HAS A NEW SIGNIFICANCE

The Duhem-Quine thesis is, strictly speaking, a point of formal logic, and as such both uncontested and incontestable. It is this: When a conclusion in a valid inference is false then all that logic can tell us in general is that one of its premises is false; logic cannot tell us generally which of the premises is false.

A scientific prediction is one deduced from an explicit hypothesis, which prediction we can prove or disprove. This is, by definition, a prereq­uisite of a scientific prediction, and we can thus see a symmetry at on point in science, between proof and disproof. We can see that the symme­try is only limited to this case. For, it seems as if, clearly, when we prove a prediction to be true we do not, thereby, prove the hypothesis from which it follows. This is the difficulty or rather the impossibility, encountered already by Hume if not earlier. There exist no way by which a prediction, if proven, leads to the proof of a hypothesis. In particular, we cannot say, if a prediction follows from two hypotheses, we make another prediction to decide between the two. If a prediction would follow from a finite number of alternative hypotheses than perhaps by a process of elimination we could prove one hypothesis by proving ever so many predictions. But, in logical fact, there are always infinitely many hypotheses from which we could have deduced the same prediction or set of predictions.

We see here a strange situation. Apparently we have a case of symmetry regarding a prediction: it can be proved if true and disproved if false. Apparently we have a case of asymmetry regarding theory: we can dis­prove a false theory by disproving a prediction based on it. Yet at once it looks perhaps possible to turn on occasion a disproof into proof and thus restore the symmetry in part.

The erroneous idea that we may have in science a finite set of possi­bilities which may all be refuted except one, and thereby establish that one - this idea has allured many thinkers. The general idea of a finite set of possibilities is known as the principle of simplicity, or of conformity of nature, or of limited variety. The reason that this idea seems so promising is a simple illusion; thought we have to accept it on occasion, as we must, for example, when making a chemical analysis on the basis of a finite known list of elements. In this case we can employ the procedure pro­posed, which is known by the name of induction by elimination; when the number of contesting hypotheses is small - two or three - the name given to the process is crucial experiment, or experimentum crucis, which originally seems to have meant the experiment of the crossroad. What Duhem’s thesis amounts to, we shall presently see, is that there is no crucial experiment (not even in chemical analysis, he said).

This sounds absurd. It is hardly conceivable that Duhem should prove the impossibility of something which happens regularly in science; when we know that Eddington’s eclipse observation was a crucial experiment between the Newtonian and the Einsteinian theories of gravity, when we know that the observations on Brownian movement were crucial between atomism and its opposition, when we can offer lists of crucial experiments in the history of quantum theory, how can Duhem say that these do not exist?

Unfortunately, the label ‘crucial experiment’ is misleading.

What Duhem said was this. We deduce a prediction from a large set of hypotheses. As we cannot prove which of these hypotheses is the culprit which has led to the false prediction, when we eliminate what we think is the culprit we forfeit our hope for a proof. We may have eliminated the wrong hypothesis. Thus, in chemical analysis we make use of certain hypotheses, often such hypotheses as the one telling us that the chemical atom is stable, or that the inert gases so-called are that, etc.

What Duhem contends here is that when making a deduction from allegedly one hypothesis to one prediction, we actually employ the whole of science. If the hypothesis is concerning gravity we use optical instru­ments to test it, thereby applying a theory of light and heat at least.

This is an extra-logical component in Duhem’s thesis, but it is one which is not worth contesting. We can be finicky and search for, perhaps, even find, perhaps, a prediction which does not involve some part of science or another. The search is not worth persuing. We may well agree with Duhem wholeheartedly that there is no proof in science of any kind, and thus no proof by any crucial experiment; that even disproof is only a very non-specific process since making it specific, i.e. putting the blame on one specific conjecture, is itself not absolutely free of conjecture (i.e. a little conjectural or a little pregnant with conjecture).

Once we are free of the desire to prove we can ask, does Duhem’s thesis have any further insight to offer? I think it does. Let us examine Popper’s view of science as conjectures and refutations. As it stands, Duhem’s thesis has little to offer regarding it: Popper’s theory is not concerned with proof or establishment, and is not averse to making any conjecture, including a conjecture which puts the blame for a given refutation on this hypothesis or that.

When the polarization of light through reflection was discovered, in the early nineteenth century, it was deemed the deathblow to the corpus­cular theory of light and the proof of the wave theory. It sounds funny but with waves being continuous and particles discrete, it was not inter­ference or even polarization or any continuous aspect of light, but rather the fact that polarization through reflection is discrete, which was so hard for the corpuscularian to explain. In a desperate attempt Jean- Batiste Boit, a celebrated 19th-century man of science, suggested to quantize the spin of the light particle, in order to account for the facts. His suggestion was ignored off-hand, and the wave theory became established. This suggestion is part and parcel of the new quantum theory - of quantum field theory to be precise.

To return to Duhem, if we really employ all of our science in every prediction, how do we come at all to the situation where, normally, we have an idea that we are testing one hypothesis? Granted, that post-hoc we can always say, it is doubtful which hypothesis has collapsed, we can still say, almost always, which one was under attack! How is it that chemical analysts use crucial experiments and doctors use differential diagnoses without hesitation?

When Jean-Servais Stas refuted Prout’s hypothesis which says that all atoms except hydrogen are compounds of hydrogen, he did so by showing that the atomic weight of chlorine is 35.55. He was in error. His result does not reflect the falsity of Prout’s hypothesis, but the falsity of Dalton’s hypothesis which says, all atoms of one element have the same weight. They do not: two atoms of the same elements may have different weights; they are then called isotopes. And when isotopes were discovered, and Aston constructed his masspectrograph and showed that some chlorine weighs 35 and some 37, an attempt was made (by Niels Bohr) to revive a version of Prout’s hypothesis (allowing as elementary particles both protons and electrons).

Duhem had no interest in refutation. He exhorted people, as all good philosophers since Bacon did, not to ignore refutations, not to become dogmatists. But the very exhortation shows a mistake: we exhort people to act correctly against their inclination; but we need not exhort those who look for a discovery to pay attention to a refutation any more than we need tell a hunter who looks for meat not to ignore the animal he has shot. If Popper is right and discovery is the same as refutation, the question becomes, how does the experimenter decide which hypothesis to track down? And why do we need the exhortation not to revive a dead game?

For the second question we may offer an answer by indicating a com­mon and standard error. But for the first question we cannot expect a full answer: hunting involves resourcefulness and intuition, it is not as stan­dard as a repeated error and so it has no general explanation. But there are some general and fairly loose rules conducive to, though not insuring, good huntint, and these may go a long way towards an answer. This chapter goes after these rules. Roughly, I shall try to argue, since confirma­tion is failed refutation, we go on failing until we succeed: we temporarily strengthen one hypothesis and thus think - often erroneousy but well enough for the time being - that we have succeeded at last to refute the previously confirmed theory. When this proves a mistake, the catch proves to be bigger then expected: we have a revolution going.

I.