Although prima facie no more than a successful private detective, Sherlock Holmes is a classic exponent of scientific method and has laid down several fundamental rules of scientific discovery and truth?detection. While he rediscovered and modified well?known principles of induction, analysis and synthesis, and decision theory, he also made significant contributions to patterns of explanation, and with his ?principle of exclusion? was an ingenious innovator. This latter cornerstone of Holmes's methodology led him to an interesting modal theory of the ?improbable (...) possible? as a competitor to the famous doctrine of the ?impossible probable? put forward by Aristotle in de Arte Poetica. Holmes's scientific discipline was seasoned by warmth, understanding, and boldness. (shrink)

The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are typically allowed only (...) with respect to known objects. This requirement explains the preoccupation of Greek geometers with questions as to which geometrical objects are ?given?, that is, known or ?data?, as in the title of Euclid's eponymous book. In problematic analysis, constructions had to rely on objects that are known only hypothetically. This seems strange unless one relies on a robust idea of ?unknown? objects in the same sense as the unknowns of algebra. The Greeks did not have such a concept, which made their grasp of the analytic method shaky. (shrink)

In this paper, I will look at two passages from the discussion of education in Book VII of Plato’s Republic: 523b-524d and 537e-539d. These passages, when taken together, present a puzzle for the coherency of the educational programme Socrates describes. Both discuss contradiction. One says that contradiction is educationally edifying, the other, that it is corrupting. This sounds like a contradiction about contradiction. As far as I know, no one has noticed this puzzle before. By the end of this paper, (...) I hope to have not only provided a solution to the apparent contradiction about contradiction that is compelling, but also one that shows that this puzzle, which might at first have seemed restricted to a textual issue about the educational programme in the Republic, is in fact one that has far reaching implications for a range of Plato’s theories across several dialogues. Along with education, corruption, and contradiction, I will discuss Plato’s theory of psychology, and his theory of forms. (shrink)

This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. The paper is divided into two parts. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the (...) Republic, better meets those criteria than do any of the three main positions. (shrink)

Following the publication of his magnum opus L’être et l’événement (Being and Event) in 1988, Alain Badiou has been acclaimed as one of France’s greatest living philosophers. Since then, he has released a dozen books, including Manifesto for Philosophy, Conditions, Metapolitics and Logiques des mondes (Logics of Worlds), many of which are now available in English translation. Badiou writes on an extraordinary array of topics, and his work has already had an impact upon studies in the history of philosophy, the (...) history and philosophy of science, political philosophy, aesthetics, psychoanalysis, and ontology. This volume takes up the challenge of explicating, extending and, in many places, criticising Badiou’s stunningly original theses. Above all, the essays collected here put Badiou’s concepts to the test in a confrontation with the four great headings that he himself has identified as essential to our humanity: science, love, art and politics. Many of the contributors have already been recognised as outstanding translators of and commentators on Badiou’s work; they appear here with fresh voices also destined to make a mark. (shrink)

Equally surprisingly, Descartes’s paranoid belief was shared by several contemporary mathematicians, among them Isaac Barrow, John Wallis and Edmund Halley. (Huxley 1959, pp. 354-355.) In the light of our fuller knowledge of history it is easy to smile at Descartes. It has even been argued by Netz that analysis was in fact for ancient Greek geometers a method of presenting their results (see Netz 2000). But in a deeper sense Descartes perceived something interesting in the historical record. We are looking (...) in vain in the writings of Greek mathematicians for a full explanation of what this famous method was. And I will argue for an answer to the question why this lacuna is there: Not because Greek geometers wanted to hide this method, but because they did not fully understand it. It is instructive to note the ambivalent attitude of the most rigorous mathematician of the period, Isaac Newton, to the method of analysis. He used it himself in his own mathematical work and in the expositions of that work. Yet when the mathematical push came to physical and cosmological shove, he formulated his Principia entirely in.. (shrink)

We attempt to discern what Badioursquo;s philosophical system provides for thinking of education in a form which separates it from its contemporary representation in the state. These notes oppose to this state form Badiou#39;s declaration that #39;the only education is an education by truthsrsquo;. We pursue this in three sections. First, we will address the significance and function of the term lsquo;conditionsrsquo;. Secondly we will address Badioursquo;s essay lsquo;Art and Philosophyrsquo; from Handbook of Inaesthetics, the only essay in fact where (...) Badiou addresses education in a specific manner and in which Badiou discusses the link between art and philosophy in terms of the lsquo;pedagogical themersquo;: A theme, he says, that has been brought to collapse. Thirdly we will attempt to discern what might make up whatnbsp; Badiou refers to as the lsquo;fourth modalityrsquo; of the link between philosophy and its conditions through a somewhat speculative discussion of the dual lsquo;militantrsquo; praxis known in Badioursquo;s work as lsquo;subtractionrsquo; and lsquo;forcingrsquo;. (shrink)