CONVENTIONALISTS AND THE PROBLEM OF INDUCTION

The best known theory of science claims that the task of empirical science is to render some theories reliable by empirical means. This theory, inductivism, is easily refuted by anyone who is willing to examine it, yet most philosophers of science currently engage in defending it, and some waste their time attacking it.

There are two extant alternatives to inductivism. The one is conven­tionalism, endorsed by Poincare, Duhem, Mach, Dingier, Eddington, and others. The third view is sometimes called criticalism, and includes chiefly Popper, and his followers to this or that degree, and others in­fluenced by his writings or who independently came to similar views.

Conventionalism views scientific theories as implicit definitions, as mathematical frameworks within which to store empirical information. As such, scientific theories are certain by virtue of being definitions. Already Poincare showed that scientific theories cannot be confirmed by facts. To be able to confirm a theory, he said, you have to be able to refute it; but it is so couched that it can always escape refutation. Take, for example, the law of conservation of energy. It is a part of mathematical theoretical physics which is given empirical content by enumerating the observed kinds of energy. But the list is not complete and so we cannot refute the law: whatever you may conceive of as a refutation of the law I may reconstrue as the discovery of a new kind of energy.

This is a thrilling argument. First, it is, indeed, valid. The only way to refute the law is to create a perpetual motion machine and observe it run, without any sort of refuelling, for ever. No one can stay around long enough to make such an observation, and no one can swear that it worked with no refuelling of any sort.

Suppose we agree, as we must, that the energy conservation law as formulated by Poincare is irrefutable; suppose we also join him in con­cluding that hence it is not confirmable. Yet suppose we are still looking for a confirmable, and hence refutable, version of the same law. I suppose then, we take the obvious step - the one he indeed mused about - and include in the law the finite list of energy-forms thus far observed, and declare the list complete. Now, we can say, our hypothesis is refutable and hence, hopefully, also confirmable. Alas! says Duhem; you can refute the claim that your list is final, or some other subsidiary claim-concerning energy transport, for example - or even the law of conservation of energy itself; but you will never show for sure that it was indeed this or that hypothesis which was refuted; and there we are right where we started.

Duhem was amazingly systematic, I think, and I find that his incon­sistencies can always be eliminated without prejudice to the core of his philosophy. He eliminated all confirmation of scientific theory, he elimi­nated all belief or reliability from science, and with this all the problems traditionally involved with reliability, yet the price was high; Duhem made science lose its major attraction: for him there is no such thing as pure science; what we call science for him was in part pure mathe­matics and in part applied mathematics which included empirical generalizations put in mathematical language. As to the reliability of generalizations, this is another matter altogether: they should be severely tested and found reliable before they are accepted. Poincare, who was more honest about difficulties in his system then Duhem, stressed that therefore he did not succeed to rid science entirely of Hume’s problem or the problem of induction; he said it was a vexing problem but we must learn to live with it. He only rid theoretical science, he flet, of Hume’s problem, by making it part and parcel of mathematics, pure or applied.

We must conclude, then, that there is a serious flaw in the conven­tionalist philosophy, which may indeed be filled in future by solving the problem of induction for empirical generalization: how do we make these reliable?

No doubt, quite a few philosophers these days study induction strictly with regard to empirical generalizations. It is not clear, however, whether these philosophers are inductivists or conventionalists, since even con­ventionalists may acknowledge the existence of the problem of induction in matters experimental. In a recent volume Carl G. Hempel has analyzed Semmelweiss’ study of the source and transmission of childbirth fever as a paradigm of proof by elimination of given alternatives, and this looks fairly inductivist. Yet, as long as the proof is not declared conclusive, the conventionalist cannot object. And, indeed, I see little objectionable in Hempel’s analysis of Semmelweiss, except perhaps his seeing it as a paradigm. This, I think, is what may, perhaps, pin down Hempel as an inductivist proper even in his latest work. I cannot say.

There is little doubt that the conventionalist faces the problem of induction regarding facts. There is little doubt that the only reasonable solution to this problem is the one offered by Mach: take even an em­pirical generalization merely as a condensed observation report. The cost of Mach’s move is, however, enormous; science loses all its predictive force. That is to say, we can project to the future an empirical generaliza­tion, as we can an abstract theory, of course; but in each and every case we have no expectation whatsoever as to the truth of falsity of the predic­tion. This seems simply empirically false. Wittgenstein said early in the century, that the sun will rise tomorrow is a mere hypothesis; I think we all feel that this is not so. Logic tells us nothing about the truth of an extrapolation, yet we all extrapolate, in fact. Hume said, extrapola­tion is a purely psychological matter. We all tend to deny that too.

It is hard for me to say what is the message of Nelson Goodman, the famous philosopher and author of the celebrated Facts, Fiction and Fore­cast. The only reasonable question which seems to trouble him is the one presented in the last paragraph, though I cannot say this unhesitatingly. The question I presented there, however, seems to me very reasonable and interesting, and I shall be happy to learn that it is, indeed, his.

The question however, is largely a matter for rational technology. Conventionalists, who are people who think theoretical science is true by definition, are usually also instrumentalists; that is to say they are usually of the opinion that the aim of science is prediction, that all theoretical science is applied mathematics and thus technology. For them, therefore, Goodman’s question is crucial. This is, perhaps, why PoincarS said, we remember, that the problem of induction is vexing: he could not shake it off.

II.