Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

In our papers on the rationality of magic, we distinghuished, for purposes of analysis, three levels of rationality. First and lowest (rationalitYl) the goal directed action of an agent with given aims and circumstances, where among his circumstances we included his knowledge and opinions. On this level the magician's treatment of illness by incantation is as rational as any traditional doctor's blood-letting or any modern one's use of anti-biotics. At the second level (rationalitY2) we add the element of rational thinking (...) or thinking which obeys some set of explicit rules, a level which is not found in magic in general, though it is sometimes given to specific details of magical thinking within the magical thought-system. It was the late Sir Edward E. Evans-Pritchard who observed that when considering magic in detail the magician may be as consistent or critical as anyone else; but when considering magic in general, or any system of thought in general, the magician could not be critical or even comprehend the criticism. Evans-Pritchard went even further: he was sceptical as to whether it could be done in a truly consistent manner: one cannot be critical of one's own system, he thought. On this level (rationalitY2) of discussion we have explained (earlier) why we prefer to wed Evans Pritchard's view of the magician's capacity for piece-meal rationality to Sir James Frazer's view that magic in general is pseudo-rational because it lacks standards of rational thinking. (shrink)

Recorded in Ithaca, NY by Cornell University., Sponsored by: Andrew D. White Professors-At-Large Program., Speaker: Professor of the History of Philosophy, Ecole des Hautes Etudes en Sciences Sociales, Paris, Andrew D. White Professor-at-Large., Lecture, October 3, 1988.

Written in political exile during the Second World War and first published in 1945, Karl Popper's The Open Society and Its Enemiesis one of the most influential books of the twentieth century. Hailed by Bertrand Russell as a 'vigorous and profound defence of democracy', its now legendary attack on the philosophies of Plato, Hegel and Marx exposed the dangers inherent in centrally planned political systems. Popper's highly accessible style, his erudite and lucid explanations of the thought of great philosophers and (...) the recent resurgence of totalitarian regimes around the world are just three of the reasons for the enduring popularity of The Open Society and Its Enemies, and for why it demands to be read both today and in years to come. This is the second of two volumes of The Open Society and Its Enemies. (shrink)

“Postmodernism” denotes efforts to replace foundationalist philosophy with contextu‐alist, immanentist forms of reason. “Postlibertarianism” denotes efforts to transcend contemporary minimal statism, questioning both its “libertarian” moral superstructure and its underlying consequentialist claims and seeking to determine whether the latter can be generalized in a way that displaces the former. Efforts to reach minimal‐statist conclusions by postmodern means seem bound to aggravate the problem that plagues contemporary minimal statism: its failure to be true to its consequentialist foundations, reflected in its long‐standing (...) devotion to dubious arguments for the intrinsic good of laissez‐faire capitalism. For postmodernism fosters the illusion that one can do without any foundations at all. Rather than recovering its consequentialist roots, therefore, postmodern minimal statism tends to rely unquestioningly on the normative foundations already accepted by the libertarian “speech community,” neither responding to alternative interpretations of the value of liberty, nor transcending the arid conversation of “liberty” in favor of investigations of the real world of contemporary capitalism and the welfare state. (shrink)

Since the seventeenth century, Western society has had a turbulent relationship with Reason. Descartes set out to reorganize all his opinions in the light of Reason, allowing, as Pascal bitterly reproached him, nothing else. In the course of the centuries which followed, the relationship with Reason became the object of a vigorous, often passionate debate. David Hume declared Reason to be impotent; Immanuel Kant observed that men suffered from "misology" as the result of their disappointed expectations of Reason; G. W. (...) F. Hegel declared that the main insight of philosophy consisted of the realization that reason masterminded and guided all history. The debate has not remained restricted to philosophy. Max Weber, the most influential modern sociologist, was obsessed with the distinctive role of Reason in Western society, and the part it played in engendering industrialism. Social anthropologists have been preoccupied both with the universality and the diversity of conceptual thought. Emile Durkheim taught them to ask why all men were rational, whilst Max Weber taught sociologists to ask why some men were more rational than others. This book brings together the philosophical, historical and sociological discussions of rationality and strives to make clear the underlying issues and the continuity of the debate under the various idioms. (shrink)