The Inferential View of Scientific Explanation

At the onset: Explanandum and Explanans (Explicandum and Explicans)

That which needs to be explained (explanandum) and that which contains the explanation (explanans)—either as a cause, antecedent event, or necessary condition.

What distinguishes philosophy of science from other studies of science is that it

1. Takes a critical, evaluative approach recommending (or criticizing) certain methods of analyzing data, drawing inferences, and offering explanations. (not merely descriptive)

2. There is also an emphasis on conceptual analysis

--e.g., explaining what a scientific explanation is (should be), or, in other words, what it means when we say that one thing "explains" another.

Philosophers often discuss the meaning of many terms whose meaning other people take for granted. This is the project of conceptual analysis. Philosophers examine closely concepts crucial to the practice of some discipline, etc. and the philosophical issues arising from these concepts. (e.g. Philosophy of Art, Philosophy of Religion, Philosophy of Science, - Philosophy of Plumbing?)

The Difference Between Explanation And Description

It is commonly agreed that science aims at not only describing regularities in the things that we observe around us, but also at explaining those phenomena. But these are distinct projects. The regularities between phases of the moon and the level of tides was noted (described) long before scientific explanations were offered for this observed regularity.

Example 1: The Redshift Phenomenon

We observe a regularity: the redshift in the spectra of stars and distant galaxies.

Science seeks to explain why we see this.

The physical principles offered to explain this (analogous to the Doppler effect in sound), is a law which holds that observed wavelengths are increased if the object is moving away from the observer and shortened if the object is moving towards the observer.

(Also, there is a derivation in general relativity theory of the redshift phenomenon, due to gravitation.)

Willem de Sitter (1872 – 1934) was a Dutch mathematician, physicist and astronomer.

In 1917, de Sitter predicted that there would be a relationship between distance and redshift.

in 1927, Georges Lemaître, a Belgian Catholic priest and physicist, published a paper in an obscure Belgian journal, Annales de la Société Scientifique de Bruxelles. In that paper, he showed that the data collected by Edwin Hubble and two other astronomers up to that time was enough to derive a linear velocity-distance relation between the galaxies, and that this supported a model of an expanding universe based on Einstein's equations for General Relativity.

This discovery was the first observational support for the Big Bang theory which had been proposed by Lemaître in 1927. The observed velocities of distant galaxies, taken together with the cosmological principle, appeared to show that the universe was expanding in a manner consistent with the Friedmann-Lemaître model of general relativity.

In 1931 Hubble wrote a letter to the Dutch cosmologist Willem de Sitter expressing his opinion on the theoretical interpretation of the redshift-distance relation:

Mr. Humason and I are both deeply sensible of your gracious appreciation of the papers on velocities and distances of nebulae. We use the term 'apparent' velocities to emphasize the empirical features of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.

Example 2: Mars “backing up” in the night sky

Retrograde refers to the observed periodic reversal in paths of the outer planets in the night sky. We observed that there are such reversals in the apparent paths the planets. And we could even predict these mathematically based on formulae derived from those observations. But observation and prediction is not the same thing as explaining. What is needed for that is a theory of the solar system which details how the planets' real motions produce the apparent motions that we observe. As a matter of fact, that did not come until long after the observations and the predictions.

It was well known at least since the days of Ptolemy (100-178) that motion of the planets could be equally well accounted for by various mathematical models. The question then becomes whether to view a mathematical description as revealing the underlying nature of the phenomenon or as merely providing a convenient description of the observable phenomena (saving the appearances). If these are merely models, they describe and predict, but they explain nothing.

Example 3: Hempel’s Thermometer

We observe that when we put a thermometer into a hot liquid the level drops initially and then rises.

But why?

“A mercury thermometer is rapidly immersed in hot water; there occurs a temporary drop of the mercury column, which is then followed by a swift rise. How is this phenomenon to be explained? The increase in temperature affects at first only the glass tube of the thermometer; it expands and thus provides a larger space for the mercury inside, whose surface therefore drops. As soon as by heat conduction the rise in temperature reaches the mercury, however, the latter expands, and as its coefficient of expansion is considerably larger than that of glass, a rise of the mercury level results.”[1]

Hempel goes on to suggest the requirements of an adequate explanation in science:

This account consists of statements of two kinds. Those of the first kind indicate certain conditions which are realized prior to, or at the same time as, the phenomenon to be explained; we shall refer to them briefly as antecedent conditions. In our illustration, the antecedent conditions include, among others, the fact that the thermometer consists of a glass tube which is partly filled with mercury, and that it is immersed into hot water. The statements of the second kind express certain general laws; in our case, these include the law of the thermic expansion of mercury and of glass, and a statement about the small thermic conductivity of glass. The two sets of statements, if adequately and completely formulated explain the phenomenon under consideration: they entail the consequence that the mercury will first drop, then rise. Thus, the event under discussion is explained by subsuming it under general laws, i.e., by showing that it occurred in accordance with those laws, in virtue of the realization of certain specified antecedent conditions.

Three Approaches To Explanation

A philosopher of science asks:

1. What is the difference between describing a phenomenon and explaining it?

2. What makes something an adequate explanation?

3. What form(s) do explanations come in?

Initially we will look at three basic accounts:

1. Inferential View (Hempel, Oppenheim) –

An explanation is a type of argument included in the premises sentences describing antecedent conditions and sentences expressing laws of nature.

Within this type there are three varieties, differing from one another with respect to the degree of confidence we can have in the conclusion of the argument given the truth of the premises. (i.e. The "Deductive-Nomological" model of explanation (D-N), The "Deductive-Statistical" model (D-S) and The "Inductive-Statistical" model (I-S)

2. Causal View (Salmon, Lewis) –

An explanation is a description of the various causes of the phenomenon: to explain is to give information about the causal history that led to the phenomenon.

3. Pragmatic View (van Fraassen) –

An explanation is a body of information that implies that the phenomenon is more likely than its alternatives, where the information is of the sort deemed "relevant" in that context, and the class of alternatives to the phenomenon are also fixed by the context. Van Frassen’s view is very similar to the inferential view in some respects, but his unique contribution is that he points out and explains why the same “why” question can have multiple, distinct, correct answers.

E.g. Why did Adam eat the apple? As opposed to…?

The Inferential Theory of Explanation

Let’s start with Hempel's inferential view.

The "Deductive-Nomological" model of explanation. (D-N)

But also the two probabilistic “siblings”

The "deductive-statistical" model (D-S)

The "inductive-statistical" model (I-S)

All three views of scientific explanation are inferential. That is, all believe the observed event can be inferred from an existing law and known field conditions. This is the "received" or standard view of explanation, still widely held and was generally agreed to by most philosophers or science and scientists until the early 1960s. It, perhaps, reflects that fact that early work in Philosophy of Science was done with “Physics” in mind. Physics was paradigmatic science and thus explanations from physics were the sort of explanations these theories of explanation were modeled on.

· The Hempel-Oppenheim paper appeared in 1948[2]

· They view explanation as a certain sort of argument: (premise sentences which collectively imply a conclusion sentence).

· The arguments they considered were deductively valid arguments: if the premises are true the conclusion has to be true.

(Something of a holdover from Aristotle)

P: All human beings are mortal.

P: Socrates is a human being.

Therefore:

CS: Socrates is mortal.

However, even if being a deductively valid argument is necessary to being an explanation, it is clearly not sufficient. Not every argument that is deductive is an explanation. More needs to be said. What further conditions need to be added to narrow this account sufficiently?

To this end, Hempel and Oppenheim offer their:

"General Conditions of Adequacy"

These are meant to specify when a deductive argument counts as an adequate explanation.

An explanation must:

(a) be a valid deductive argument (hence "deductive")

(b) contain essentially at least one general law of nature as a premise (hence "nomological")

(c) have empirical content

(i.e., it must be empirically falsifiable/ logically possible for an observation-statement to contradict it)

These conditions are formal, structural, semantic features. The presence of these features can all be determined simply by looking at the language before us. But to complete the conditions of adequacy, Hempel and Oppenheim add a fourth, "empirical" condition.

(d) The premises (statements in the explanans) must all be true.

This further condition cannot be known by simply examining the sentences themselves. One must actually investigate the world to know whether the sentences are true or not.

Thus, on the inferential view, explanations all have the following structure (where the antecedent conditions and laws of nature make up the "explanans").

C1, C2, ... , Cn (antecedent conditions)

L1, ... , Ln (law(s) of nature]

Therefore,

E [explanandum]

We can look at the statistical variants of this pattern later.

(An Aside) Laws of Nature

Central to their account is the notion of a “Law of Nature.” They take a law of nature to be a true "law-like" sentence.

(It seems that they are not saying that a Law of Nature is expressed in/by a sentence; it is the sentence. Perhaps this is not crucial here.)

This means that a law is a linguistic entity and they suggest that it is distinguished by its peculiar, linguistic features. So we have a big basket of sentences, only some of which are laws of nature. They attempt to specify the criteria by which we can pick out all and only the laws of nature.

According to Hempel and Oppenheim, laws are to be distinguished from other non-law sentences in a language in that law sentences are

1. universal

2. have unlimited scope

3. contain no designation of particular objects

4. contain only "purely qualitative" predicates.

EX: "All gases that are heated under constant pressure expand in volume."

In short, Laws express true universal claims. But even so, how are we to distinguish a “laws of nature” sentence from other true sentences expressing accidental universal generalizations (i.e., general universal truths that happen to be true, though they are not true as a matter of physical law). Where laws are held to necessitate their explanandum, in cases of accidental generalizations, there is no “necessity” to them. For example, suppose that all the apples that ever get into my refrigerator are yellow. Then the following is a true generalization:

“All the apples in my refrigerator are yellow."

This sentence seems to be true, universal, unlimited in scope, and containing only purely qualitative predicates. But we hardly want to say it is a “Law of Nature” that only yellow apples get into my fridge. One might object that the statement does not meet one of their criteria: #3 contain no designation of particular objects. Laws of nature are supposed to refer to universal classes of objects (or phenomena).

Consider the sentence which is a Law of Nature:

"All gases that are heated under constant pressure expand in volume."

This is the very reason that Hempel and Oppenheim include the requirement that to be a law of nature a sentence must NOT designate any particular objects.

But we can easily get around that with a bit of creative linguistic trickery.

“All the apples in any and all refrigerators owned by Kenton Harris are yellow."

Or, alternatively, use some physical description in terms of "purely qualitative" predicates that constitute a definite description for my refrigerator from the class of all refrigerators in the universe (a definite description which would reference the -entire- unit class of my refrigerator such as its serial number). Such a description would pick out all the members of a (unit) class and thus be universal and not explicitly naming a particular object. Would the existence of such a sentence convince you that you have discovered a new law of nature?

(No.)

Moreover, consider the following two true sentences.

G: No gold sphere has a mass greater than 100,000 kilograms.

U: No enriched uranium sphere has a mass greater than 100,000 kilograms.

Since the critical mass of enriched uranium is just a few kilograms, U is rightly considered lawful while G is not. Granted that U may be a relatively “low-level” variety of law, given its particularity and that it follows from more general, and therefore more properly considered, laws. Nevertheless, there is a necessity to U, whereas G expresses a contingently true generalization.

This returns us to the question of what, precisely, is a law of nature. Our modern understanding of the term “law of nature” is an issue philosophers continue to argue at length. For example, philosopher John W. Carroll[3] compares similar statements.

“All gold spheres are less than a mile in diameter.”

And

“All uranium-235 spheres are less than a mile in diameter.”

Our observations of the world tell us that there are no gold spheres larger than a mile wide, and we can be pretty confident there never will be. Still, we have no reason to believe that there couldn’t be one, and so the statement is not considered a law. On the other hand, the statement “All uranium-235 spheres are less than a mile in diameter.” could be thought of as a law of nature because, according to what we know about nuclear physics, once a sphere of uranium-235 grew to a diameter greater than about 6 inches (because critical mass for uranium-235 is about 15 kilograms), it would demolish itself in a nuclear explosion. (Boom!)

Hence we can be sure that such spheres do not exist. The distinction matters because it illustrates two important features about our concept of a “Law of Nature.” First, contra Hempel-Oppenheim, not all true generalizations we observe can be thought of as laws of nature, but second, most laws of nature are thought to exist as part of a larger, interconnected system of laws.

Laws of Nature and Counterfactuals

A counterfactual claim is a subjunctive, condition-counter-to-(actual)-fact. Nevertheless, we think some counterfactuals are true and others false.

1. If I had not been offered a job at FIU in 2003, I would have pursued a career in private industry.

2. If Hitler had won WWII, Israel would not have been founded in 1948.

3. If you had just been a few inches taller, you would have a 4.0 GPA.

4. If the sun were made of pudding, I would be a famous soccer player.

All of these four claims are counterfactuals; their antecedents express conditions counter to fact. But while #1 is true, and #2 is likely true, #3 is likely false and #4 is nonsense, or quite near it. Counterfactuals are tricky; what precisely are the truth conditions of a counterfactual or how might we otherwise know them to me true?[4]

One reason that the true universal statements about apples in my refrigerator and gold might not be laws of nature, a reason NOT captured by the Hempel-Oppenheim analysis of laws, is that they do not support inferences to counterfactual statements. On the basis of the true universal alone, we do not suppose counterfactuals. For instance from the (apparently) true universal “All planets that support intelligent life have one and only one moon.” We do not suppose that, if the Earth had had two moons, it would not have supported intelligent life. Nor from my “apple” universal do we suppose that, if a red apple were to be placed into my refrigerator, it would turn yellow. And again, we do not suppose that if we were to collect 100,000 kilograms of gold into a sphere, it would explode.

Genuine laws of nature, by contrast, are supposed to support legitimate counterfactual inferences. From the law “All gases that are heated under constant pressure expand.” we can infer that if a sample of gas in a particular container were heated under constant pressure, it would expand. This seems true even if we never actually heat that sample of gas under constant pressure. Similarly, we can infer that if were to successfully gather 100,000 kilograms of uranium and try to fashion it into a sphere, we would fail.

(Boom!)

The difference between statements G and U does not seem to be something that can be captured purely linguistically. Thus, Hempel and Oppenheim's view that laws of nature are sentences of a certain sort must be fundamentally mistaken.

What laws of nature are is still a matter of dispute. But, as we are primarily concerned with scientific explanation here, let’s assume some satisfactory account can be given of “Law of Nature” to alleviate this issue and look at some more specific problems with the inferential account of explanation.

Counterexamples To The Inferential View Of Scientific Explanation: Asymmetry and Irrelevance

The Hempel-Oppenheim analysis of scientific explanation has the following four key features.

(a) Inferential - Explanations are arguments: to explain why E occurred is to provide information that would have been sufficient to predict beforehand that E would occur.

(b) Covering Law - Explanations explain by showing that E could have been predicted from the laws of nature, along with a complete specification of the initial conditions.

(c) Explanation-Prediction Symmetry - The information (i.e., laws, antecedent conditions) appearing in an adequate explanation of E could have been used to predict E; conversely, any information that can be used to predict E can be used after the fact to explain why E occurred. Thus there is a perfect symmetry between predicting X and explaining X. A prediction of X is just as appropriately regarded as an explanation of X and vise versa.

(d) No Essential Role for Causality - Laws of nature do not have to describe causal processes. Thus “causes” seem to play no role in these scientific explanations.

Counterexamples target one or more of these features.

First Problem: Asymmetry: Hempel-Oppenheim assert that explanation and prediction are symmetric, whereas that does not seem to be the case, as the following examples show.

(1) Eclipse - You can predict when and where a solar eclipse will occur using the laws governing the orbit of the Earth around the Sun, and the orbit of the Moon around the Earth, as well as the initial configuration these three bodies were in at an earlier time. Given that the Sun, Moon and Earth are in certain position relative to each other now (field conditions) and given certain known laws governing their motions (laws of nature) the eclipse will occur at time T.

But you can also make the same prediction by extrapolating backwards in time from the subsequent positions of these three bodies.

Given that the Sun, Moon and Earth are in certain position relative to each other now (field conditions) and given certain known laws governing their motions (laws of nature) the eclipse did occur at time T.

In other words, we can retrodict (infer) that the eclipse had occurred by running a simulation backward. However, only the first which references law and conditions prior to the eclipse would count as an explanation of why the eclipse occurs when and where it did. But that the sun and moon are in the positions they are in now taken together with certain laws of motion does NOT explain why an eclipse did occur. Thus, inference and explanation are NOT symmetric here.

(2) Flagpole - Using the laws of trigonometry and the law that light travels in straight lines, you can predict the length of the shadow that a flagpole of a certain height will cast when the Sun is at a certain elevation. The known height of the flagpole and the law-governed behavior of light thus explain the what the shadow is the length that it is.

But note, one can also determine what the height of the flagpole is by measuring the length of its shadow and the elevation of the Sun. Nevertheless, the length of the shadow does not explain the height of the flagpole. Only the first of these two derivations/inferences would count as an explanation.

(3) Barometer - Using the laws governing weather patterns, storm formation, and the effect of air pressure on the behavior of barometers, you can predict that when a barometer falls that a storm will soon follow.

You can also predict that when a storm is approaching, the barometer will fall.

However, in this case, neither of these inferences are explanatory, since both are explained by antecedent atmospheric conditions.

In each of the cases the inferential relations between the sets of facts is symmetric, but the explanatory relationship is not. This suggests that the nature of explanation is not (fully) captured by the current inferential account.

Second Problem: Irrelevance: the Hempel-Oppenheim analysis would in some cases endorse information as explanatory when it is irrelevant to the explanandum.

(1) Birth Control Pills - All men who take birth control pills never get pregnant. Thus, from the fact that John is taking birth control pills we can infer logically that he won't get pregnant.

All men who take birth control pills fail to get pregnant.

John is a man who takes birth control pills

Therefore

John will fail to get pregnant.

By their criteria, the true universal together with the field conditions explains why John does not get pregnant. However, this would hardly be an explanation of John's failing to get pregnant since he couldn't have gotten pregnant whether or not he took birth control pills.

(2) Hexed Salt - All salt that has had a hex placed on it by a witch will dissolve in unsaturated water. Hence, we can logically infer from the fact that a sample of salt that had a hex placed on it by a witch that it will dissolve in water.

However, this wouldn't give us an explanation of why the salt dissolved in the unsaturated water since the salt would have dissolved even if it hadn't been hexed.

Note in both these cases the failure to support counterfactual reasoning.

The Causal Theory of Explanation

A third set of problems arise from the contention that to explain a phenomenon is merely to provide information sufficient to predict that it will occur. Some explanations for events do not in fact provide us with the ability to have predicted the event would have occurred. This is more easily seen in the inductive-statistical model of explanation.

The I-S differs from D-N explanation only in that the laws that are cited in the explanation can be statistical.

Example, it is a law of nature that 90% of electrons in a 90-10 superposition of spin-up and spin-down will go up if passed through a vertically oriented Stern-Gerlach magnet. (Or so I have been told. 😊)

With this information we can construct a statistical syllogism similar to the D-N inferences.

P1. Ninety percent of electrons in a 90-10 superposition of spin-up and spin-down will go up if passed through a vertically oriented Stern-Gerlach magnet. (Law of Nature)

P2. This electron is in a 90-10 superposition of spin-up and spin-down and is passed through a vertically oriented Stern-Gerlach magnet. (Statement of Initial Conditions)

Therefore

CS: This electron goes up. (Explanandum) [90% chance]

This argument pattern is obviously similar to that exhibited by D-N explanation, the only difference being that the law in the inductive argument stated above is statistical rather than a universal generalization. On the inferential view, this argument constitutes an explanation since the initial conditions and laws confer a high probability (though not a 100% probability) on the explanandum. (i.e. If you knew that these laws and initial conditions held of a particular electron, you could predict with high confidence that the electron would go up.)

First, this seems odd. How does the fact that an event frequently occurs explain the fact that the event frequently occurs? It strikes me as a case of an unsatisfying “dispositional” explanation. This is something like saying that my boastfulness explains my pompous and boorish behavior. “And what does it mean to say I am boastful?” you ask. Well I mean that I am such as to frequently behave pompously and boorishly. Similarly, I might “explain” that the window shattered when struck with a hammer because it is fragile. And what does it mean to say a think is fragile? It means it is such as to shatter when it is hit with a hammer. Thus one is saying that the reason the window shattered when struck with a hammer is because the window is such as to shatter when struck with a hammer. I think non-statistical laws may suffer from that same problem. Why do unsupported objects close to the surface of the Earth fall at a rate of 32 feet per second/ per second? Oh, because they always do that!

Second, you can't always use explanatory information as the basis for a prediction. That is because we frequently offer explanations of events with low probability. For instance two heterogeneous brown-eyed individuals having a brown-eyed child is highly probable. Two heterogeneous brown-eyed individuals having a blue-eyed child is improbable. Yet the corresponding probability of both events seem to be explained by exactly the same processes and “laws.”

(Numbers in the examples below are for purposes of illustration only.)

Atomic Blasts & Leukemia.

We might explain why a person contracted leukemia by pointing out the person was once only two miles away from an atomic blast, and that exposure to an atomic blast from that distance increases one's chances of contracting leukemia in later life, this despite the fact that only 1 in 1,000 persons exposed to an atomic blast eventually contract leukemia. Nevertheless, exposure to an atomic blast explains the leukemia since people who haven't been exposed to an atomic blast have a much lower probability (say, 1 in 10,000) of contracting leukemia. But notice that, while once being only two miles away from an atomic blast can be said to explain the fact that an individual contracted leukemia, it does not make it so probable that an individual will contract leukemia that you would predict this result (e.g. greater that 50%).

Smoking & Lung Cancer.

We can explain why someone contracted lung cancer by pointing out that the person had smoked two packs of cigarettes a day for forty years. Actually this is offered and accepted as a pretty good explanation of why this person got lung cancer. This is an explanation since people who smoke that much have a much higher probability (say, 1 in 100) of contracting lung cancer than non-smokers (say, 1 in 10,000). Still, the vast majority of smokers (99 percent) will never contract lung cancer. Thus, it would be false to say this makes it probable that the person will get lung cancer.

The point here is that, In each of these cases, you can't predict that the result will occur since the information does not confer a high probability on the result. Nevertheless, the information offered constitutes an explanation of that result, since it increases the probability that that result will occur.

Wesley Salmon’s Statistical Explanation (which he later rejects)

In the 1960s and 1970s, Wesley Salmon developed a view of statistical explanation that postulated that, contrary to what Hempel claimed earlier, high probability was NOT necessary for an explanation, but only positive statistical relevance.

Definition. A hypothesis h is positively relevant (correlated) to e if h makes e more likely, i.e., pr(h|e) > pr(~h|e).

The problem Salmon faced was distinguishing cases where the information could provide a substantive explanation from cases where the information reported a mere correlation and so could not. This often occurs when what explains one of the correlates also explains the other (common cause). They are positively correlated because they have a common explanation. For example, having nicotine stains on one's fingers is positively correlated with contracting lung cancer, but you could not explain why a person contracted lung cancer by pointing out that the person had nicotine stains on their fingers.

Distinguishing these cases proved to be impossible using purely formal (statistical) relations. Obviously, some other type of information was needed to make the distinction. Ultimately, Salmon rejected the received view of explanation. Eventually Salmon came to believe that to explain a phenomenon is NOT to offer information sufficient for a person to predict that the phenomenon will occur, but to give information about the causes of that phenomenon. On this view, an explanation is NOT a type of argument containing laws of nature as premises but an assembly of statistically relevant information about an event's causal history.

Two Reasons in Support of Causal Explanations

1. The Explanans must precede the explanadum

The initial conditions given in the explanatory information have to precede the explanandum temporally to constitute an explanation of the explanandum. Hempel's theory has no restriction of this sort.

The eclipse example illustrates this fact: you can just as well use information about the subsequent positions of the Sun and Moon to derive that an eclipse occurred at an earlier time as use information about the current positions of the Sun and Moon to derive that an eclipse will occur later.

The former is a case of retrodiction, whereas the latter is a (familiar) case of prediction. This is an example of the prediction-explanation symmetry postulated by Hempel. However, as we saw earlier when discussing the problem of asymmetry, only the forward-looking derivation counts as an explanation.

Interestingly, Salmon points out that the temporal direction of explanation matches the temporal direction of causation, which is forward-looking (i.e., causes must precede their effects in time).

2. Not all derivations from laws count as explanations.

Salmon argues that some D-N "explanations" (e.g., a derivation from the ideal gas law and a description of initial conditions) are not explanations at all. The ideal gas law simply describes a set of constraints on how various parameters (pressure, volume, and temperature) are related; it does not explain why these parameters are related in that way.

Why these constraints exist (in the sense of the sufficient reason) is a substantive question that is answered by the kinetic theory of gases.

Another example: People knew for centuries how the phases of the Moon were related to the height of tides, but simply describing how these two things are related did not constitute an explanation. An explanation was not provided until Newton developed his theory of gravitation.

Salmon argues that the difference between explanatory and non-explanatory laws is that the former describe causal processes, whereas non-explanatory laws (such as the ideal gas law) only describe empirical regularities.

Salmon’s Causal Account of Explanation

An explanation is a body of information about the causes of a particular event.

Salmon's theory of causal explanation has three elements.

(1) Statistical Relevance - the explanans (C) increases the probability of the explanandum (E), i.e., pr(E|C) > pr(E).

(2) Causal Processes - the explanans and the explanandum are both parts of different causal processes

(3) Causal Interaction - these causal processes interact in such a way as to bring about the event (E) in question

Ah, but then, what precisely is a “causal process?”

Salmon's view is that causal processes are characterized by two features.

1. A causal process is a sequence of events in a continuous region of spacetime.

2. A causal process can transmit information (a "mark")

I will not elaborate here.

Now we turn to Explanation

Common Cause

According to Salmon, a powerful explanatory principle is that whenever there is a coincidence (correlation) between the features of two processes, the explanation is an event common to the two processes that accounts for the correlation. This is a "common cause." To cite an example discussed earlier, there is a correlation between lung cancer (C) and nicotine stains on a person's fingers (N). That is,

Pr (C|N) > Pr(C).

The probability of C given N is greater than the probability of C alone.

The common cause of these two events is a lifetime habit of smoking two packs of cigarettes each day. Let this fact be (S).

Relative to S, C and N are independent of one another and thus neither is the cause of the other., i.e.,

Pr (C|N&S) = Pr(C|S).

The probability of C given N&S is no different than the probability of C given S alone. Therefore, N has nothing to do with the probability of C.

Thus N adds nothing to the probability of C. The same can be said about C in relation to N.

This is sometimes expressed as "S screens C off from N" That is, once S is brought into the picture N becomes irrelevant. This is part of a precise definition of "common cause," which is constrained by the formal probabilistic conditions.

Salmon's attempt here is to analyze a type of explanation that is commonly used in science, but the notion of causal explanation can be considered more broadly than he does. For example, David Lewis points out that the notion of a causal explanation is quite fluid. In his essay on causal explanation[5], he points out that there is an extremely rich causal history behind every event. Lewis too argues that to explain an event is to provide some information about its causal history.

The question arises, what kind of information? Where to “start” and where to “end?” There might be many situations in which we might only want a partial description of the causal history. Consider trying to assign blame for an automobile accident in a court trial. We need not cite all the physical principles at work to account for the accident.

We might consider:

1. whether gas was available for him to drive his car.

2. whether he was old enough to have received a driver's license by the time of the accident.

3. whether he was likely to have lived to the age that he did.

These features all figure into the causal history of the event, but they are not needed for the kind of explanation we seek. While all of these are part of the "causal history" leading up to the person having an accident while drunk, but we would not want to cite any of these as causing or explaining the accident. ("Explaining Well vs. Badly.") One might object that the availability of gas was not "the" cause of the person's accident. But it is a mistake to think we can really single out “the cause.” We can (must) focus on a given chunk of the causal history leading up to the event to get at the explanation we are looking for.

Lewis separates the causal history--any portion of which can in principle be cited in a given explanation--from the portion of that causal history that we are interested in or find most salient at a given time. We might not be interested in some of the information about any portion of the causal history, Lewis says, but it remains the case that to explain and event is to give information about the causal history leading up to that event. Or we may just want to know something about the type of causal history that leads to events of that sort, and so on.

To explain then is to give information about a causal history, but giving information about a causal history is not limited to citing one or more causes of the event in question. Lewis allows negative information about the causal history to count as an explanation:

· There was nothing to prevent it from happening.

· There was no state for the collapsing star to get into.

· There was no connection between the CIA agent being in the room and the Shah's death. It was just a coincidence.

Problems With the Causal Account of Explanation

If this account is correct (exhaustive), then there should be no explanations that fail to cite information about the causal history of the explanandum. Is this so? Remember the D-N explanation was long thought to model legitimate explanations and it does not cite causal histories. Do all purported D-N explanations fail to be explanations? Salmon seems to say as much. He argues that

1. Non-causal laws allow for "backwards" explanations.

2. Cry out to be explained themselves.

3. Are in fact simply descriptions of empirical regularities that themselves need to be explained.

The same might occur in the redshift case, if the law connecting the redshift with the velocity was simply an empirical generalization. (Also, consider Newton's explanation of the tides.)

Van Fraassen's Pragmatic View Of Explanation

There are two basic challenges that can be given to the causal view:

1. Sometimes non-causal generalizations can explain (see above)

2. Laws can be explained by other laws. But such a relationship between laws does not seem to be causal. Laws do not cause other laws, since neither is an event.

The Basic Elements Of The Pragmatic View Of Explanation

Van Fraassen gives a somewhat pragmatic, epistemic view of explanation. An explanation is a particular type of answer to a “why-question.” A satisfying explanation is an answer that provides relevant information that "favors" the event to be explained over its alternatives.

These features are determined by the context in which the why-question is asked.

According to van Fraassen, a why-question consists of:

(1) A presupposition (Why X)

(2) S contrast class (Why X rather than Y, Z, and so on)

(3) An implicitly understood criterion of relevance.

Information given in response to a particular why-question constitutes an explanation of the presupposition if the information is relevant and "favors" the presupposition over the alternatives in its contrast class.

E.g.

· Why did Adam eat the apple? (as opposed to Charlie?)

· Why did Adam eat the apple? (as opposed to baking it into a pie?)

· Why did Adam eat the apple? (as opposed to a pear?)

Context fixes relevant alternatives and thus, what it is that needs to be explained.

Both the contrast class and the criterion of relevance are contextually determined, based on interests of those involved. Therefore, According to van Fraasen, subjective interests define what count as an explanation in that context, but then it's an objective matter whether that information really favors the presupposition over the alternatives in its contrast class.

Contrasts Between The Pragmatic And Causal Views Of Explanation

Any type of information can be counted as relevant. Of course, it's a scientific explanation if only information provided by science counts. However, even so, there might be different kinds of scientific explanation; not any old information will do. Again, context (interests) determines when something counts as an explanation, that is, when we would find an explanation interesting or salient.

According to Lewis, what makes it an explanation is that it gives information about the causal history leading up to a given event; whether we find that explanatory information interesting or salient is another matter. By contrast, on the pragmatic view a mere description of the causal history leading up to an event --even a God-like complete one - -is not an explanation of any sort. According to the pragmatic view, even God could never have an explanation of an event, unless he had interests. This is because it must serve some actual interest to be an explanation.

Asymmetries Between Inference and Explanations Not Really a Problem

VanFraassen suggests that asymmetries only exist because of the context; thus, they can be reversed with a change in context. To illustrate this point, he offers a story when the height of a tower is explained by the length of its shadow, rather than the other way around. In van Fraassen's story, a character offers the following explanation of the height of a tower:

“That tower marks the spot where the Chevalier killed the maid with whom he had been in love to the point of madness. And the height of the tower? He vowed that shadow would cover the terrace where he first proclaimed his love, with every setting sun-that is why the tower had to be so high.

Van Fraassen here suggests that explanations are arguments, but only relative to context. We assess the explanatory merits of the derivations by tacitly supposing contexts that occur in everyday life. With a little imagination, we can see that there are alternative contexts in which the argument we normally would dismiss would count as explanatory.

Lewis' Objection to the Tower example:

Van Fraassen's story supposedly describes a context in which the length of the shadow explains the height of the tower. But this will solve the traditional problem of the asymmetries of explanation only if one can claim that the argument underlying the quoted passage is the argument that the unimaginative have dismissed as nonexplanatory. But the explanation van Fraassen relates does not in fact take the form of deducing the height of the tower from the length of the shadow (with the elevation of the sun and the principles of optics as the only other premises).

What is really doing the explaining is the intentions and beliefs of the Chevalier. This is what causes the tower to be of a certain height. We must begin with some initial conditions about the psychological characteristics of the Chevalier (He wanted to build a tower with certain properties. He knew certain physical facts.) Using general principles of rationality, we infer a statement to the effect that the Chevalier came to believe that, if he built a tower of the appropriate height on the appropriate spot, it would meet his desiderata.

Thus Lewis claims that van Fraassen is mistaken. His story does not provide a context in which the argument wrongly dismissed as explanatory shows its explanatory worth (mere length explains height) by a shift in context alone.

“Moreover, since van Fraassen points out, quite explicitly, the dependency on desires, we take him to appreciate that his story does not solve the traditional problem of the asymmetries of explanation.

Further, can you think of a story in which the redshift would explain the galaxies moving away? Where human intention is not possible, it seems difficult; this would seem to confirm Lewis' diagnosis of the Tower story.

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[1] Hempel, Carl,” Studies in the Logic of Explanation” http://people.loyno.edu/~folse/hempelstudies.htm

[2] Carl G. Hempel and Paul Oppenheim “Studies in the Logic of Explanation” Philosophy of Science Vol. 15, No. 2 (Apr., 1948), pp. 135-175 (41 pages)

[3] Laws of Nature, John W. Carroll Cambridge University Press (1994)

[4] One popular way of understanding the truth conditions of counterfactuals employs the use of possible worlds discourse. To say that a counterfactual is true is to say that in the nearest possible world where the antecedent obtains the consequent obtains.

[5] Lewis, David [1973]: `Causation’ Journal of Philosophy 70, pp. 556-567.