An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric $\bar h_{\mu \nu } $ is proportional to a probability amplitude φuv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired in (...) a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor Tμv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric $\bar h_{\mu \nu } $ and associated equations in the probability amplitudes φuv. The gauge condition φ v uv =0 (Lorentz condition) and conservation of energy and momentum Tv μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φuv. (shrink)

Inleidend studieboek op universitair niveau over de Nederlandse rechtswetenschap.

Apart from the scientific unknowns and technological barriers that complicate the development of medical neuroimaging applications, various relevant actors might have different ideas on what is considered advancement or progress in this field. We address the challenge of identifying societal actors and their different points of view concerning neuroimaging technologies in an early phase of neuroimaging development. To this end, we conducted 16 semistructured interviews with societal actors, including governmental policy makers, health professionals, and patient representatives, in the Netherlands. We (...) show how the contextual aspects of applications and underlying features of the ideal health system determine the desirability. Neuroimaging developments are perceived as innovations that will optimize the current health system or as opportunities to change existing structures and practices of the current health system more radically. Insights into and understanding of these visions show incongruence between visions regarding desirable medical neuroimaging use and potential conflicting visions regarding the embedding of neuroimaging applications. We conclude that it is possible to prospectively identify incongruent visions and analyze when these visions will most likely come into conflict with each other. Such an analysis might provide a reflective space, beyond personal and political interest, suitable as a starting point for joint reflection and mutual learning in order to manage medical neuroimaging innovations towards more responsible applications. (shrink)

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)

What precisely, W. J. T. Mitchell asks, are pictures (and theories of pictures) doing now, in the late twentieth century, when the power of the visual is said to be greater than ever before, and the "pictorial turn" supplants the "linguistic turn" in the study of culture? This book by one of America's leading theorists of visual representation offers a rich account of the interplay between the visible and the readable across culture, from literature to visual art to the mass (...) media. (shrink)

W. J. Mander presents the first ever synoptic history of British Idealism, the school of thought which dominated English-language philosophy from the 1860s to the early 20th century. He restores to its proper place this neglected period of philosophy, introducing the exponents of Idealism and explaining its distinctive concepts and doctrines.

Through clear explanation of its characteristic concepts and doctrines, and paying close attention to the published works of its philosophers, the volume ...

Most of what has been written about Buber and education tend to be studies of two kinds: theoretical studies of his philosophical views on education, and specific case studies that aim at putting theory into practice. The perspective taken has always been to hold a dialogue with Buber's works in order to identify and analyse critically Buber's views and, in some cases, to put them into practice; that is, commentators dialogue with the text. In this article our aims are of (...) a different kind. First and fundamentally, we demonstrate the political and social ontological basis of Buber's thought; that is, we show that Buber, the philosopher of dialogue, held an authentic dialogue with his time, and demonstrate that Buber's work, in this case I and Thou, holds a dialogue with its Zeitgeist; that is the text dialogues with its Zeitgeist. This approach leads us to our second aim, which is to demonstrate that Buber's thought remains relevant to our times, particularly when it serves as a dialogical educational tool with which to resolve conflict of all types and to aid dialogue towards peace in inter-community relations. (shrink)

"[Mitchell] undertakes to explore the nature of images by comparing them with words, or, more precisely, by looking at them from the viewpoint of verbal language.... The most lucid exposition of the subject I have ever read."—Rudolf Arnheim, _Times Literary Supplement_.

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)

W. J. Mander provides a brief introduction to and critical assessment of the thought of the greatest of the British Idealist philosophers, F. H. Bradley (1846-1924), whose work has been largely neglected in this century. After a general introduction to Bradley's metaphysics and its logical foundations, Mander shows that much of Bradley's philosophy has been seriously misunderstood. Mander argues that any adequate treatment of Bradley's thought must take full account of his unique dual inheritance from the traditions of British empiricism (...) and Hegelian rationalism. The scholarship of recent years is assessed, and new interpretations are offered of Bradley's views about truth, predication, and relations, and of his arguments for idealism. (shrink)

This is the first full assessment of British philosophy in the 19th century. Specially written essays by leading experts explore the work of the key thinkers of this remarkable period in intellectual history, covering logic and scientific method, metaphysics, religion, positivism, the impact of Darwin, and ethical, social, and political theory.

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

This paper argues that a strong thesis of divine providence, whereby God is understood as in complete control of all things, entails pantheism, the thesis that the universe is not ontologically distinct from God. In normal discourse, we distinguish a plan from, on the one hand, the state of affairs which realizes that plan—its execution or expression—and, on the other hand, the person or group whose plan it is. However, with respect to an omnipotent God who displays complete providence, neither (...) of these two distinctions holds. We cannot separate person from plan, or plan from world, and in consequence, neither can we separate person from world, ergo pantheism. Accordingly, the argument of this paper comes in two parts maintaining, first, the impossibility of distinguishing between God’s plan and its execution and, second, the impossibility of distinguishing God himself from his plan. (shrink)

Although the notion of spatiality has always lurked in the background of discussions of literary form, the self-conscious use of the term as a critical concept is generally traced to Joseph Frank's seminal essay of 1945, "Spatial Form in Modern Literature."1 Frank's basic argument is that modernist literary works are "spatial" insofar as they replace history and narrative sequence with a sense of mythic simultaneity and disrupt the normal continuities of English prose with disjunctive syntactic arrangements. This argument has been (...) attacked on several fronts. An almost universal objection is that spatial form is a "mere metaphor" which has been given misplaced concreteness and that it denies the essentially temporal nature of literature. Some critics will concede that the metaphor contains a half-truth, but one which is likely to distract attention from more important features of the reading experience. The most polemical attacks have come from those who regard spatial form as an actual, but highly regrettable, characteristic of modern literature and who have linked it with antihistorical and even fascist ideologies.2 Advocates of Frank's position, on the other hand, have generally been content to extrapolate his premises rather than criticize them, and have compiled an ever-mounting list of modernist texts which can be seen, in some sense, as "antitemporal." The whole debate can best be advanced, in my view, not by some patchwork compromise among the conflicting claims but by a radical, even outrageous statement of the basic hypothesis in its most general form. I propose, therefore, that far from being a unique phenomenon of some modern literature, and far from being restricted to the features which Frank identifies in those works , spatial form is a crucial aspect of the experience and interpretation of literature in all ages and cultures. The burden of proof, in other words, is not on Frank to show that some works have spatial form but on his critics to provide an example of any work that does not. · 1. Frank's essay first appeared in Sewanee Review 53 and was revised in his The Widening Gyre . Frank's basic argument has not changed essentially even in his most avante-garde statements; he still regards spatial form "as a particular phenomenon of modern avante-garde writing." See "Spatial Form: An Answer to Critics," Critical Inquiry 4 : 231-52. A useful bibliography, "Space and Spatial Form in Narrative," is being complied by Jeffrey Smitten .· 2. This charge generally links the notion of spatial form with Wyndham Lewis and Ezra Pound, the imagist movement, the "irrationality" and pessimistic antihistoricism of modernism, and the conservative Romantic tradition. Frank discusses the complex motives behind these associations in the work of Robert Weimann and Frank Kermode in his "Answer to Critics," pp. 238-48. W. J. T. Mitchell, editor of Critical Inquiry, is the author of Blake's Composite Art, and The Last Dinosaur Book: The Life and Times of a Cultural Icon. The present essay is part of Iconology: The Image in Literature and the Visual Arts. "Diagrammatology" appeared in the Spring 1981 issue of Critical Inquiry. Leon Surette responds to the current essay in "‘Rational Form in Literature’". (shrink)

In this study, W. J. Waluchow argues that debates between defenders and critics of constitutional bills of rights presuppose that constitutions are more or less rigid entities. Within such a conception, constitutions aspire to establish stable, fixed points of agreement and pre-commitment, which defenders consider to be possible and desirable, while critics deem impossible and undesirable. Drawing on reflections about the nature of law, constitutions, the common law, and what it is to be a democratic representative, Waluchow urges a different (...) theory of bills of rights that is flexible and adaptable. Adopting such a theory enables one not only to answer to critics' most serious challenges, but also to appreciate the role that a bill of rights, interpreted and enforced by unelected judges, can sensibly play in a constitutional democracy. (shrink)

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)

W. J. Mander examines the nature of idealist ethics, that is to say, the form and content of ethical belief most typically adopted by philosophical idealists. His inquiry has two aims. The first is historical: from the record of past philosophy, Mander demonstrates that there exists a discernible idealist approach to moral philosophy; a tradition of 'idealist ethics', and examines its characteristic marks and varieties. The second aim is apologetic. He argues that such idealist ethics offers an attractive way of (...) looking at moral questions and that it has much to contribute to contemporary discussion. In particular he argues that Idealist ethics have the power to cut through the sterile opposition between moral realism and moral anti-realism. To be an idealist is precisely to hold that the universe is so constituted that things are real if and only if they are ideal; to hold that uncovering in something the work of mind makes it more not less significant. (shrink)

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.

In this paper I argue that Wittgenstein is correct when he says of the Standard Metre stick that we can neither say that it is or is not a metre in length – despite what our intuitions may tell us to the contrary. Specifically, the paper deals with Kripke's criticism of Wittgenstein's claim in Naming And Necessity and with Salmon's attempt to arbitrate between the two views. I conclude that, not only is Wittgenstein correct, but that both Kripke and Salmon (...) (and possibly the majority of philosophers) simply do not understand the concept of measurement. (shrink)

A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈,F〉, whereis an algebra of the appropriate type, andFa subset of the domain of, called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logicE, which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, (...) wherenow is a modal algebra, andFis a filter of. If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jónsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10].The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general. (shrink)

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.