CONCLUSION

Thus far I have treated corroboration without going into detail except to say it is a failed refutation. Popper has written a few memoirs on the specific qualities of corroboration.

A theory-like hypothesis is rich in content in its very generality; a fact­like hypothesis seems very ad hoc when judged as theory-like; this is why it is taken seriously only ad hoc, only to justify a stated observation report!

An ad hoc hypothesis is less contentful, and so, according to Popper, less testable. Yet, its very arbitrariness makes it improbable that it will be asserted, taken seriously, etc. This accords with Hume’s criterion: whatever is improbable that it be asserted without being an observation report, but probable as a result of observation, is taken as an observation report. (Hume, within the tradition, meant taking a statement to be an observation report to be the same as believing that statement to be true; this, we saw, is an error.) The very ad hoc character of the observation report which makes it not improbable enough to qualify as a theoretical hypothesis, is what makes it, when reported, qualify as an observation, or as fact-like hypothesis; without this quality a report made on the witness stand is rejected as eyewitness testimony, though it may be endorsed as expert witness testimony.

Examples abound; let me mention a few striking ones: the alleged fact that only iron has magnetic qualities, that there is a symmetry between negative and positive electricities, that all planets rotate in the same direc­tion. Each of these examples led to far reaching theories, and each of them has been refuted - but not easily and not at once.

Often, to conclude, the ad hoc nature of a fact-like statement is rooted in the theoretical background against which it is couched; given a different theoretical background and it fully falls into place, as the expression goes. If an observation report is at once a corollary of our scientific theory, then it is unproblematic. If it conflicts with our scientific theory, either we reject the theory or try to find an excuse for not rejecting it. When, however, a small theory which well integrates in our theoretical background is attacked by a well corroborated fact-like theory and all its defences are refuted, then a revolution may be under way. Such events may be rare, but they are the more intersting ones. At times we alter our whole theoretical outlook around a rather fact-like theory which then gets refuted. We then look silly from any viewpoint except that which takes the process to be a bootstrap operation!

appendix: precision in theory and in measurement

An intuitive idea concerning degrees of precision is widely accepted, and it is that we increase precision of theories by paying attention to ever decreasing orders of magnitude of measurements which we incorporate in these theories. We increase precision of measuring or of predicting measurement of length, for instance, if we pay attention not only to centimeters but also to millimeters, microns, angstroms, and so on. And our theories are precise to centimeters, then to millimeters, and so on respectively. The idea is that increased precision is the process of capturing a point within nested intervals, and that this is reflected both in experi­mental and in theoretical progress.

That this idea is popular amongst physicists in this or that variant is an empirical fact. It is also a fact that many physicists, e.g. R. Schlegel, in Completeness in Science, consider Heisenberg’s principle to be a law limiting the degree of accuracy which will ever be achieved; consequently, some part of physics - containing both theory and observation-reports - is not only here to stay but also never to be superseded. It sounds strange that after the Einsteinian revolution and all that, scientists may view any part of science as final, but I think I may claim here to be making an observation of a fact, strange as the fact may be.

The most obvious criticism - valid or not, this remains to be seen - of the view of increased precision of theories as decreased order of magnitude of imprecision of measurements (observed or predicted) is this: Evey result of measurement can be amplified. The obviousness of the previous statement makes one puzzle whether it is relevant to our present discus­sion, and, on the assumption that it is, how could anyone overlook it. The puzzle will disappear once it is noted that the controversy is not concerning the amplifiability of small effects but concerning its relevance.

Amplifiability was used by Schrodinger to argue that quantum theory cannot be a complete description of nature because a solution to a quan­tum equation is often a weighted sum of possibilities of an outcome of a quantum process and the outcome may be amplified to kill a cat so that the solution would be amplified to a weighted sum of the possibility that in the end the cat will be dead and the possibility that it will remain alive, but only one of these two will be realized. The point of Schrodinger’s argument is that the statistical interpretation of Born may render the weighted possibilities into relative frequency in the small but not when one member of a random sequence is isolated and amplified. Whether Schroedinger’s criticism is valid or not is hard to say; the answer to it is that, upon repeating Schroedinger’s thought-experiment, we get a relative frequency of dead cats but no prediction concerning any individual mem­ber of the sequence, just as in life-insurance. (We assume that probabilities are weighted possibilities.)

This point was taken up by Reichenbach in his Philosophical Founda­tions of Quantum Mechanics to dismiss the idea that possibly the world is indeterministic in the small but deterministic in the large. Doubtless this criticism is valid and, indeed, no one has ever seriously advocated the thesis Reichenbach criticizes. The question whether Schrodinger’s criti­cism is valid, then, depends very much on whether indeterminism may be viewed as a complete view of nature in the sense that only a part of the future is predetermined by the laws of nature and the function of science is to be able to predict in principle the whole of that part and nothing else. This idea is that the nested intervals converge not to a point but to an elementary interval which is the objective limit of precision in physics. What exactly is this interval is hard, if not impossible, to say, as Einstein, Podolsky, and Rosen have ventured to argue.

So much for the quantum aspect of the ideas of increased precision of theories as decreased order of magnitude of imprecision of measurement and the criticism of it from amplification.

That this is so is obvious from the fact that we do increase the order of precision of observation without altering ourselves at all as instruments of measurement. All increased precision of observation beyond a rapidly achievable limit is achieved by amplification. The amplification which was historically important was optical magnification, whether of the op­tical instruments in question or of the scale on which they were mounted, etc. But the limit of magnification is that of resolution power, and resolu­tion power is a wider concept of a degree of precision available than magnification; for example it is an essential factor in spectroscopy which can hardly be called optical magnification. A little reflection will show that any increased precision claimed in any field of micro-measurement includes a claim concerning resolution-power and amplification of sepa­rated parts within the limits of the claimed resolution-power. It is a known fact that all micro-observations are beyond the reach of the untrained whatever his eyesight, etc. This shows how very theoretically loaded such observations are, and the kind of theory involved concerns the objects whose ‘images’ are separated and separately amplified. Without theoret­ical instruction we cannot identify the reading of an instrument as an amplified micro-effect.

There are amplifications that have nothing to do with optics. A crucial experiment between Galileo’s theory of gravity (a=g = const) and New­ton’s (a=const 1/r²) within eighteenth century conditions, is possible by amplifying any phenomenon of gravitation by sheer repetition; a pen­dulum clock adjusted on one altitude will be unadjusted according to Newton but not according to Galileo once it is shifted to a different altitude or geographical latitude. And however small the maladjustment might be, it would be detectible over a sufficiently long period (if the instruments’ resolution-power permits) - as indeed it was (and to Newton’s advantage of course).

Thus, the amplification does occur under conditions specified by a theory. Theory makes us identify (a) a micro-effect amplified by unusual instruments (pendulum clocks) with (b) macro-effects allegedly magnified by unusual natural (lunar orbit) conditions. The suggestion, therefore, that within a given limit of accuracy a theory still holds even when super­seded is false, since the qualification concerns not so much the limits of accuracy but their dependence on certain conditions which may vary naturally or artificially. Classical statistical mechanics holds within limits of accuracy which depend on temperatures and which are thus very wide almost everywhere - the notable exception being those parts of the earth’s crust which are occupied by laboratories. Newtonian mechanics holds in the same way where the limits of accuracy depend on relative speed and strength of gravitational fields.

Even when the effect in question is naturally small in our environment, we may fill our environment with amplifiers and thus render the old theory into a less and less useful instrument of measurement and prediction in daily life; or change our environment by travelling to parts where the conditions for the imprecision of the once accepted theory become increasingly common.

Professor Phillip Morrison has commented on the above saying that precision may apply to totally’different kinds of widening of our field of observation, such as rendering ultraviolet light visible. Not only is there the idea of precision in the mode of rendering ultraviolet light visible but also the degree of precision of a theory may be reassessed after such conversion. It is no doubt the case that the theory of increased precision via nested intervals does not easily or fully apply there. My point pre­viously was merely that where the theory does apply it applies only under strict conditions to be described by a superseding theory and he has ex­tended it to cases where the theory should apply but fails to.

The current ideas on precision, then, have to be replaced; precision is only deceptively obvious, and to handle it more adequately we have to relativize it and make it more dependent on specific conditions.

Popper has claimed that degrees of precision are monotonic functions of degrees of falsifiability. He has also relativized his idea of degrees of falsifiability, relative to given fields of potential falsifiers. It follows that he has relativized degrees of precision. I do not know, however, how satisfactory this implicit relativization is, and I doubt that it is entirely so; as I shall argue in Chapter IX below, both his theory of degrees of falsifiability and his view of degrees of precision as monotonic functions of degrees of falsifiability may be questioned. In particular, since the degree of precision of a given theory can be adequately described only with the aid of a superseding theory, the degree of precision of the super­seding theory itself can be said to be higher only when a crucial experi­ment between the two can be designed, either by devising new means of separation and amplification or by constructing or discovering those con­ditions under which, the new theory tells us, the old theory becomes highly imprecise.

The above observation may be obscured by the fact that observations are often stated within limits of accuracy in reports which refer to current theory but not to preceding theory. The limits of accuracy in such cases are sometimes the limits of the accuracy available to the observer. These facts indeed sometimes run counter to the above observation. The ques­tion is whether highly precise observations of this kind are of any value. The answer to this question, I think, cannot be given a priori on philo­sophical grounds. No sets of observation absolutely fit the theory at hand, and when the fit is considered close enough and when not is relative. In particular, a new theory with a better fit may be triumphant for a while and then people may worry about the fit not being perfect and look for a still better theory, etc. So the same data may support the same theory in the old situation and condemn it in the new. There exist historical instances to this case, such as from classical chemistry, from modern spectroscopy, and from general relativity.

Thus, when an observer highly increases the degree of accuracy of observation while referring only to one current theory, his observations may be useless if the fit is judged good enough, or useful if he calls the fit into question - quite in accord with the above observation of the relativity of degrees of accuracy. For instance, when the atomic weight of oxygen was deemed close enough to 16 there was neither any point in increasing the accuracy of the measurement of its deviation from 16 to further decimals nor even any point in isolating its isotopes to find the more precise atomic weight of the predominant isotope. Things changed dras­tically, of course, when 16 was not good enough any more because nuclear physics should yield the exact deviation from this weight (when the mass of a proton is taken to be 1).

The above example may indicate that precision is not a value in itself but a tool for furthering the ends of science from day to day and, more generally, it may be useful in constructing interesting explanations and in testing them. The sentiment expressed here is broadly the same as that expressed by Popper, but the details may differ. It seems that Popper equates explanation and testability, if not in his Logik der Forschung then at least in an appendix to the Logic of Scientific Discovery where he presents explanation (E) as monotonously dependent on confirmation (C) which, again, is monotonously dependent on testability. Were tes­tability, explanation, and precision all monotonously interdependent, precision would be much simpler.