Imre Lakatos’ Proofs and Refutations is a book well known to those who work in the philosophy of mathematics, though it is perhaps not widely referred to. Its general thrust is out of tenor with the foundationalist perspective that has dominated work in the philosophy of mathematics since the early years of the 20th century. It seems to us, though, that the book contains striking insights into the nature of proof, and the purpose of this paper is to explore and (...) apply some of these. (shrink)

In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain (...) that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied. (shrink)

Why did Copernicus's research programme supersede Ptolemy's?’, Lakatos and Zahar argued that, on Zahar's criterion for ‘novel fact’, Copernican theory was objectively scientifically superior to Ptolemaic theory. They are mistaken, Lakatos and Zahar applied Zahar's criterion to ‘a historical thought-experiment’—fictional rather than real history. Further, in their fictional history, they compared Copernicus to Eudoxus rather than Ptolemy, ignored Tycho Brahe, and did not consider facts that would be novel for geostatic theories. When Zahar's criterion is applied to real history, the (...) results are distinctly different. Finally, most of the historical and conceptual problems in applying Zahar's criterion to the Copernican Revolution primarily arise from a deep difficulty in Lakatos's programme: the necessity of individuating research programmes and identifying their originators. 1 Working closely with David Dahl was crucial in developing this paper. Robert Westman's valiant effort to keep me on the historical straight and narrow drastically limited my tendency to a priori historical pronouncements. The Vassar Philosophy Department, John Tompsich, and Jean Sterling were also helpful. (shrink)

The purpose of this paper is to explore various pedagogical tools that facilitate productive and effective classroom discussion in philosophy courses. Adequate preparation for classroom discussion is not merely a matter of doing the assigned reading, but requires students to take careful notes on the reading, to read the text systematically, and to compose questions. Instead of teaching students remedial reading skills, the author suggests a series of assignments (in and outside of class) that help students develop critical reading skills. (...) The author recommends that students hone their engagement with philosophical themes and discussion topics by completing writing assignments prior to class and by working in class with small discussion groups. Teachers can supplement this practice by utilizing the blackboard to outline questions, assignments, and important ideas from the text. The more students engage with the material from various angles, the better they are equipped to effectively contribute to classroom discussion and the easier it is for instructors to facilitate their philosophical growth. (shrink)

There is a common (although not universal) claim among historians and philosophers that Copernican theory predicted the phases of Venus. This claim ignores a prominant feature of the writings of, among others, Copernicus, Galileo and Kepler-the possibility that Venus might be self illuminating or translucent. I propose that such over-simplifications of the history of science emerges from "psychological predictivism", the tendency to infer from "E is good evidence for H" to "H predicts E." If this explanation is correct, then in (...) cases where evidence is less blatant the history of science (and philosophies of science that rely on it) has probably been seriously distorted in a predictivist direction. (shrink)