Thomas Kuhn's shadow hangs over almost every field of intellectual inquiry. His book The Structure of Scientific Revolutions has become a modern classic. His influence on philosophy, social science, historiography, feminism, theology, and (of course) the natural sciences themselves is unparalleled. His epoch-making concepts of 'new paradigm' and 'scientific revolution' make him probably the most influential scholar of the twentieth century. Sharrock and Read take the reader through Kuhn's work in a careful and accessible way, emphasizing Kuhn's detailed studies of (...) the history of science, which often assist the understanding of his more abstract philosophical work. These historical studies provide vital insight into what Kuhn was actually trying to achieve in his The Structure of Scientific Revolutions: an endeavour far less extreme than either his 'foes' or his 'fans' claim. In the book's second half, Sharrock and Read provide excellent explications, defences and, where appropriate, criticisms of Kuhn's central concept of 'incommensurability', and tackle head on the crucial issue of whether Kuhn's insights concerning the natural sciences can be extrapolated to other disciplines, such as the social sciences. This is the first comprehensive introduction to the work of Kuhn and it will be of particular interest to students and scholars in philosophy, theory of science, management science and anthropology. (shrink)

The last section of “Lecture at Zilsel’s” [9, §4] contains an interesting but quite condensed discussion of Gentzen’s first version of his consistency proof for P A [8], reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen’s result (in game-theoretic terms), fill in the details (with some corrections) of Godel's reformulation, and discuss the relation between the two proofs.

AT PHAEDO 96A-C Plato portrays Socrates as describing his past study of "the kind of wisdom known as περὶ φυσέως ἱστορία." At 96c-97b, Socrates says that this study led him to realize that he had an inadequate understanding of certain basic concepts which it involved. In consequence, he says at 97b, he abandoned this method and turned to a method of his own. But at this point in the dialogue, instead of proceeding immediately to describe his method, Plato has him (...) interjecting a complaint concerning Anaxagoras and his view that everything should be explained in terms of Mind. His complaint is that Mind would order things in the best possible way and that, therefore, an account of things in terms of Mind would amount to showing that they are ordered in the best possible way. But Anaxagoras did not show this and, instead, offered other kinds of explanations of the various phenomena. Socrates is not just criticizing Anaxagoras here for not doing what he set out to do; he makes it clear, for example at 99b-c, that he believes that the best kind of explanation of the phenomena would be to show that they are ordered in the best possible way. But he was unable to discover an explanation of this kind, either for himself or from others, and so turned to a method which he calls "second best". The actual description of this method is contained in two passages, 99e5-100a7 and 101d5-e1. Between these passages, Socrates invokes the doctrine of Forms and, in particular, the formula. (shrink)

There are some puzzles about G¨ odel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, G¨ odel’s writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term “finit” (in German) or “finitary” or “finitistic” primarily to (...) refer to Hilbert’s conception of finitary mathematics. On two occasions (only, as far as I know), the lecture notes for his lecture at Zilsel’s [G¨ odel, 1938a] and the lecture notes for a lecture at Yale [G¨ odel, *1941], he used it in a way that he knew—in the second case, explicitly—went beyond what Hilbert meant. Early in his career, he believed that finitism (in Hilbert’s sense) is openended, in the sense that no correct formal system can be known to formalize all finitist proofs and, in particular, all possible finitist proofs of consistency of first-order number theory, P A; but starting in the Dialectica paper.. (shrink)