The Deductive-Nomological Model of Scientific Explanation

     We begin by observing that not all "explanations," of course are "scientific explanations"; there
is nothing particularly "scientific" about explaining how to play chess, or the meaning of a text or work
of art.  Religious and philosophical "explanations" would not normally count as "scientific," and certainly
pseudo-scientific "explanations" like those provided by astrology or alchemy are intended to be excluded.
Thus defenders of the consensus were concerned to formulate the criteria which make an explanation
a scientific explanation.

     Aristotle is generally given credit for being the first philosopher to clearly enunciate the view
that scientific knowledge is distinguished by the fact that it aspires to explain the causes of "what is."
Aristotelian metaphysics analyzes knowledge about reality into statements about the entities or "beings"
which comprise the actual world (generally translated as "substances").  Scientific knowledge explains why
substances are what they are by appeal to four aitia or "explanatory factors" (generally translated as
"causes").  Aristotle develops a complex analysis of these causes in terms of his conceptual dichotomies
of sensible and intelligible, "universal" and "particular," and "actual" and "potential," etc.  The upshot of
this analysis is that knowledge of the four causes requires the active intellect's comprehension of the
universal intelligible form embodied in the sensible particular substances.  This form is most definitely
in the substance and makes it what it is and what it will become; it is not to be confused with a concept
in the mind of the cognitive subject but it is the object which the mind grasps or understands when
knowledge is attained.  In disagreement with his master Plato, who proposed a separate, eternal,
changeless realm for the Forms, Aristotle argued that the form does not exist apart from the physical
particular substance which it "informs"; but, like Plato, he holds that it is not itself a physical particular
thing grasped by the senses, but a universal essence grasped by the mind.

In the scientific revolution of the seventeenth century a new form of explanation emerged in
which no appeal was made to Aristotelian forms or essences.  In the "mechanical philosophy" of the new
natural philosophers like Galileo and Descartes, and ultimately Newton, the observed motions of bodies
was accounted for by deducing them from basic mathematically expressed statements of regularities
between observable, and measurable, aspects of phenomena.  Thus the idea of explanation in terms of
forms came to be replaced with the idea of explanation in terms of deduction from "laws of nature." In
seeking a justification for the new science of their time, the diverse philosophers of the Enlightenment
at least agreed in rejecting the old Aristotelian conception of causal explanation.  On the rationalist side
of Enlightenment thinking, something like the ancient doctrine of forms lived on, in a new "mentalized"
version, in the doctrine of innate ideas or principles as the foundations of knowledge.  But inasmuch
as it is the empiricist line which came to dominate in the consensus we are exploring, our story leads
us to follow this thread.

     Now it is -at the very least- an open question whether or not deduction from a "causal law" (understood in the Humean sense as merely the statement that phenomena of one sort have been regularly followed (in the past) by phenomena of another sort) constitutes an "explanation" of the occurrence of the latter phenomenon at all, for under such a restricted interpretation adopted by Humean empiricism, "laws" state in effect only that certain phenomena in fact have been connected temporally. Under this Humean epiricistic view, the statement of a law does not even address the issue of why this regularity occurs.  Even at best such an account of laws relinquishes any hope of ascribing necessity to the occurrences of nature; at worst it could be that it states no more than mere co-incidences. Some empiricists would just abandon recourse to "explanation" as a distinguishing characteristic of scientific knowledge and admit that such laws are no more than short hand ways of summarizing "descriptions" of observed regularities.  But most empiricists would be in favor of revising the understanding of what it is to "explain" phenomena such that just such a deduction from laws so interpreted is, by definition, an "explanation."

     The image of science held by the empiricist consensus accepts the cognitive goal of science as
explaining observable phenomena and regularities amongst them. Although defenders of the consensus
agreed that philosophy of science should provide a precise clarification of the criteria for a "scientific
explanation,"  unfortunately the actual content of science includes explanations of many very different
sorts and there are a variety of ways of characterizing these differences.  In particular because they
tended to take physics as the most perfected of the sciences, and because it seems to embody mostly a
deductive form of explanation, consensus defenders originally identified the criterion of a scientific
explanation in the claim that it could be logically cast (or recast by the philosopher) as having the form
of a valid deductive argument.

       Statements of          +          Statements of       =>     Statements Describing
     Initial Conditions                 Laws & Theories             Explained Phenomena

    Here "=>" symbolizes the relation of "valid deductive implication".

     The premises of the argument which forms the explanation consist of two kinds of statements:
        a) statements describing "initial conditions" and
        b) statements of "laws & theories"

These two classes of statments forming the explanation are referred to by the Latin word the "explanans".

The conclusion of the argument, which is alleged to be validly deduced from the explanans, is the statement(s) describing the phenomenon which is being explained; it is called the "explanandum".

Explananda (plural of explanandum) come in two forms:

     a) Explanations of particular phenomena:  Some explananda are statements describing some particular occurrence in the world, often referred to as a "fact," a "phenomenon," or an "event." The statements of such explananda are taken as being directly known by sensory experience. They are explained by being validly deduced from statement(s) of some general law or laws and statements describing the "initial conditions" actually obtaining in the case of the particular phenomenon to be explained.

     b) Explanations of general laws: Other explananda are statements of laws themselves, for example those which express regularities between certain observable phenomena.  These are called "empirical (or observational) laws".  They can be explained by deduction validly from "higher level" laws, some of which may include reference to unobservable entities, processes, or events.  These are known as theoretical laws."

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     Shortly after World War II, Carl Hempel, under the influence of the older generation of positivists, set about expressing this rather vague conviction already held by most positivists in a precise way. {Click here to see Hempel's Paper.) The view he described came to be known as "the deductive nomological model" (meaning in effect "deduction from laws") or the "covering law" model of scientific explanation (since an ideal explanation "subsumed" the phenomenon to be explained "under a law" which "covers" phenomena of that sort).  This model never purported to cover all scientific explanations, for from the start Hempel emphasized that statistical explanations were of a different sort.  Nevertheless, the dominant view was that an explanation having the deductive nomological form was an ideal towards which many explanations could be interpreted as approaching more or less successfully.

     It is important to realize the basic logical point that to say that the argument is deductively "valid" is merely to say that the conclusion, the explanandum, follows with necessity from the explanans.  Or in other words (speaking less formally) given the initial conditions and the correct laws, one can deduce what observable phenomena will occur given those conditions.  However, the important point to recognize here is that merely the fact that an explanation can be expressed as such a valid deductive argument does not establish the claim that the premises of that argument, i.e., the "laws," and the "initial conditions" are in fact true.  The question of the "justification" of the explanation, i.e. the question of what evidence we have for the truth of the laws, becomes a quite distinct question from the question of what is a "scientific explanation," or in other words whether or not ideal acceptable scientific explanations do have the form of valid arguments.

     For this reason we must bear in mind that the D-N model is a model of an ideal form for a
scientific explanation; it does not itself address the epistemic question of why this explanation is justified
as acceptable.  At least three different models of justification, known as "inductivism," "hypothetico-
deductivism," and "falsificationism" are all more or less equally compatible with the D-N model of what
is a scientific explanation.  After traditional inductivism came to be regarded as discredited, the
remaining rivals of "hypothetico-deductivism," which was a "confirmationism" derived from the
"verificationism" of the original logical positivists, and the "falsificationism" of Karl Popper could live
equally well with the D-N image of explanations.

The DN Model of scientific explanation has interesting implications for the relationship between "explanation" and "prediction" in science.  The argument which is put forward as the explanation (the "explanans") can be formulated either after or before the phenomenon to be explained (the "explanandum") occurs.  If the scientist gives us such an argument after we know of the occurrence of  the explanandum phenomenon, we call it an "explanation"; but if the deduction is made prior to the occurrence of the phenomenon, it is known as a "prediction." "Explanation" and "prediction" are thus in effect the same argument, differing only in when they happen to be formulated.  This was often expressed by saying they were "symmetric."

This symmetry, however, is only a formal symmetry in the logical relations between the statements.  From an epistemological point of view, the evidential value of predictions of hitherto unknown phenomena is far greater than the explanations the theory provides of the
phenomena it was developed to explain.  In other words the fact that a theory allows us to deduce, given initial conditions, the occurrence of those very phenomena which the theory was developed to explain, is only a minimal condition which any candidate for an acceptable theory must meet.  However, if that same theory, given different initial conditions, allows us to predict a hitherto unknown phenomenon, then this achievement is considered much stronger evidence in favor of the acceptability of that theory.  We express this by saying that even though "explanation" and "prediction" are logically "symmetric," from the epistemic point of view which asks why should we accept this explanation, succesful prediction of novelty counts for much more than explanation of what is already known.  This fact in turn casts doubt on the empiricist attempt to reduce the question of the acceptability of a theory to the purely logical relation explanans and explanandum.

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     The account of "laws" is of crucial concern in the elaboration of the D-N model.  Laws differ from statements describing initial conditions in that these latter are "particular" statements referring to individual instances whereas laws are "general" or "universal" statements stating that all members of one class of possible instances are related in a certain way to another class.  The truth value of particular statements, empiricists presumed, could and should be established by a process of "observation."

However, laws being universal in scope cannot be so justified.  According to "inductivism" a process of "inductive reasoning" leads from particular statements known by observation to general statements of laws.  But no inductive process can establish that the truth of its conclusion follows necessarily from the observational premisses with which it begins.

Hypothetico-deductivism holds that such general laws are not arrived at inductively, but proposed first as hypotheses and then employed in (hopefully) successful explanations.  After an array of such successes a hypothesis (perhaps gradually) shifts from hypothetical acceptance to being called an accepted "law."

Now some statements which are honored with the name "law" in scientific parlance are in effect definitions.  Since these statements are true by virtue of the meanings thereby attributed to the terms, such statements are considered "analytic," and our confidence in their truth does not rest on any sensory observation.  But if all premisses in an argument are analytic, all statements that can be validly deduced are equally analytic.  Analytic statements are true independently of the way the world is, they are thus independent of any empirical facts.  Another way to put this is that they are true in any logically possible world.

However the explananda in an empirical science are contingentnon-analytic facts about this actual world, and thus cannot be known to be true analytically.  Thus the premisses of an acceptable explanation must include at least one law which has "empirical content," or "empirical import," which is to say that if it is true, it is not true solely on the basis of meanings of terms, but its truth rests on the particular facts of this actual world.  Our belief in the truth of such laws with empirical import, when universal in scope, is always open to the possibility of future evidence undermining our justification.  Thus no non-analytic "law" can ever be known to be true, leading to the epistemological acceptance of fallibilism.
 

We are tempted to say being iron causes the magnet necessarily to attract the object whereas being elected President does not cause a person to be (or become) a white male; the former admits of no exceptions while the latter, though it is true at present might and perhaps one day will no longer be so.  This strategy for distinguishing genuine laws from "accidental generalizations," however, brings into the account of scientific explanation a non-empirical idea of causal necessity which empiricists were anxious to avoid.

The path that empiricists typically did pursue was to re-express causal relations as propositions which would "support" not only deductions of particular actually observed phenomena, but also "subjunctive conditionals" or  "counterfactuals"  of the form, "If such and such is (or would be) a so and so, then it would be (or would have been) thus and so." [To use the above examples, the genuine law, "All pieces of iron are attracted by magnets." would allow me to infer of this brass key: "Had this key been made of iron (contrary to fact), it would have been attracted by this magnet." However, the true but accidental generalization "All Presidents have been white males." would not allow me to infer that "If Whoopi Goldberg is elected President, she will be (or become) a white male."]  This tactic then suggested that empiricist needed to develop a logic of subjunctive conditionals which would explain how one arrives at the truth value of statements that refer to mere possibility or events that did not happen (counterfactual).  This goal was never attained, thus leading to considerable uneasiness over how to specify genuine laws. Defenders of the consensus had many disputes surrounding this issue.

     We should note that because the D-N model regards explanations as arguments, explanations are in effect things in a language, for an "argument" must by definition be something expressed in a language.  This of course accords well with the consensus view that "science" (or "scientific knowledge") is a vast body of statements.  What scientists aspire to do is to add to, and perhaps improve the precision of, this body of statements; that is the goal or purpose of scientific research.  The philosophy of science, in contrast to science itself, provides no new knowledge itself, but is envisioned as concerned with the logical analysis of this body of statements, a project which requires recasting the often "messy" shorthand language of real science by translating it into a logically precise ideal language and exhibitingthe logical interrelations between the statements of this language.

Problems with the DN Model of Explanation:

a) Problems with "Predictions":

As noted above, according to the DN model of explanation, explanations and predictions are really the same thing, differeng only with respect to when the "explanandum" occurs.  Thus if the DN model is an acceptable account of scientific explanations, then anything that can be explained, could equally well have been predicted.

Unfortunately many sciences, such a evolutionary biology or geology produce explanations which are considered quite acceptable scientific explanations, but which are utterly incapable of predicting, phenomena.  Two possible responses to this difficulty are open.

One could argue that the unpredictability of such sciences is due to the fact that the phenomena concerned are of such massive complexity that a total knowledge of the initial conditions is practically (or perhaps even physically) impossible to attain, but were it attainable, predictability of even such phenomena would be possible. One way of expressing this outlook would be to say that an omniscient being given the conditions in the "Big-bang" could deduce the whole subsequent history of planet Earth and the evolution of living organisms on it.  This of course is a considerable claim which, in the very nature of the case, cannot be established empirically.

     Another alternative was to admit that the D-N model was gives us an account of only one of a variety of possible explanations which were ultimately irreducible to D-N form.  The devotion of most defenders of the empiricist consensus to the "unity of science" made them loathe to take this path, for it certainly sowed the seeds of disunity among what they perceived as the different branches of a "unified  science."
 

From the start Hempel noted that statistical explanations are not reducible to DN form. Statements to the effect that events of a certain sort have a high statistical correlation with events of another sort, do not allow us to deduce (and therefore to predict) that the explanandum event will occur, yet many sciences offer explanations of just this sort.

 Thus, for example, if Jones smokes two packs of cigarettes per day, the fact that he develops lung cancer is accepted as "explained" by the statistical generalization that "Ninety per cent of people who smoke two packs of cigarettes per day develop lung cancer."  However, although this generalization is taken as a satisfactory explanation of Jones's cancer, it would not have allowed one to predict that Jones would get lung cancer, because he might have been part of the ten per cent who do not.

Statistical sorts of explanations given in fields like genetics or quantum physics may well be irreducible and should not be seen as half-way houses en route to a fully deductive account.  Nevertheless, such explanations are the best many sciences can aspire to achieve.

    Matters are made worse by the prevalence of "functional" or "teleological" explanations in the life sciences which account for their explananda by explaining structures in terms of the functions they perform and the purposes of the performance of such functions.  Human conscious agents often explain their actions this way, but it is a mistake to imagine that such explanations make sense only by imputing conscious purposes to entities.  One might explain bodily organs through their role in the functions of digestion or respiration without imagining that these organs, or any process which gave rise to them, has a conscious end in view.  Equally, one might give a functional account of a steam engine or a nuclear reactor which is considered quite "scientific" although no suspicion of consciousness accrues to the explananda.  These teleological explanations again might be thought to give way one day to purely mechanical explanations which could be cast in D-N form, but it seems to be at least an open question whether the biological science would be enriched or impoverished by such a reduction, should it ever be possible to achieve it.

d) Problems with "Genetic explanations":

     Finally, many seemingly quite acceptable scientific explanations are "genetic" in form, explaining the explanandum phenomenon in effect by establishing a chronology of events that led up to present day observations.  The account of the shapes and positions of the continents in terms of plate tectonics and the break-up of the super-continent "Pangea" or the Cretaceous extinction as a consequence of a collision with an extraterrestrial object may well be perfectly scientific but these "narratives" do not fit the D-N form.

     The D-N Model faced difficulties such as a) through d) above because the concept of "explanation" has an inherently pragmatic dimension.  This is the philosopher's way of saying that what is considered "acceptable" as an explanation cannot be defined out of the context in which such an explanation is offered.  In different contexts when we ask for an "explanation" we have different "purposes" or "goals" or "interests" which we hope to be fulfilled by providing an "acceptable" scientific explanation.  The philosopher calls the defense of the acceptability of belief in terms of its satisfaction of certain interests a "pragmatic" defense.  In one context a mechanical explanation which follows strict D-N form may be just what we expect, but in another context where we are interested in a connection between structure and function, a teleological explanation may be called for, and a mechanical explanation in deductive form would seem ludicrously  inappropriate.

Consequently the claim that different types of explanation are appropriate in different contexts calls for a pragmatic account of explanation not successfully captured by the D-N model.  At the best, we can say that the D-N model allowed a relatively precise specification of one type of scientific explanation. Its successful explication would indeed be an achievement important for philosophy of science, but even
were all the problems with the DN Model eliminated, it would at best tell part, but not all, of the story of scientific explanation.