WHAT IS A MESS?

To conclude, let me say this. If we know what the mess is, as Feyerabend indicates, then we are already on the way to clean it up (or, as he says, we already have). A question well put, to put it otherwise, is half a solu­tion.

Since this is put in a suspicious form of a proverb, or of folkwisdom, let me adapt it, quite ad hoc (in a very different sense of ad hoc) to the accepted framework (quite metaphysical, though in the guise of meth­odological) of the accepted theory of explanation.

It was William Whewell who first described scientific systems as hier­archies of explanation. Yet he stressed that the explanations are far from being stratified. (To the extent that systems were known before, meth­odologists, expecially Sir Francis Bacon, took it for granted that they were stratified.) Today’s explicans, said Whewell, is tomorrow’s explican- dum, but together with newly discovered facts. Hence, the explicandum is part theory part fact. Examples abound: the new magnetic theory of elementary magnetic dipoles (Poisson) explains the old theories (Gilbert to Coulomb) plus facts such as the facts of magnetization by random processes.

There is a problem here: how do we choose a new fact to go with the new theory to be explicanda for a still newer theory? Whewell does not say. He takes it for granted that intuitively we see a connexion and want to explain it. But then, how come we always have a fact handy to go with a given theory in such a fashion?

Things look much better from a Popperian viewpoint. Popper starts - he is in error to insist on this starting point, but this is another matter - from any given testable theory, and says we should try to refute it. He says, if we cannot refute it, we feel stale and then try to explain it by a better theory, i.e.

Here we have a hypothesis about the history of science: we try to find the most universal theories as well as to refute them. Hence, we try to put as many theories together as explicanda, plus their refutations. We have no theory, in Popper’s view, as to which pairs of given theories are best suited as candidates of explicanda for the new theory of the near future. For this, of course, we need a metaphysics. Also, then, Popper does not say which theory and which facts may be paired together. But clearly, he has an obvious feeling that a refuted theory is a good expli­candum when coupled with its refutation.

Thus, we can say, an optimum case is, old explicans and its refutation and... = new explicandum.

And now comes the crucial point. As stated the new explicandum is inconsistent, of course, and so can be explained only by a contradiction and by any contradiction.

Examples abound, but the simplest is Kepler’s Law plus the irregular­ities that, Newton says, were puzzling astronomers in his time.

Clearly there is an answer to my crucial point and it is very forceful and convincing and true. It is also very simple: the new explicandum is not the old explicans verbatim plus its refutation, but the old explicans in some modification or other plus the refutation - and this takes care precisely of the inconsistency in question.

Precisely. Except that the question is, which modification is chosen and how. Here comes my point: a well formulated explicandum, or a well modified one, is half the explicans. Of course, we may try to modify the explicandum differently so as to attain different versions of both explicandum and explicans, thus leading to crucial experiments galore.

This explains a very important and puzzling fact. Every research phys­icist knows that new insights to a problem may be attained by the mere transformation of an equation, more easily a set of equations, from one wording to another.

The answer is that different wordings ‘suggest’ different kinds of prima facie modifications and ‘suggest’ or ‘lead to’ different kinds of explicans.

What this shows is that we often do not know what is our explicandum, that the explicandum often comes in a mess, and that cleaning it up is half the job. Often the job is done in one stroke and the explicans offers the explicandum.

The point of the present chapter was this, often we offer ad hoc hypoth­eses as excuses pro tern. Further, often we offer token ad hoc hypotheses, obviously lame and half-articulated ones, but still acceptable merely be­cause they are understood to be excuses pro tem anyway. Still further, we may offer no ad hoc hypothesis at all, but a mere token for it. Now the most ad hoc hypothesis is the ad hoc modification of a given theory to avoid a given refutation. Often we use a token rather than the ad hoc modification. One way or another, once the refuted theory in modifica­tion plus its refutation are explained by a new testable theory, the mod­ification plus its refutation are explained by a new testable theory, the modification is ad hoc no longer.

In reality, I feel, we are never free of all ad hoc measures. But we keep replacing them, thus keeping our credit high.