Exercises for Chapter 2:
1. Defend or criticize: “The D-N model, or covering-law model, does not elucidate the nature of explanation. If someone wants to know why x occurs under condition y, being told what always occurs under condition y does not elucidate anything.”
Science begins in wonder, and science seeks explanation in order to satisfy that wonder. (See textbook, p. 26.) The difference between scientific explanation and the explanations found in “the other trades” of human beings lies in method and norms, not in the object explained. What is called scientific explanation is directed toward “wonder,” that is, the quest for an answer to “why.”
So we may as well begin by attending to the way a “question” is posed—rather than hurrying to formulate the norms of an answer.
For example, the question in this problem, “to know why x occurs under condition y,” is not a realistic or reasonable way to ask. In actual practice, when someone asks a question, they often do not know the condition y. As for this y that “always occurs under condition y,” setting aside whether it can even be found, even if it could be found, the task of listing the conditions belongs to the explainer, not the one seeking the explanation. Which boundary conditions y are relevant to, or necessary for, the occurrence of x must be determined through scientific analysis; and before receiving a satisfactory scientific explanation, the questioner is simply puzzled about “why x occurs.” The wording of this problem has a trap in it—“someone wants to know why x occurs under condition y” is only one case of scientific explanation, but it is not necessarily the case that for every explanandum one must list its sufficient conditions.
Therefore, before discussing the application of the D-N model, it is necessary to consider the different types of explananda in scientific explanation.
One distinction is to divide explananda into necessary events and probabilistic events: the former are explained using the D-N model, and the latter by the I-S model. But this division has its shortcomings, because events in reality are often very hard to list in such a way as to guarantee that they must occur in this form rather than that form; the line between necessity and probability is blurry. More crucially, when we ask “why,” how do we know whether the cause of a certain phenomenon is probabilistic or necessary?
I think that when discussing scientific explanation, the first thing to note is the syntactic type of the explanandum. That is to say, the very first thing is to distinguish between an explanation of a single event and an explanation of a general phenomenon.
A single event is something like “why x occurs,” for example, “this piece of ice floats on water,” “Zhang San has measles,” “a rainbow appeared somewhere this afternoon,” and so on. A general phenomenon, by contrast, is “why (under condition y) x (or a phenomenon like x) always (or often) occurs,” for example, “ice always floats on water,” “90% of people who have had intimate contact with a measles patient will be infected,” “rainbows appear from time to time,” and so on.
And the so-called “why must x necessarily occur under condition y” is an illicit question. For when we ask “why x,” x is always something that we have already experienced and perceived; just as it would be inappropriate to ask “why does God exist” before we have proven that God exists, so too, when we merely “believe” in some kind of “necessity” but have not yet demonstrated it, it is unreasonable to ask why it is necessary.
It should be noted that asking “why does x occur rather than anything else” does seem to be a legitimate question, but this question still does not contain a demand for “necessity.” Moreover, the principle of sufficient reason is merely a belief; just as only someone who believes in a perfectly good God would be puzzled by the question “why is this world full of evil,” only someone who unconditionally and devoutly believes in the principle of sufficient reason could ask “what is the sufficient reason that made this thing occur this way rather than that way.” But since, according to empiricist logic, the only things we can know for certain are the phenomena we experience, then only questions about empirical facts are legitimate, whereas challenging the creed itself is a philosophical matter; to take that creed as a presupposition and then question on that basis is the religious way of proceeding.
Therefore, the demand to “explain why something necessarily occurs under condition y” is not something the questioner reasonably puts forward. At most, it is an additional demand one imposes on oneself as an explainer, and this demand is obviously too high.
The questioner is asking, not setting an exam question. To put it jokingly, there is a “meta-law” among middle-school math exam questions—“what needs to be proved is always correct.” That is because the problems have all been designed by the teacher with the proof already in mind, but this “law” obviously cannot be applied to scientific explanation. Only after we have already found a satisfactory scientific explanation can we say “…necessarily…” (though even that is questionable), and what we need to discuss now is precisely how a scientific explanation can be satisfactory. Before we have given a scientific explanation, it is impossible to reasonably ask a question such as “why does x necessarily occur under condition y.” Therefore, although proving why x necessarily occurs is indeed one way to explain why x occurs, it is not a necessary requirement.
The questioner’s demands are first and foremost practical, and the explanatory strategies for questions with different demands are different!
General phenomena, such as “ice always floats on water,” can themselves be called “laws.” An explanation of a law can make use of laws that are more “basic,” and the most basic laws are what are called “scientific laws.” General laws and scientific laws are not substantively different in syntax: both are of the form “under such-and-such a circumstance, such-and-such always (often, possibly) occurs,” only scientific laws are more basic, more reliable, more universally applicable, and so on.
An explanation of a single event does not necessarily need to trace back to the most fundamental scientific laws; using relatively basic laws can already be satisfactory. For example, “why does this piece of ice float on water” can be explained by “ice always floats on water.” Of course, that is still not satisfying enough, but explaining it by “objects lighter than water in density always float on water” is about right. Further, we can replace water with liquid in general and quantify, in terms of density ratios, the specific state of an object floating on top of a liquid; but for the person who asked “why does this piece of ice float on water,” that probably need not be too cumbersome.
For an explanation of a single event, one usually does not require a demonstration of necessity; it is enough to show that the event’s occurrence is “reasonable” and “in accordance with the laws.” For example, to explain “why does Zhang San have measles,” it is enough to provide an account that makes one believe the event’s occurrence is sensible and reasonable. To pursue “why did Zhang San necessarily (in this way rather than that way) get measles” is excessive. Even for some “necessary events” that have been demonstrated, if we continue to ask why their “boundary conditions” are such-and-such, sooner or later we will always have to appeal to contingency. Let alone probabilistic events: for example, science can never explain the necessity of “I just now tossed a coin and got heads,” and often cannot even explain that it was a high-probability event; it can only explain that getting heads on a coin toss is reasonable. For the question “why did I toss a coin ten times and get heads every time,” neither the D-N model nor the I-S model is likely to be of much help. But these low-probability events still require scientific explanation. Once science abandons the task of explaining them, mystical explanations will have a chance to come into play. Science needs to offer a more reasonable explanation than “these coincidences happened because of the devil’s curse,” and this requires scientific explanation to lower its own overly lofty demands.
The explanation of general phenomena is different. Many people say that scientific explanation is always simultaneously both “demonstration” and “prediction.” I think this view at most applies only to the explanation of general phenomena.
A general phenomenon itself, as a “law,” often appears in the explanation of a single event—for example, using “ice always floats on water” to explain “this piece of ice floats on water.” But if the law itself is not basic enough, or if the person asking “why does this piece of ice float on water” really means “why does ice always float on water,” then such an explanation is not sufficiently satisfactory, and we need to seek an explanation of the “law.” In general, science explains laws by finding laws that are more basic; how far one must trace back depends on the questioner’s requirements.
One may think that as long as one carries out an effective deductive exposition using relatively basic laws, the explanation is complete—though it may not be sufficiently satisfying. However, if one thinks that explanations such as using “ice always floats on water” to explain “this piece of ice floats on water,” or using “objects with lower density always float on water” to explain “ice always floats on water,” are not satisfying enough, then the questioner is, in effect, “following up.” That is to say, what needs to be explained is no longer the original question, but a further requirement has been introduced. Yet strictly with respect to the question “why does ice always float on water,” “objects with lower density always float on water” already completes a full explanation.
Here, I abandon “convincingness” as a necessary condition for scientific explanation. In fact, scientific explanations often do not satisfy, and in some cases are even inferior to analogical explanations or even fairy tales. So let us give a lower threshold for what counts as scientific explanation: as long as one uses a more “basic” law to explain a law, or uses a “law” to explain a concrete event, this may be called an “explanation”; the added condition is that if the laws and methods used in the explanation are both “scientific” (the term here is ambiguous; it is impossible to complete a discussion of what science is in just a few paragraphs, so here we may provisionally understand “scientific” as “recognized by the scientific community”), then this explanation is a “scientific explanation.”
We have said that scientific explanation always uses “more basic” laws—that is, more reliable and more universal laws—to explain laws. Pursued to the end, this will involve the “most basic” laws, namely scientific laws. Of course, exactly which laws count as “scientific laws” is not clearly delimited, and perhaps in the social sciences there is hardly any such thing as “laws” at all. For the moment, let us examine only some obvious cases of basic laws in the natural sciences—for example, the law of conservation of energy.
How, then, is it possible to scientifically explain a law as basic as “conservation of energy”? I think that, as the saying goes, when things reach an extreme they must turn back; for these fundamental laws, the only effective and reasonable way to explain them is to reverse the direction and use concrete actual events! That is, use a large number of “single events” to explain the basic law. In fact, it can only be this way. Unless one resorts to “philosophical explanation” or “religious explanation,” if one wants to explain “why energy is conserved,” the only thing science can say is: “Because a great many experiments and a long history of experience strongly support that the conservation of energy cannot be violated.” — I fear there is no better way to explain the most basic scientific laws.
In summary, I think the relationships among the various objects of scientific explanation are as follows:
┏→law—(explanation)→law—(explanation)→law—(explanation)→concrete event┐
↑＿＿＿＿＿＿＿＿＿＿＿(explanation)＿＿＿＿＿＿＿＿＿＿＿＿＿＿↓
If, within a set of explanations, one can complete a full circle from law to event—that is, both use deductive derivation starting from the law to show that the occurrence of the event is reasonable, and at the same time the correspondence between the event that actually occurred and the event inferred in advance in turn confirms the correctness of the law and the derivation—then that set of explanations is the most successful. Of course, many times we do not need that whole package of explanation, and often it is enough merely to make someone believe that “the event’s occurrence is reasonable” or that “the law or regularity is valid.” In addition, in the social sciences one generally skips the link of basic laws and directly explains concrete events and general regularities in mutual terms.
In the age of Big Science, science itself has formed a vast system. It possesses some relatively fixed basic laws, and the laws support and coordinate one another; numerous observational results and actual events fit the laws very closely—at least with few contradictions. It is precisely the effectiveness and reliability of this enormous system that ensure the effectiveness and reliability of scientific explanation.
To sum up: the D-N model clarifies a viable approach to scientific explanation in certain cases, but it does not satisfy all the questioner’s demands. Scientific explanation is directed toward “real” “problems,” not toward designing questions for oneself and then seeking answers.
April 7, 2006
Latest Comments
Gu2006-04-12 16:37:38 [Reply]
Self-addendum:
Strictly speaking, the law of conservation of energy may perhaps still be inferred from something more basic. In fact, in quantum mechanics, the three major conservation laws are all related to certain properties of spacetime. For example, time-translation invariance—that is, no matter when I begin the experiment, the result is the same—leads to the law of conservation of energy; spatial-translation invariance—that is, no matter whether I do the experiment here or there, the result is the same—leads to the law of conservation of momentum; and rotational invariance—that is, if one turns the entire apparatus through an angle and performs the experiment, the structure is the same—leads to the law of conservation of angular momentum. In addition, when one takes into account the relativity of time-space, and examines translations in time-space more carefully, one obtains invariance under Lorentz transformations, and this invariance leads to relativity, and within it the conservation of mass-energy, and so on.- Gu
2006-04-12 16:45:15
A few more words:
These most basic spacetime invariances can no longer be explained by anything more basic, unless one resorts to circular explanation. They seem so correct and unquestionable, but in fact they are not absolutely reliable! In fact, there is another invariance that is intuitively obvious—mirror invariance, that is, if one turns the whole apparatus into its mirror image, the experimental result will also be mirror-symmetric with respect to the original outcome. And the invariance this gives rise to is the legendary “law of parity conservation.” But as is well known, this law has been shown by Yang Zhenning, Li Zhengdao, and Wu Jianxiong to fail under the weak interaction. So might the other three also occasionally fail? No one can guarantee that. - yellow86
2010-02-20 22:08:45 Anonymous 121.5.20.2
Hehe
Did you do the other problems in this chapter?
Translated from the Chinese original with AI assistance. The original text is authoritative.
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