Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this (...) book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999. (shrink)

A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.

The 1996 European Summer Meeting of the Association of Symbolic Logic was held held the University of the Basque Country, at Donostia (San Se bastian) Spain, on July 9-15, 1996. It was organised by the Institute for Logic, Cognition, Language and Information (ILCLI) and the Department of Logic and Philosophy of Sciences of the University of the Basque Coun try. It was supported by: the University of Pais Vasco/Euskal Herriko Unib ertsitatea, the Ministerio de Education y Ciencia (DGCYT), Hezkuntza Saila (...) (Eusko Jaurlaritza), Gipuzkoako Foru Aldundia, and Kuxta Fun dazioa. The main topics of the meeting were Model Theory, Proof Theory, Re cursion and Complexity Theory, Models of Arithmetic, Logic for Artifi cial Intelligence, Formal Semantics of Natural Language and Philosophy of Contemporary Logic. The Program Committee consisted of K. Ambos Spies (Heidelberg), J.L. Balcazar (Barcelona), J.E. Fenstad (Oslo), D. Israel (Stanford), H. Kamp (Stuttgart), R. Kaye (Birmingham), J.M. Larrazabal (San Sebastian), D. Lascar (Paris, chairman), A. Marcja (Firenze), G. Mints (Stanford), M. Otero (Madrid), S. Ronchi della Rocca (Torino), K. Segerberg (Uppsala) and L. Vega (Madrid). The organizing Committee consisted of X. Arrazola (San Sebastian), A. Arrieta (San Sebastian), R. Beneyeto (Valencia), B. Carrascal (San Se bastian), K. Korta (San Sebastian), J.M. Larrazabal (San Sebastian, chair man), J.C. Martinez (Barcelona), J.M. Mendez (Salamanca), F. Migura (Victoria) and J. Perez (Victoria). (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

This original and lively book uses texts from ancient medicine, epic, lyric, tragedy, historiography, philosophy, and religion to explore the influence of Greek ideas on health and disease on Greek thought. Fundamental issues are deeply implicated: causation and responsibility, purification and pollution, the mind-body relationship and gender differences, authority and the expert, reality and appearances, good government, and good and evil themselves.

In The Ambitions of Curiosity, first published in 2002, one of the world's foremost philosophers of science explores the origins and growth of systematic inquiry in Greece, China, and Mesopotamia. Professor Lloyd examines which factors stimulated or inhibited this development, and whose interests were served. He asks who set the agenda? What was the role of the state in sponsoring, supporting or blocking research, in such areas as historiography, natural philosophy, medical research, astronomy, technology, pure and applied mathematics? How were (...) each of those fields defined and developed in different ancient societies? How did truly innovative thinkers persuade their own contemporaries to accept their work? Professor Lloyd explores the different routes those developments took in China, Greece and Mesopotamia, and demonstrates the unexpected results of many research efforts, as well as the tensions between state control and individual innovation and the different ways they were resolved - problems that remain central to scientific research today. (shrink)

How were the aims of philosophy and the responsibilities of philosophers conceived in ancient Greece and China? How were the learned elite recruited and controlled; how were their speculations and advice influenced by the different types of audiences they faced and the institutions in which they worked? How was a yearning for invulnerability reconciled with a sense of human frailty? In each chapter of this fascinating analysis ancient Greek and Chinese ideas and practices are used as a basis for critical (...) reflections on the predicaments we continue to face today, with a particular focus on the key Greek ideas of the equal participation of all citizens in the political process, and on the key Chinese one of a dedication to the ideal of the welfare of all under heaven. (shrink)

How far can we construct a framework within which to compare different traditions of philosophy and science across civilizations? The first problem lies with the terms “philosophy” and “science” themselves, for they carry particular associations in Western thought, some of which contribute to the mistaken view that they are uniquely Western activities. This brief article refutes that view, examining how we can compare the philosophical and scientific achievements of different cultures, and further challenging the sharp positivist dichotomy between “science” and (...) “philosophy” that stems from equating the former with facts, the latter with values. (shrink)

In April 1939, G. E. Moore read a paper to the Cambridge University Moral Science Club entitled ‘Certainty’. In it, amongst other things, Moore made the claims that: the phrase ‘it is certain’ could be used with sense-experience-statements, such as ‘I have a pain’, to make statements such as ‘It is certain that I have a pain’; and that sense-experience-statements can be said to be certain in the same sense as some material-thing-statements can be — namely in the sense that (...) they can be safely counted on. When Moore later read his paper to Wittgenstein, Wittgenstein took violent exception to it, and the two entered into a heated exchange. The only known notes of this exchange are a previously unpublished verbatim record of part of it, taken by Norman Malcolm. This paper is an edition of Malcolm’s notes. These notes are valuable for both philosophical and scholarly reasons. They give us a glimpse of a sustained exchange between Wittgenstein and a real-life interlocutor; they contain a defence by Wittgenstein of the idea that a word’s use can illuminate its meaning; and they provide evidence of Wittgenstein’s philosophical engagement with the topic of certainty, and with Moore’s thought on it, long before he began to write the notes which make up On Certainty, in 1949. (shrink)

This book challenges the common assumption that the predominant focus of the history of science should be the achievements of Western scientists since the so-called Scientific Revolution. The conceptual frameworks within which the members of earlier societies and of modern indigenous groups worked admittedly pose severe problems for our understanding. But rather than dismiss them on the grounds that they are incommensurable with our own and to that extent unintelligible, we should see them as offering opportunities for us to revise (...) many of our own preconceptions. We should accept that the realities to be accounted for are multi-dimensional and that all such accounts are to some extent value-laden. In the process insights from current anthropology and the study of ancient Greece and China especially are brought to bear to suggest how the remit of the history of science can be expanded to achieve a cross-cultural perspective on the problems. (shrink)

How far can we construct a framework within which to compare different traditions of philosophy and science across civilizations? The first problem lies with the terms “philosophy” and “science” themselves, for they carry particular associations in Western thought, some of which contribute to the mistaken view that they are uniquely Western activities. This brief article refutes that view, examining how we can compare the philosophical and scientific achievements of different cultures, and further challenging the sharp positivist dichotomy between “science” and (...) “philosophy” that stems from equating the former with facts, the latter with values. (shrink)