BOOTSTRAP OPERATIONS IN TESTING
So let me proceed to my own view of the matter. In general, whether within pure science alone or within science and rational technology taken together, I think corroboration is no matter for belief, yet it has an important role in both.
Very briefly, we corroborate working hypotheses, and auxiliary hypotheses, when we calibrate our instruments in order to blunt the edge of Duhem’s thesis: calibration has to be successful before tests can proceed, or else we declare the results of the test a priori invalid and worthless. And the corroboration with uncalibrated instruments means that the instrument is probably not stable enough and not precise enough to refute the hypothesis tested; and so we use the instruments only if they survive the onslaught, if we corroborate claims for their stability. In other words, we try to make it at least a bit hard to blame the instruments for undesirable results of any test prior to that test. This is why we have always an a priori idea of which hypothesis to blame if the experiment will refute the prediction it comes to test. But this does not mean that calibration excludes all possibility of blaming our instruments; and so, this does not invalidate Duhem’s argument. The reason for this is obvious: calibration is never complete; but it explains the fact that Duhem’s thesis is so abstract: in concrete situations we take measures to exclude it.To show that calibration is never complete we may take actual cases where successful calibration not only permits using a Duhemian ploy of saving the tested hypothesis at the expense of the auxiliary hypotheses, but also where this was done in history. I have in mind bootstrap operations, in particular.
It is convenient to take bootstrap operations because they exclude the inductivist view of science a priori. Inductivism does, of course, permit and even encourages the use of one theory for the purpose of discovering another.
But the inductivist views the use of a theory in discovery not as bootstrap - it is for him climbing a mountain (or in special instances climbing a ladder). The mountain climber (and the ladder climber) makes sure to the best of his ability that a step he is going to take will put his forward foot on solid grounds. Of course, the mountain climber can never make absolutely sure that his next step will be safe until he has put it behind him. Yet, his success in making any step rests on the stability of the place on which he has rested his foot in the previous step. In a bootstrap operation the opposite seems to be the case: the support cannot sustain one well enough, yet one uses it just long enough to make the next one. Literally, of course, the image is exaggerated to the point of impossibility - we cannot pull ourselves by our bootstraps alone - yet the allusion is to ever so many situations which are notoriously precarious yet which we voluntarily enter in the hope to exit very quickly from, and into a better position than ever before. An example may be walking fast in a swamp or a speculation in a bull market by a penniless customer who, however, has enough credit to speculate; the customer resells at a higher rate before he has to pay. An image may be that of treading water; but this only keeps our heads above water until rescue comes and is so not a sufficiently adequate image.Examples of bootstrap operations in science abound, though historians of science have not yet studied them as much as they deserve. The simplest examples are indeed theories used to calculate results which conflict with the very same theories in order to eliminate the conflict. The most obvious examples are the steps leading to the personal equation; - the equation came to eliminate discrepancy between theory and observations (without the theory there would have been no discrepancy discovered) - or Roemer’s theory of the speed of light which comes to rescue the Keplerian theory of Jupiter’s moons; or Bradley’s theory of abberation which rescued Newtonian celestial mechanics. The bootstrap operation is in the lact that these theories - Kepler’s or Newton’s - could not be developed without the use of some prior optical theories, which they now helped to replace! Better optics leads to better astronomy and vice versa.
A still simpler example would be the use of the perfect gas law to develop the kinetic theory of gases, without which Van der Waals could not possibly have developed his replacement of the perfect gas law. Another example, somewhat less familiar, would be the use of very classical optical theory and radiation theory to develop astrospectroscopy to the point it could be used as an aid to the development of quantum theory. The clearest and most startling example, however, is something like Newton’s use of Kepler’s third law to establish the constants peculiar to the solar system (masses of planets) so as to be able to calculate the irregularities, i.e., the deviations from Kepler’s laws (all three laws, that is) which the system exhibits. Or, to take another and more troublesome example, on occasion we use the old (sometimes relativized) quantum theory to identify spectral lines which we measure exactly, and compare the results of the measurement with the new quantum theory; but when there is a discrepancy we may, and at times do, alter the identification of the line under study. If these kinds of practice do not feel like a bootstrap operation, if all this does not give the logically minded reader a slight shudder, then that’s the end to the problem: he can just as well ignore it or delight in his own solution to it as the case may be.What is felt to be needed here, quite intuitively, is both a clarification of the logic of the situation, and an added measure of constraint. We may feel some fear that Newton contradicts himself when using Kepler while planning to calculate the deviations from Kepler. This is no catastrophe to begin with, but a challenge all the same. It is now agreed by all and sundry that Newton’s calculus was not in order, and that it has meanwhile been successfully put to order by his nineteenth century successors. Perhaps the same holds for his astronomy. This has not been shown to be the case, but a suspicion is lurking all the same. And even if there is no inconsistency, there may still be too much arbitrariness in the whole enterprise.
If we can alter almost any part of our system, then any change seems ad hoc. If we can change the identification of any spectral line, then what good is spectroscopic test? Even when no change is required, the attractive taste may have gone. And, of course, we have a purely-logical argument to shake confidence in the situation. We have tried to blunt Duhem’s thesis by confirming our auxiliary hypotheses; but, Duhem would retort, in order to do this, the auxiliary hypotheses must be refutable. Are they?Here we see most clearly the need for further constraint. Yes, we sometimes overthrow our auxiliary hypotheses, sometimes we rescue them with the aid of further auxiliary hypotheses. Are these not cycles on cycles and fleas on fleas? This must make us feel quite uncomfortable.
Take the auxiliary hypotheses which go into any spectroscopic calculation (except very few of the very easiest). Once you realize that a quantum spectroscopist can alter his identification of a given spectral line if he fails to calculate its characteristics (mainly wavelength and intensity, but also spread), you wonder how much trust you put in his results on occasions when they do fit. It seems as if he cannot lose but only win. It seems as if his ability to win does not reflect on the trustworthiness or otherwise of his specific theory. It seems as if the quantum spectroscopist has too much leeway. Too much for our taste, that is.
IV.