Kuhn vs Popper - About James H. Collier

Lakatos believed he had improved on Popper’saccount by showing how – at least in mathematicalinquiry – the discovery of error is followed bysomething more than the simple removal of thefalsified theory. Rather, in the process that Lakatoscalled ‘lemma incorporation’, a counter-example toa theory is retransmitted as a boundary conditionfor applying a successor version of the theory. Thus,error elimination is made into a genuinely collectivelearning experience, whereby a prima facienegative episode in the theory’s history becomes afeature of its logical structure.Moreover, from a pedagogical standpoint, thisprocess is better seen as dialectical than strictlydeductive. Dialectics lays bare patterns of reasoningthat are normally mystified by mathematicians’appeals to the ‘intuitiveness’ of a proof’s axiomsand lemmas. The social, indeed rhetorical, dimensionof mathematical inquiry is therefore finallyexposed. Lakatos would have us focus more on howone from among several competing sets of axiomscame to be selected than on how, once selected, thisset manages to entail a set of conclusions.Why does Lakatos’ preoccupation with dialecticsmatter in the Kuhn–Popper debate? The answer isencapsulated in what analytic philosophers call theunderdetermination thesis – the idea that any body ofevidence can be explained by any number of61