We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.

Recent developments in quantum theory have focused attention on fundamental questions, in particular on whether it might be necessary to modify quantum mechanics to reconcile quantum gravity and general relativity. This book is based on a conference held in Oxford in the spring of 1984 to discuss quantum gravity. It brings together contributors who examine different aspects of the problem, including the experimental support for quantum mechanics, its strange and apparently paradoxical features, its underlying philosophy, and possible modifications to the (...) theory. (shrink)

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose ‘configuration space’ (or history-theory analogue) is the set of objects Ob(Q) in a category Q. We develop a scheme based on constructing (...) an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold Q ≃ G/H, where G and H are Lie groups. In particular, we choose as the analogue of G the monoid of “arrow fields” on Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the ‘category quantisation monoid’, we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over Ob(Q). For the example of a category of finite sets, we construct an explicit representation structure of this type. (shrink)

This collection of research papers explores the implications of quantum cosmology and the status of the laws of nature for theological and philosophical issues regarding God's action in the world. The main goal is to contribute to constructive theology as it engages current research in the natural sciences, and to investigate the philosophical and theological elements in ongoing theoretical research in the natural sciences.

"This edition, which replaces the original Loeb edition..., offers text, translation, and annotation that are fully current with modern scholarship"--Front flap of dust jacket, volume 1.

_Verificationism_ is the first comprehensive history of a concept that dominated philosophy and scientific methodology between the 1930s and the 1960s. The verificationist principle - the concept that a belief with no connection to experience is spurious - is the most sophisticated version of empiricism. More flexible ideas of verification are now being rehabilitated by a number of philosophers. C.J. Misak surveys the precursors, the main proponents and the rehabilitators. Unlike traditional studies, she follows verificationist theory beyond the demise of (...) positivism to examine its reappearance in the work of modern philosophers. Most interestingly, she argues that despite feminism's strenuous opposition to positivism, verificationist thought is at the heart of much of contemporary feminist philosophy. _Verificationism_ is an excellent assessment of a major and influential system of thought. (shrink)

In his celebrated masterpiece, Symposium, Plato imagines a high-society dinner-party in Athens in 416 BC at which the guests - including the comic poet Aristophanes and, of course, Plato's mentor Socrates - each deliver a short speech in praise of love. The sequence of dazzling speeches culminates in Socrates' famous account of the views of Diotima, a prophetess who taught him that love is our means of trying to attain goodness. And then into the party bursts the drunken Alcibiades, the (...) most popular and notorious Athenian of the time, who insists on praising Socrates himself rather than love, and gives us a brilliant sketch of this enigmatic character. The power, humour, and pathos of Plato's creation engages the reader on every page. This new translation is complemented by full explanatory notes and an illuminating introduction. (shrink)

least this was his later view. He had begun with the more obvious but more naive view that need was the key to the process and that removal of the need ...

C.J. Bartley places Ramunuja in his intellectual context. This study is particularly concerned with Ramanuja's engagement with opposing schools of thought and practice, rendering it a valuable contribution to the history of Indian thought.

This edition of Martin Ostwald's revised version of J. B. Skemp's 1952 translation of _Statesman_ includes a new selected bibliography, as well as Ostwald's interpretive introduction, which traces the evolution in Plato's political philosophy from _Republic_ to _Statesman to Laws_--from philosopher-king to royal statesman.

Banking, in common with other areas of finance, is often considered an amoral field focused purely on risk and return. However, ethics does have an important role to play, both traditionally and as business and banking evolve. Based on a speech to a European Union conference on financing small and medium–sized enterprises (SMEs), this paper seeks to provide an overview of ethics in banking using three terms. Integrity is important to generate the trust necessary for any banking system to flourish, (...) responsibility highlights contemporary banks’ need to take into account the consequences of their lending policies, and affinity refers to a set of relatively novel ways in which depositors and borrowers can be brought closer together than they are in conventional western banking. (shrink)

Banking, in common with other areas of finance, is often considered an amoral field focused purely on risk and return. However, ethics does have an important role to play, both traditionally and as business and banking evolve. Based on a speech to a European Union conference on financing small and medium–sized enterprises , this paper seeks to provide an overview of ethics in banking using three terms. Integrity is important to generate the trust necessary for any banking system to flourish, (...) responsibility highlights contemporary banks’ need to take into account the consequences of their lending policies, and affinity refers to a set of relatively novel ways in which depositors and borrowers can be brought closer together than they are in conventional western banking. (shrink)

Classifying the Zhuangzi Chapters . Liu Xiaogan, trans, by William E. Savage, 1994, Ann Arbor, Center for Chinese Studies, University of Michigan, xxii + 217 pp., ISBN 0 89264 106 1.

The social, educational and political writings of Jean-Jacques Rousseau have become enormously influential in the 200 years since his death. But the breadth as well as the depth of Rousseau's achievement - he was amongst other things a creative writer and musical composer as well as a philosopher - is not always appreciated. In around 100 articles, alphabetically arranged and fully cross-referenced, N. J. H. Dent explores all facets of Rousseau's work and thoughts, while his subject's remarkable life is summarized (...) in a biographical introduction. Details of works by and about Rousseau are listed in an extensive bibliography. For students or general readers seeking an introduction to Rousseau's work, and for those already familiar with the material who require a convenient reference source, this dictionary is essential reading. (shrink)

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, (...) the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties). (shrink)

Christology seems to fall fairly clearly into two divisions. The first is concerned with the truth of the two propositions: ‘Christ is God’ and ‘Christ is a man’. The second is concerned with the mutual compatibility of these propositions. The first part of Christology tends to confine itself to what is sometimes called ‘positive theology’: that is to say, it is largely given over to examining the Jons revelationis —let us not prejudge currently burning issues by asking what this is—to (...) see what evidence can be found for the truth of these propositions. Clearly, the methods used will be above all those of New Testament exegesis. The second part of Christology will necessarily consist entirely of that speculative theology which is contrasted with positive theology. Even if the earliest speculation on this topic is to be found in the New Testament itself and thus becomes fair game for the exegetes, any attempt to relate the primary truths, ‘Christ is God’ and ‘Christ is a man’, to eachother is a work of reflection, and in the terminology I am using speculative. (shrink)