On method in science.

When examining the writings of those who have thought long and hard about the nature of science one finds the same difficulties appearing again and again.⁵⁹ There is, for the most part, a great enthusiasm that science is progressing in some sense, that we are learning ever more about the world around us, that we are continually solidifying that knowledge, that our increasingly sophisticated technology is testament to the power of science. Yet, when pressed, not only can we not agree on the method of science, we can't quite agree on what science is, or even whether what it talks about is real! Looking over the history described in this paper we can get some inkling as to why this state of affairs persists.

The progress seems real enough, from the question of light's speed being meaningless, to discussion of whether it is finite or not, to increasing evidence for finite speed, to ever `better' estimates of its value. It might seem that scientific knowledge is the conjunction of the facts accumulated so far, that theories live or die according to their verification or falsification by these facts, and that, eventually, the truth will be inferred from the collection of facts.

Kuhn's work [33] describes a framework for this progress - within a scientific `paradigm' normal science is pursued as a puzzle-solving activity, this eventually produces anomalies, anomalies accumulate until a crisis is reached, a new paradigm is somehow introduced , normal science proceeds again, and so on. For example, normal science was pursued within a paradigm where light was without speed, astronomical anomalies began to appear, leading ultimately to a theory where light had a finite speed, whereupon normal science set about solving problems to establish its value. In a more elaborate history, many such Kuhnian cycles would have been detectable.

But what about method? Long ago Aristotle wrote that knowledge, being ``a state of capacity to demonstrate'', required the teaching of the principles of demonstration and so the teaching of science necessarily ``$\ldots$proceeds sometimes through induction and sometimes by deduction''([3] 1139^b19 - 36). But each is tricky to apply - Francis Bacon, that strongest of proponents of inductive method, allowed his perception of the incredible speed at which stars move in their orbit about the Earth to form his inductive base and so concluded that an infinite speed of light was reasonable; no lesser talents than Aristotle and Descartes by pure deduction demonstrated that light could not possibly have finite speed. Using induction and deduction in combination as in the hypothetico-deductive approach is no easier. It appears explicitly only twice in the above history - once by Aristotle to dismiss the argument of Empedocles, and once by Descartes to dismiss that of Beeckman - and wrong in both cases! At various times each of these has been suggested as the method of science. A slightly different tack is to take one such method and raise it to the status of a criterion to distinguish science from non-science. Karl Popper did this in 1934 with the hypothetico-deductive approach. Contemptuous of the widely held view that the use of inductive methods distinguished science from non-science, Popper proposed instead that ``it must be possible for an empirical scientific system to be refuted by experience.'' ⁶⁰ That is, to merit the name scientific a theory must be falsifiable;⁶¹ a decisive experiment which refutes the theory is a crucial falsifying experiment. By this criterion, the geocentric theory of the universe is scientific being falsifiable by any orbital system not centred about the Earth; Galileo's discovery of the moons of Jupiter refuted this theory. Similarly the scientific theories of light held by Aristotle and Descartes were refuted by Römer's determination of the speed of light. This criterion is turned into method by having scientists focus on trying to refute theory; theories are corroborated only by surviving the most stringent of testing.

But normal science is conservative. Crucial experiments are typically only recognized as such long after the fact - Cassini et al showed at the time that Römer's observations could be accommodated by existing theory.⁶² If theories were thrown out when first refuted, the result would be chaos. Instead normal science motors along, sometimes fine tuning its theory to accommodate the new information, sometimes patching the theory with auxiliary hypotheses, and sometimes just tossing the information into the back seat where Popper's refutations become Kuhn's anomalies. As the anomalies accumulate, the ride gets rougher and some members of the scientific community become increasingly uneasy that a crisis is around the corner.

It is here that Kuhn's work is most interesting and most troublesome. Kuhn likens the transition from one paradigm to the next to that of a gestalt shift in visual perception. Like a gestalt shift, a paradigm shift is sudden and without reason. Unlike a gestalt shift, a paradigm shift does not allow the scientist to switch between paradigms; no neutral third viewpoint exists from which both paradigms can be seen - if there were then this would be the new paradigm. This is not to say that the new paradigm cannot be reasoned about and justified to some satisfaction, but rather that it may not be possible to do so by comparing it to the old. For once the transition is complete, the convert's view of the field will have changed - its methods, its concepts, its questions, even its data - and the old paradigm can only be viewed from the perspective of the new. In a word, the two paradigms are incommensurate. Concepts, theory, methods, and data that are meaningful according to one might not be according to the other.

Consider the concept of light. According to Aristotle, light required an intervening transparent substance (like air or water); it could not exist in a vacuum. Things are transparent, of course, only because they contain a `certain substance' which is `also found in the eternal upper body' (possibly aether? itself a concept Aristotle tells us he has changed from that of Anaxagoras⁶³). `Of this substance, light is the activity.' But it is not movement. Moreover, the visibility in the dark of bioluminescent plants and animals does not depend upon light! ⁶⁴ From this Aristotle says he has explained light. Not only is Aristotle's concept different from ours, but to really understand what he means by light we would need to become immersed in his paradigm. Scientific concepts like light change in irreversible ways; some like aether disappear altogether - even after thousands of years of service.

Nor are concepts alone determined by the paradigm. So too are the `empirical facts' - Francis Bacon's data included fantastic speeds for the movement of the stars about the Earth; Glaseknapp demonstrated that different theory produced different `observed' speeds of light. Even relatively raw `sense data' can be dependent upon theory. Soon after Galileo announced the discovery of Jupiter's moons, he had others verify his observations using his telescopes. Many could not see the satellites; those who could see multiple lighted spots could not be certain that these were not artefacts of the new instrument. Only once the optics of telescopes was developed could there be confidence in the verity of the observations.<sup>65</sup> Modern instruments produce observations that are irrevocably `theory laden.'

Paradigm shifts, incommensurability, and theory laden data have all contributed to what Ian Hacking [27] calls ``a crisis in rationality'' - at least for philosophers of science. Is there such a thing as scientific reasoning? Are the entities with which science deals real or are they human constructs? Does it make sense to think that there is in fact an ideal truth to which science might converge?