In Descartes's Meditations, one of the key texts of Western philosophy, the thinker rejects all his former beliefs in the quest for new certainties. Discovering his own existence as a thinking entity in the very exercise of doubt, he goes on to prove the existence of God, who guarantees his clear and distinct ideas as a means of access to the truth. He develops new conceptions of body and mind, capable of serving as foundations for the new science of nature. (...) Subsequent philosophy has grappled with Descartes's legacy, questioning many of its conclusions and even his basic approach, but his arguments set the agenda for many of the greatest philosophical thinkers, and their fascination endures.This new translation includes the Third and Fourth Objections and Replies in full, and a selection from the rest of Descartes's exchanges with contemporaries that helped to shape and expound his philosophy. (shrink)

The Meditations, one of the key texts of Western philosophy, is the most widely studied of all Descartes' writings. This authoritative translation by John Cottingham, taken from the much acclaimed three-volume Cambridge edition of the Philosophical Writings of Descartes, is based upon the best available texts and presents Descartes' central metaphysical writings in clear, readable modern English. As well as the complete text of the Meditations, the reader will find a thematic abridgement of the Objections and Replies (which were originally (...) published with the Meditations) containing Descartes' replies to his critics. These extracts, specially selected for the present volume, indicate the main philosophical difficulties which occurred to Descartes' contemporaries and show how Descartes developed and clarified his arguments in response. This edition contains a new comprehensive introduction to Descartes' philosophy by John Cottingham and the classic introductory essay on the Meditations by Bernard Williams. (shrink)

This is the first critical edition since the nineteenth century of Bacon's principal philosophical work in English, The Twoo Bookes of Francis Bacon. Of the proficience and advancement of Learning, divine and humane - traditionally known as The Advancement of Learning.

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them (...) angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank. (shrink)

In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to a large extent (...) with argument assessment in non-mathematical contexts. I demonstrate this claim by considering the assessment of axiomatic or deductive proofs, probabilistic evidence, computer-aided proofs, and the acceptance of axioms. I also consider Jody Azzouni’s ‘derivation indicator’ view of proofs because it places derivations—which may be thought to invoke formal logic—at the center of mathematical justificatory practice. However, when the notion of ‘derivation’ at work in Azzouni’s view is clarified, it is seen to accord with, rather than to count against, the informal logical view I support. Finally, I pose several open questions for the development of a theory of mathematical argument. (shrink)

Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals (...) why these proofs—written in the vernacular to this very day—succeed in conforming to those norms. (shrink)

Only paperback edition of great legal classic. Lucid, accessible coverage of liability, criminal law, torts, contracts, more, from historical perspective. New introduction by Sheldon M. Novick. Table of Cases.

The aim of the paper is to present a typology of argument schemes. In first place, we found it helpful to define what an argument scheme is. Since many argument schemes found in contemporary theories stem from the ancient tradition, we took in consideration classical and medieval dialectical studies and their relation with argumentation theory. This overview on the main works on topics and schemes provides a summary of the main principles of classification. In the second section, Walton’s theory is (...) briefly explained to introduce the schemes classification and its different levels. At least, the final part shows the main application of the schemes in computing and AI. -/- . (shrink)