In the mathematical documents which have come down to us from these peoples, there are no theorems or demonstrations, and the fundamental concepts of ...

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.

In this paper, I consider a variety of objections against the covering-law model of scientific explanation, show that Aristotle was already aware of them and had solutions for them, and argue that these solutions are correct. These solutions involve the notions of nonHumean causality and of essential properties. There are a great many familiar objections, both methodological and epistemological, to introducing these concepts into the methodology of science, but I show that these objections are based upon misunderstandings of these concepts.

RésuméEpicure, Descartes, Kant appartiennent à une même lignée philosophique, l' intuitionnisme. Par leur méthode; ils ne séparent pas la vérité des precédés par iesquels on parvient à elle et, de façon plus ou moins directe, ils restreignent la validité du tiers‐exclu et des preuves par l' absurde. Par leur anthropologic: en revendiquant passionément la liberté. Par leur théodicée: en conciliant de façon originale mécanisme et finalité, celle‐ci étant posée en vertu' une sorte d' acte de foi rationnelle mais conservant son (...) impénétrabilitéà la raison. (shrink)