THE EMPIRICAL SUPPORT OF SOME SCIENTIFIC THEORIES REQUIRES EXPLANATION
This is the way I see the two traditions in contemporary philosophy, roughly the conventionalists, instrumentalists, pragmatists, positivists, and analysts on the one side, and the irrationalists, including the existentialists, on the other; this is how I saw them ever since I became somewhat familiar with the contemporary philosophical scene (I do not claim much familiarity with it).
I have rejected the irrationalists offhand, partly because of my faith in rationality and in science, partly because they recommend arbitrary esoteric religions, from one of which I had just run away. The irrationalist school I rejected after understanding it or at least after feeling that I had understood it; the rationalist school simply did not make sense, to me. Amongst my teachers in science some believed that science is a branch of applied formal mathematics, that the formulas of science are stable and hence important, whereas their interpretations are ephemeral and hence of little value. One of my teachers quoted in class with great approval Philipp Frank’s comparison of applied mathematics to sewing machines and the interpretations of its formulas to clothings which are subject to the whims of fashion. I could not believe that men of science would debunk science so freely and voluntarily. To be sure, the mathematical relations between Einstein’s formulas and Newton’s formulas are mathematically not very interesting, and yet for the technicians they are very important and quite satisfactory. But the intellectual value of the Einsteinian revolution, the new picture of the world that he has created, the exciting questions about the nature of space and time - all these I could not believe my teachers were giving up or viewing as mere fashion. They insisted that the interpretation of a formula is never of great importance; in particular, they stressed, the interpretation of the formulas of quantum or wave mechanics are not important. These formulas, it is well known, are open to both the wave interpretation and the corpuscular interpretation, but either interpretation is rather problematic. Is the lack of interest in them but an attempt to ignore a problem? Max Born, in his attack on Schrodinger of 1953, has claimed that the problem belongs to the philosopher, not to the scientist. The problematic interpretations constitute answers to the question what is, really, an electron? This question, said Born, is entirely metaphysical, and hence outside the domain of science. My teachers in science went further. They said metaphysics always lags behind science, and so it is better ignored. This argument seemed to me to be besides the point, and dangerously erroneous. It is very difficult to develop a scientific theory, and the process of development may start with a new metaphysics which slowly becomes more scientific. It is easy to be tough toward theories which are as yet unsuccessful; it is harder to try and be appreciative of half-baked ideas.2So much for the formafist instrumentalist philosophy of science; as to the inductivist philosophy of science, it looked to me even more puzzling than the formalist philosophy. Its main theses, you remember, are two. First, that scientific theories are highly probable so that they are not likely to be overthrown. I have heard Born estimate in a public lecture the likelihood of a revolution against the quantum-theory at odds of one against one thousand or thereabout. Second, that if, per improbabile, a scientific theory is rejected, its main features are salvaged and reincorporated into the new theory. The first point, concerning the probability of scientific theory, fills the literature. The second, concerning modification, is passed over rather glibly, and for a good reason. What was considered the main features of a theory prior to the revolution, turns out after the revolution to be the less significant features of it. The indivisibility of atoms, surely the central element of Dalton’s theory, has not survived the revolution, and the same can be said about the constancy of mass and the ability of forces to act at a distance in relation to Newtonian mechanics.
If we observe closely any salvage operation, we shall clearly see that what is salvaged is first, all the facts which the old theory had explained, and second, some of the formulas of the old theory which are yielded from the new theory as first approximations. So, at heart, the salvage operation is explicable by a formalist instrumentalist philosophy, not by an inducti- vist philosophy; but the inductivist philosophy yields only high probability, whereas the formalist instrumentalist philosophy yields utter certainty! What use, then, do we have for the theory of probability?The answer to this question concerns positive evidence. If the formal theory is certain, its domain of applicability is not. Indeed, one may view a revolution in science as a revision of the views of the domain of applicability of a given theory. This view was advanced by Duhem, and recently repeated by J. B. Conant and Thomas Kuhn. What they all tend to pass over with no comment, is the fact that when ascribing a domain of applicability to a formula we are making a hypothesis, and that the hypothesis may be supported by striking positive evidence. For example, the domain of applicability of Maxwell’s equations depended on whether he has described correctly the relations between the speed of light in vacuum and the ratio between the units of electricity and of magnetism, and whether he has described correctly the relations between dielectricity and re- frangibility, etc. On all these points Maxwell got answers from his theory that were later spectacularly supported by experiment. Why? How? Was he a magician? Was he a prophet? Was he lucky? These questions are most intriguing and the answer to them is less easy to come by than one imagines when one simply rejoices in the success of science instead of asking how it comes to be.
The fact that scientific theories are so spectacularly supported by positive evidence was explained by Bayes, Laplace, Whewell, Helmholtz, and many other thinkers, on the following lines.
There are two possible explanations of the existence of positive evidence: first, that the theory it comes to support is true, and second, that though false, the theory agrees with facts by accident. The more improbable the evidence is, they said, the less likely it is that it fits the theory by accident and hence the more likely it is that the theory is true.This argument, whether correct or not, belongs to the theory of probability or of games of chance or of relative frequency. Therefore, if the argument is correct, then he who endorses only theories which fit the facts well will be less often in need of changing or modifying his view than he who endorses testable theories which were not yet empirically tested; and the more improbable the evidence in favour of given theories, the less likely it is that they be overthrown or modified. This is the. corollary from the probability theory of positive evidence which, historically, gaye it its great importance.
Now, this corollary explains why in the 19th century there was little discussion about the difference between certainty and high probability. If we wish to be right as often as possible we aim at high probability, preferring certainty; but we do not complain about having attained only high probability any more than the owner of a vending machine whose machine accepts true coins and rejects false ones correctly with the exception of one in one hundred or so. Subsequent to this, we may see that the modern idea that the Einsteinian revolution has proved that we can aim only at high probability but not at certainty, is not as much of a change as was claimed. Further, the spirit of the 19th-century philosophy of science viewed any need for modification as a defect, quickly to be eliminated. It fully agreed with the probability theory of positive evidence which speaks only of the likelihood of a theory to be true or false, not to be in need of big modifications or small ones. Once modifiability is introduced, there is no knowing how the probability theory requires from us to treat positive evidence and its import.
It is thus not surprising that when speaking of modifications philosophers seldom speak of the probability of the need for modification. The classical theory of probability, at least, applies only when every theory which is in need of modification is considered to be false. Classically, then, no matter what probability a theory has, it also is either true or false: amongst the probable theories, the majority are true; and amongst the improbable ones, the majority are false. It is this classical rational readiness to judge the truth of hypotheses by the strictest standards that many contemporary philosophers dislike. These contemporary philosophers wish to use probability not in the sense of likelihood to be absolutely true but in some weaker sense of truth; probability is often viewed today as truth-surrogate.3This change is not very surprising: the corollary to the classical theory which tells us that he who believes positive evidence is seldom in error, is false. Take any 19th-century thinker who believed only well-supported theories - William Hyde Wollaston should qualify very well - and ask how many of his beliefs are literally true. The answer is, of course, that none of them will pass today without some modification. This is, I suppose, what became obvious to some philosophers thanks to Einstein, and this is why they have tried to provide a new sense to the notion of the probability of a hypothesis, as I said. For my part, I still wonder, how were false theories such as Maxwell’s so fantastically supported by empirical evidence? Was it really a most unlikely coincidence? It is very tempting to say that a miracle happened - perhaps to reward men of science for their efforts, perhaps to encourage them to make further efforts. How else can we explain the facts?
To my surprise I find this a most unpopular question. Even Popper seldom faces it. Most scientists and most philosophers just rejoice in having positive evidence; perhaps they think that asking questions spoils the fun.
A young colleague of mine has quite recently chosen, for some purpose or another, to discuss cases of happiness which are obvious and undiluted; he chose meeting one’s mother in the airport, and the confirmation of one’s hypothesis. When I read that I was grieved; I can well see how obvious and undiluted a case of happiness the meeting of one’s mother after along absence may be; but is it so incredible that one may hold a false hypothesis and tragically have it empirically supported again and again just when it would be so wonderful if he had given it up and tried new avenues? Is confirming one’s hypothesis really as straightforwardly desirable as meeting one’s mother after a long absence? Undoubtedly, people do get impressed by some positive evidence, and rightly so; also, it is a fact that they would all too often put their faith in a theory impressively supported by evidence; but is it so obvious that they are right? Once people believed in miracles as a matter of course; once people believed in the written letter as a matter of course; nowadays the desirability of believing in theories with empirical evidence supporting them is a matter of course. What of it? At all times and places some people believed in some omens and signs or others; does this prove anything? Is one faith so obviously much better than the others? Before we can leave this question, we may find it not so outrageously eccentric that someone wishes to know why is empirical support more imposing than miracles. But I guess I am crying out from the depth of my personal prejudices, which I am quite ready to expose.III.