Lecture 2


The Inferential View Of Scientific Explanation

Last time we discussed philosophy of science very abstractly. I said that it was difficult to separate completely from other studies of science, since it draws on these other disciplines (sociology, history, psychology, as well as the sciences themselves) for its "data." What distinguishes philosophy of science from other studies of science is that it (1) takes a critical, evaluative approach--e.g., it aims at explaining why certain methods of analyzing data, or as we shall see today, the notion of explanation--are good ones. There is also an emphasis on conceptual analysis--e.g., explaining what explanation is, 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.) I also noted that the best way to see how philosophy of science is differentiated from other studies of science is by examining special cases, i.e., by doing philosophy of science. We will start our investigation by examining the notion of explanation.

The Difference Between Explanation And Description

It is commonplace, a truism, to say that science aims at not only describing regularities in the things that we observe around us--what is often called observable or empirical phenomena--but also at explaining those phenomena. For example, there is the phenomenon of redshift in the spectra of stars and distant galaxies. The physical principles behind redshift are sometimes explained by analogy with the Doppler effect, which pertains to sound: observed wavelengths are increased if the object is moving away from us, shortened if the object is moving towards us. (Also, there is a derivation in general relativity theory of the redshift phenomenon, due to gravitation.) In 1917, de Sitter predicted that there would be a relationship between distance and redshift, though this prediction was not generally recognized until Hubble (1929), who was inspired by de Sitter's analysis. Another example: There's a periodic reversal in the apparent paths of the outer planets in the sky. This can be predicted purely mathematically, based on past observations, but prediction does not explain why the reversal occurs. What is needed is a theory of the solar system, which details how the planets' real motions produce the apparent motions that we observe. Final example: Hempel's thermometer example (an initial dip in the mercury level precedes a larger increase when a thermometer is placed into a hot liquid).

Three Approaches To Explanation

A philosopher of science asks: What is the difference between describing a phenomenon and explaining it? In addition, what makes something an adequate explanation? Philosophers have defended three basic answers to this question.

  1. Inferential View (Hempel, Oppenheim) - An explanation is a type of argument, with sentences expressing laws of nature occurring essentially in the premises, and the phenomenon to be explained as the conclusion. Also included in the premises can be sentences describing antecedent conditions.
  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.

In the next few weeks, we will examine each of these accounts in turn, detailing their strengths and weaknesses. Today we will start with Hempel's inferential view, which goes by several other names that you might encounter.

The "received" view of explanation (reflecting the fact that philosophers generally agreed with the inferential view until the early 1960s)

The "deductive-nomological" model of explanation (along with its probabilistic siblings, the "inductive-statistical" and "deductive-statistical" models of explanation)

The Inferential Theory of Explanation

The original Hempel-Oppenheim paper, which appeared in 1948, analyzed what has come to be known as "deductive-nomological" (D-N) explanation. Hempel and Oppenheim consider patterns of explanation of a particular sort and try to generalize that pattern. As already noted, they view explanation as a certain sort of argument, i.e., a set of premises (sentences) which collectively imply a conclusion. The arguments they considered were deductive, i.e., arguments such that if the premises are true the conclusion has to be true as well.

All human beings are mortal.

Socrates is a human being.

Socrates is mortal.

Not every argument that is deductive is an explanation, however. How can we separate those that are from those that are not?

To accomplish this task, Hempel and Oppenheim describe their "General Conditions of Adequacy" that define 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 logically possible for an observation-statement to contradict it)

The first three conditions are "logical" conditions, i.e., formal, structural features that a deductive argument must have to count as an explanation. To complete the conditions of adequacy, Hempel and Oppenheim add a fourth, "empirical" condition.

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

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

C1, ... , Cn [antecedent conditions (optional)]

L1, ... , Ln [laws of nature]

Therefore, E [explanandum]

Later, we will be looking at a statistical variant of this pattern, which allows the laws of nature to be statistical, and the resulting inference to be inductive.

Laws Of Nature

Since Hempel and Oppenheim's analysis is stated in terms of laws of nature, it is important to state what a law of nature is on their view. Hempel and Oppenheim take a law to be a true "law-like" sentence. This means that a law is a linguistic entity, to be distinguished by its peculiar linguistic features. According to Hempel and Oppenheim, laws are to be distinguished from other sentences in a language in that they are (1) universal, (2) have unlimited scope, (3) contain no designation of particular objects, and (4) contain only "purely qualitative" predicates.

The problem Hempel and Oppenheim face is distinguishing laws from accidental generalizations, i.e., general truths that happen to be true, though they are not true as a matter of physical law. 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." However, we do not deem this sentence to be a law of nature. One reason that this might be so is that this statement only applies to one object in the universe, i.e., my refrigerator. Laws of nature, by contrast, refer to whole classes of objects (or phenomena). (Consider the sentence "All gases that are heated under constant pressure expand.") It is for this reason that Hempel and Oppenheim include the requirement that to be a law of nature a sentence must not designate any particular objects.

Discuss: Can we get around this requirement by a bit of linguistic trickery? Consider if we replace the designation "in my refrigerator" by "in any Lyle Zynda-owned refrigerator," or, even better, by some physical description in terms of "purely qualitative" predicates that single out my refrigerator from the class of all refrigerators in the universe. Would the existence of such a sentence convince you that you have discovered a new law of nature? Moreover, consider the following two 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.

The former is not a law of nature, though the latter is (though it is of a relatively low-level variety of law).

One reason that the statements about apples and gold might not be laws of nature, a reason not adequately captured by the Hempel-Oppenheim analysis of laws, is that they do not support inferences to counterfactual statements. For example, it cannot be inferred from the fact that all the apples that ever get into my refrigerator are yellow that if a red apple were to be placed into my refrigerator, it would turn yellow. Laws of nature, by contrast, support counterfactual inferences. From the fact that 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. (We can reasonably infer this even if we never 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. (We could not infer a similar statement about gold from the true generalization that no gold sphere has a mass greater than 100,000 kilograms.)

The difference between statements G and U has never been captured purely syntactically. 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.

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

The Hempel-Oppenheim analysis of scientific explanation has the following overlapping features. (Review and explain each.)

(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.

(d) No Essential Role For Causality - Laws of nature do not have to describe causal processes to be used legitimately in scientific explanations.

Many counterexamples have been given to the Hempel-Oppenheim analysis of scientific explanation that target one or more of these features. The first group of counterexamples reveals that the Hempel-Oppenheim analysis faces the Problem of 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. You can also make the same prediction by extrapolating backwards in time from the subsequent positions of these three bodies. However, only the first would count as an explanation of why the eclipse occurred when and where it did.

(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. You can also predict what the height of the flagpole is by measuring the length of its shadow and the elevation of the Sun. However, only the first derivation 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, neither of these are explanatory, since both are explained by antecedent atmospheric conditions.

The second group of counterexamples reveals that the Hempel-Oppenheim analysis of explanation faces the Problem of Irrelevance: the Hempel-Oppenheim analysis sometimes endorses information as explanatory when it is irrelevant to the explanandum.

(4) 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. 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.

(5) Hexed Salt - All salt that has had a hex placed on it by a witch will dissolve in water. Hence, we can logically infer from the fact that a sample of salt had a hex placed on it by a witch that it will dissolve in water. However, this wouldn't give us an explanation of the dissolution since the salt would have dissolved even if it hadn't been hexed.