservable, should be construed literally as having truth values, whether true or false. This semantic commitment contrasts primarily with those of so-called instrumentalist epistemologies of science, which interpret descriptions of unobservables simply as instruments for the prediction of observable phenomena, or for systematizing observation reports. Traditionally, instrumentalism holds that claims about unobservable things have no literal meaning at all (though the term is often used more liberally in connection with some antirealist positions today). Some antirealists contend that claims involving unobservables should not be interpreted literally, but as elliptical for corresponding claims about observables". 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.Chakravartty
"Scientific realism"
§4 "Antirealism: Foils for scientific realism", §4.1 "Empiricism", in ''SEP'', 2013: "Traditionally, instrumentalists maintain that terms for unobservables, by themselves, have no meaning; construed literally, statements involving them are not even candidates for truth or falsity. The most influential advocates of instrumentalism were the logical empiricists (or logical positivists), including Rudolf Carnap and Carl Hempel, associated with the Vienna Circle group of philosophers and scientists as well as important contributors elsewhere. In order to rationalize the ubiquitous use of terms which might otherwise be taken to refer to unobservables in scientific discourse, they adopted a non-literal semantics according to which these terms acquire meaning by being associated with terms for observables (for example, 'electron' might mean 'white streak in a cloud chamber'), or with demonstrable laboratory procedures (a view called ' operationalism'). Insuperable difficulties with this semantics led ultimately (in large measure) to the demise of logical empiricism and the growth of realism. The contrast here is not merely in semantics and epistemology: a number of logical empiricists also held the neo-Kantian view that ontological questions 'external' to the frameworks for knowledge represented by theories are also meaningless (the choice of a framework is made solely on pragmatic grounds), thereby rejecting the metaphysical dimension of realism (as in Carnap 1950)".

* Okasha, ''Philosophy of Science'' (Oxford U P, 2002)
p. 62
"Strictly we should distinguish two sorts of anti-realism. According to the first sort, talk of unobservable entities is not to be understood literally at all. So when a scientist puts forward a theory about electrons, for example, we should not take him to be asserting the existence of entities called 'electrons'. Rather, his talk of electrons is metaphorical. This form of anti-realism was popular in the first half of the 20th century, but few people advocate it today. It was motivated largely by a doctrine in the philosophy of language, according to which it is not possible to make meaningful assertions about things that cannot in principle be observed, a doctrine that few contemporary philosophers accept. The second sort of anti-realism accepts that talk of unobservable entities should be taken at face value: if a theory says that electrons are negatively charged, it is true if electrons do exist and are negatively charged, but false otherwise. But we will never know which, says the anti-realist. So the correct attitude towards the claims that scientists make about unobservable reality is one of total agnosticism. They are either true or false, but we are incapable of finding out which. Most modern anti-realism is of this second sort".

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'' (IS 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'' (DS model).Woodward
"Scientific explanation"
§2 "The DN model", §2.3 "Inductive statistical explanation", in Zalta, ed, ''SEP'', 2011.Stuart Glennan, "Explanation", § "Covering-law model of explanation", in Sarkar & Pfeifer, eds, ''Philosophy of Science'' (Routledge, 2006)
p. 276
Georg Henrik von Wright, another critic, named the totality ''subsumption theory''.Manfred Riedel, "Causal and historical explanation", in Manninen & Tuomela, eds, ''Essays on Explanation and Understanding'' (D Reidel, 1976)
pp. 3–4

Decline

Amid failure of neopositivism's fundamental tenets, Hempel in 1965 abandoned verificationism, signaling neopositivism's demise.
Fetzer
"Carl Hempel"
§3 "Scientific reasoning", in '' SEP'', 2013: "The need to dismantle the verifiability criterion of meaningfulness together with the demise of the observational/theoretical distinction meant that logical positivism no longer represented a rationally defensible position. At least two of its defining tenets had been shown to be without merit. Since most philosophers believed that Quine had shown the analytic/synthetic distinction was also untenable, moreover, many concluded that the enterprise had been a total failure. Among the important benefits of Hempel's critique, however, was the production of more general and flexible criteria of ''cognitive significance'' in Hempel (1965b), included in a collection of his studies, ''Aspects of Scientific Explanation'' (1965d). There he proposed that ''cognitive significance'' could not be adequately captured by means of principles of verification or falsification, whose defects were parallel, but instead required a far more subtle and nuanced approach.

Hempel suggested multiple criteria for assessing the ''cognitive significance'' of different theoretical systems, where significance is not categorical but rather a matter of degree: 'Significant systems range from those whose entire extralogical vocabulary consists of observation terms, through theories whose formulation relies heavily on theoretical constructs, on to systems with hardly any bearing on potential empirical findings' (Hempel 1965b: 117). The criteria Hempel offered for evaluating the 'degrees of significance' of theoretical systems (as conjunctions of hypotheses, definitions, and auxiliary claims) were (a) the clarity and precision with which they are formulated, including explicit connections to observational language; (b) the systematic—explanatory and predictive—power of such a system, in relation to observable phenomena; (c) the formal simplicity of the systems with which a certain degree of systematic power is attained; and (d) the extent to which those systems have been confirmed by experimental evidence (Hempel 1965b). The elegance of Hempel's study laid to rest any lingering aspirations for simple criteria of 'cognitive significance' and signaled the demise of logical positivism as a philosophical movement". From 1930 onward, Karl Popper attacked positivism, although, paradoxically, Popper was commonly mistaken for a positivist.Popper, "Against big words", ''In Search of a Better World'' (Routledge, 1996)
pp. 89–90
Hacohen, ''Karl Popper: The Formative Years'' (Cambridge U P, 2000)
pp. 212–13
Even Popper's 1934 book embraces DN model,Woodward, "Scientific explanation", in Zalta, ed, ''SEP'', 2011
abstract
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.Bechtel, ''Discovering Cell Mechanisms'' (Cambridge U P, 2006), es
pp. 24–25
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 (IS model), Salmon introduced '' statistical-relevance model'' (SR 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.

Strengths

As theory of knowledge, epistemology differs from ontology, which is a subbranch of metaphysics, theory of reality. Ontology proposes categories of being—what sorts of things exist—and so, although a scientific theory's ontological commitment can be modified in light of experience, an ontological commitment inevitably precedes empirical inquiry.Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988)
ch 1
subch "Areas of philosophy that bear on philosophy of science", § "Metaphysics", pp. 8–9, § "Epistemology", p. 11.

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. Thus, the epistemic success of Newtonian theory's law of universal gravitation is reduced to—thus explained by—Albert Einstein's general theory of relativity, although Einstein's discards Newton's ontic claim that universal gravitation's epistemic success predicting Kepler's laws of planetary motion 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.Reutlinger, Schurz & Hüttemann
"Ceteris paribus"
§ 1.1 "Systematic introduction", in Zalta, ed, ''SEP'', 2011. 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.Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), ch 5, subch "Theory reduction model and the unity of science program" pp. 72–76. (''Boundary conditions'' are specified conditions whereby the phenomena of interest occur. ''Bridge laws'' translate terms in one science to terms in another science.)Bem & de Jong, ''Theoretical Issues'' (Sage, 2006)
pp. 45–47

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". Yet by problem of symmetry, 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, but an answer clearly incorrect. 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 he factually took them, and the law of their preventing pregnancy—as covering law model poses no restriction to bar that observation from the explanans.

Many philosophy of science, philosophers have concluded that causality is integral to scientific explanation.O'Shaughnessy, ''Explaining Buyer Behavior'' (Oxford U P, 1992)
pp. 17–19
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''. 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.

Scientific explanations increasingly pose not determinism's universal laws, but probabilism's chance, ''ceteris paribus'' laws. Smoking's contribution to lung cancer fails even the inductive-statistical model (IS model), requiring probability over 0.5 (50%). (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, a probabilistic counterfactual causality.Making no commitment as to the particular causal ''role''—such as necessity, or sufficiency, or component strength, or mechanism—''counterfactual causality'' is simply that alteration of a factor from its factual state prevents or produces by any which way the event of interest.

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,Schwarz
"Recent developments in string theory"
''Proc Natl Acad Sci U S A'', 1998; 95:2750–7, es
Fig 1
resembling covering law model.Ben-Menahem, ''Conventionalism'' (Cambridge U P, 2006)
p. 71
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,Spohn, ''Laws of Belief'' (Oxford U P, 2012)
p. 306
hinging on atomic theory of matter, atomic/molecular theory of matter. Mach as well as Ostwald viewed matter as a variant of energy, and molecules as mathematical illusions,Newburgh ''et al''
"Einstein, Perrin, and the reality of atoms"
, ''Am J Phys'', 2006, p. 478. as even Boltzmann thought possible.For brief review of Boltmann's view, see ch 3 "Philipp Frank", § 1 "Thomas Samuel Kuhn, T S Kuhn's interview", in Blackmore ''et al'', eds, ''Ernst Mach's Vienna 1895–1930'' (Kluwer, 2001)
p. 63
as Frank was a student of Boltzmann soon after Mach's retirement. See "Notes"
pp. 79–80
#12 for views of Mach and of Ostwald, #13 for views of contemporary physicists generally, and #14 for views of Albert Einstein, Einstein. The more relevant here is #12: "Mach seems to have had several closely related opinions concerning atomism. First, he often thought the theory might be useful in physics as long as one did not believe in the scientific realism, reality of atoms. Second, he believed it was difficult to apply the atomic theory to both psychology and physics. Third, his own theory of elements is often called an 'atomistic theory' in psychology in contrast with both gestalt theory and a continuum theory of experience. Fourth, when critical of the reality of atoms, he normally meant the Greek sense of 'indivisible substance' and thought Boltzmann was being evasive by advocating divisible atoms or 'corpuscles' such as would become normal after J J Thomson and the distinction between electrons and atomic nucleus, nuclei. Fifth, he normally called physical atoms 'things of thought' and was very happy when Ostwald seemed to refute the reality of atoms in 1905. And sixth, after Ostwald returned to atomism in 1908, Mach continued to defend Ostwald's 'energeticist' alternative to atomism".

In 1905, via statistical mechanics, Albert Einstein predicted the phenomenon Brownian motion—unexplained since reported in 1827 by botanist Robert Brown (Scottish botanist from Montrose), Robert Brown. Soon, most physicists accepted that atoms and molecules were unobservable yet real. Also in 1905, Einstein explained the electromagnetic field's energy as distributed in ''particles'', doubted until this helped resolve atomic theory in the 1910s and 1920s. Meanwhile, all known physical phenomena were gravitational or timeline of electromagnetic theory, 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,Tavel, ''Contemporary Physics'' (Rutgers U P, 2001), pp
66
Einstein in 1905 ''a priori knowledge, a priori'' unified all inertial frame of reference, reference frames to state special ''principle'' of relativity, which, by omitting aether,Cordero, ''EPSA Philosophy of Science'' (Springer, 2012)
pp. 29–30
converted space and time into ''relative'' phenomena whose relativity aligned classical electrodynamics, electrodynamics with the Newtonian principle Galilean invariance, Galilean relativity or invariance. Originally epistemic or instrumentalism, instrumental, this was interpreted as ontic or scientific realism, realist—that is, a causal mechanical explanation—and the ''principle'' became a ''theory'', refuting Newtonian gravitation. By predictive success Solar eclipse of May 29, 1919, 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).Cushing, ''Quantum Mechanics'' (U Chicago P, 1994)
pp. 113–18
Despite clashing explanations,Schrödinger's Schrödinger equation, wave mechanics posed an electron's charge smeared across space as a wavefunction, waveform, later reinterpreted as the electron probability amplitude, manifesting across space probabilistically but nowhere definitely while eventually building up that deterministic waveform. Heisenberg's matrix mechanics confusingly talked of ''operator (quantum mechanics), operators'' acting on ''quantum states''. Richard Feynman introduced QM's path integral formulation, path integral formalism—interpretable as a particle traveling all paths imaginable, canceling themselves, leaving just one, the most efficient—predictively identical with Heisenberg's matrix mechanics, matrix formalism and with Schrödinger equation, Schrödinger's wave formalism. the two theories made identical predictions. Paul Dirac's 1928 Dirac equation, model of the electron was set to special relativity, launching quantum mechanics, QM into the first quantum field theory (QFT), quantum electrodynamics (QED).Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999)
pp. 393–95
From it, Dirac interpreted and predicted the electron's antiparticle, soon discovered and termed ''positron'',Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999)
p. 394
but the QED failed electrodynamics at high energies. Elsewhere and otherwise, strong nuclear force and weak nuclear force were discovered.

In 1941, Richard Feynman introduced QM's path integral formulation, path integral formalism, which if taken toward ''interpretation'' as a causal mechanical model clashes with Heisenberg's matrix mechanics, matrix formalism and with Schrödinger equation, Schrödinger's wave formalism, although all three are empirically identical, sharing predictions.From 1925 to 1926, independently but nearly simultaneously, Werner Heisenberg as well as Erwin Schrödinger developed quantum mechanics (Zee in Feynman, ''QED''
p. xiv
. Schrödinger introduced Schrödinger equation, wave mechanics, whose wave function is discerned by a partial differential equation, now termed the ''Schrödinger equation'' (p xiv). Heisenberg, who also stated the uncertainty principle, along with Max Born and Pascual Jordan introduced matrix mechanics, which rather confusingly talked of ''operator (quantum mechanics), operators'' acting on ''quantum states'' (p xiv). If taken as causal mechanically explanatory, the two formalisms vividly disagree, and yet are indiscernible empirically, that is, when not used for ''interpretation'', and taken as simply ''scientific formalism, formalism''
p. xv
.
In 1941, at a party in a tavern in Princeton, New Jersey, visiting physicist Herbert Jehle mentioned to Richard Feynman a different formalism suggested by Paul Dirac, who developed bra–ket notation, in 1932 (p xv). The next day, Feynman completed Dirac's suggested approach as ''sum over histories'' or ''sum over paths'' or ''path integral formulation, path integrals'' (p xv). Feynman would joke that this approach—which sums all possible paths that a particle could take, as though the particle actually takes them all, canceling themselves out except for one pathway, the particle's most efficient—abolishes the uncertainty principle
p. xvi
. All empirically equivalent, Schrödinger's wave formalism, Heisenberg's matrix formalism, and Feynman's path integral formalism all incorporate the uncertain principle (p xvi).

There is no particular barrier to additional formalisms, which could be, simply have not been, developed and widely disseminated
p. xvii
. In a particular physical discipline, however, and on a particular problem, one of the three formalisms might be easier than others to operate
pp. xvi–xvii
. By the 1960s, path integral formalism virtually vanished from use, while matrix formalism was the "canonical"
p. xvii
. In the 1970s, path integral formalism made a "roaring comeback", became the predominant means to make predictions from quantum field theory, QFT, and impelled Feynman to an aura of mystique
p. xviii
. Next, working on QED, Feynman sought to model particles without fields and find the vacuum truly empty. As each known fundamental force is apparently an effect of a field, Feynman failed. Louis de Broglie's waveparticle duality had rendered atomism—indivisible particles in a void—untenable, and highlighted the very notion of discontinuous particles as self-contradictory.

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,Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999)
p. 395
Schweber

(Princeton U P, 1994). subsuming chemistry, optics, and statistical mechanics.Feynman, ''QED'' (Princeton U P, 2006)
p. 5
QED thus won physicists' general acceptance. Paul Dirac criticized its need for renormalization as showing its unnaturalness,Torretti, ''Philosophy of Physics'', (Cambridge U P, 1999)
pp. 395–96
and called for an aether.Cushing, ''Quantum Mechanics'' (U Chicago P, 1994)
pp. 158–59
In 1947, Willis Lamb had found unexpected motion of electron configuration, electron orbitals, Lamb shift, shifted since the vacuum is not truly empty. Yet ''emptiness'' was catchy, abolishing aether conceptually, and physics proceeded ostensibly without it, even suppressing it. Meanwhile, "sickened by untidy math, most philosophy of physics, philosophers of physics tend to neglect QED".

Physicists have feared even mentioning ''aether'',
* Vongeh
"Higgs discovery rehabilitating despised Einstein Aether"
''Science 2.0'', 2011.
* renamed ''vacuum'',Riesselman

''Inquiring Minds'', Fermilab, 2008. 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.Pigliucci, ''Answers for Aristotle'' (Basic Books, 2012)
p. 119
"But the antirealist will quickly point out that plenty of times in the past scientists have posited the existence of unobservables that were apparently necessary to explain a phenomenon, only to discover later on that such unobservables did not in fact exist. A classic case is the aether, a substance that was supposed by nineteenth-century physicists to permeate all space and make it possible for electromagnetic radiation (like light) to propagate. It was Einstein's special theory of relativity, proposed in 1905, that did away with the necessity of aether, and the concept has been relegated to the dustbin of scientific history ever since. The antirealists will relish pointing out that modern physics features a number of similarly unobservable entities, from quantum foam, quantum mechanical 'foam' to dark energy, and that the current crop of scientists seems just as confident about the latter two as their nineteenth-century counterparts were about aether". Einstein was noncommittal to aether's nonexistence, simply said it superfluous. Abolishing Newtonian motion for electrodynamic primacy, however, Einstein inadvertently reinforced aether,Wilczek, ''Lightness of Being'' (Basic Books, 2008)
pp. 78–80
and to explain motion was led back to aether in general relativity.Laughlin, ''A Different Universe'' (Basic Books, 2005)
pp. 120–21
Yet resistance to relativity theory became associated with earlier theories of aether, whose word and concept became taboo. Einstein explained special relativity's compatibility with an aether,Einstein, "Ether", ''Sidelights'' (Methuen, 1922)
pp. 14–18
but Einstein aether, too, was opposed. Objects became conceived as pinned directly on spacetime, space and time by abstract geometric relations lacking ghostly or fluid medium.Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999)
p. 180

By 1970, QED along with weak force, weak nuclear field was reduced to electroweak theory (EWT), and the strong force, strong nuclear field was modeled as quantum chromodynamics (QCD). Comprised by EWT, QCD, and Higgs field, this Standard Model of particle physics is an "effective theory", not truly fundamental. As gluons, QCD's particles are considered nonexistent in the everyday world, QCD especially suggests an aether, routinely found by physics experiments to exist and to exhibit relativistic symmetry.Laughlin, ''A Different Universe'', (Basic Books, 2005)
pp. 120–21
"The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. ... Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. It turns out that such matter exists. About the time that relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo". Confirmation of the Higgs particle, modeled as a condensation within the Higgs field, corroborates aether, although physics need not state or even include aether. Organizing regularities of ''observations''—as in the covering law model—physicists find superfluous the quest to discover ''aether''.

In 1905, from special relativity, Einstein deduced mass–energy equivalence, particles being variant forms of distributed energy, how particle accelerator, 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,Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999)
p. 396
the particles and their masses being states of aether,Wilczek
"The persistence of ether"
''Phys Today'', 1999; 52:11,13, p. 13. apparently unifying all physical phenomena as the more fundamental causal reality,Wilczek, ''Lightness of Being'' (Basic Books, 2008), ch 8 "The grid (persistence of ether)"
p. 73
"For natural philosophy, the most important lesson we learn from quantum chromodynamics, QCD is that what we perceive as empty space is in reality a powerful medium whose activity molds the world. Other developments in modern physics reinforce and enrich that lesson. Later, as we explore the current frontiers, we'll see how the concept of 'empty' space as a rich, dynamic medium empowers our best thinking about how to achieve the unification of forces". as long ago foreseen. Yet a ''quantum'' field is an intricate abstraction—a ''mathematical'' field—virtually inconceivable as a ''classical'' field's physical properties.Kuhlmann
"Physicists debate"
''Sci Am'', 2013. Nature's deeper aspects, still unknown, might elude any possible field theory.

Though discovery of causality is popularly thought science's aim, search for it was shunned by the Isaac Newton, Newtonian research program,
even more Newtonian than was Isaac Newton. By now, most theoretical physics, 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. Given uncertainties of scientific realism,Challenges to scientific realism are captured succinctly by Bolotin, ''Approach to Aristotle's Physics'' (SUNY P, 1998)
pp. 33–34
commenting about modern science, "But it has not succeeded, of course, in encompassing all phenomena, at least not yet. For it laws are mathematical idealizations, idealizations, moreover, with no immediate basis in experience and with no evident connection to the ultimate causes of the natural world. For instance, Newton's first law of motion (the law of inertia) requires us to imagine a body that is always at rest or else moving aimlessly in a straight line at a constant speed, even though we never see such a body, and even though according to his own theory of universal gravitation, it is impossible that there can be one. This fundamental law, then, which begins with a claim about what would happen in a situation that never exists, carries no conviction except insofar as it helps to predict observable events. Thus, despite the amazing success of Newton's laws in predicting the observed positions of the planets and other bodies, Einstein and Infeld are correct to say, in ''The Evolution of Physics'', that 'we can well imagine another system, based on different assumptions, might work just as well'. Einstein and Infeld go on to assert that 'physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world'. To illustrate what they mean by this assertion, they compare the modern scientist to a man trying to understand the mechanism of a closed watch. If he is ingenious, they acknowledge, this man 'may form some picture of a mechanism which would be responsible for all the things he observes'. But they add that he 'may never quite be sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison'. In other words, modern science cannot claim, and it will never be able to claim, that it has the definite understanding of any natural phenomenon". 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.
Covering law model is among Carl G Hempel's admired contributions to philosophy of science.Fetzer, ch 3, in Fetzer, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000)
p. 111

See also

Types of inference
* Deductive reasoning
* Inductive reasoning
* Abductive reasoning

Related subjects
* Explanandum, Explanandum and explanans
* Hypothetico-deductive model
* Models of scientific inquiry
* Philosophy of science
* Scientific method

Notes

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Further reading

* Carl G. Hempel, ''Aspects of Scientific Explanation and other Essays in the Philosophy of Science'' (New York: Free Press, 1965).
* Randolph G. Mayes
"Theories of explanation"
in Fieser Dowden, ed, ''Internet Encyclopedia of Philosophy'', 2006.
* Ilkka Niiniluoto, "Covering law model", in Robert Audi, ed.
''The Cambridge Dictionary of Philosophy'', 2nd edn
(New York: Cambridge University Press, 1996).
* Wesley C. Salmon

(Minneapolis: University of Minnesota Press, 1990 / Pittsburgh: University of Pittsburgh Press, 2006).

{{positivism

Scientific method
Philosophy of science
Conceptual models