The deductive-nomological model (DN model),
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—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, it
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, 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, revision
to DN model emphasized maximal specificity
for relevance of the conditions and axioms
stated. Together with Hempel's inductive-statistical
model, the DN model forms scientific explanation's
covering law model, which is also termed,
from critical angle, subsumption theory.
== Form ==
The term deductive distinguishes the DN model's
intended determinism from the probabilism
of inductive inferences. The term nomological
is derived from the Greek word νόμος
or nomos, meaning "law". The DN model holds
to a view of scientific explanation whose
conditions of adequacy (CA)—semiformal but
stated classically—are derivability (CA1),
lawlikeness (CA2), empirical content (CA3),
and truth (CA4).In the DN model, a law axiomatizes
an unrestricted generalization from antecedent
A to consequent B by conditional proposition—If
A, then B—and has empirical content testable.
A law differs from mere true regularity—for
instance, George always carries only $1 bills
in his wallet—by supporting counterfactual
claims and thus suggesting what must be true,
while following from a scientific theory's
axiomatic structure.The phenomenon to be explained
is the explanandum—an event, law, or theory—whereas
the premises to explain it are explanans,
true or highly confirmed, containing at least
one universal law, and entailing the explanandum.
Thus, given the explanans as initial, specific
conditions C1, C2 . . . Cn plus general laws
L1, L2 . . . Ln, the phenomenon E as explanandum
is a deductive consequence, thereby scientifically
explained.
== Roots ==
Aristotle's scientific explanation in Physics
resembles the DN model, an idealized form
of scientific explanation. The framework of
Aristotelian physics—Aristotelian metaphysics—reflected
the perspective of this principally biologist,
who, amid living entities' undeniable purposiveness,
formalized vitalism and teleology, an intrinsic
morality in nature. With emergence of Copernicanism,
however, Descartes introduced mechanical philosophy,
then Newton rigorously posed lawlike explanation,
both Descartes and especially Newton shunning
teleology within natural philosophy. At 1740,
David Hume staked Hume's fork, highlighted
the problem of induction, and found humans
ignorant of either necessary or sufficient
causality. Hume also highlighted the fact/value
gap, as what is does not itself reveal what
ought.Near 1780, countering Hume's ostensibly
radical empiricism, Immanuel Kant highlighted
extreme rationalism—as by Descartes or Spinoza—and
sought middle ground. Inferring the mind to
arrange experience of the world into substance,
space, and time, Kant placed the mind as part
of the causal constellation of experience
and thereby found Newton's theory of motion
universally true, yet knowledge of things
in themselves impossible. Safeguarding science,
then, Kant paradoxically stripped it of scientific
realism. Aborting Francis Bacon's inductivist
mission to dissolve the veil of appearance
to uncover the noumena—metaphysical view
of nature's ultimate truths—Kant's transcendental
idealism tasked science with simply modeling
patterns of phenomena. Safeguarding metaphysics,
too, it found the mind's constants holding
also universal moral truths, and launched
German idealism, 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—rejecting conjectures
about unobservables, thus rejecting search
for causes. Positivism predicts observations,
confirms the predictions, and states a law,
thereupon applied to benefit human society.
From late 19th century into the early 20th
century, the influence of positivism spanned
the globe. Meanwhile, evolutionary theory's
natural selection brought the Copernican Revolution
into biology and eventuated in the first conceptual
alternative to vitalism and teleology.
== Growth ==
Whereas Comtean positivism posed science as
description, logical positivism emerged in
the late 1920s and posed science as explanation,
perhaps to better unify empirical sciences
by covering not only fundamental science—that
is, fundamental physics—but special sciences,
too, such as biology, psychology, economics,
and anthropology. After defeat of National
Socialism with World War II's close in 1945,
logical positivism shifted to a milder variant,
logical empiricism. All variants of the movement,
which lasted until 1965, are neopositivism,
sharing the quest of verificationism.Neopositivists
led emergence of the philosophy subdiscipline
philosophy of science, researching such questions
and aspects of scientific theory and knowledge.
Scientific realism takes scientific theory's
statements at face value, thus accorded either
falsity or truth—probable or approximate
or actual. Neopositivists held scientific
antirealism as instrumentalism, holding scientific
theory as simply a device to predict observations
and their course, while statements on nature's
unobservable aspects are elliptical at or
metaphorical of its observable aspects, rather.DN
model received its most detailed, influential
statement by Carl G Hempel, first in his 1942
article "The function of general laws in history",
and more explicitly with Paul Oppenheim in
their 1948 article "Studies in the logic of
explanation". Leading logical empiricist,
Hempel embraced the Humean empiricist view
that humans observe sequence of sensory events,
not cause and effect, as causal relations
and casual mechanisms are unobservables. DN
model bypasses causality beyond mere constant
conjunction: first an event like A, then always
an event like B.Hempel held natural laws—empirically
confirmed regularities—as satisfactory,
and if included realistically to approximate
causality. In later articles, Hempel defended
DN model and proposed probabilistic explanation
by inductive-statistical model (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). Georg Henrik von Wright,
another critic, named the totality subsumption
theory.
== Decline ==
Amid failure of neopositivism's fundamental
tenets, Hempel in 1965 abandoned verificationism,
signaling neopositivism's demise. From 1930
onward, Karl Popper had refuted any positivism
by asserting falsificationism, which Popper
claimed had killed positivism, although, paradoxically,
Popper was commonly mistaken for a positivist.
Even Popper's 1934 book embraces DN model,
widely accepted as the model of scientific
explanation for as long as physics remained
the model of science examined by philosophers
of science.In the 1940s, filling the vast
observational gap between cytology and biochemistry,
cell biology arose and established existence
of cell organelles besides the nucleus. Launched
in the late 1930s, the molecular biology research
program cracked a genetic code in the early
1960s and then converged with cell biology
as cell and molecular biology, its breakthroughs
and discoveries defying DN model by arriving
in quest not of lawlike explanation but of
causal mechanisms. Biology became a new model
of science, while special sciences were no
longer thought defective by lacking universal
laws, as borne by physics.In 1948, when explicating
DN model and stating scientific explanation's
semiformal conditions of adequacy, Hempel
and Oppenheim acknowledged redundancy of the
third, empirical content, implied by the other
three—derivability, lawlikeness, and truth.
In the early 1980s, upon widespread view that
causality ensures the explanans' relevance,
Wesley Salmon called for returning cause to
because, and along with James Fetzer helped
replace CA3 empirical content with CA3' strict
maximal specificity.Salmon introduced causal
mechanical explanation, never clarifying how
it proceeds, yet reviving philosophers' interest
in such. Via shortcomings of Hempel's inductive-statistical
model (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 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.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—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. 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. (Boundary conditions are specified
conditions whereby the phenomena of interest
occur. Bridge laws translate terms in one
science to terms in another science.)
== 
Weaknesses ==
By DN model, if one asks, "Why is that shadow
20 feet long?", another can answer, "Because
that flagpole is 15 feet tall, the Sun is
at x angle, and laws of electromagnetism".
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 philosophers have concluded that causality
is integral to scientific explanation. 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%).) 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. 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.
== Covering action ==
Through lawlike explanation, fundamental physics—often
perceived as fundamental science—has proceeded
through intertheory relation and theory reduction,
thereby resolving experimental paradoxes to
great historical success, resembling covering
law model. In early 20th century, Ernst Mach
as well as Wilhelm Ostwald had resisted Ludwig
Boltzmann's reduction of thermodynamics—and
thereby Boyle's law—to statistical mechanics
partly because it rested on kinetic theory
of gas, hinging on atomic/molecular theory
of matter. Mach as well as Ostwald viewed
matter as a variant of energy, and molecules
as mathematical illusions, as even Boltzmann
thought possible.In 1905, via statistical
mechanics, Albert Einstein predicted the phenomenon
Brownian motion—unexplained since reported
in 1827 by botanist Robert Brown. 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 electromagnetic,
whose two theories misaligned. Yet belief
in aether as the source of all physical phenomena
was virtually unanimous. At experimental paradoxes,
physicists modified the aether's hypothetical
properties.Finding the luminiferous aether
a useless hypothesis, Einstein in 1905 a priori
unified all inertial reference frames to state
special principle of relativity, which, by
omitting aether, converted space and time
into relative phenomena whose relativity aligned
electrodynamics with the Newtonian principle
Galilean relativity or invariance. Originally
epistemic or instrumental, this was interpreted
as ontic or realist—that is, a causal mechanical
explanation—and the principle became a theory,
refuting Newtonian gravitation. By predictive
success in 1919, general relativity apparently
overthrew Newton's theory, a revolution in
science resisted by many yet fulfilled around
1930.In 1925, Werner Heisenberg as well as
Erwin Schrödinger independently formalized
quantum mechanics (QM). Despite clashing explanations,
the two theories made identical predictions.
Paul Dirac's 1928 model of the electron was
set to special relativity, launching QM into
the first quantum field theory (QFT), quantum
electrodynamics (QED). From it, Dirac interpreted
and predicted the electron's antiparticle,
soon discovered and termed positron, 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 formalism, which if taken toward
interpretation as a causal mechanical model
clashes with Heisenberg's matrix formalism
and with Schrödinger's wave formalism, although
all three are empirically identical, sharing
predictions. 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 selfcontradictory.Meeting in 1947, Freeman
Dyson, Richard Feynman, Julian Schwinger,
and Sin-Itiro Tomonaga soon introduced renormalization,
a procedure converting QED to physics' most
predictively precise theory, subsuming chemistry,
optics, and statistical mechanics. QED thus
won physicists' general acceptance. Paul Dirac
criticized its need for renormalization as
showing its unnaturalness, and called for
an aether. In 1947, Willis Lamb had found
unexpected motion of electron orbitals, shifted
since the vacuum is not truly empty. Yet emptiness
was catchy, abolishing aether conceptually,
and physics proceeded ostensibly without it,
even suppressing it. Meanwhile, "sickened
by untidy math, most philosophers of physics
tend to neglect QED".Physicists have feared
even mentioning aether, renamed vacuum, which—as
such—is nonexistent. General philosophers
of science commonly believe that aether, rather,
is fictitious, "relegated to the dustbin of
scientific history ever since" 1905 brought
special relativity. Einstein was noncommittal
to aether's nonexistence, simply said it superfluous.
Abolishing Newtonian motion for electrodynamic
primacy, however, Einstein inadvertently reinforced
aether, and to explain motion was led back
to aether in general relativity. Yet resistance
to relativity theory became associated with
earlier theories of aether, whose word and
concept became taboo. Einstein explained special
relativity's compatibility with an aether,
but Einstein aether, too, was opposed. Objects
became conceived as pinned directly on space
and time by abstract geometric relations lacking
ghostly or fluid medium.By 1970, QED along
with weak nuclear field was reduced to electroweak
theory (EWT), and the strong nuclear field
was modeled as quantum chromodynamics (QCD).
Comprised by EWT, QCD, and Higgs field, this
Standard Model of particle physics is an "effective
theory", not truly fundamental. As 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.
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 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, the particles
and their masses being states of aether, apparently
unifying all physical phenomena as the more
fundamental causal reality, as long ago foreseen.
Yet a quantum field is an intricate abstraction—a
mathematical field—virtually inconceivable
as a classical field's physical properties.
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 Newtonian
research program, even more Newtonian than
was Isaac Newton. By now, most theoretical
physicists infer that the four, known fundamental
interactions would reduce to superstring theory,
whereby atoms and molecules, after all, are
energy vibrations holding mathematical, geometric
forms. Given uncertainties of scientific realism,
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.
== See also ==
Types of inference
Deductive reasoning
Inductive reasoning
Abductive reasoningRelated subjects
Explanandum and explanans
Hypothetico-deductive model
Models of scientific inquiry
Philosophy of science
Scientific method
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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, Four Decades of Scientific
Explanation (Minneapolis: University of Minnesota
Press, 1990 / Pittsburgh: University of Pittsburgh
Press, 2006).
