Monday, October 08, 2012

Whewell on Newton's Laws III: The First Law

Tucked away in the introduction to a (now) little-read book, On the Motion of Points Constrained and Resisted, which was actually the second volume of his most developed physics textbook (an active advocate for the ineliminable importance of science in a liberal education, he wrote many), we find what is perhaps Whewell's most straightforward comment on the relation between the causal axioms that describe the Fundamental Idea of Cause, and how this Idea relates to Newton's Laws. For the first, he isolates the first causal axiom:

It is the object of science to reduce phenomena to their causes: the fundamental principle of science is

PROPOSITION I. No change can take place without a cause. (MPCR ix)

The cause relevant to motion is that of force, and in some sense Newton's First Law, Every body perseveres in its state of rest or uniform motion in a straight line, except insofar as it is compelled to change that state by an impressed force, is just the causal axiom applied to forces: we have a change, namely, deviation from state of rest or uniform motion in a straight line, and we have identified the relevant cause, impressed force. However, this obscures an absolutely essential element of Whewell's discussion; capturing this element requires us to think a bit more about the issue of the modal disparity that Whewell's account of induction addresses.

On the one hand, there is excellent reason for regarding Newton's Laws as something derived from experience. They have not, for instance, always been accepted, and, indeed, there were plenty of proposed principles of motion prior to Newton that are not strictly consistent with Newton's Laws. This does not, in and of itself, guarantee that the Laws must be derived from experience, because not all intrinsically self-evident truths are obvious to everyone -- mathematics and logic are both full of self-evident principles that cannot be recognized as such unless one has done considerable conceptual work. But when we look both at the kinds of errors that prevented people from developing the Laws and at the work that had to be done in order to clarify the principles of motion, we find that a considerable amount on both sides is experimental in character. So, for instance, to stick with the First Law, Aristotle failed to have anything like it for obviously experimental reasons. As Whewell says in the second volume of his Philosophy of the Inductive Sciences (PIS2, 589), giving just one example,

Thus with regard to the first law of motion, Aristotle allowed that natural motions continue unchanged, though he asserted the motions of terrestrial bodies to be constrained motions, and therefore, liable to diminution. Whether this was the cause of their diminution was a question of fact, which was, by examination of facts, decided against Aristotle.

Likewise, recognizing that an object moving uniformly in a straight line would continue to do so unless something intervened required some clever experimental work for handling things like friction. Similar things can be said about the other two. So the history of science shows a clear experimental component in the Laws. And this is confirmed by the fact that many disciplines -- chemistry, biology, psychology, history, in short, since we distinguish what is real and what is not causally, all fields that deal with understanding the real world -- use causal reasoning, but they can't simply draw things like Newton's Laws directly from the relevant causal axioms.

On the other hand, the Laws cannot be mere descriptions of experience. For one thing, any such description is by its very nature merely a description of past experience, and on its own gives us no reason to think that things will continue. The Laws simply do not function in scientific reasoning in the way that, say, a report of what happened in a series of observations does. When people draw conclusions using the Laws, they aren't merely saying what will happen if the trend continues; they are stating as a fact what will happen on the information given, and can identify precisely what would have to happen in order to change that fact. Further, one can recognize immediately that there is something abstract about them: there has never been an empirical situation the exact empirical description of which exactly matched Newton's three laws, because no empirical description could guarantee that nothing essential was left out, nor an it agree complete precision and unrestricted statements.

Whewell therefore stakes out a middle way between two distinct positions on Newton's Laws, both of which had advocates in his day. On the one hand, there are those who hold that Newton's Laws are self-evident truths; Whewell doesn't think this position does justice to the actual history of their development, and he rejects out of hand any account of scientific discoveries, laws, or postulates that cannot properly place them in their actual historical context. Descartes had argued that experiment had a place in scientific inquiry, but the place he had given it was only as a crutch, a way to make conceptual clarification easier. Whewell insists throughout that experiment is not merely an adjunct to conceptual clarification; it is a fundamental contributor to scientific progress, and was a fundamental contributor to the development of Newton's Laws, and these two points are historical facts. This is an ongoing concern for Whewell; in the preface to another one of his physics textbooks, An Introduction to Dynamics, he says (ID, x):

It is a peculiar feature in the fortune of principles of such high elementary generality and simplicity as characterise the laws of motion, that when they are once firmly established, or supposed to be so, men turn with weariness and impatience from all questionings of the grounds and nature of their authority. We often feel disposed to believe that truths so clear and comprehensive are necessary conditions, rather than empirical attributes, of their subjects: that they are legible by their own axiomatic light, like the first truths of geometry, rather than discovered by the blind gropings of experience. And even when the experimental foundation of these principles is allowed, there is still no curiosity about the details of the induction by which they are established.

On the other hand, we do have people who claim that Newton's Laws are merely economical summaries of experience; Whewell doesn't think this position does justice to the powerful role they actually play in scientific reasoning, and since his project is in some sense laying out the conditions for the possibility of successful scientific reasoning as we actually find it, he obviously rejects any position that gives the Laws, or any other scientific principles, a weaker character than they actually have in the standard scientific arguments in which they are used. Further, as a matter of history, Newton's Laws were not simply read off of experiment; developing them required considerable conceptual refinement -- indeed, they were a major advance in conceptual refinement themselves, and ultimately made possible further conceptual clarifications that had never before been possible. There is a purely rational element to the development of the Laws, and the history of inquiry into forces shows this quite clearly. As he says in the beginning of yet another physics textbook, An Elementary Treatise on Mechanics (ETM, 1):

The appearance and occurrences of the material world suggest to us the conception of motion, and of changes of motion. Moreover, we find that we can often, by our own volition and exertion, influence the motions of bodies, and occasion changes of motion. We perceive too, that bodies appear to influence each other's motion in the same manner. By considering these occurrences in a general and abstract manner we obtain the conception of Force. Force is conceived as that general and abstract property by which one body causes, changes, or prevents motion in another body.

Abstraction is ineliminable.

Thus the reality, according to Whewell, is that each Law is a union of an abstract necessary principle (derived from the Idea of Cause) and an empirical specification. They therefore do exhibit necessity and universality, but it is a conditional necessity and a conditional universality; the condition itself is determined empirically.

In the First Law, for instance, we start with the causal axiom that no change can take place without a cause. But in order to apply this to the relevant field we first need (1) a reasonably clear conception of a particular kind of change, which requires that we already have done a considerable amount of work making sense of phenomena, identifying stable patterns that can be reasoned upon -- in this case the conception of motion and changes of motion mentioned above. Even this is not sufficient, however. Given a well-formed conception of a kind of change, (2) we can apply the causal axiom to recognize that there must be a cause. Given that we conceive of forces as a particular kind of external cause of change, we begin to get something recognizably like the First Law on this basis, but we can only get to the First Law if (3) we eliminate internal causes of the change. In this case, we need to know (to quote a paper that Whewell appended to later editions of the Philosophy of the Inductive Sciences), "that there is not in the mere lapse of time any cause of the retardation of moving bodies" (PIS2, 579). This requires various kinds of experimental set-up. What one can determine this way is that all discernible retardation effects are due to external causes, and therefore do not depend on time-lapse alone. Strictly speaking, this leaves open the possibility that we could have missed something. It could be, for instance, that the purely time-based change of motion is so subtle it cannot be detected with the instruments we have. It could also be that a time-lapse can only have this effect under very specific conditions that we have not yet discovered. This is element of the Law is one "which we can, in our imagination at least, contradict and replace by others, and which, historically speaking, have been established by experiment" (PIS2, 593); as such, it is potentially revisable. In effect, Whewell is beginning to identify the limits of Newtonian physics, the conditions under which it would have to be revised; interestingly, he began doing it at a time in which there were no serious limits in sight, just research problems, and in which the fundamental principles of Newtonian physics seemed to many to be on the order of logical truths.

Nonetheless it is important to recognize that this intrinsic revisability does not mean that Whewell is giving up the necessity of the First Law taken as a whole. This does not do justice to the power of experiment. While experiments and observations cannot guarantee of themselves that there is nothing left out, they can guarantee that nothing is left out within a certain range of possibilities to a certain degree of precision. Take, for instance, one of the earliest scientific theories to be well-established by observation, the basic astronomical system of Hipparchus, which was put in its canonical and paradigmatic form by Ptolemy. We have gone well beyond this. Nonetheless, the system did establish things that are recognizably still true, for instance, certain features of the apparent motions of the planets, and yet other things that are necessary, for instance, that the apparent motions of the planet can be described, to any degree of precision practical purposes may require, entirely in terms of equable circles. In fact, since the major figures in the Ptolemaic tradition were fully aware that they were only accounting for apparent motion, there's a very real sense in which the Ptolemaic theory is true in the same sense it ever was -- we superceded it not by proving it false in the sense that its advocates accepted it, but by establishing quite precisely its limits so that the whole of the Ptolemaic model of the apparent motion of the planets became yet one more phenomenon to explain, and by developing a theory of the real motion of the planets powerful enough to explain that phenomenon. Whewell, in other words, has a much more robust notion of scientific progress than even many people in his day had, and certainly much more robust than most people have today: it is impossible to imagine Whewell being impressed by Karl Popper or his claims that theories are only falsifiable. On the contrary, they are strictly provable; it just happens that they are only strictly provable for certain conditions and up to certain limits, and perhaps the most important experimental discoveries are those that allow us to discern exactly what these conditions and limits are. So with the First Law. The Newtonians, on Whewell's view, established it for all time. At the same time, it is still revisable, as experiment shows that there are conditions attached to it that we did not realize, conditions which mean that it is only true and established for a certain range of phenomena to a certain degree of precision. There is no need to choose between a scientific inquiry that can establish things with rigor and certainty and a scientific inquiry that is tentative and capable of revision: you can have both at once.

The history of the development of the First Law is very long, with some interesting episodes, but of the three Laws, it is far and away the least interesting, both historically and philosophically. Principles of the same general structure have been around for almost as long as we have records of people trying to explain changes of motion; it took a long time to work out the details, in large part for experimental reasons, but, aside from issues about uniform motion in circles and lines, there's really nothing extraordinary about the course of its history. Likewise, and for much the same reason, it is the least philosophically interesting of the Laws, not really capable of shaking much up: we're used to explanatory principles of this general sort, having had them practically as long as the human race can collectively remember. The Second and Third Law are more interesting on the historical and philosophical fronts, and since Whewell's approach to the Laws of Motion cannot be properly grasped without taking into account both of these fronts, we will in the next post look at some of the interesting features of these two, although we will not by any means be able to do justice to the more complex details.

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