John Dupré: The Disorder of Things

Falsificationism

The central difficulty for falsificationism comes at the very beginning, with the process of inferring empirical conclusions from a theory and attempting to falsify them. The problem is that such inferences will typically require vastly more by way of premises than merely the theory that is supposedly being exposed to possible falsification. But then it is quite unclear what can be concluded from a negative result to an experiment. Perhaps the theory is wrong, but perhaps some other of the many auxiliary premises is the culprit. Given the likelihood that scientists will have strong commitments to the theories they devote their professional lives to investigating, it seems entirely reasonable that they should seek out any other possible explanation of an apparently anomalous result before rejecting their theories. But if that is true, and if they will almost always have alternative possibilities to investigate, it is hard to find any plausible role for the goal of falsification in actual scientific practice. [...]

A classic case is that of the inference by Leverrier and Adams for unexplained irregularities in the orbit of Uranus to the existence of the planet Neptune. [footnote 7 omitted HS] These irregularities were not, needless to say, taken as refuting Newtonian mechanics, but rather as motivating a search for the erroneous assumption, a search that culminated in the prediction of the existence and orbit of Uranus. More telling still, Leverrier also noticed deviations in the orbit of Mercury. But here no such explanation was found prior to the replacement of Newtonian with relativistic mechanics. Thus this latter case proved in the end to constitute, by our current lights, a genuine falsification of Newtonian mechanics. But no one took it as such until a new theory that actually predicted the phenomena in question had been developed as a serious rival to the Newtonian account.

John Dupré. 1993. The Disorder of Things. Cambridge MA: Harvard University Press. Pages 230-1.

Mathematical Methods in Science

Most obvious of such aspects [aspects of scientific work that greatly amplify epistemic prestige HS] is the enormously enhanced respect that accrues to parts of science that give a central role to mathematical methods. It is not at all my aim to banish mathematics from science. Mathematics has a wide range of uses in various scientific enterprises, many of them entirely legitimate. The probabilistic views of causality discussed in the preceding chapter, for example, reinforce the importance of the mathematical analyses of statistical data. And large parts of physics and physical chemistry appear to have proved amenable to systematization in terms of mathematically often quite precise laws. But the extension of this approach to many areas in which no such empirical successes can be claimed is part of what I refer to abusively as scientistic.

That this aspect of scientism -- perhaps we should call it "mathematicism" -- is a sociologically significant contributor to scientific prestige seems hard to dispute. It is again perhaps best illustrated by the preeminent influence of economics, with its characteristic appeal to abstruse mathematical models of little empirical worth, among the social sciences. A number of factors probably contribute to this situation. Most relevant to my general theme, more or less inchoate commitments to reductionism surely play some part in the continuing role of physics, and indirectly its mathematical methods, as the paradigm to the methods of which other sciences should aspire. [footnote 1 A phenomenon often referred to as physics envy. [...]] More broadly still, believers in an ultimately orderly universe often suppose that mathematics provides the language necessary to capture such metaphysical order. Straightforwardly sociological factors surely also contribute to mathematicism. It seems very plausible, for example, that mathematical complexities the mastery of which requires substantial training, by setting up barriers to entry (to borrow a concept, this time, from economics), serve to increase the financial and other rewards that accrue to membership of scientific professions. Or even more simply, a mystifying veneer of mathematics will sometimes serve to conceal the banality of what is offered as scientific wisdom. At any rate, the omnipresent neo-Pythagoreanism of contemporary science is surely not adequately justified by its empirical successes. If it is motivated by any legitimately theoretical considerations, I suspect that these amount to some kind of commitment to a universe amenable to one systematic and orderly description; a universe in the existence of which, I have argued, we have every reason to disbelieve.

John Dupré. 1993. The Disorder of Things. Cambridge MA: Harvard University Press. Pages 223-4.