Explanation

An explanation is an account that makes something understandable: it tells us why an event happened, why a state of affairs holds, or how something works. Children ask "why?" almost as soon as they can talk, scientists spend careers looking for explanations, and courts, doctors, mechanics, and historians all trade in them. Yet saying precisely what an explanation is, and what separates a good one from a bad one, has turned out to be one of the most stubborn problems in philosophy.

This article introduces the main ideas. It covers the ordinary concept of explanation, how explanations differ from arguments and justifications, the classical philosophical accounts of the twentieth century (above all Carl Hempel's deductive-nomological model), the famous counterexamples that undermined it, and the main alternatives that followed: statistical relevance and causal-mechanical theories, unificationist theories, pragmatic theories, and more recent interventionist and mechanistic accounts. It closes with debates about non-causal explanation, the psychology of explanation, common misconceptions, and a set of frequently asked questions.

The basic vocabulary

Philosophers usually divide an explanation into two parts:

• The explanandum (Latin for "that which is to be explained") is the fact, event, or regularity we want to understand: for example, that a particular bridge collapsed, or that the planets move in ellipses.
• The explanans ("that which explains") is the material offered to account for it: perhaps facts about the bridge's design and the load on it, together with principles of engineering.

An explanation, then, is a relation between an explanans and an explanandum. The philosophical question is what that relation has to be.

Explanations come in many everyday forms. We explain someone's action by citing their beliefs and desires: she took off her coat because she felt hot and believed removing it would cool her down. We explain a machine's failure by pointing to a broken part. We explain a historical event by describing the circumstances and choices that led to it. We explain a biological trait by its function or evolutionary history. A theory of explanation aims to say what these have in common, or, failing that, to sort them into kinds.

Explanations, arguments, and justifications

Explanation versus argument

Explanations and arguments can look alike, since both often consist of statements linked by words such as "because" and "so." But they do different jobs.

• An argument starts from a claim that is in doubt and offers reasons to believe it. Its goal is to establish that something is true.
• An explanation usually starts from a claim that is already accepted and tries to show why it is true or what brought it about. Its goal is understanding rather than proof.

Consider two neighbors. If they disagree about whether a cat has fleas, one might argue: "The cat keeps scratching and there are tiny dark specks in its fur, so it has fleas." Once both agree the cat has fleas, they might ask why, and one might explain: "The weather has been damp, and fleas thrive in damp conditions." The same subject, the same kind of sentence structure, but different aims.

The two are easy to confuse for several reasons: people are often unclear about which one they are doing; they use similar connecting words; the verb "explain" frequently turns up in what are really arguments ("let me explain why you're wrong"); and explanations are often used as part of arguments. In particular, a common form of reasoning infers that a hypothesis is true because it would explain the evidence well, which is discussed below as inference to the best explanation.

Explanation versus justification

"Explanation" is also sometimes used to mean justification: an account of why a belief is reasonable, or how someone knows what they claim to know. Justification concerns reasons for believing; explanation concerns reasons why something is so. A detective's evidence justifies believing that the butler did it; the butler's motive and opportunity explain why he did it. An explanation need not be a proof, and a proof need not be explanatory.

Ancient beginnings: Aristotle's four causes

The idea that there are different kinds of answer to "why?" goes back at least to Aristotle in the fourth century BCE. In his Physics and Metaphysics, Aristotle distinguished four kinds of aitia, a Greek word traditionally translated as "cause" but often better rendered as "explanatory factor" or "reason why." Many modern scholars regard Aristotle's theory of causes as, in effect, a theory of explanation.

For centuries these four were treated as the basic kinds of explanation. The rise of modern science in the seventeenth century narrowed the focus. Final causes, explanations in terms of purpose, were largely banished from physics, and "cause" came to mean primarily what Aristotle called the efficient cause. Purpose-based explanation survived in human affairs and was later reinterpreted in biology through the idea of natural selection, where traits can be explained by the function they served for ancestors. Modern writers also distinguish other types: functional, historical, psychological, reductive, and teleological explanations, among others.

Hempel and the deductive-nomological model

The model

The modern philosophical debate begins with a 1948 paper by Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation," published in Philosophy of Science. Hempel developed the view further over the next two decades; his 1965 book Aspects of Scientific Explanation and Other Essays in the Philosophy of Science contains its most authoritative statement.

On the deductive-nomological (DN) model, to explain something is to show that it follows logically from general laws together with particular facts. "Deductive" refers to the logical derivation; "nomological" comes from the Greek nomos, law. Hempel and Oppenheim set out conditions an explanation must meet:

1. The explanandum must be a logical consequence of the explanans.
2. The explanans must contain at least one general law, and the law must actually be needed for the derivation.
3. The explanans must have empirical content: it must be testable.
4. The sentences in the explanans must be true.

A simple example has this shape:

• Law: all gases expand when heated at constant pressure.
• Particular fact: this sample of gas was heated at constant pressure.
• Therefore: this sample of gas expanded.

Because explanations on this model are arguments, the DN model is often called the "covering-law" model: the event to be explained is "covered" by a law. Hempel summarized the underlying idea by saying that an explanation shows that the phenomenon "was to be expected" given the explanatory facts.

Explanation and prediction

One consequence of the DN model is a close link between explanation and prediction. If an explanation is a derivation from laws and initial conditions, then the same information, had it been available beforehand, would have allowed us to predict the event. Hempel held that explanation and prediction have the same logical structure and differ only in when the reasoning is done. This idea is often called the symmetry thesis. It made explanation respectable for the logical empiricist tradition to which Hempel belonged: an explanation was not a vague feeling of understanding but a precise logical relation that could be checked.

Statistical explanation

Many explanations do not involve exceptionless laws. Doctors explain recovery by treatment, though treatment does not always work. Hempel therefore added the inductive-statistical (IS) model. Here the explanandum is shown to be highly probable, rather than certain, given statistical laws and particular facts. A common illustration concerns a patient with a streptococcus infection who is given penicillin and recovers. If most such patients recover after penicillin, the treatment explains this patient's recovery. Hempel required that the explanans confer high probability on the explanandum: if the probability of recovery given penicillin were low, the information could not serve as an IS explanation even if the patient happened to recover.

A related form is often stated as: most heavy tobacco users develop lung disease; this person was a heavy tobacco user; therefore this person probably developed lung disease. (The example illustrates form, not medical statistics.)

Hempel also recognized a special difficulty for statistical explanations, called ambiguity: the same individual can belong to many reference classes with different probabilities. He proposed a requirement, which he called maximal specificity, to require that the explanation use the most specific relevant class known.

Why the DN model mattered

Even its critics acknowledge that the DN model was the starting point for virtually every later theory of explanation. It was precise, general, and tied to the actual practice of physics, where explanations often do take the form of derivations from equations. The model was widely criticized from the 1960s onward, and few philosophers now accept it as it stands. But its failures were instructive, and the counterexamples to it became a kind of shared test set that any new theory had to pass.

The classic counterexamples

Asymmetry: the flagpole and the barometer

A flagpole of a certain height stands in the sun, casting a shadow of a certain length. From the height of the pole, the angle of the sun, and the laws of optics (light travels in straight lines), we can derive the length of the shadow. That derivation seems to explain why the shadow is as long as it is.

But the derivation also runs in reverse. From the length of the shadow, the angle of the sun, and the same laws, we can derive the height of the pole. This second derivation satisfies all the DN conditions. Yet it seems absurd to say that the shadow explains why the flagpole is that tall. The pole's height is explained by how it was made, not by its shadow.

The philosopher Sylvain Bromberger, in work culminating in a 1966 paper titled "Why-Questions," pressed examples of this kind. A related case involves a pendulum, whose period can be derived from its length and whose length can be derived from its period by the same law, though only the first derivation seems explanatory. The lesson is that explanation has a direction that logical derivation lacks.

The barometer case makes a related point. A falling barometer reading is reliably followed by a storm. Together with a suitable generalization, the barometer reading lets us derive or predict the storm. But, as the Internet Encyclopedia of Philosophy puts it, "it is counterintuitive to say that the barometer explains the occurrence of the storm." Both the barometer reading and the storm are effects of a common cause, a drop in atmospheric pressure. Prediction and explanation come apart.

Irrelevance: birth control pills and hexed salt

Wesley Salmon offered an example in 1971. Suppose a man takes his wife's birth control pills regularly, and a law states that anyone who takes birth control pills regularly does not become pregnant. From this we can derive that the man did not become pregnant. The derivation is valid and the premises are true, yet the explanation is clearly defective: the pills are irrelevant, since men do not become pregnant anyway.

Henry Kyburg had raised a similar case in 1965 involving salt that has been "hexed" by a person wearing special clothing. Hexed salt dissolves in water. But the hexing is irrelevant: all salt dissolves in water. Salmon summed up the lesson in a memorable phrase: irrelevancies are harmless in arguments but fatal in explanations.

Low probability: paresis

Michael Scriven, in a 1959 paper in Science on explanation and prediction in evolutionary theory, pointed to a medical case. Paresis is a form of neurological disease that develops in some people with untreated latent syphilis. Only a minority of such people develop paresis, so having untreated syphilis does not make paresis probable. Yet the standard medical explanation of why a given patient has paresis is that they had untreated syphilis. If this is a good explanation, then Hempel's high-probability requirement for statistical explanation is wrong, and the symmetry thesis fails: syphilis explains paresis, though it could not have been used to predict it with confidence.

Explanation without laws: the inkwell

Scriven also argued that many perfectly good explanations cite no laws at all. If someone knocks over an inkwell with their knee, the explanation of the stain on the carpet is simply that the knee hit the desk and tipped the inkwell. No one formulates a general law about knees and inkwells. Defenders of Hempel replied that such explanations are incomplete "explanation sketches" that implicitly rely on laws, but critics found this unconvincing as an account of what makes them explanatory.

What the counterexamples teach

Statistical relevance and causal-mechanical models

Salmon's statistical-relevance model

Wesley C. Salmon proposed an alternative in 1971. On the statistical-relevance (SR) model, an explanation is not an argument at all. It is an assembly of information about which factors are statistically relevant to the outcome: factors that change its probability. Taking birth control pills does not change a man's probability of becoming pregnant, so it is not explanatory. Untreated syphilis raises the probability of paresis from essentially zero to something substantial, so it is explanatory, even though the probability remains below one half.

The SR model drops Hempel's high-probability requirement. Low-probability outcomes can be explained, as long as the relevant factors and probabilities are correctly identified. Formally, Salmon described explanations in terms of a "homogeneous partition" of the relevant population into cells within which no further factor makes a difference.

But statistical relevance alone does not settle direction. The barometer reading is statistically relevant to the storm. Different causal structures can produce the same pattern of correlations. Salmon himself came to see that something more was needed.

The causal-mechanical model

In his 1984 book Scientific Explanation and the Causal Structure of the World, Salmon developed a causal-mechanical (CM) model. On this view, to explain something is to show how it fits into the causal structure of the world, by tracing the causal processes and interactions that led up to it and the mechanisms that compose it.

Salmon distinguished causal processes, such as a moving baseball or a beam of light, from pseudo-processes, such as a moving shadow or a spot of light sweeping across a wall. His original test was mark transmission: a causal process can carry a modification ("mark") forward in time, while a pseudo-process cannot. Paint a baseball red and it stays red as it flies; but you cannot mark a shadow at one point and have the mark travel with it.

Critics noted problems. Christopher Hitchcock (1995) argued that the model cannot say why some features of a process are explanatorily relevant and others are not. A chalk mark on a billiard ball is transmitted, but it is the ball's momentum, not the chalk, that explains the collision's result. In response to such worries, and under the influence of Phil Dowe's "conserved quantity" theory, Salmon later revised his account (around 1994) so that a causal process is one that transmits a conserved quantity such as energy, momentum, or charge. He also conceded, in later work, that statistical relevance information is needed alongside the causal story.

The CM model handles the flagpole: the sun's light travels from the sun, past the pole, to the ground, so the causal process runs from pole to shadow, not the other way round. It handles the barometer: there is no causal process from barometer to storm.

Unificationist theories

The idea

A different tradition holds that explanation is fundamentally about unification: showing that many apparently separate phenomena are instances of a few basic patterns. Newton's theory of gravitation explained both the fall of objects on Earth and the orbits of the planets by one law. Maxwell's equations unified electricity, magnetism, and light. On the unificationist view, this is what explanation is: the reduction of the number of independent facts we have to accept as brute.

Friedman and Kitcher

Michael Friedman gave an early formal statement in "Explanation and Scientific Understanding," published in the Journal of Philosophy in 1974. He proposed that science increases understanding by reducing the total number of independent phenomena we must accept. Philip Kitcher found technical problems with Friedman's version (1976) and developed his own account, first in "Explanatory Unification" (1981) and most fully in a 1989 essay, "Explanatory Unification and the Causal Structure of the World."

Kitcher's version focuses on argument patterns. An explanation derives a phenomenon using a pattern of derivation that can be used again and again to derive many other phenomena. Patterns are evaluated by how many conclusions they yield, how few patterns are needed, and how "stringent" they are, meaning how tightly they constrain what can be plugged in. The set of patterns that best unifies everything we accept is what Kitcher calls the explanatory store.

Handling the counterexamples

Kitcher argued that unificationism explains explanatory asymmetry without appealing to causation. We have a powerful pattern that explains the dimensions of objects in terms of their origin and development: how they were built or how they grew. We could add a pattern that derives the heights of objects from their shadows, but this would apply only to objects that cast shadows and would leave everything else to be explained some other way. The "origin and development" pattern unifies more, so it is the explanatory one.

Critics have questioned whether this works. Eric Barnes (1992) argued that in Newtonian mechanics, retrodicting earlier states from later ones seems just as unified as predicting later states from earlier ones, so unification alone cannot recover the direction of explanation. Others argued that unification is a sign of good explanation rather than its essence, or that some explanations, such as of a single unique historical event, do not seem to unify anything.

Pragmatic theories

Explanations as answers to questions

Pragmatic theories hold that explanation cannot be understood apart from the context in which it is requested: who is asking, what they already know, and what they want. A simple version says that explanations are whatever people will accept as answers to certain kinds of questions. More developed versions are more careful.

The most influential is Bas van Fraassen's account in The Scientific Image (1980). Van Fraassen treats an explanation as an answer to a why-question, and he holds that why-questions are contrastive. To ask "Why did Adam eat the apple?" might mean "Why Adam, rather than Eve?" or "Why the apple, rather than the pear?" or "Why eat it, rather than throw it away?" Each contrast calls for a different answer.

Formally, van Fraassen analyzes a why-question as involving a topic (the fact to be explained), a contrast class (the alternatives it is being contrasted with), and a relevance relation (what counts as a relevant answer in this context). An answer says that the topic, rather than the other members of the contrast class, holds because of some fact that bears the relevance relation to the question. He summed up his view by describing explanation as "a three-term relation between theory, fact, and context."

Peter Achinstein's The Nature of Explanation (1983) is another classic pragmatic account. He treats explanation as an act in which one person attempts to produce understanding in another by answering a question in a certain way.

Contrast in everyday explanation

The contrastive point is often illustrated with the story of the American bank robber Willie Sutton, who, asked why he robbed banks, is reported to have replied that that's where the money is. The questioner wanted to know why he robbed at all; Sutton answered why banks rather than other targets. Alan Garfinkel used this kind of example in Forms of Explanation (1981) to argue that what counts as an explanation depends on the contrast space in the background.

Criticism

Kitcher and Salmon, in a 1987 paper, objected that van Fraassen's theory places no real constraints on the relevance relation. If anything can count as relevant in some context, then astrological "influences" could count as explanatory if the context said so. Defenders of pragmatic theories reply that the objective constraints come from science, while context determines which of the objectively correct answers is wanted. Many philosophers now accept that pragmatic factors affect which explanation is appropriate, while denying that pragmatics alone determines what is explanatory.

Recent accounts

Interventionism

The most widely discussed recent theory of causal explanation is James Woodward's interventionist account, developed in Making Things Happen (2003). On this view, C causes E if an intervention on C, a kind of idealized experimental manipulation, would change E or the probability of E. An explanation succeeds by answering what Woodward calls "what-if-things-had-been-different" questions: it shows how the explanandum would have changed if the explanatory factors had been different.

This handles the classic cases neatly. Manipulating the barometer needle would not change the weather, so the barometer does not explain the storm. Changing a man's pill-taking would not change whether he becomes pregnant, so the pills are irrelevant. Changing the flagpole's height changes its shadow, but changing the shadow (by shining another light, say) does not change the pole.

Woodward and Christopher Hitchcock also developed the idea of invariance. A generalization is invariant to the extent that it continues to hold under a range of interventions. Hooke's law, which relates the stretch of a spring to the force applied, holds only within a limited range before the spring deforms. The inverse-square law of gravitation holds over a far wider range. More invariant generalizations, on this view, support deeper explanations. The account does not require strict laws of nature, which makes it attractive for biology and the social sciences, where exceptionless laws are rare.

Mechanistic explanation

In the life sciences, explanation often consists in describing a mechanism: the parts of a system, what they do, and how they are organized to produce a phenomenon. A widely cited paper by Peter Machamer, Lindley Darden, and Carl Craver, "Thinking about Mechanisms" (Philosophy of Science, 2000), helped launch what is called the "new mechanist" program, alongside earlier work by William Bechtel and Robert Richardson (1993) and Stuart Glennan (1996). These accounts emphasize entities and their activities: binding, opening, pushing, inhibiting.

Craver used the Hodgkin-Huxley model of the nerve impulse, a set of equations that accurately describes how voltage changes across a nerve membrane, to argue that an accurate mathematical description is not by itself a full mechanistic explanation. In its original form it was, in his phrase, a "mechanism sketch": it predicted the behavior well but did not say what physical parts in the membrane produce it.

The kairetic account

Michael Strevens, in Depth (2008), offered a "two-factor" theory. The first factor is causal influence of the sort described by fundamental physics. The second is a procedure for removing details that make no difference to the outcome. A good explanation, on this "kairetic" account, cites only the difference-makers, abstracted to the right level of generality. This aims to explain why high-level explanations, such as an explanation of a population's growth that ignores the details of individual organisms, can be better than descriptions packed with microscopic detail.

A summary of the main theories

Non-causal explanation

A lively recent debate concerns whether all explanations are causal. Several examples suggest not.

• The bridges of Königsberg. In 1736 the mathematician Leonhard Euler showed that it is impossible to walk through the city of Königsberg crossing each of its seven bridges exactly once. The explanation is not causal: it lies in the mathematical structure of the network of land masses and bridges. Every attempt fails for the same reason, which has to do with how many bridges meet at each land mass.
• Periodical cicadas. Some species of cicadas in North America emerge in cycles of 13 or 17 years, both prime numbers. Alan Baker (2005) discussed a proposed explanation in which prime cycle lengths minimize overlap with predators or other species with shorter cycles, and argued that the mathematics plays a genuinely explanatory role.
• Honeycomb. Baker and others also discussed the hexagonal shape of honeycomb cells, explained in part by the mathematical fact that a hexagonal grid divides a plane into equal areas with the least total perimeter.
• Dividing strawberries. Marc Lange (2013) offered a simple case: a mother cannot divide 23 strawberries evenly among her 3 children without cutting any, and the explanation is just that 23 is not divisible by 3. No causal story adds anything.

Woodward (2018) distinguished two kinds of apparently non-causal explanation: those where the explanatory factors cannot be targets of intervention (such as the number of dimensions of space), and those where the dependence is mathematical rather than contingent. Strevens has argued that many apparently mathematical explanations are causal after all, because the mathematics represents causal constraints. Lange has argued that some impossibility explanations resist this treatment. Debates also continue about whether certain explanations in physics, such as those using the mathematical technique called renormalization, are non-causal.

Inference to the best explanation

Explanation does not only answer "why?"; it also guides belief. In 1965 the philosopher Gilbert Harman gave the name "inference to the best explanation" to a familiar pattern of reasoning: we infer that a hypothesis is true because it would provide the best explanation of the evidence. A detective concludes that the butler did it because that hypothesis best explains the clues. A doctor infers a diagnosis that best explains the symptoms. Scientists accept theories that best explain the data. Peter Lipton's Inference to the Best Explanation (1991) is a standard book-length treatment.

This pattern raises questions. What makes one explanation "best": simplicity, scope, fit with other knowledge, or something else? Why should the best explanation be the true one? Van Fraassen argued that the method can only deliver the best explanation among those considered so far, which may be "the best of a bad lot," and so is not an objective guide to truth. Defenders reply that inference to the best explanation is woven so deeply into everyday and scientific reasoning that rejecting it would undermine much of what we take ourselves to know. It also plays a central role in arguments for scientific realism, the view that the success of scientific theories is best explained by their being approximately true.

Explanation and understanding

Many philosophers hold that the point of explanation is to produce understanding. But understanding is a slippery notion. Hempel was wary of it, because the feeling of understanding is psychological and can be present when an explanation is wrong, or absent when it is right. His aim was to give an objective account of explanation that did not depend on how anyone felt.

Salmon, by contrast, argued that scientific understanding is more than the ability to predict. He used the image of a Laplacean demon, an imaginary intellect that knows all the laws and the current state of the universe and so can predict everything. Such a being could predict perfectly without understanding the causal structure that produces what it predicts. Understanding, for Salmon, required knowing the mechanisms.

Wesley Salmon also distinguished three broad conceptions of explanation that run through the literature: an epistemic conception, on which explaining is a matter of making the explanandum expected or fitting it into a body of knowledge (Hempel and the unificationists); a modal conception, on which explaining is showing that the explanandum had to happen; and an ontic conception, on which explaining is locating the explanandum in the causal structure of the world (his own later view). Recent work on understanding, in epistemology and philosophy of science, asks whether understanding is a kind of knowledge, whether it can be had from false but useful models, and how it relates to the ability to reason about a system.

The psychology of explanation

Psychologists study how people actually explain things and evaluate explanations. One well-known finding is the "illusion of explanatory depth," documented by Leonid Rozenblit and Frank Keil in a 2002 paper in Cognitive Science. People asked to rate how well they understand how everyday devices work, such as zippers, toilets, or cylinder locks, gave fairly high ratings. When asked to write out a detailed step-by-step explanation, they discovered how little they knew, and their ratings dropped. The illusion appears to be stronger for explanatory knowledge of mechanisms than for some other kinds of knowledge, such as facts or procedures.

Research on children's "why" questions and on how adults choose among explanations suggests that people have preferences for explanations that are simple, broad in scope, and that cite causes or functions. These preferences are often useful but can mislead, for example when people favor purpose-based explanations of natural phenomena that have no purpose.

Explanation in artificial intelligence

The rise of machine learning has created a practical demand for explanation. Systems that recommend medical treatments, approve loans, or flag fraud often work by learning statistical patterns in data, and their internal workings can be hard even for experts to interpret. The field of "explainable AI" develops methods for describing why a system produced a given output: for example, by identifying which inputs most affected a decision, or by showing what change to the input would have produced a different output.

The philosophical theories above are directly relevant. Explanations that show how the output would change if an input were different are a form of the counterfactual, "what-if-things-had-been-different" explanation that Woodward described. The pragmatic insight that explanations answer contrastive questions also applies: a loan applicant usually wants to know why they were rejected rather than accepted, not a full account of everything the system computed. And the distinction between explanation and justification matters: an account of what a system did is not the same as a justification of whether it should have done it.

Common misconceptions

"An explanation is just a description"

A description says what happened; an explanation says why. A detailed account of every move in a chess game describes it; an account of why one player's strategy failed explains it. Many explanations contain descriptions, but not every description explains.

"If you can predict it, you can explain it"

The barometer case shows that reliable prediction need not be explanatory. Conversely, the paresis case suggests that explanations need not support confident prediction. Hempel's symmetry thesis is now widely rejected in its strong form.

"Correlation is explanation"

Statistical association can suggest explanatory relations, but it can also arise from common causes, coincidence, or the way data were selected. This is why theories that rely only on statistical relevance have trouble with direction, and why interventionist accounts emphasize what would happen under manipulation.

"There is one correct theory of explanation for every case"

Many philosophers now doubt that a single model fits all sciences. Explanations in physics, biology, psychology, history, and mathematics may differ in their aims and in what they can draw on, for example in whether strict laws are available. Some see the different theories as capturing different, complementary aspects of explanation.

"Purpose-based explanations are always unscientific"

Modern science rejects the idea that rocks fall because they aim to reach the ground. But functional explanations are central in biology (the heart pumps blood; that is what it is for), and they can be interpreted in terms of evolutionary history or the role a part plays in a system. Teleological language is not automatically a mistake.

A worked hypothetical

The following example is hypothetical and is intended to show how different theories would treat one case.

A small town's river floods one spring. Residents ask why.

• A DN-style explanation would cite the amount of rain and snowmelt, the capacity of the river channel, and the principle that water exceeding channel capacity overflows the banks, then derive the flood.
• A statistical-relevance explanation would identify which factors raised the probability of flooding that year, such as unusually heavy rainfall and an early thaw, compared with years without floods.
• A causal-mechanical explanation would trace the physical process: rain and meltwater flowing into tributaries, the rising water level, the point where it overtopped a particular bank.
• A unificationist explanation would show how the flood fits general hydrological patterns that also explain floods elsewhere.
• A pragmatic account would note that a farmer, an engineer, and an insurance adjuster might each be asking a different contrastive question: why this year rather than last year, why this bank rather than the opposite bank, why the levee failed rather than held.
• An interventionist explanation would say what would have changed the outcome: had the levee been half a meter higher, or had the upstream reservoir released water earlier, the town would not have flooded.

Each captures something real. Which one counts as "the" explanation depends on what the questioner needs.

Frequently asked questions

What is the difference between explanation and description?

Description answers "what?"; explanation answers "why?" or "how?" An explanation connects the fact to be explained with something else, such as causes, laws, mechanisms, or patterns, that makes it understandable.

Why was Hempel's model so influential if it has so many problems?

It was the first precise, general theory of scientific explanation, it fit much of physics well, and it set the terms of debate. Its counterexamples were so clear and so widely discussed that they became the standard benchmarks for every later theory.

Are all good explanations causal?

Many philosophers think that most scientific explanations are causal, and causal theories handle the classic counterexamples well. But examples from mathematics and some areas of physics, such as Euler's bridges, have led others to argue that some explanations are non-causal. This remains an open debate.

What does "contrastive" explanation mean?

It means that a request for explanation usually has an implicit "rather than." Asking why something happened is often asking why it happened rather than some specific alternative. The same event can have different explanations depending on the contrast in view.

Can a false theory explain anything?

On Hempel's model, no, because the explanans must be true. In practice, scientists often use idealized models that are strictly false, such as frictionless planes or perfectly rational agents, to explain real phenomena. How such models can explain is an active topic of research.

How does explanation relate to understanding?

Most philosophers think explanations aim at understanding, but they disagree about whether understanding can be defined independently of explanation, whether the feeling of understanding is a reliable guide, and whether understanding is a form of knowledge.

Is inference to the best explanation a valid form of reasoning?

It is not deductively valid: the best available explanation can be false. It is widely regarded as a reasonable and indispensable form of non-deductive reasoning, though philosophers disagree about how to justify it and how to judge which explanation is best.

Summary

Explanation is the business of making things understandable. Aristotle distinguished four kinds of answer to "why?" In the twentieth century, Hempel's deductive-nomological model tried to reduce explanation to logical derivation from laws, and its failures, captured in the flagpole, barometer, birth control, and paresis examples, showed that explanation involves direction, relevance, and something more than prediction. Salmon's causal-mechanical model, Friedman's and Kitcher's unificationism, and van Fraassen's pragmatic theory each captured part of the picture. More recent accounts by Woodward, the new mechanists, and Strevens focus on manipulation, mechanisms, and difference-making, while debates about mathematical and other non-causal explanations test the limits of causal approaches. Few philosophers now expect a single formula. But the effort to find one has produced one of the richest literatures in the philosophy of science and has practical relevance for fields from medicine to artificial intelligence.

Sources

• Explanation, Wikipedia
• 20th Century Theories of Scientific Explanation, Stanford Encyclopedia of Philosophy
• Causal Approaches to Scientific Explanation, Stanford Encyclopedia of Philosophy
• Theories of Explanation, Internet Encyclopedia of Philosophy
• Deductive-nomological model, Wikipedia
• Four causes, Wikipedia
• Rozenblit and Keil, "The misunderstood limits of folk science: an illusion of explanatory depth," Cognitive Science (2002)
• Inference to the best explanation, Wikipedia