It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW Ψ and the mean peak width wψ of a general wave function ψ and show that the productW Ψ w φ is bounded from below if φ is the Fourier transform of ψ. It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments. (shrink)

This is the fourth volume of the Clarendon edition of Robert Burton's Anatomy of Melancholy and the first of three volumes of Commentary. It contains commentary on the text up to p. 327 of volume one - i.e. The Argument of the Frontispeice, Democritus to the Reader, and Partition 1 as far as the end of Section 2, Member 3, Subsection 15: 'Misery of Schollers'. In his study of morbid psychology as it was understood in his day, Burton cites many (...) other writers. No previous edition of the Anatomy has identified all of these or verified all his quotations. In addition to explanatory notes and translations of all the passages in Latin, this edition attempts to locate all Burton's sources in the actual books he himself owned or to which he probably had access. The last of the three volumes of commentary will contain a Biobibliography listing over 1,500 authorities referred to by Burton, many very obscure, and will give not only bibliographical details but information about the writers. (shrink)

L’article examine la reprise que le « prince des Averroïstes » Jean de Jandun fait de cette phrase délicate d’Averroès, tirée de son Grand Commentaire du De anima d’Aristote : « forte igitur philosophia invenitur in maiori parte subiecti in omni tempore ». On cherche à montrer par l’analyse des textes que l’interprétation du maître ès arts s’écarte radicalement de la pensée du Cordouan qu’il prétend suivre. Tandis qu’Averroès suppose l’existence continue d’au moins un philosophe dans le monde, Jean de (...) Jandun, rejetant comme irréaliste l’idée d’un homme parfait en qui s’incarnerait tout le savoir, et tributaire d’une erreur de traduction arabo-latine qui donne « sujet » pour « lieu », soutient qu’il n’y a chaque fois de perfection que si l’on totalise tous les savoirs particuliers des différents penseurs en activité sur la terre. Autrement dit, la philosophie est parfaite, certes, mais il n’y a pas de philosophe parfait. C’est coniunctim que la science est achevée, et non pas divisim. Un tel constat, qui rapproche l’analyse de Jean de celle menée par Dante au début de sa Monarchia, permet deux révisions : d’une part, l’idée d’un « averroïsme » latin réactionnaire, se contentant de répéter les paroles du maître, est à revoir ; d’autre part, cela signifie qu’il n’y a pas chez Jean les bases théoriques de l’idéal éthico-intellectualiste dont l’historiographie moderne assure qu’il en fut le champion parisien. (shrink)

This examination considers the influence of the seventeenth century Cambridge Platonist Cudworth upon the thought of the late eighteenth century German thinker Herder. It focuses upon Herder's use of Cudworth's philosophy to create a revised version of Spinoza's metaphysics. Both Cudworth and Herder were concerned with the problem of determinism. Cudworth outlined a number of difficulties relating to this problem in the thought of Spinoza and proposed amendments, particularly the introduction of the middle principle of plastik, which would mediate between (...) the Ideas of transcendent reason and mechanical materialism. We find these amendments to Spinoza's philosophy also employed in Herder's contribution to the Pantheism Controversy, in which he too offers a revised Spinozism and introduces his own middle principle of Kraft. This demonstrates an important but under-explored English contribution to a key development in German intellectual history. The Pantheism Controversy was an epoch-making event, helping to bring an end to the German Enlightenment and to inaugurate the Romantic movement. Herder's version of Spinoza's thought revived the philosopher's fortunes, and Herder's notion of Kraft became central to Romantic aesthetics. Finally, Herder's use of Cudworth demonstrates the important but overlooked source of Platonic realism in German Romantic thought. (shrink)

Little is in print on the development in Britain of university disciplines including the academic study of education. This paper provides a historical narrative of the study of adolescence from the 1870 Education Act to the contemporary day. Adolescence textbooks are examined in the context of changes in the education system, such as the demand for secondary education and the expansion of teacher education. Changing emphases in adolescence research are traced through various publications to illustrate curriculum developments. The important contributions (...) of Dame Olive Wheeler, Professor W. D. Wall and other leading writers on adolescence are evaluated. It is clear that in over a century of national educational provision British teachers have never faced a great choice of adolescence texts and the paper concludes with some reflections on this observation. (shrink)

In response to Michael Allsopp's essay ‘Deontic and epistemic authority in Roman Catholic ethics: The case of Richard McCormick’ it is argued that a carefully nuanced analysis reveals further epistemological implications of “reason informed by faith.” Three areas of McCormick's ethical analyses are considered which respond to basic questions about our moral knowledge, being and choosing 1) How do our value commitments arise? 2) From what perspective do we appreciate and interpret our value commitments?; 3) How do our value commitments (...) yield concrete moral norms? Moral theology ought to yield reason informed by faith which is Christocentric and anchored in charity, universalizing in its appeal, with appropriate subsidiarity, in addition it should be personalistic, modest and tentative, ecumenical, inductive, pluralistic, aspirational, and specialistic. It is concluded that McCormick's Catholic moral theology (its bases, development, and even disputes) identifies and develops essential “points of contact” for theological-ethical and public policy discourse. (shrink)

Christianity has understood the environment as a gift to nurture and steward, a book of divine revelation disclosing the divine mind, a wild garden in need of cultivation and betterment, and as a resource for the creation of a new Eden. This Cambridge Companion details how Christianity, one of the world's most important religions, has shaped one of the existential issues of our age, the environment. Engaging with contemporary issues, including gender, traditional knowledge, and enchantment, it brings together the work (...) of international scholars on the subject of Christianity and the Environment from a diversity of fields. Together, their work offers a comprehensive guide to the complex relationship between Christianity and the environment that moves beyond disciplinary boundaries. To do this, the volume explains the key concepts concerning Christianity and the environment, outlines the historical development of this relationship from antiquity to the present, and explores important contemporary issues. (shrink)

Spectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural extension of Atom Exchangeability to polyadic languages. It has been shown1that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed languageLis the set of sentences ofLwhich must be assigned probability 1 by every probability function satisfying Sx, by examining separately the (...) theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures forL, and it emerges that Sx is inconsistent with the principle of Super-Regularity. As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property. (shrink)

The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices (...) satisfy the Jónsson–Kiefer property. (shrink)

In the paper I offer a brief sketch of one of the sources of utilitarianism. Our biological ancestry is a matter of fact that is not altered by the way we describe ourselves. With philosophical theories it is otherwise. Utilitarianism can be described in ways that make it look as if it is as old as moral philosophy – as J. S. Mill thought it was. For my historical purposes, it is more useful to have an account that brings out (...) what is specific about Benthamism and its descendants. Let us try to make do with the following. First, utilitarianism asserts that the fundamental requirement of morality is that we are to maximize good, for everyone and not just for the agent. This basic principle presupposes that it makes sense to think of aggregating goods to make a total, and of comparing amounts of good thus aggregated. Second, the good to be brought about is located in feelings of pleasure, and the evil to be avoided in feelings of pain. These feelings have inherent value or disvalue regardless of how they are caused to exist and regardless of their own consequences. Third, all moral principles can be derived from the requirement that good be maximized. The principles involved in evaluating agents as well as in giving moral direction to action are nothing but applications of the basic principle. (shrink)

J. B. Schneewind's "The Invention of Autonomy" has been hailed as a major interpretation of modern moral thought. Schneewind's narrative, however, elides several serious interpretive issues, particularly in the transition from late medieval to early modern thought. This results in potentially distorted accounts of Thomas Aquinas, Hugo Grotius, and G. W. Leibniz. Since these thinkers play a crucial role in Schneewind's argument, uncertainty over their work calls into question at least some of Schneewind's larger agenda for the history of ethics.

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...) main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)

Philosophy and the scientific revolution / Daniel Garber -- Old history and introductory teaching in early modern philosophy : a response to Daniel Garber / Lisa Downing -- Meaning and metaphysics / Susan Neiman -- Evil and wonder in early modern philosophy : a response to Susan Neiman / Mark Larrimore -- The forgetting of gender / Nancy Tuana -- The forgetting of gender and the new histories of philosophy : a response to Nancy Tuana / Eileen O’Neill -- The (...) idea of early modern philosophy / Knud Haakonssen -- Response to Knud Haakonssen / Jeffrey Edwards -- Arguments over obligation : teaching time and place in moral philosophy / Ian Hunter -- Response to Ian Hunter / T.J. Hochstrasser -- Teaching the history of moral philosophy / J.B. Schneewind -- Historicism, moral judgment, and the good life : a response to J.B. Schneewind / Jennifer A. Herdt -- Integrating history of philosophy with history of science after Kant / Michael Friedman -- Response to Michael Friedman / Juliet Floyd -- Thought versus history : reflections on a French problem / Denis Kambouchner -- Response to Denis Kambouchner / Bé́atrice Longuenesse -- Teaching the history of philosophy in 19th-century Germany / Ulrich Johannes Schneider -- Response to Ulrich Johannes Schneider / Karl Ameriks -- Comment : philosophy in practice / Lorraine Daston -- A note from inside the teapot / Anthony Grafton -- Philosophy, history of philosophy, and L’histoire de l’esprit humain : a historiographical question and problem for philosophers / Jonathan Israel -- History and/or philosophy / Donald R. Kelly -- Historians look at the new histories of philosophy : roundtable discussion. (shrink)