View source for Deductive-nomological model

The '''deductive-nomological model''' ('''DN model'''), also known as '''[[Carl Gustav Hempel|Hempel]]'s model''', the '''Hempel–[[Paul Oppenheim|Oppenheim]] model''', the '''[[Karl Popper|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 inference|deductive]] structure—that is, 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 [[scientific law|law]]s.  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 [[axiom]]s 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 inference|deductive]]'' distinguishes the DN model's intended [[determinism]] from the [[probabilism]] of [[inductive inference]]s.<ref name=Woodward-DNmodel/>  The term ''nomological'' is derived from the Greek word ''[[:wikt:νόμος|νόμος]]'' or ''nomos'', meaning "law".<ref name=Woodward-DNmodel>Woodward, [http://plato.stanford.edu/archives/win2011/entries/scientific-explanation "Scientific explanation"], §2 "The DN model", in ''[[The Stanford Encyclopedia of Philosophy|SEP]]'', 2011.</ref> 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).<ref name=Fetzer-p113>James Fetzer, ch 3 "The paradoxes of Hempelian explanation", in Fetzer, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000), [https://books.google.com/books?id=Nvctcrj08wAC&pg=PA113 p 113].</ref>

In the DN model, a law [[axiom]]atizes an [[enumerative induction|unrestricted generalization]] from antecedent ''A'' to consequent ''B'' by [[conditional sentence|conditional proposition]]—''If A, then B''—and has empirical content testable.<ref>Montuschi, ''Objects in Social Science'' (Continuum, 2003), [https://books.google.com/books?id=bQ24-BV8WSAC&pg=PA62&dq= pp 61–62].</ref>  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,<ref>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), [http://mechanism.ucsd.edu/research/philosophyofscience.html ch 2], subch "DN model of explanation and [[hypothetico-deductive model|HD model]] of theory development", pp 25–26.</ref> while following from a scientific theory's axiomatic structure.<ref name=Bechtel-axiomatic>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), [http://mechanism.ucsd.edu/research/philosophyofscience.html ch 2], subch "Axiomatic account of theories", pp 27–29.</ref>

The phenomenon to be explained is the '''''explanandum'''''—an event, [[scientific law|law]], or [[scientific theory|theory]]—whereas the [[premise]]s to explain it are '''''explanans''''', true or highly confirmed, containing at least one universal law, and entailing the explanandum.<ref name=Suppe>Suppe, "Afterword—1977", "Introduction", §1 "Swan song for positivism", §1A "Explanation and intertheoretical reduction", [https://books.google.com/books?id=SpvZsxCA0TIC&pg=PA619 pp 619–24], in Suppe, ed, [https://books.google.com/books?id=SpvZsxCA0TIC ''Structure of Scientific Theories'', 2nd edn] (U Illinois P, 1977).</ref><ref name=Shaffner/>  Thus, given the explanans as initial, specific conditions ''C<sub>1</sub>, C<sub>2</sub> . . . C<sub>n</sub>'' plus general laws ''L<sub>1</sub>, L<sub>2</sub> . . . L<sub>n</sub>'', the phenomenon ''E'' as explanandum is a deductive consequence, thereby scientifically explained.<ref name=Suppe/>

== Roots ==

[[Aristotle]]'s scientific explanation in ''[[Physics (Aristotle)|Physics]]'' resembles the DN model, an idealized form of scientific explanation.<ref name=Shaffner>Kenneth F Schaffner, [https://books.google.com/books?id=hQ-z5oriurYC&pg=PA79 "Explanation and causation in biomedical sciences"], pp 79–125, in Laudan, ed, ''Mind and Medicine'' (U California P, 1983), [https://books.google.com/books?id=hQ-z5oriurYC&pg=PA81&dq= p 81].</ref>  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 [[ethics|morality]] in nature.<ref name=Montalenti>G Montalenti, [https://books.google.com/books?id=NMAf65cDmAQC&pg=PA3 ch 2 "From Aristotle to Democritus via Darwin"], in Ayala & Dobzhansky, eds, ''Studies in the Philosophy of Biology'' (U California P, 1974).</ref>  With emergence of [[Copernicanism]], however, [[René Descartes|Descartes]] introduced [[mechanical philosophy]], then [[Isaac Newton|Newton]] rigorously posed lawlike explanation, both Descartes and especially Newton shunning teleology within [[natural philosophy]].<ref>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 [[problem of demarcation|outside]] [[natural philosophy|science]]'s inquiry (Bolotin, ''Approach to Aristotle's Physics'', [https://books.google.com/books?id=LLqB1IfeSZ0C&pg=PA31&dq= 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.</ref>  At 1740, [[David Hume]]<ref>Nicknames 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.</ref> staked [[Hume's fork]],<ref>By Hume's fork, the truths of mathematics and logic as [[formal sciences]] are universal through "relations of ideas"—simply abstract truths—thus knowable [[a priori knowledge|without experience]].  On the other hand, the claimed truths of [[empirical science]]s are [[contingency (philosophy)|contingent]] on "fact and real existence", knowable only [[a posteriori|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", [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA156&dq= p 156]).</ref> highlighted the [[problem of induction]],<ref>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 [[uniformitarianism|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'', [https://books.google.com/books?id=Y2u8C_ur8VIC&pg=PA381&dq=uniformity+of+nature+problem+of+induction p 381]; Flew, ''Dictionary'', "Hume", [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA156&dq= p 156].</ref> and found humans ignorant of either necessary or sufficient causality.<ref>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:
<br><br>
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 (logic)|tautology]]—a statement whose terms' [[syntax|arrangement]] and [[semantics|meanings]] render it is logically true by mere definition—which, as an [[analytic-synthetic distinction|''analytic'' statement]], is uninformative about the actual world.  A statement referring to and contingent on the world's actualities is a [[analytic-synthetic distinction|''synthetic'' statement]], rather.)
<br><br>
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.
<br><br>
From a [[David Hume|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.
<br><br>
Though apparently enjoying the scandals that trailed his own explanations, Hume was very practical and his skepticism was quite uneven (Flew [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA156&dq=induction+scandal+sceptical+common+sense+logical+natural 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 [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA154&dq=anti-Copernican p 154]).  Hume thus placed his own [[epistemology|theory of knowledge]] on par with [[Newton's theory|Newton's theory of motion]] (Buckle [https://books.google.com/books?id=jiq14nexzu0C&pg=PA70&dq=Hume's+Newton+crowning#v=twopage pp 70–71], Redman [https://books.google.com/books?id=1faeMedY8k8C&pg=PA182&dq=theism+moral+causal+induction#v=twopage pp 182–83], Schliesser [http://plato.stanford.edu/archives/win2008/entries/hume-newton § abstract]).  Hume found [[enumerative induction]] an unavoidable custom required for one to live (Gattei [https://books.google.com/books?id=oPPu1JvMBFoC&pg=PA28#v=twopage 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.</ref><ref name=Kundi/>  Hume also highlighted the [[Hume's law|fact/value gap]], as what ''is'' does not itself reveal what ''ought''.<ref>Hume noted that authors ubiquitously continue for some time stating facts and then suddenly switch to stating [[normative|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", [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA157&dq=Hume's+law p 157] & "Naturalistic fallacy", [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA240&dq=naturalistic+fallacy#v=twopage pp 240–41]; Wootton, ''Modern Political Thought'', [https://books.google.com/books?id=78eaIfCg2mcC&pg=PA306&dq=Hume+communal+reinforcement p 306].)</ref>

[[Critique of Pure Reason|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|Newton's theory of motion]] universally true,<ref>
Kant inferred that the [[category (Kant)|mind's constants]] arrange space holding [[Euclidean geometry]]—like Newton's [[absolute space]]—while objects interact temporally as modeled in [[Newton's theory|Newton's theory of motion]], whose [[Newton's law of universal gravitation|law of universal gravitation]] is a truth ''[[synthetic a priori]]'', that is, contingent on experience, indeed, but known universally true without universal experience.  Thus, the [[category (Kant)|mind's innate constants]] [[synthetic a priori|cross the tongs]] of [[Hume's fork]] and lay Newton's [[universal gravitation]] as ''[[a priori knowledge|a priori]]'' truth.</ref> yet knowledge of [[ding-an-sich|things in themselves]] impossible.<ref name=Kundi/>  Safeguarding [[natural philosophy|science]], then, Kant paradoxically stripped it of [[scientific realism]].<ref name=Kundi/><ref name=Chakravartty/><ref name=Bolotin-realism/>  Aborting [[Francis Bacon]]'s [[inductivist]] mission to dissolve the veil of appearance to uncover the ''[[noumena]]''—[[metaphysics|metaphysical]] view of nature's [[essentialism|ultimate truths]]—Kant's [[transcendental idealism]] tasked science with simply modeling patterns of ''[[phenomena]]''.  Safeguarding metaphysics, too, it found the [[category (Kant)|mind's constant]]s holding also [[categorical imperative|universal moral truths]],<ref>Whereas a [[hypothetical imperative]] is practical, simply what one ought to do if one seeks a particular outcome, the [[categorical imperative]] is morally universal, what everyone always ought to do.</ref> and launched [[German idealism]], increasingly speculative.

[[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]]<ref name=Bourdeau>Bourdeau, "Auguste Comte", §§ "Abstract" & [http://plato.stanford.edu/entries/comte/#Int "Introduction"], in Zalta, ed, ''SEP'', 2013.</ref>—rejecting conjectures about [[unobservable]]s, thus rejecting search for ''causes''.<ref>Comte, ''A General View of Positivism'' (Trübner, 1865), [https://books.google.com/books?id=59hUAAAAcAAJ&pg=PA49&dq=atheism+repudiated+causes+laws pp 49–50], including the following passage: "As long as men persist in attempting to answer the insoluble questions which occupied the attention of the childhood of our race, by far the more rational plan is to do as was done then, that is, simply to give free play to the imagination.  These spontaneous beliefs have gradually fallen into disuse, not because they have been disproved, but because humankind has become more enlightened as to its wants and the scope of its powers, and has gradually given an entirely new direction to its speculative efforts".</ref>  Positivism predicts observations, confirms the predictions, and states a ''law'', thereupon [[applied science|applied]] to benefit human society.<ref>Flew, ''Dictionary'' (St Martin's, 1984), "Positivism", [https://books.google.com/books?id=MmJHVU9Rv3YC&pg=PA283&dq=positivism+prediction p 283].</ref>  From late 19th century into the early 20th century, the influence of positivism spanned the globe.<ref name=Bourdeau/>  Meanwhile, evolutionary theory's [[natural selection]] brought the [[Copernican Revolution]] into biology and eventuated in the first conceptual alternative to [[vitalism]] and [[teleology]].<ref name=Montalenti/>

==Growth==

Whereas Comtean positivism posed science as ''description'', [[logical positivism]] emerged in the late 1920s and posed science as ''explanation'', perhaps to better [[unity of science|unify empirical sciences]] by covering not only [[fundamental science]]—that is, [[fundamental interactions|fundamental physics]]—but [[special science]]s, too, such as biology, psychology, economics, and [[anthropology]].<ref name=Woodward-Background>Woodward, [http://plato.stanford.edu/archives/win2011/entries/scientific-explanation "Scientific explanation"], §1 "Background and introduction", in ''[[The Stanford Encyclopedia of Philosophy|SEP]]'', 2011.</ref>  After defeat of [[National Socialism]] with World War II's close in 1945, logical positivism shifted to a milder variant, ''logical empiricism''.<ref name=Friedman-pxii>Friedman, ''Reconsidering Logical Positivism'' (Cambridge U P, 1999), [https://books.google.com/books?id=e9TjZc9wNUAC&pg=PR12 p xii].</ref>  All variants of the movement, which lasted until 1965, are neopositivism,<ref>Any ''positivism'' placed in the 20th century is generally ''neo'', although there was [[Ernst Mach]]'s positivism nearing 1900, and a general positivistic approach to science—traceable to the [[inductivist]] trend from [[Francis Bacon|Bacon]] at 1620, the [[Isaac Newton|Newtonian]] [[research program]] at 1687, and [[Auguste Comte|Comptean]] positivism at 1830—that continues in a vague but usually disavowed sense within popular culture and some sciences.</ref> sharing the quest of [[verificationism]].<ref>Neopositivists are sometimes called "verificationists".</ref>

Neopositivists led emergence of the philosophy subdiscipline [[philosophy of science]], researching such questions and aspects of scientific theory and knowledge.<ref name=Friedman-pxii/>  [[Scientific realism]] takes scientific theory's statements at [[face value]], thus accorded either falsity or truth—probable or approximate or actual.<ref name=Chakravartty>Chakravartty, [http://plato.stanford.edu/archives/sum2013/entries/scientific-realism "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".</ref>  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.<ref name=Chakravartty-Okasha>
*Chakravartty, [http://plato.stanford.edu/archives/sum2013/entries/scientific-realism "Scientific realism"], §4 "Antirealism: Foils for scientific realism", §4.1 "Empiricism", in ''SEP'', 2013: "Traditionally, [[instrumentalism|instrumentalist]]s 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 empiricist]]s (or logical positivists), including [[Rudolf Carnap|Carnap]] and [[Carl Hempel|Hempel]], famously 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 [[scientific realism|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 [[pragmatism|pragmatic]] grounds), thereby rejecting the [[metaphysical]] dimension of [[scientific realism|realism]] (as in Carnap 1950)".
*Okasha, ''Philosophy of Science'' (Oxford U P, 2002), [https://books.google.com/books?id=W2jCrzKYqxMC&pg=PA62 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".</ref>

DN model received its most detailed, influential statement by [[Carl Gustav Hempel|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".<ref name=Woodward-introduction/><ref>{{cite journal | last1 = Hempel | first1 = Carl G | last2 = Oppenheim | first2 = Paul | date = Apr 1948 | title = Studies in the logic of explanation | journal = Philosophy of Science | volume = 15 | issue = 2| pages = 135–175 | jstor = 185169 | doi = 10.1086/286983 }}</ref>  Leading logical empiricist, Hempel embraced the [[David Hume|Humean]] empiricist view that humans observe sequence of sensory events, not cause and effect,<ref name=Woodward-Background/> as causal relations and casual mechanisms are unobservables.<ref name=Bechtel-mechanism/>  DN model bypasses causality beyond mere [[constant conjunction]]: first an event like ''A'', then always an event like ''B''.<ref name=Woodward-Background/>

Hempel held [[natural laws]]—empirically confirmed regularities—as satisfactory, and if included realistically to approximate causality.<ref name=Suppe/>  In later articles, Hempel defended DN model and proposed probabilistic explanation by ''[[inductive-statistical model]]'' (IS model).<ref name=Suppe/>  DN model and IS model—whereby the probability must be high, such as at least 50%<ref name=Woodward-ISmodel/>—together form ''covering law model'',<ref name=Suppe/> as named by a critic, [[William Dray]].<ref>von Wright, ''Explanation and Understanding'' (Cornell U P, 1971), [https://books.google.com/books?id=33wCi2bg5x0C&pg=PA11 p 11].</ref>  Derivation of statistical laws from other statistical laws goes to the ''[[deductive-statistical model]]'' (DS model).<ref name=Woodward-ISmodel>Woodward, [http://plato.stanford.edu/archives/win2011/entries/scientific-explanation "Scientific explanation"], §2 "The DN model", §2.3 "Inductive statistical explanation", in Zalta, ed, ''SEP'', 2011.</ref><ref name=Glennan>Stuart Glennan, "Explanation", § "Covering-law model of explanation", in Sarkar & Pfeifer, eds, ''Philosophy of Science'' (Routledge, 2006), [https://books.google.com/books?id=od68ge7aF6wC&pg=PA276&dq= p 276].</ref>  [[Georg Henrik von Wright]], another critic, named the totality ''subsumption theory''.<ref name=Riedel>Manfred Riedel, "Causal and historical explanation", in Manninen & Tuomela, eds, ''Essays on Explanation and Understanding'' (D Reidel, 1976), [https://books.google.com/books?id=It3ji_AuO3sC&pg=PA3&dq=Covering+subsumption pp 3–4].</ref>

==Decline==

Amid failure of [[neopositivism]]'s fundamental tenets,<ref>
Neopositivism's fundamental tenets were the verifiability criterion of ''cognitive meaningfulness'', the [[analytic-synthetic distinction|analytic/synthetic gap]], and the observation/theory gap.  From 1950 to 1951, Carl Gustav Hempel renounced the verifiability criterion.  In 1951 [[Willard Van Orman Quine]] attacked the analytic/synthetic gap.  In 1958, [[Norwood Russell Hanson]] blurred the observational/theoretical gap.  In 1959, [[Karl Raimund Popper]] attacked all of verificationism—he attacked, actually, any type of positivism—by asserting falsificationism.  In 1962, [[Thomas Samuel Kuhn]] overthrew [[foundationalism]], which was erroneously presumed to be a fundamental tenet of neopositivism.
</ref> Hempel in 1965 abandoned verificationism, signaling neopositivism's demise.<ref name=Fetzer-reFall>
Fetzer, [http://plato.stanford.edu/archives/spr2013/entries/hempel "Carl Hempel"], §3 "Scientific reasoning", in ''[[The Stanford Encyclopedia of Philosophy|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 famous 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".
</ref>  From 1930 onward, Karl Popper had refuted any positivism by asserting [[falsificationism]], which Popper claimed had killed positivism, although, paradoxically, Popper was commonly mistaken for a positivist.<ref name=Popper>Popper, "Against big words", ''In Search of a Better World'' (Routledge, 1996), [https://books.google.com/books?id=L33XSZE77OkC&pg=PA89#v=twopage pp 89-90].</ref><ref name=Hachoben>Hacohen, ''Karl Popper: The Formative Years'' (Cambridge U P, 2000), [https://books.google.com/books?id=3VtHcYGp2pIC&pg=PA212&dq=Habermas+broad+Popper+killed+logical+positivism#v=twopage pp 212–13].</ref>  Even Popper's 1934 book<ref>''[[Logik der Forschung]]'', published in Austria in 1934, was translated by Popper from German to English, ''[[The Logic of Scientific Discovery]]'', and arrived in the [[English-speaking world]] in 1959.</ref> embraces DN model,<ref name=Shaffner/><ref name=Woodward-introduction>Woodward, "Scientific explanation", in Zalta, ed, ''SEP'', 2011, [http://plato.stanford.edu/archives/win2011/entries/scientific-explanation abstract].</ref> widely accepted as the model of scientific explanation for as long as physics remained the model of science examined by philosophers of science.<ref name=Bechtel-mechanism/><ref name=cplaws/>

In the 1940s, filling the vast observational gap between cytology<ref>As scientific study of cells, cytology emerged in the 19th century, yet its technology and methods were insufficient to clearly visualize and establish existence of any cell [[organelle]]s beyond the [[cell nucleus|nucleus]].</ref> and [[biochemistry]],<ref>The first famed biochemistry experiment was [[Edward Buchner]]'s in 1897 (Morange, ''A History'', [https://books.google.com/books?id=Qe93vz5ZLVsC&pg=PA11&dq= p 11]).  The biochemistry discipline soon emerged, initially investigating [[colloid]]s in biological systems, a "biocolloidology" (Morange [https://books.google.com/books?id=Qe93vz5ZLVsC&pg=PA12&dq= p 12]; Bechtel, ''Discovering'', [https://books.google.com/books?id=WrEquK3hoDwC&pg=PA94&dq=biocolloidology+colloids+exemplifies+organic+proteins p 94]).  This yielded to macromolecular theory, the term ''macromolecule'' introduced by German chemist [[Hermann Staudinger]] in 1922 (Morange [https://books.google.com/books?id=Qe93vz5ZLVsC&pg=PA12&dq= p 12]).</ref> [[cell biology]] arose<ref>Cell biology emerged principally at [[Rockefeller University|Rockefeller Institute]] through new technology ([[electron microscope]] and [[ultracentrifuge]]) and new techniques ([[cell fractionation]] and advancements in staining and fixation).</ref> and established existence of cell [[organelle]]s besides the [[cell nucleus|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.<ref name=Bechtel-mechanism>Bechtel, ''Discovering Cell Mechanisms'' (Cambridge U P, 2006), esp [https://books.google.com/books?id=WrEquK3hoDwC&pg=PA24&dq=empiricists+Salmon#v=twopage pp 24–25].</ref>  Biology became a new model of science, while [[special sciences]] were no longer thought defective by lacking universal laws, as borne by physics.<ref name=cplaws/>

In 1948, when explicating DN model and stating scientific explanation's semiformal ''conditions of adequacy'', [[Carl Hempel|Hempel]] and [[Paul Oppenheim|Oppenheim]] acknowledged redundancy of the third, ''[[empiricism|empirical content]]'', implied by the other three—''derivability'', ''lawlikeness'', and ''truth''.<ref name=Fetzer-p113/>  In the early 1980s, upon widespread view that causality ensures the explanans' relevance, [[Wesley Salmon]] called for returning ''cause'' to ''because'',<ref>James Fetzer, ch 3 "The paradoxes of Hempelian explanation", in Fetzer J, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000), [https://books.google.com/books?id=Nvctcrj08wAC&pg=PA121&dq=causality pp 121–122].</ref> and along with [[James H. Fetzer|James Fetzer]] helped replace CA3 ''empirical content'' with CA3' ''strict maximal specificity''.<ref>Fetzer, ch 3 in Fetzer, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000), [https://books.google.com/books?id=Nvctcrj08wAC&pg=PA129&dq=better p 129].</ref>

Salmon introduced ''causal mechanical'' explanation, never clarifying how it proceeds, yet reviving philosophers' interest in such.<ref name=Bechtel-mechanism/>  Via shortcomings of Hempel's inductive-statistical model (IS model), Salmon introduced ''[[statistical-relevance model]]'' (SR model).<ref name=Shaffner/>  Although DN model remained an idealized form of scientific explanation, especially in [[applied science]]s,<ref name=Shaffner/> most philosophers of science consider DN model flawed by excluding many types of explanations generally accepted as scientific.<ref name=Glennan/>

==Strengths==

As theory of knowledge, [[epistemology]] differs from [[ontology]], which is a subbranch of [[metaphysics]], theory of reality.<ref name=Bechtel-metaphysics-epistemology/>  Ontology poses which 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.<ref name=Bechtel-metaphysics-epistemology>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), [http://mechanism.ucsd.edu/research/philosophyofscience.html ch 1], subch "Areas of philosophy that bear on philosophy of science", § "Metaphysics", pp 8–9, § "Epistemology", p 11.</ref>

[[Natural law]]s, 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]]''.<ref>H Atmanspacher, R C Bishop & A Amann, "Extrinsic and intrinsic irreversibility in probabilistic dynamical laws", in Khrennikov, ed, ''Proceedings'' (World Scientific, 2001), [https://books.google.com/books?id=9B6b5WKuNWwC&pg=PA51&dq=ontic+epistemic+general pp 51–52].</ref><ref>Fetzer, ch 3, in Fetzer, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000), [https://books.google.com/books?id=Nvctcrj08wAC&pg=PA118 p 118], poses some possible ways that natural laws, so called, when [[epistemic]] can fail as [[ontic]]: "The underlying conception is that of bringing order to our ''knowledge'' of the universe.  Yet there are at least three reasons why even complete knowledge of every empirical regularity that obtains during the world's history might not afford an adequate inferential foundation for discovery of the world's laws.  First, some laws might remain uninstantiated and therefore not be displayed by any regularity.  Second, some regularities may be accidental and therefore not display any law of nature.  And, third, in the case of probabilistic laws, some frequencies might deviate from their generating nomic probabilities 'by chance' and therefore display natural laws in ways that are unrepresentative or biased".</ref>

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.<ref name=Bechtel-axiomatic/><ref name=Suppe/>  Thus, the epistemic success of [[Isaac Newton|Newton]]ian theory's [[law of universal gravitation]] is reduced to—thus explained by—[[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]]<ref>This theory reduction occurs if, and apparently only if, the Sun and one planet are modeled as a two-body system, excluding all other planets (Torretti, ''Philosophy of Physics'', [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P60&dq= pp 60–62]).</ref> 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 interactions|fundamental physics]]—or are [[special sciences]], whether [[astrophysics]], chemistry, biology, [[geology]], psychology, economics, and so on.<ref name=cplaws>Reutlinger, Schurz & Hüttemann, [http://plato.stanford.edu/archives/spr2011/entries/ceteris-paribus "Ceteris paribus"], § 1.1 "Systematic introduction", in Zalta, ed, ''SEP'', 2011.</ref><ref>Spohn, ''Laws of Belief'' (Oxford U P, 2012), [https://books.google.com/books?id=MSXrFBvIZIUC&pg=PA305&dq=fundamental+special+sciences p 305].</ref><ref>Whereas fundamental physics has sought [[scientific law|law]]s of [[determinism|universal regularity]], special sciences normally include ''[[ceteris paribus]]'' laws, which are predictively accurate to high [[probability]] in "normal conditions" or with "all else equal", but have exceptions [Reutlinger ''et al'' § 1.1].  Chemistry's laws seem [[deterministic|exceptionless]] in their domains, yet were in principle reduced to fundamental physics [Feynman [https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PA5&dq=chemistry p 5], Schwarz [https://www.ncbi.nlm.nih.gov/pubmed/9501161 Fig 1], and so are special sciences.</ref>  All special sciences would network via covering law model.<ref>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), ch 5, subch "Introduction: Relating disciplines by relating theories" pp 71–72.</ref>  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.<ref name=Bechtel-TheoryReduction>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), ch 5, subch "Theory reduction model and the [[unity of science]] program" pp 72–76.</ref><ref name=Bem-Long/>  (''Boundary conditions'' are specified conditions whereby the phenomena of interest occur.  ''Bridge laws'' translate terms in one science to terms in another science.)<ref name=Bechtel-TheoryReduction/><ref name=Bem-Long>Bem & de Jong, ''Theoretical Issues'' (Sage, 2006), [https://books.google.com/books?id=DgDGJi2F2vsC&pg=PA45&dq=deductive-nomological+boundary+conditions+bridge+laws pp 45–47].</ref>

==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]]".<ref name=Suppe/>  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.<ref name=Suppe/>  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.<ref name=OShaughnessy>O'Shaughnessy, ''Explaining Buyer Behavior'' (Oxford U P, 1992), [https://books.google.com/books?id=magj7kNrbpsC&pg=PA17&dq= pp 17–19].</ref>  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''.<ref name=OShaughnessy/>  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]].<ref name=OShaughnessy/><ref name=Spohn-idealgas/>

Scientific explanations increasingly pose not [[determinism]]'s universal laws, but [[probabilism]]'s chance,<ref name=Karhausen/> ''[[ceteris paribus]]'' laws.<ref name=cplaws/>  Smoking's contribution to [[lung cancer]] fails even the inductive-statistical model (IS model), requiring probability over 0.5 (50%).<ref>Bechtel, ''Philosophy of Science'' (Lawrence Erlbaum, 1988), [http://mechanism.ucsd.edu/research/philosophyofscience.html ch 3], subch "Repudiation of DN model of explanation", pp 38–39.</ref>  (Probability standardly ranges from 0 (0%) to 1 (100%).)  An [[applied science]] that applies [[statistics]] seeking associations between events, [[epidemiology]] 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.<ref name=Rothman-Greenland>{{Cite journal 
| last1 = Rothman | first1 = K. J. 
| last2 = Greenland | first2 = S. 
| doi = 10.2105/AJPH.2004.059204 
| title = Causation and Causal Inference in Epidemiology 
| journal = American Journal of Public Health 
| volume = 95 
| pages = S144–S150 
| year = 2005 
| pmid = 16030331 
| pmc = 
| hdl = 10.2105/AJPH.2004.059204 
| hdl-access = free 
}}</ref>  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,<ref>Boffetta, [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3024843 "Causation in the presence of weak associations"], ''Crit Rev Food Sci Nutr'', 2010; '''50'''(S1):13–16.</ref> responsible for some cases that without smoking would not have occurred,<ref name=Rothman-Greenland/> a probabilistic [[counterfactual]] causality.<ref name=counterfactual>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.</ref><ref>In epidemiology, the counterfactual causality is not [[deterministic]], but [[probabilistic]] (Parascandola & Weed, "Causation in epidemiology", ''J Epidemiol Community Health'', 2001; '''55''':905–12) {{PMID|11707485}}.</ref>

==Covering action==

Through lawlike explanation, [[fundamental interactions|fundamental physics]]—often perceived as [[fundamental science]]—has proceeded through intertheory relation and theory reduction, thereby resolving experimental [[paradox]]es to great historical success,<ref name=Schwarz>Schwarz, [https://www.ncbi.nlm.nih.gov/pubmed/9501161 "Recent developments in string theory"], ''Proc Natl Acad Sci U S A'', 1998; '''95''':2750–7, esp [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC19640/figure/F1 Fig 1].</ref> resembling covering law model.<ref name=Ben-Menahem>Ben-Menahem, ''Conventionalism'' (Cambridge U P, 2006), [https://books.google.com/books?id=bgRA2LOjcMAC&pg=PA71&dq=mechanical+deductive-nomological+model+ether p 71].</ref>  In early 20th century, [[Ernst Mach]] as well as [[Wilhelm Ostwald]] had resisted [[Ludwig Boltzmann]]'s reduction of [[thermodynamics]]—and thereby [[Boyle's law]]<ref>Instances of falsity limited Boyle's law to special cases, thus [[ideal gas law]].</ref>—to [[statistical mechanics]] partly ''because'' it rested on [[kinetic theory of gas]],<ref name=Spohn-idealgas>Spohn, ''Laws of Belief'' (Oxford U P, 2012), [https://books.google.com/books?id=MSXrFBvIZIUC&pg=PA306&dq=gas p 306].</ref> hinging on [[atomic theory of matter|atomic/molecular theory of matter]].<ref name=NewburghEtAl/>  Mach as well as Ostwald viewed matter as a variant of energy, and molecules as mathematical illusions,<ref name=NewburghEtAl>Newburgh ''et al'', [http://physlab.lums.edu.pk/images/f/fe/Ref1.pdf "Einstein, Perrin, and the reality of atoms"] {{Webarchive|url=https://web.archive.org/web/20170803105918/https://physlab.lums.edu.pk/images/f/fe/Ref1.pdf |date=2017-08-03 }}, ''Am J Phys'', 2006, p 478.</ref> as even Boltzmann thought possible.<ref name=Kuhn-Frank>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), [https://books.google.com/books?id=hCfk8tZix6oC&pg=PA63&dq=Mach+Boltzmann+atoms p 63], as Frank was a student of Boltzmann soon after Mach's retirement. See "Notes", [https://books.google.com/books?id=hCfk8tZix6oC&pg=PA79&dq=atomism 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 [[electron]]s 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".</ref>

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]].<ref name=NewburghEtAl/>  Soon, most physicists accepted that atoms and molecules were unobservable yet real.<ref name=NewburghEtAl/>  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.<ref>
Physicists had explained the electromagnetic field's energy as ''mechanical'' energy, like an ocean wave's bodily impact, not water droplets individually showered (Grandy, ''Everyday Quantum Reality'', [https://books.google.com/books?id=v-Tmtb-XvwcC&pg=PA22&dq= pp 22–23]).  In the 1890s, the problem of [[blackbody radiation]] was paradoxical until [[Max Planck]] theorized ''[[quantum]]'' exhibiting [[Planck's constant]]—a minimum unit of energy.  The quanta were mysterious, not viewed as ''particles'', yet simply as units of ''energy''.  Another paradox, however, was the [[photoelectric effect]].
<br><br>
As shorter wavelength yields more waves per unit distance, lower wavelength is higher wave frequency.  Within the [[electromagnetic spectrum]]'s visible portion, frequency sets the color.  Light's intensity, however, is the wave's amplitude as the wave's height.  In a strictly wave explanation, a greater intensity—higher wave amplitude—raises the mechanical energy delivered, namely, the wave's impact, and thereby yields greater physical effect.  And yet in the photoelectric effect, only a certain color and beyond—a certain frequency and higher—was found to knock electrons off a metal surface. Below that frequency or color, raising the intensity of the light still knocked no electrons off.
<br><br>
Einstein modeled Planck's quanta as each a particle whose individual energy was Planck's constant multiplied by the light's wave's frequency: at only a certain frequency and beyond would each particle be energetic enough to eject an electron from its orbital.  Although elevating the intensity of light would deliver more energy—more total particles—each individual particle would still lack sufficient energy to dislodge an electron.  Einstein's model, far more intricate, used [[probability theory]] to explain rates of elections ejections as rates of collisions with electromagnetic particles.  This revival of the [[particle theory of light|particle hypothesis of light]]—generally attributed to Newton—was widely doubted.  By 1920, however, the explanation helped solve problems in [[atomic theory]], and thus [[quantum mechanics]] emerged.  In 1926, [[Gilbert N Lewis]] termed the particles ''[[photon]]s''.  [[quantum electrodynamics|QED]] models them as the electromagnetic field's [[messenger particle]]s or force carriers, emitted and absorbed by electrons and by other particles undergoing transitions.
</ref>  Meanwhile, all known physical phenomena were gravitational or [[timeline of electromagnetic theory|electromagnetic]],<ref>Wolfson, ''Simply Einstein'' (W W Norton & Co, 2003), [https://books.google.com/books?id=FwNJ_PDRnbkC&pg=PA67&dq=Wrap p 67].</ref> whose two theories misaligned.<ref>Newton's gravitational theory at 1687 had postulated [[absolute space and time|absolute space and absolute time]].  To fit [[Thomas Young (scientist)|Young]]'s [[transverse wave]] theory of light at 1804, space was theoretically filled with [[Augustin Fresnel|Fresnel]]'s [[luminiferous aether]] at 1814.  By [[James Clerk Maxwell|Maxwell]]'s electromagnetic field theory of 1865, light always holds a constant speed, which, however, must be relative to something, apparently to aether.  Yet if light's speed is constant relative to aether, then a body's motion through aether would be relative to—thus vary in relation to—light's speed.  Even Earth's vast speed, multiplied by experimental ingenuity with an [[interferometer]] by [[Michelson–Morley experiment|Michelson & Morley at 1887]], revealed no apparent ''aether drift''—light speed apparently constant, an absolute.  Thus, both Newton's gravitational theory and Maxwell's electromagnetic theory each had its own relativity principle, yet the two were incompatible.  For brief summary, see Wilczek, ''Lightness of Being'' (Basic Books, 2008), [https://books.google.com/books?id=iWhxK12fbA4C&pg=PA78&dq= pp 78–80].</ref>  Yet belief in aether as the source of all physical phenomena was virtually unanimous.<ref>Cordero, ''EPSA Philosophy of Science'' (Springer, 2012), [https://books.google.com/books?id=e0B_VtFeSi4C&pg=PA27&dq=ether pp 26–28].</ref><ref>Hooper, ''Aether and Gravitation'' (Chapman & Hall, 1903), [https://books.google.com/books?id=cgoQAQAAMAAJ&pg=PA126&dq=Aether pp 122–23].</ref><ref name=Lodge>{{cite journal | last1 = Lodge | first1 =  | year = 1909 | title = The ether of space | url = https://books.google.com/books?id=FgYiAQAAMAAJ&pg=PA202&dq=action+constitute+distance+electron+empty+space+gravitation+Optical | journal = Sci Am Suppl | volume = 67 | issue = | pages = 202–03 | doi = 10.1038/scientificamerican03271909-202supp }}</ref><ref>Even Mach, who shunned all hypotheses beyond direct sensory experience, presumed an aether, required for motion to not violate [[mechanical philosophy]]'s founding principle, ''No instant inter[[action at a distance]]'' (Einstein, "Ether", ''Sidelights'' (Methuen, 1922), [https://books.google.com/books?id=vwZlfF3sVJEC&pg=RA1-PA617&dq=special pp 15–18]).</ref>  At experimental paradoxes,<ref>
Rowlands, ''Oliver Lodge'' (Liverpool U P, 1990), [https://books.google.com/books?id=7BfLxqkSgBEC&pg=PA159&dq= pp 159–60]: "[[Sir Oliver Lodge|Lodge]]'s [[luminiferous aether|ether]] experiments have become part of the historical background leading up to the establishment of [[special relativity]] and their significance is usually seen in this context.  Special relativity, it is stated, eliminated both the ether and the concept of absolute motion from physics.  Two experiments were involved: that of Michelson and Morley, which showed that bodies do not move with respect to a stationary ether, and that of Lodge, which showed that moving bodies do not drag ether with them.  With the emphasis on relativity, the [[Michelson–Morley]] experiment has come to be seen as the more significant of the two, and Lodge's experiment becomes something of a detail, a matter of eliminating the final, and less likely, possibility of a nonstationary, viscous, all-pervading medium.

It could be argued that almost the exact opposite may have been the case.  The Michelson–Morley experiment did not prove that there was no absolute motion, and it did not prove that there was no stationary ether.  Its results—and the [[FitzGerald–Lorentz contraction]]—could have been predicted on [[Oliver Heaviside|Heaviside]]'s, or even [[James Clerk Maxwell|Maxwell]]'s, theory, even if no experiment had ever taken place.  The significance of the experiment, though considerable, is purely historical, and in no way factual.  Lodge's experiment, on the other hand, showed that, if an ether existed, then its properties must be quite different from those imagined by mechanistic theorists.  The ether which he always believed existed had to acquire entirely new properties as a result of this work".</ref> physicists modified the aether's hypothetical properties.<ref>Mainly [[Hendrik Lorentz]] as well as [[Henri Poincaré]] modified [[classical electrodynamics|electrodynamic theory]] and, more or less, developed special theory of relativity before Einstein did (Ohanian, ''Einstein's Mistakes'', [https://books.google.com/books?id=4DunN-eD3VIC&pg=PA282&dq= pp 281–85]).  Yet Einstein, free a thinker, took the next step and stated it, more elegantly, without aether (Torretti, ''Philosophy of Physics'', [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P180&dq=Lorentz+Einstein p 180]).</ref>

Finding the [[luminiferous aether]] a useless hypothesis,<ref name=Tavel>Tavel, ''Contemporary Physics'' (Rutgers U P, 2001), pp [https://books.google.com/books?id=SELS0HbIhjYC&pg=PA60], [https://books.google.com/books?id=SELS0HbIhjYC&pg=PA66&dq=Lorentz+contraction+ether 66].</ref> Einstein in 1905 ''[[a priori knowledge|a priori]]'' unified all [[inertia]]l [[frame of reference|reference frames]] to state special ''principle'' of relativity,<ref>Introduced soon after Einstein explained Brownian motion, special relativity holds only in cases of [[inertia]]l motion, that is, unaccelerated motion.  Inertia is the state of a body experiencing no acceleration, whether by change in speed—either quickening or slowing—or by change in direction, and thus exhibits constant [[velocity]], which is speed plus direction.</ref> which, by omitting aether,<ref name=Cordero-p29-30>Cordero, ''EPSA Philosophy of Science'' (Springer, 2012), [https://books.google.com/books?id=e0B_VtFeSi4C&pg=PA29&dq=ether pp 29–30].</ref> converted space and time into ''relative'' phenomena whose relativity aligned [[classical electrodynamics|electrodynamics]] with the Newtonian principle [[Galilean invariance|Galilean relativity or invariance]].<ref name=Schwarz/><ref>To explain absolute light speed without aether, Einstein modeled that a body at motion in an electromagnetic field experiences [[length contraction]] and [[time dilation]], which [[Hendrik Lorentz|Lorentz]] and [[Henri Poincaré|Poincaré]] had already modeled as [[Lorentz-FitzGerald contraction]] and [[Lorentz transformation]] but by hypothesizing [[dynamics (mechanics)|dynamic]] states of the aether, whereas Einstein's special relativity was simply [[kinematics|kinematic]], that is, positing no causal mechanical explanation, simply describing positions, thus showing how to align measuring devices, namely, clocks and rods.  (Ohanian, ''Einstein's Mistakes'', [https://books.google.com/books?id=4DunN-eD3VIC&pg=PA282&dq= pp 281–85]).</ref>   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'',<ref>Ohanian, ''Einstein's Mistakes'' (W W Norton, 2008), [https://books.google.com/books?id=4DunN-eD3VIC&pg=PA282&dq= pp 281–85].</ref> refuting Newtonian gravitation.<ref name=Cordero-p29-30/><ref>Newton's theory required [[absolute space and time]].</ref>  By predictive success [[Solar eclipse of May 29, 1919|in 1919]], [[general relativity]] apparently overthrew [[Newton's theory]], a revolution in science<ref>Buchen, [https://www.wired.com/thisdayintech/2009/05/dayintech_0529 "May 29, 1919"], ''Wired'', 2009.<br>Moyer, [https://dx.doi.org/10.1007/978-1-4684-3596-2_4 "Revolution"], in ''Studies in the Natural Sciences'' (Springer, 1979), p 55.<br>Melia, ''Black Hole'' (Princeton U P, 2003), [https://books.google.com/books?id=nmBLT-X5bOQC&pg=PA83 pp 83–87].</ref> resisted by many yet fulfilled around 1930.<ref>Crelinsten, ''Einstein's Jury'' (Princeton U P, 2006), [https://books.google.com/books?id=W1Dt15vWYGQC&pg=PA296&dq=1928 p 28].</ref>

In 1925, [[Werner Heisenberg]] as well as [[Erwin Schrödinger]] independently formalized [[quantum mechanics]] (QM).<ref name=QMformalisms/><ref name=Cushing-p113-18>Cushing, ''Quantum Mechanics'' (U Chicago P, 1994), [https://books.google.com/books?id=kTewHaL8fvgC&pg=PA113&dq= pp 113–18].</ref>  Despite clashing explanations,<ref name=Cushing-p113-18/><ref name=QMs>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)|operator]]s'' acting on ''[[quantum state]]s''. [[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's [[Schrödinger's equation|wave]] formalism.</ref> the two theories made identical predictions.<ref name=QMformalisms/>  [[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).<ref name=Torretti-p393-95>Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P393&dq= pp 393–95].</ref>  From it, Dirac interpreted and predicted the electron's [[antiparticle]], soon discovered and termed ''[[positron]]'',<ref name=Torretti-p394>Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P394&dq= p 394].</ref> but the QED failed electrodynamics at high energies.<ref name=Torretti-p395/>  Elsewhere and otherwise, [[strong nuclear force]] and [[weak nuclear force]] were discovered.<ref>Recognition of strong force permitted [[Manhattan Project]] to engineer [[Little Boy]] and [[Fat Man]], dropped on Japan, whereas effects of weak force were seen in its aftermath—[[radioactive fallout]]—of diverse health consequences.</ref>

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's [[Schrödinger's equation|wave]] formalism,<ref name=QMs/> although all three are empirically identical, sharing predictions.<ref name=QMformalisms>From 1925 to 1926, independently but nearly simultaneously, [[Werner Heisenberg]] as well as [[Erwin Schrödinger]] developed quantum mechanics (Zee in Feynman, ''QED'', [https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR14&dq= p xiv]).  Schrödinger introduced [[Schrödinger equation|wave mechanics]], whose [[wave function]] is discerned by a [[partial differential equation]], now termed ''[[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)|operator]]s'' acting on ''[[quantum state]]s'' (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]]'' ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR15&dq= p xv]).
<br><br>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 ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR16&dq= 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).
<br><br>
There is no particular barrier to additional formalisms, which could be, simply have not been, developed and widely disseminated ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR17&dq= 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 ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR16&dq= pp xvi–xvii]).  By the 1960s, path integral formalism virtually vanished from use, while matrix formalism was the "canonical" ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR17&dq= 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 ([https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PR18&dq= p xviii]).</ref>  Next, working on QED, Feynman sought to model particles without fields and find the vacuum truly empty.<ref name=Wilczek1999p13/>  As each known [[fundamental force]]<ref>The four, known [[fundamental interactions]] are gravitational, electromagnetic, weak nuclear, and strong nuclear.</ref> is apparently an effect of a field, Feynman failed.<ref name=Wilczek1999p13/>  [[Louis de Broglie]]'s [[waveparticle duality]] had rendered [[atomism]]—indivisible particles in a void—untenable, and highlighted the very notion of discontinuous particles as selfcontradictory.<ref>Grandy, ''Everyday Quantum Reality'' (Indiana U P, 2010), [https://books.google.com/books?id=v-Tmtb-XvwcC&pg=PA24&dq= pp 24–25].</ref>

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,<ref name=Torretti-p395>Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P395&dq= p 395].</ref><ref name=Schweber>Schweber, [https://books.google.com/books/about/QED_and_the_Men_who_Made_it.html?id=61n5dE7FJQgC ''QED and the Men who Made it''] (Princeton U P, 1994).</ref> subsuming [[chemistry]], [[optics]], and [[statistical mechanics]].<ref name=Schwarz/><ref name=Feynman>Feynman, ''QED'' (Princeton U P, 2006), [https://books.google.com/books?id=Uv-uxB0sRKEC&pg=PA5&dq=chemistry p 5].</ref>  QED thus won physicists' general acceptance.<ref name=Torretti-p395-96/>  [[Paul Dirac]] criticized its need for renormalization as showing its unnaturalness,<ref name=Torretti-p395-96>Torretti, ''Philosophy of Physics'', (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P395&dq=Dirac pp 395–96].</ref> and called for an aether.<ref name=Cushing-p158-59>Cushing, ''Quantum Mechanics'' (U Chicago P, 1994), [https://books.google.com/books?id=kTewHaL8fvgC&pg=PA158&dq=ether+Dirac+medium+vacuum#v=twopage pp 158–59].</ref>  In 1947, [[Willis Lamb]] had found unexpected motion of [[electron configuration|electron orbitals]], [[Lamb shift|shift]]ed since the vacuum is not truly empty.<ref>Close, [https://www.pbs.org/wgbh/nova/physics/blog/tag/ether "Much ado about nothing"], ''Nova'', PBS/WGBH, 2012:

"This new quantum mechanical view of nothing began to emerge in 1947, when [[Willis Lamb]] measured spectrum of hydrogen.  The electron in a hydrogen atom cannot move wherever it pleases but instead is restricted to specific paths.  This is analogous to climbing a ladder: You cannot end up at arbitrary heights above ground, only those where there are rungs to stand on.  Quantum mechanics explains the spacing of the rungs on the atomic ladder and predicts the frequencies of radiation that are emitted or absorbed when an electron switches from one to another.  According to the state of the art in 1947, which assumed the hydrogen atom to consist of just an electron, a proton, and an electric field, two of these rungs have identical energy. However, Lamb's measurements showed that these two rungs differ in energy by about one part in a million.  What could be causing this tiny but significant difference?

"When physicists drew up their simple picture of the atom, they had forgotten something: Nothing.  Lamb had become the first person to observe experimentally that the vacuum is not empty, but is instead seething with ephemeral electrons and their anti-matter analogues, positrons.  These electrons and positrons disappear almost instantaneously, but in their brief mayfly moment of existence they alter the shape of the atom's electromagnetic field slightly.  This momentary interaction with the electron inside the hydrogen atom kicks one of the rungs of the ladder just a bit higher than it would be otherwise.
<br>
"This is all possible because, in quantum mechanics, energy is not conserved on very short timescales, or for very short distances.  Stranger still, the more precisely you attempt to look at something—or at nothing—the more dramatic these energy fluctuations become.  Combine that with Einstein's E=mc<sup>2</sup>, which implies that energy can congeal in material form, and you have a recipe for particles that bubble in and out of existence even in the void.  This effect allowed Lamb to literally measure something from nothing".</ref>  Yet ''emptiness'' was catchy, abolishing aether conceptually, and physics proceeded ostensibly without it,<ref name=Wilczek1999p13/> even suppressing it.<ref name=Cushing-p158-59/>  Meanwhile, "sickened by untidy math, most [[philosophy of physics|philosophers of physics]] tend to neglect QED".<ref name=Torretti-p395-96/>

Physicists have feared even mentioning ''aether'',<ref name=Vongehr>
*Vongehr [http://www.science20.com/alpha_meme/higgs_discovery_rehabilitating_despised_einstein_ether-85497 "Higgs discovery rehabilitating despised Einstein Aether"], ''Science 2.0'', 2011.
*{{cite arxiv |eprint=0912.3069|last1=Vongehr|first1=Sascha|title=Supporting Abstract Relational Space-Time as Fundamental without Doctrinism against Emergence|class=physics.hist-ph|year=2009}}</ref> renamed ''vacuum'',<ref name=Cushing-p158-59/><ref name=Riesselmann>Riesselmann [http://www.fnal.gov/pub/inquiring/questions/ether.html "Concept of ether in explaining forces"], ''Inquiring Minds'', [[Fermilab]], 2008.</ref> which—as such—is nonexistent.<ref name=Cushing-p158-59/><ref>Close, [https://www.pbs.org/wgbh/nova/physics/blog/tag/ether "Much ado about nothing"], ''Nova'', PBS/WGBH, 2012.</ref>  General philosophers of science commonly believe that aether, rather, is fictitious,<ref>On "historical examples of empirically successful theories that later turn out to be false", Okasha, ''Philosophy of Science'' (Oxford U P, 2002), [https://books.google.com/books?id=W2jCrzKYqxMC&pg=PA65&dq=ether p 65], concludes, "One that remains is the wave theory of light, first put forward by [[Christian Huygens]] in 1690.  According to this theory, light consists of wave-like vibrations in an invisible medium called the ether, which was supposed to permeate the whole universe.  (The rival to the wave theory was the particle theory of light, favoured by Newton, which held that light consists of very small particles emitted by the light source.)  The wave theory was not widely accepted until the French physicist Auguste Fresnel formulated a mathematical version of the theory in 1815, and used it to predict some surprising new optical phenomena.  Optical experiments confirmed Fresnel's predictions, convincing many 19th-century scientists that the wave theory of light must be true.  But modern physics tells us that the theory is not true: there is no such thing as the ether, so light doesn't consist of vibrations in it.  Again, we have an example of a false but empirically successful theory".</ref> "relegated to the dustbin of scientific history ever since" 1905 brought [[special relativity]].<ref name=Pigliucci>Pigliucci, ''Answers for Aristotle'' (Basic Books, 2012), [https://books.google.com/books?id=laZensALMSgC&pg=PA119&dq=antirealist+aether 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".</ref>  Einstein was noncommittal to aether's nonexistence,<ref name=Tavel/> simply said it superfluous.<ref name=Cordero-p29-30/>  Abolishing Newtonian motion for electrodynamic primacy, however, Einstein inadvertently reinforced aether,<ref name=Wilczek-p78-80>Wilczek, ''Lightness of Being'' (Basic Books, 2008), [https://books.google.com/books?id=iWhxK12fbA4C&pg=PA78&dq= pp 78–80].</ref> and to explain motion was led back to aether in [[general relativity]].<ref name=Laughlin>Laughlin, ''A Different Universe'' (Basic Books, 2005), [https://books.google.com/books?id=djQKg_XBsLEC&pg=PA120&dq=ironic pp 120–21].</ref><ref name=Einstein/><ref>[[Lorentz aether theory|Lorentz aether]] was at absolute rest—acting ''on'' matter but not acted on ''by'' matter.  Replacing it and resembling [[Ernst Mach]]'s aether, Einstein aether is [[spacetime]] itself—which is the [[gravitational field]]—receiving motion from a body and transmitting it to other bodies while propagating at light speed, [[gravitational waves|waving]].  An unobservable, however, Einstein aether is not a privileged [[frame of reference|reference frame]]—is not to be assigned a state of absolute motion or absolute rest.</ref>  Yet resistance to [[relativity theory]]<ref>Relativity theory comprises both special relativity (SR) and general relativity (GR).  Holding for inertial reference frames, SR is as a limited case of GR, which holds for all reference frames, both inertial and accelerated.  In GR, all motion—inertial, accelerated, or gravitational—is consequent of the geometry of 3D space stretched onto the 1D axis of time.  By GR, no force distinguishes acceleration from inertia.  Inertial motion is consequence simply of ''uniform'' geometry of spacetime, acceleration is consequence simply of ''nonuniform'' geometry of spacetime, and gravitation is simply acceleration.</ref> became associated with earlier theories of aether, whose word and concept became taboo.<ref name=Laughlin-quote/>  Einstein explained special relativity's compatibility with an aether,<ref name=Einstein>Einstein, "Ether", ''Sidelights'' (Methuen, 1922), [https://books.google.com/books?id=vwZlfF3sVJEC&pg=RA1-PA617&dq=special pp 14–18].</ref> but Einstein aether, too, was opposed.<ref name=Vongehr/>  Objects became conceived as pinned directly on [[spacetime|space and time]]<ref>In Einstein's 4D spacetime, 3D space is stretched onto the 1D axis of time flow, which [[time dilation|slows]] while space additionally [[space contraction|contracts]] in the vicinity of mass or energy.</ref> by abstract geometric relations lacking ghostly or fluid medium.<ref name=Vongehr/><ref name=Torretti-p180>Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P180&dq=Lorentz+Einstein p 180].</ref>

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).<ref name=Torretti-p395/>  Comprised by EWT, QCD, and [[Higgs field]], this [[Standard Model]] of [[particle physics]] is an "effective theory",<ref>As an effective field theory, once adjusted to particular domains, Standard Model is predictively accurate until a certain, vast energy scale that is a cutoff, whereupon more fundamental phenomena—regulating the effective theory's modeled phenomena—would emerge. (Burgess & Moore, ''Standard Model'', [https://books.google.com/books?id=PLYECqs2geEC&pg=PR11&dq=effective p xi]; Wells, ''Effective Theories'', [https://books.google.com/books?id=kKKAfrfCofcC&pg=PA56&dq=Natural+Standard+Model pp 55–56]).</ref> not truly fundamental.<ref name=Torretti-p396/><ref name=Jegerlehner>{{cite journal |arxiv=1304.7813 |quote=We understand the [[Standard Model|SM]] as a low energy effective emergence of some unknown physical system—we may call it 'ether'—which is located at the [[Planck scale]] with the [[Planck length]] as a 'microscopic' length scale.  Note that the cutoff, though very large, in any case is finite.|doi=10.5506/APhysPolB.45.1167|bibcode=2014AcPPB..45.1167J|title=The Standard Model as a Low-energy Effective Theory: What is Triggering the Higgs Mechanism?|year=2014|last1=Jegerlehner|first1=F.|journal=Acta Physica Polonica B|volume=45|issue=6|pages=1167}}</ref>  As [[gluons|QCD's particles]] are considered nonexistent in the everyday world,<ref name=Wilczek1999p13/> QCD especially suggests an aether,<ref name=Wilczek-p73/> routinely found by physics experiments to exist and to exhibit relativistic symmetry.<ref name=Laughlin-quote>Laughlin, ''A Different Universe'', (Basic Books, 2005), [https://books.google.com/books?id=djQKg_XBsLEC&pg=PA121&dq= 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".</ref>  Confirmation of the [[Higgs particle]], modeled as a condensation within the [[Higgs field]], corroborates aether,<ref name=Vongehr/><ref name=Jegerlehner/> although physics need not state or even include aether.<ref name=Vongehr/>  Organizing regularities of ''observations''—as in the covering law model—physicists find superfluous the quest to discover ''aether''.<ref name=Ben-Menahem/>

In 1905, from [[special relativity]], Einstein deduced [[mass–energy equivalence]],<ref>Mass–energy equivalence is formalized in the equation E=mc<sup>2</sup>.</ref> particles being variant forms of distributed energy,<ref>Einstein, "Ether", ''Sidelights'' (Methuen, 1922), [https://books.google.com/books?id=vwZlfF3sVJEC&pg=RA1-PA616&dq=special p 13]: "[A]ccording to the special theory of relativity, both matter and radiation are but special forms of distributed energy, ponderable mass losing its isolation and appearing as a special form of energy".</ref> how [[particle accelerator|particles colliding at vast speed]] experience that energy's transformation into mass, producing heavier particles,<ref>Braibant, Giacomelli & Spurio, ''Particles and Fundamental Interactions'' (Springer, 2012), [https://books.google.com/books?id=e8YUUG2pGeIC&pg=PA2&dq=electron+proton+neutron+collisions p 2]: "Any particle can be created in collisions between two high energy particles thanks to a process of transformation of energy in mass".</ref> although physicists' talk promotes confusion.<ref>[[Brian Greene]] explained, "People often have the wrong image of what happens inside the [[Large Hadron Collider|LHC]], and I am just as guilty as anyone of perpetuating it.  The machine does not smash together particles to pulverise them and see what is inside.  Rather, it collides them at extremely high energy.  Since, by dint of Einstein's famous equation, [[mass-energy equivalence|E=mc<sup>2</sup>]], energy and mass are one and the same, the combined energy of the collision can be converted into a mass, in other words, a particle, that is heavier than either of the colliding [[proton]]s.  The more energy is involved in the collision, the heavier the particles that might come into being" [Avent, [https://www.economist.com/blogs/babbage/2012/07/qa-brian-greene "The Q&A"], ''Economist'', 2012].</ref>  As "the contemporary locus of [[metaphysical]] research", QFTs pose particles not as existing individually, yet as ''excitation modes'' of fields,<ref name=Torretti-p396>Torretti, ''Philosophy of Physics'' (Cambridge U P, 1999), [https://books.google.com/books?id=vg_wxiLRvvYC&pg=P396&dq= p 396].</ref><ref name=Kuhlmann/> the particles and their masses being states of aether,<ref name=Wilczek1999p13>Wilczek, [http://ctpweb.lns.mit.edu/physics_today/phystoday/Ether.pdf "The persistence of ether"], ''Phys Today'', 1999; '''52''':11,13, p 13.</ref> apparently unifying all physical phenomena as the more fundamental causal reality,<ref name=Riesselmann/><ref name=Jegerlehner/><ref name=Wilczek-p73>Wilczek, ''Lightness of Being'' (Basic Books, 2008), ch 8 "The grid (persistence of ether)", [https://books.google.com/books?id=iWhxK12fbA4C&pg=PA73&dq=Ether+QCD 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".</ref> as long ago foreseen.<ref name=Lodge/>  Yet a ''quantum'' field is an intricate abstraction—a ''mathematical'' field—virtually inconceivable as a ''classical'' field's physical properties.<ref name=Kuhlmann>Kuhlmann, [http://www.scientificamerican.com/article.cfm?id=physicists-debate-whether-world-made-of-particles-fields-or-something-else "Physicists debate"], ''Sci Am'', 2013.</ref>  Nature's deeper aspects, still unknown, might elude any possible field theory.<ref name=Torretti-p396/><ref name=Kuhlmann/>

Though discovery of causality is popularly thought science's aim, search for it was shunned by the [[Isaac Newton|Newtonian]] [[research program]],<ref name=Kundi>{{Cite journal 
| author= Kundi M 
| title = Causality and the interpretation of epidemiologic evidence 
| doi = 10.1289/ehp.8297 
| journal = Environmental Health Perspectives 
| volume = 114 
| issue = 7 
| pages = 969–974 
| year = 2006 
| pmid =  16835045
| pmc =1513293 
}}</ref> even more Newtonian than was [[Isaac Newton]].<ref name=Wilczek1999p13/><ref>Whereas Newton's ''Principia'' inferred absolute space and absolute time, omitted an aether, and, by [[Newton's law of universal gravitation]], formalized [[action at a distance]]—a supposed force of gravitation spanning the entire universe instantly—Newton's later work ''Optiks'' introduced an aether binding bodies' matter, yet denser outside bodies, and, not uniformly distributed across all space, in some locations condensed, whereby "aethereal spirits" mediate electricity, magnetism, and gravitation. (Whittaker, ''A History of Theories of Aether'' (Longmans, Green & Co: 1910), [https://archive.org/stream/historyoftheorie00whitrich#page/18/mode/2up pp 17–18])</ref>  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.<ref name=Schwarz/>  Given uncertainties of [[scientific realism]],<ref name=Bolotin-realism>Challenges to [[scientific realism]] are captured succinctly by Bolotin, ''Approach to Aristotle's Physics'' (SUNY P, 1998), [https://books.google.com/books?id=LLqB1IfeSZ0C&pg=PA33&dq= 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".</ref> 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.<ref>Norton, [http://www.pitt.edu/~jdnorton/papers/003004.pdf "Causation as folk science"], in Price & Corry, eds, ''Mature Causation, Physics, and the Constitution of Reality'' (Oxford U P, 2007), esp [https://books.google.com/books?id=oCXe4DvqUFMC&pg=PA12&dq= p 12].</ref>  Even [[epidemiology]] is maturing to heed the severe difficulties with presumptions about causality.<ref name=Kundi/><ref name=Karhausen>{{Cite journal 
| doi = 10.1023/A:1009970730507 
| last1 = Karhausen | first1 = L. R. 
| title = Causation: The elusive grail of epidemiology 
| journal = Medicine, Health Care and Philosophy 
| volume = 3 
| issue = 1 
| pages = 59–67 
| year = 2000 
| pmid = 11080970
}}</ref><ref name=Rothman-Greenland/>  Covering law model is among [[Carl Gustav Hempel|Carl G Hempel]]'s admired contributions to [[philosophy of science]].<ref>Fetzer, ch 3, in Fetzer, ed, ''Science, Explanation, and Rationality'' (Oxford U P, 2000), [https://books.google.com/books?id=Nvctcrj08wAC&pg=PA111&dq= p 111].</ref>

==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==
{{Reflist|2}}

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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, [http://www.iep.utm.edu/e/explanat.htm "Theories of explanation"], in Fieser Dowden, ed, ''[[Internet Encyclopedia of Philosophy]]'', 2006.
*Ilkka Niiniluoto, "Covering law model", in Robert Audi, ed., [https://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambridge.Dictionary.of.Philosophy#page/n0/mode/2up ''The Cambridge Dictionary of Philosophy'', 2nd edn] (New York: Cambridge University Press, 1996).
*Wesley C. Salmon, [https://books.google.com/books/about/Four_Decades_of_Scientific_Explanation.html?id=FHqOXCd06e8C ''Four Decades of Scientific Explanation''] (Minneapolis: University of Minnesota Press, 1990 / Pittsburgh: University of Pittsburgh Press, 2006).

{{philosophy of science}}
{{positivism}}

[[Category:Scientific method]]
[[Category:Philosophy of science]]
[[Category:Conceptual models]]