Philosophical Issues in Scientific Foundations

The issues discussed above are related not only in that they are philosophical issues, but also in that they are philosophical issues that influence the work­ings of science. In this section, we consider a sampling of issues related to science that are philosophically interesting, but are such that they (at least typically) do not directly influence the actual workings of science.

3.1 Scientific explanation

Recall that in §2.1, we looked at the basic confirmation and disconfirm­ation aspect of science; that is, the process of generating predictions and then checking to see if the predictions are correct. And we saw that even this basic aspect of science had intriguing (and largely philosophical) issues just beneath the surface. In this section we probe into a topic with close ties to issues we found in that section; namely, issues related to scientific explanation.

Let us begin by returning to an earlier example. Consider again the theory that planets move about the sun in elliptical orbits, with the sun at one focus of the ellipse. Again, this idea was first proposed by Kepler in the early 1600s and is now often referred to as Kepler’s first law of

planetary motion. Also important is what we now usually refer to as Kepler's second law of planetary motion. Let us take a moment to under­stand this second law.

Consider the elliptical orbit of a planet, say Mars, with the sun at one focus of the ellipse. Suppose we think of this as a sort of elliptical pie. And imagine we cut this elliptical pie as follows. Along the crust (that is, Mars' orbit) we will mark the points where Mars is at, say, 30-day intervals over the course of a year. (This will mean we will have 12 marks along the crust, one for Mars' position at the beginning of each 30-day interval.

In addition to having substantial predictive power (for example, Kepler's first and second laws provided substantially more accurate predictions than any competing theory), Kepler's laws also seem to have substantial explana­tory power. For example, suppose we are observing the night sky, and we ask why Mars appears where it does. We could answer this question using Kepler's laws. The full explanation would not be trivial, but neither is it terribly complex. In providing an explanation, we might start with the position of the earth and Mars, in their respective orbits, at the beginning of the year. Then, using Kepler's first and second laws, we could deduce where the earth and Mars will be at this moment. That would then show us where, from our perspective on earth, Mars should appear in the night sky. And that explains why Mars appears where it is tonight - Mars' posi­tion in the night sky is a deductive consequence of Kepler's laws together with some initial conditions (in this case, the positions of the earth and Mars at the beginning of the year).

If we look more closely at this style of explanation, the pattern is as fol­lows: from a scientific law or laws (in this case, Kepler's laws of planetary motion), together with some set of initial conditions (here, the initial positions of the earth and Mars at the beginning of the year), we deduce that such and such should be observed (here, the current position of Mars in the night sky).

The style of explanation just described has come to be called the “covering law” model of explanation. Although many scholars have con­tributed to this model of explanation, this style of explanation is most closely associated with Carl Hempel (1905-94) (for an early account, see Hempel and Oppenheim 1948, Hempel 1965a). And indeed, this account of explanation seems, intuitively, to be on the right track.

As a brief aside, the model of explanation illustrated above is often termed the “deductive-nomological” model (or D-N model; “deductive” because of the deductive nature of the reasoning involved and “nomological” because of the involvement of laws). Also, there is a variety of related models of explanation which, because of time and space constraints, we will not explore here. Most notable among these (and usually viewed as another type of covering law style explanation) is the “inductive-statistical” (or I-S) model, which is similar to the D-N model except that the inferences involved are inductive inferences from statistical laws (for an early investigation, see Hempel 1962). It is worth noting that a variety of alternative approaches to the D-N and I-S style of explanation have also been defended over the years.^[24] For this section, we will focus primarily on the covering law model, as illustrated by the example above involving Kepler's laws, and attempt to convey a flavor of the difficulties this model has encountered.

One basic problem with the covering law model is that it seems to miss a certain asymmetry that is present in explanation. This “asymmetry” issue requires some explanation, and, as usual, an example might help. Consider again the case above, where we used Kepler's laws, together with the position of the earth and Mars at the beginning of the year, to explain the current position of Mars. Notice that the covering law model of explanation allows us to run this example in the other direction.

But this just seems wrong. It seems we should be able to explain future events from past events, but not vice versa. That is, although past events seem able to explain current events, it does not seem right to try to explain past events from current events. And that is the sense in which explan­ation is asymmetric. And again, the covering law model seems simply to miss this characteristic of explanation.

It seems we need to supplement the covering law model, or look for alternative accounts of scientific explanation, or both. In the remainder of this section, I will try to sketch (very) briefly some of these approaches.

One initially appealing way of supplementing the covering law account is by appealing to the notion of causation. We do seem to have strong intuitions that past events can cause current events, but not vice versa. That is, causation seems to have the sort of symmetry lacking in the covering law model. So perhaps an account of explanation along the general lines of the covering law model, supplemented with an account of causation, might do the trick.

However, causation is a notoriously slippery subject. One of the earliest substantive analyses of the concept of causation dates back to the Scottish philosopher David Hume (1711-76) (Hume 1975). In a nutshell, Hume argued that causation is not something we observe in nature; rather, what we literally observe are events followed reliably by other events. These “con­stant conjunctions” between events (for example, events such as two pool balls colliding are reliably followed by events such as the pool balls moving away from each other) are all we actually observe.

I think you can see some of the issues raised by these sorts of Humean concerns about causation. For example, if scientific explanation depends on the notion of causation, and causation is not “out there” in nature but is instead contributed by our minds, then we have to suspect that explanations in science are not the sort of objective, independent accounts I think we initially tend to think of them as.

This is, of course, just a brief sketch of some difficult issues. Suffice it to say that, although much interesting work has been done in recent decades on the notion of causation, and its potential role in helping to under­stand scientific explanation, nothing close to any sort of a consensus view on these matters has evolved (Sosa and Tooley 1993, Woodward 2003). Causation is, as noted, an incredibly slippery issue.

As mentioned earlier, some alternative accounts of explanation, ones not based on the covering law model, have been (and are being) explored. For example, some have proposed that a sort of explanatory unification is central to explanation (Friedman 1974, Kitcher 1981). To take one quick case, in Newtonian physics certain similarities among phenomena (say the similarity in the forces you experience as a result of acceleration or deceleration, and the gravitational forces you experience from being near a large body such as the earth) have to be taken as a sort of curious and unrelated coincidence. In contrast, on Einstein’s general relativity (Einstein 1916), these two phenomena are seen as resulting from the same set of basic laws. In this sense, Einstein’s theory unifies these previously disparate phenomena, and as noted, this sort of unification is seen by some as key to explanation.

These are, of course, not the only options and avenues being explored concerning explanation in science, and needless to say, even a cursory survey of all the alternatives is beyond the scope of this essay.

3.2 Scientific laws

At various points in our discussion so far, we have appealed to the notion of a scientific law. And indeed, scientific laws seem to play a central role in science. Kepler’s laws of planetary motion, for example, are an indis­pensable part of Kepler’s account of the motion of planets. Laws also seem to be central to more philosophical approaches to science we have discussed - for example, the covering law model of scientific explanation.

But what is a scientific law? For the sake of a concrete example, let us again think about one of Kepler’s laws of planetary motion, say the equal areas law. Again, this law says that a line from the sun to a planet will sweep out equal areas in equal time. Our initial inclination is to view this law as capturing some sort of fundamental, and presumably exceptionless, regularity about the universe (or at least a fundamental regularity about planetary motion).

We also, at least initially, tend to view this as an objective regularity, that is, as a regularity that exists independently of us. So, for example, our initial inclinations are to think that even if humans had never evolved on earth, planetary orbits still would have worked in accordance with Kepler's law, that is, a line drawn from the sun to a planet would still have swept out equal areas in equal time.

So, in this section, let us focus on just these two features we tend to associate with scientific laws, namely, that laws such as Kepler's equal areas law capture an exceptionless regularity about the universe, and that such laws are objective, that is, independent of us.

Let us begin with some considerations about regularities. Notice that regularities, even exceptionless regularities, are everywhere. But we are not inclined to count most of these regularities as scientific laws. For example, as far as I can recall, I have always put my pants on left-leg first, and prob­ably always will. Suppose this in fact turns out to be the case, that is, I always have and always will put my pants on left-leg first. Then this would be an exceptionless regularity, but it certainly is not a scientific law. Likewise, it is an exceptionless regularity that there has never been a single English sentence of a million words (and almost certainly never will be), but this regularity is also not a scientific law. And so on for countless other regularities.

Intuitively, there seems to be a substantial difference between accidental regularities (for example, my dressing routine) and regularities that we tend to think of as scientific laws (for example, Kepler's equal areas law of planet­ary motion). And in fact, there is a fairly standard account of this difference.

The difference between accidental and law-like regularities is usually accounted for by appealing to what are called “counterfactual conditionals.” Counterfactual conditionals (or just “counterfactuals”) are something everyone is familiar with, though you may not be familiar with the term. The idea is straightforward. Suppose you say, “If I had studied harder for that test, then I would have gotten an A on it,” or “If the battery in my alarm had not died, then I would have been on time for my appointment.” Note that these are conditional sentences (that is, “if/then” sorts of sentences), in which the antecedent of the conditional (the “if” part) is false; hence the name “counterfactual conditional” (that is, contrary to fact). And again, we use counterfactual conditionals all the time to express what would have happened if antecedent conditions had been other than they actually were.

Now consider again Kepler's equal areas law, and suppose we focus on a particular planet, say Jupiter. Notice that Kepler's law would have held for Jupiter even if a wide variety of facts about Jupiter had been different. For example, if Jupiter had been more massive than it is, or less massive, or had a rocky composition rather than being a gas giant, or was located at a different distance from the sun, and so on. In all these cases, it still would have held true that a line drawn from the sun to Jupiter would have swept out equal areas in equal time. In short, Kepler's law remains correct even under a wide variety of counterfactual conditions.

In contrast, we can easily imagine any number of conditions under which the regularity about my dressing behavior would no longer have held. For example, my pants regularity probably would not have held had my parents taught me to put on pants in a different manner, or perhaps if I had been left-handed, or if as a child I had sustained an ankle sprain that made it difficult to put my pants on left-leg first, or any number of other perfectly trivial counterfactual conditions. So in contrast with the regularity expressed by Kepler's law, my pants-putting-on behavior is not true under a variety of counterfactual conditions.

In short, there seems to be a sort of necessity about the regularities captured by scientific laws, where that necessity is lacking in accidental regularities. And that necessity seems to be nicely captured by counterfactual statements. In particular, law-like regularities remain true under a variety of counterfactual conditions, whereas accidental regularities do not. As such, counterfactuals seem key in distinguishing law-like regularities from accidental regularities.

However, it does not take long to uncover surprisingly difficult issues involving counterfactuals (see Quine 1964, Goodman 1979). To look into one issue among many, counterfactuals seem to be inescapably context- and interest-dependent. For example, consider the counterfactual above, when we imagined you saying to yourself, “If I had studied harder for that test, then I would have gotten an A on it.” Whether this counterfactual is true or not depends substantially on the context surrounding the counter- factual, as well as on other background information. For example, sup­pose you wound up missing the test entirely, perhaps because the battery in your alarm clock was dead. In that case, the counterfactual would be false. Likewise, the counterfactual would have been false if you had the wrong notes for the exam (in which case it is likely no amount of studying would earn you an A). And so on for countless other contextual issues.

These sorts of considerations raise a variety of issues. For example, if we need counterfactuals to distinguish law-like regularities from accidental regularities, and the truth of counterfactuals is context-dependent, and what the relevant context is depends on our interests in various situations, then it begins to look like which regularities count as laws are likewise depend­ent on our interests. And in this case, scientific laws begin to look as if they are dependent on us, rather than being objective and independent.^[26]

Or another issue: largely because of the context-dependence of counter- factuals, it has been difficult to provide an account of under what condi­tions counterfactuals are true and false.^[27] So if the distinction between accidental and law-like regularities depends upon the truth of the relevant counterfactuals associated with those regularities, and it is difficult to give a principled account of the truth and falsity of those counterfactuals, then it seems we will have difficulty giving a principled account by which we can distinguish accidental from law-like regularities.

Other issues concerning law-like regularities arise as well. To look at one of these issues, although quite briefly, consider again Kepler's laws of planetary motion. As it turns out, there is an important sense in which these are not exceptionless regularities. We have already seen (in §2.2) that in the 1800s it was recognized that there were some peculiarities with the orbit of Uranus, and in particular, the motion of Uranus was found not to be in strict accordance with Kepler's laws. As another example, in July of 1994 a quite substantial comet (Comet Shoemaker-Levy 9) collided with Jupiter. The collision's effect on Jupiter's orbit was not large, but it was enough of an impact to slightly affect Jupiter's orbit, such that Kepler's laws did not quite hold for that time period near the comet's collision.

Although the dramatic collision of the comet and Jupiter was an unusual event, less dramatic events influence planetary orbits all the time. The gravitational effects of Neptune on Uranus, as well as the gravitational effects of various bodies (other planets, comets, asteroids, and so on), will likewise affect the orbit of a planet, and in ways so as to make Kepler's laws not strictly apply.

The usual view is that the regularities expressed by scientific laws (and indeed, almost all regularities, whether accidental or law-like) apply with the understanding that certain “all else equal” clauses apply. For example, if Uranus were not affected by the gravitational influences of Neptune, or had comet Shoemaker-Levy 9 not smashed into Jupiter in July of 1994, and were these planets not influenced by the gravitational influences of other planets, and not influenced by the gravitational influences of the millions of asteroids in the asteroid belt, and not influenced by the presence of the Galileo spacecraft, and not influenced by other similar factors, then Kepler's laws would hold.

These sorts of “all else equal” clauses are typically referred to as “ceteris paribus” clauses, and such ceteris paribus clauses seem an indispensable part of scientific laws. Ceteris paribus clauses seem to have a number of problematic features, of which we will only briefly note a couple. First, do not overlook that such clauses have close ties to counterfactual conditionals, and as such bring with them the issues discussed above concerning coun- terfactuals. In addition, ceteris paribus clauses are notoriously vague. For example, in the example above involving Jupiter, what exactly counts as influences “like” the ones described? Whether one thing is like another again seems very much context- and interest-dependent. So once again, if scientific laws require interest-dependent criteria, it would appear difficult to main­tain that scientific laws are objective, that is, independent of us, not to men­tion difficult to give a principled account of when such conditions hold.

There are far more issues surrounding the role played by ceteris paribus clauses in science than just those outlined above.^[28] But as with previous discussions, the discussion above will, I hope, at least convey a flavor of some of these issues.

3.3 Hume’s problem of induction

As noted earlier in this essay, an important component of science is the making of predictions about what we would expect to observe. Nor is this sort of reasoning unique to science - we all use this sort of reasoning all the time, probably every day. Also notice - and this is of particular relevance for the main topic of this section - that this sort of reasoning is reasoning about what we can expect to observe in the future. Again, there is nothing seemingly unusual about this - we reason about the future all the time in everyday life, and reasoning about the future is certainly a critical aspect of science.

Concerning reasoning about the future, Hume (whose views on caus­ation we have already encountered) seems to have been the first to notice some important points about such reasoning (Hume 1975). The first point Hume noticed was this: if we are to trust our reasoning about the future, we have to assume that what happens in the future will be similar to what has happened in the past.

To see this, consider what the world would be like if what happened in the future was not like what has happened in the past. For example, suppose we lived in a world where each day was very different from the day before. Maybe the force of gravity changes from day to day; maybe the sun rises in the east one day and from some other random location the next day; maybe the weather changes randomly and unpredictably, being below freez­ing one day and 100 degrees the next; and so on. In such a world, we could not make the sorts of predictions about the future that we take for granted.

So, to repeat the first key point of Hume, to trust our reasoning about the future, we have to assume that what happens in the future will be simi­lar to what has happened in the past. But now comes Hume's second key point: there seems to be no way to justify this assumption, that is, there seems to be no way to justify the assumption that what happens in the future will be like what has happened in the past.

Note that one way we could not justify this assumption is by using circular reasoning, that is, by using the assumption to justify itself. To see a simple case of circular reasoning (and why it does not work to justify a claim), consider this example. My new students sometimes tell me they have heard I sometimes goof around with the class, and, reasonably enough, would like to know when they can trust what I am saying, and distinguish it from when I am just goofing. Suppose I answer by going to the board at the front of the class, and writing:

What DeWitt writes on the board is trustworthy.

And I tell the class that that is how they can tell: if I write something on the board, it is trustworthy.

But now a particularly inquisitive student raises a perfectly reasonable question, namely, why should they trust what I just wrote on the board? And suppose I reply, “Because I wrote it on the board, and as you can see by what's written on the board, what DeWitt writes on the board is trustworthy.”

That is blatantly circular reasoning. I am using the claim “what DeWitt writes on the board is trustworthy” to justify the claim “what DeWitt writes on the board is trustworthy.” And that sort of circular reasoning - using a claim to justify itself - is no justification at all.

But notice - and this is really at the heart of Hume's second key point - that exactly this sort of circularity is lurking with the key claim that what happens in the future will be like what has happened in the past. Why? Because the only way we seem to have to justify this claim is noting that what happened today is similar to what happened yesterday, and what happened yesterday was similar to what happened the day before, and so on. That is, we are justifying the claim “what happens in the future will be similar to what has happened in the past” by appealing to past experience. But as Hume noted, any such reasoning - that is, any reasoning about the future based on past experience - must already assume that what happens in the future will be similar to what has happened in the past. That is, in trying to justify the claim “what happens in the future will be similar to what has happened in the past,” we have to assume the truth of that exact claim, that is, that what happens in the future will be similar to what has happened in the past. And as with the “what DeWitt writes on the board” case, this is circular and thus no justification at all.

So Hume noticed a very general, and very curious, point about any reasoning concerning the future; namely all such reasoning rests on an assumption that cannot be logically justified. And the more general impli­cation is difficult to avoid: if all reasoning about the future rests on a logically unjustified assumption, then our conclusions based on such rea­soning, that is, our conclusions about what is likely to happen in the future, are equally logically unjustified.

4.