CAN REFUTATION BE FINAL?

It is hard to present Popper’s views, particularly on the topic at hand, without regard to current misunderstandings of them. Besides being a bore, misunderstandings are also fascinating as they are excellent diagnos­tic tools for elucidating both popular prejudices and the weaknesses of authors who are regularly misunderstood.

The evidently false allegation concerning Popper’s philosophy is very strange.

Briefly, Popper’s slogan is, we cannot verify a theory, but we can refute it; whereas logic is useless for verification, it is sufficient for refutation; whereas logic never enables us to justify, it does enable us to overthrow. This is one of the few theses of Popper’s philosophy which has been repeatedly quoted and misquoted. Even when repeated without being properly ascribed to Popper, it is easy to detect his hallmark because of a logical mistake he made in this context - one which he has corrected, but which has remained a misnomer for the thesis expounded at the beginning of this paragraph. The error remains widespread.

The doctrine, ‘we can use logic to refute but not to verify’, is known as the asymmetry thesis, or as the application of the modus toile ns. or simply as the modus tollens. Popper states, in a lengthy footnote to the English version of his magnum opus, he was logically confused. Since almost all English-speaking readers are familiar only with the English version of his Logic of Scientific Discovery of 1959, and since almost all German readers of his Logik der Forschung of 1935 are familiar only with the second and later editions which incorporate translations of the English additions, it is surprising that the learned public sticks so stub­bornly to a logical error presented to them along with its correction.

Popper employs deductive logic as a model of science. We begin, according to this model, with universal statements and initial conditions from which we deduce final conditions; the final conditions are either explicanda, old observation reports thus explained, or test statements, new observation statements to be checked and affirmed or their negations affirmed as the case may turn out. Now, let us present universal statements in the modern style, e.g. instead of ‘all swans are white’ let us say ‘for everything, if it is a swan, then it is also white’.

Yet scholars well versed in logic, quite averse to confusing the meta- and the object-language, follow the early Popper here, confuse inferences with conditionals, call the falsification rule by its misnomer modus tollens, and make a mess of things.

Popper’s asymmetry thesis (I should say, Bacon’s), the thesis of the asymmetry between refutation and verification, is simply this: ordinary logic cannot help us verify a theory but it can help us refute it. The asymmetry is logically so trite, it takes but a glance to see it: from an observation report, which specifies the occurrence of some event in some space-time region (to use Popper’s terminology and apparatus), we can deduce the existence of that event somewhere in the universe; we do so by simply replacing the reference to space-time co-ordinates with a more vague expression, such as ‘somewhere’ or ‘there exists’, and such. We can verify an existential statement in this manner, says Popper. But we cannot refute such an existential statement - a purely existential state­ment, as he calls it - as this requires scanning the whole space-time mani­fold, which may be infinite. We can verify some but not refute any purely existential statements. By a simple logical exercise we can show that this amounts to the following claim - we can refute some but not verify any universal statements. Or rather, instead of‘we’ I should write ‘observation reports’. Observation reports may refute but cannot verify universal statements; they can verify but not refute existential statements. End of Popper’s or Bacon’s doctrine of the asymmetry between refutation and verification.

This doctrine of asymmetry was taken to mean that (according to Popper), if we can refute a theory then we can do so once and for all. And, since we can verify its negation, it seems fairly reasonable to say that when we speak of its refutation we have in mind something as final as we mean by ‘verification’.

The critical reader may be disturbed by my discussion of conclusive evidence against some reading of a text by Popper, when the text in question is one concerning counter-evidence and the question is, ‘is the reading of the text correct which reads it to say that counter-evidence can be conclusive?’ I shall not dwell on this point here, though it certainly deserves examination.

The methodical reader may be disturbed by something else: thus far nothing has been said about Popper’s view on empirical justification of universal hypotheses, and I have reported that he says that there is none. Yet above it has been affirmed, without so much as an explanation, that Popper does think some empirical justification of universal hypoth­eses is possible - namely corroboration or a hypothesis having withstood a test. Corroboration is, presumably, the empirical basis of a hypothesis or a part of that basis. The methodical reader is not alone here. Practically all commentators on Popper, casual or systematic, sympathetic or hostile, have been puzzled over Popper’s position on this point - myself included.

Personal evidence aside, the fact that many commentators puzzle over Popper’s theory of support and the fact that some differ about what it says, the fact that even Popper himself joined the band of commentators, is sufficient evidence to allow us to conclude (here again we have evidence justifying a conclusion though not logically yielding it) that in 1959, in the extended version of his opus magnum, Popper’s theory of corroboration was not sufficiently clear.

Much emotion and ink were spilled over this issue of asymmetry between verification and refutation. Popper’s chief opponents, namely A. J. Ayer, Rudolf Carnap, C. G. Hempel, and Herbert Feigl, all de­dared that where Popper sees asymmetry, there is in fact full symmetry: there is, in perfect accord with his own doctrine, full symmetry between verification and confirmation on one hand, and falsifications and dis­confirmation on the other: as long as an observation report may be with­drawn, as he says it may, we have only strong reasons but not conclusive reasons for rejecting a theory, just as for accepting a theory.

No doubt, this sounds blockheaded in view of the fact that logical verification in science is impossible but logical contradiction is possible. Yet Popper’s opponents are right, for the following reasons.

When Popper says that an observation report verifies a purely ex­istential statement he means that we know for sure that if the one is true then the other is also true, or that as long as we accept the one we eo ipso accept the other. This is not verification but entailment. Admittedly, it is quite traditional for followers of Bacon’s or even of Locke’s to say that a theory is verified emprically if an only if it follows from, or is entailed by, a set of observation reports. And Popper here unwisely follows accept­ed usage and declares all corollaries to observation reports verified. In this sense, the thesis of asymmetry between verification and refutation is trivial and when you tell Popper’s detractors that this is what he has in mind - lam reporting now - they look incredulous and say, this is im­possible!

After some labour, I discovered that what they mean to say is this. Disreputable philosophers make assertions which have double meanings: one trite and obviously true, one fantastic and (seemingly) obviously false. Under attack they affirm the trite sense but soon after they revert to the other. Surely, Popper’s detractors say, I am not imputing this vile technique to him.

Here another difficulty arises: it is taken for granted that corollaries from trite theses are trite. Yet such corollaries may solve serious and troublesome problems! Earlier, in Chapter III above, I ascribed to Popper such significant conclusions from a series of fairly trite assertions. An example may be useful. Obviously, the mere acceptance of an observation report, however tentatively, has some theoretical consequences, such as the rejection, however tentatively, of a scientific theory, however well established. Add to this the rule that one should always accept observa­tion reports until they are refuted - which is Popper’s variant of Boyle’s rule - and it follows that though observations cannot logically confirm or corroborate theories, they can lead to scientific revolutions; indeed by these rules they must.

I dissent from Popper’s version of Boyle’s rule. Other rules, it seems to me, including ones accepted by Popper, sometimes permit us to accept a theory - in different senses of accept - and hence to question the asym­metry. Yet there remains the logical fact that an observation report can entail a purely existential statement but not contradict one, just as it can contradict some universal statement but not entail one. This hard logical fact (Bacon’s and Popper’s) remains, and I feel that it is all too easy to ignore it as merely logical. For my part, I think it is both the crux of all critical philosophy, Popper’s and my own included, and its rejection or obfuscation creates a barrier between the critical and the uncritical. At­tempts to break through the barrier lead only to misunderstandings, as we shall see.

III.