The present article deals with the power of the axiom of choice within the second-order predicate logic. We investigate the relationship between several variants of AC and some other statements, known as equivalent to AC within the set theory of Zermelo and Fraenkel with atoms, in Henkin models of the one-sorted second-order predicate logic with identity without operation variables. The construction of models follows the ideas of Fraenkel and Mostowski. It is e. g. shown that the well-ordering theorem for unary (...) predicates is independent from AC for binary predicates and from the trichotomy law for unary predicates. Moreover, we show that the AC for binary predicates follows neither from the trichotomy law for unary predicates nor from Zorn's lemma for unary predicates nor from the formalization of the axiom of choice for disjoint families of sets for binary predicates, and that the trichotomy law for unary predicates does not follow from AC for binary predicates. (shrink)

Conceptual spaces are a frequently applied framework for representing concepts. One of its central aims is to find criteria for what makes a concept natural. A prominent demand is that natural concepts cover convex regions in conceptual spaces. The first aim of this paper is to analyse the convexity thesis and the arguments that have been advanced in its favour or against it. Based on this, I argue that most supporting arguments focus on single-domain concepts (e.g., colours, smells, shapes). Unfortunately, (...) these concepts are not the primary examples of natural concepts. Building on this observation, the second aim of the paper is to develop criteria for natural multi-domain concepts. The representation of such concepts has two main aspects: features that are associated with the concept and the probabilistic correlation pattern which the concept captures. Conceptual spaces, together with probabilistic considerations, provide a helpful framework to approach these aspects. With respect to feature representation, the existence of characteristic features (i.e., that apples have a specific taste) is essential. Moreover, natural concepts capture peaks of a probabilistic distribution over complex spaces. They carve up nature at its joints, that is, at areas with no or low probabilistic density. This last aspect is shown to be closely related to the convexity demand. (shrink)

The present report is a, somewhat lengthy, addendum to "A new deconstructive logic: linear logic," where the elimination of cuts from derivations in sequent calculus for classical logic was studied ‘from the point of view of linear logic’. To that purpose a formulation of classical logic was used, that - as in linear logic - distinguishes between multiplicative and additive versions of the binary connectives.The main novelty here is the observation that this type-distinction is not essential: we can allow classical (...) sequent derivations to use any combination of additive and multiplicative introduction rules for each of the connectives, and still have strong normalization and confluence of tq-reductions.We give a detailed description of the simulation of tq-reductions by means of reductions of the interpre- tation of any given classical proof as a proof net of PN2 (the system of second order proof nets for linear logic), in which moreover all connectives can be taken to be of one type, e.g., multiplicative.We finally observe that dynamically the different logical cuts, as determined by the four possible combinations of introduction rules, are independent: it is not possible to simulate them internally, i.e., by only one specific combination, and structural rules. (shrink)

Mas A. Mardkayin arzhēkʻner -- Mas B. Hawatkʻ ew mnapashtutʻiwn -- Mas G. Ěntanekan mtorumner.

The intentionality of sensation -- The first person -- Substance -- The subjectivity of sensation -- Events in the mind -- Comments on Professor R.L. Gregory's paper on perception -- On sensations of position -- Intention -- Pretending -- On the grammar of "Enjoy" -- The reality of the past -- Memory, "experience," and causation -- Causality and determination -- Times, beginnings, and causes -- Soft determinism -- Causality and extensionality -- Before and after -- Subjunctive conditionals -- "Under a (...) description" -- Analysis competition--tenth problem -- A reply to Mr. C.S. Lewis's argument that "naturalism" is self-refuting. (shrink)

G. E. Moore was a central figure in twentieth-century philosophy. Along with Russell and Wittgenstein, he pioneered analytic philosophy, and his Principia Ethica shaped the contours of twentieth-century ethics. Indeed, until the publication of Rawls's A Theory of Justice, no single book in moral philosophy was to equal Principia's influence. Unfortunately, however, Principia Ethica has so dominated critical discussions of Moore's work that even experts on his moral philosophy have tended to ignore his Ethics, which he published eight years later. (...) But Ethics is Moore's only other book on moral philosophy, and one of only a handful of post-Principia publications dealing with ethics. Its detailed discussions of utilitarianism, free will, and the objectivity of moral judgements find no real counterpart in Principia while its account of right and wrong and of the nature of intrinsic value deepen our understanding of his moral philosophy. The republication of Ethics thus rounds out our understanding of Moore's ethical thought. But the book's value goes beyond its historical or scholarly interest. A short but philosophically rich text, Ethics stands independent of Principia and repays careful study in its own right. By raising a number of fundamental questions in ethics, questions that remain live today, by proffering clear, credible, and often innovative answers to them, and by doing so with a philosophical skill that is still impressive, Moore's short book is a minor classic. Almost a century after its original publication, it still amply rewards those who read it.This new edition of Moore's Ethics includes his essay 'The Nature of Moral Philosophy' as well as editorial notes, an introduction, and a guide to further reading. (shrink)

An elaborately extended analysis of what Singer believes to be the basic form of moral argument: If everyone did that, the consequences would be undesirable, therefore you ought not to do that. This argument in conjunction with several principles of a modified utilitarianism are interpreted as grounding rational morality. The place of reason in ethics, classical utilitarianism, the distinction between moral rules, laws, and principles, and the distinction between prudence and morality are discussed in detail. The general argument of the (...) book is rather complicated and at times the transitions seem weak.--E. R. G. (shrink)

G. E. Moore was a central figure in twentieth-century philosophy. Along with Russell and Wittgenstein, he pioneered analytic philosophy, and his Principia Ethica shaped the contours of twentieth-century ethics. Indeed, until the publication of Rawls's A Theory of Justice, no single book in moral philosophy was to equal Principia's influence. Unfortunately, however, Principia Ethica has so dominated critical discussions of Moore's work that even experts on his moral philosophy have tended to ignore his Ethics, which he published eight years later. (...) But Ethics is Moore's only other book on moral philosophy, and one of only a handful of post-Principia publications dealing with ethics. Its detailed discussions of utilitarianism, free will, and the objectivity of moral judgements find no real counterpart in Principia while its account of right and wrong and of the nature of intrinsic value deepen our understanding of his moral philosophy. The republication of Ethics thus rounds out our understanding of Moore's ethical thought. But the book's value goes beyond its historical or scholarly interest. A short but philosophically rich text, Ethics stands independent of Principia and repays careful study in its own right. By raising a number of fundamental questions in ethics, questions that remain live today, by proffering clear, credible, and often innovative answers to them, and by doing so with a philosophical skill that is still impressive, Moore's short book is a minor classic. Almost a century after its original publication, it still amply rewards those who read it.This new edition of Moore's Ethics includes his essay 'The Nature of Moral Philosophy' as well as editorial notes, an introduction, and a guide to further reading. (shrink)

Hall's final statement of his "intentionalistic empiricism" in epistemology and ethics. He takes emotional experience to be basic; perceptions are only an abstracted portion of this experience. Truth as a property of empirical propositions, and legitimacy as a property of value propositions, are interpreted as unanalyzable relations between propositions and facts or values. The test of truth and legitimacy is coherence. The examples of emotionally expressive language found throughout the second half of this work show sensitivity to the variety in (...) such a language.--E. R. G. (shrink)

This book is built upon the premiss that there is more than a heuristic connection between Heidegger's thought and his accounts of the Pre-Socratics. Accordingly, by studying what Heidegger has said about them and why he has said it, Seidel offers explanations of some key Heideggerian themes, such as history, being, truth, and language. Seidel brings to this task a sound and thorough reading of both the Pre-Socratics and Heidegger and succeeds in illuminating some of Heidegger's basic concepts.—W. G. E.

This book comprises Cameron's Terry Lectures at Yale, given in 1964-1965 before a disappointingly small audience. Disappointing, primarily because the lectures represent a serious analysis of a significant, though often neglected, aspect of classical natural law, natural theology doctrines. This is the concept of vicarious authority with its corresponding claim of an independent access to truth on the part of one subject to authority. This is surely an important historical as well as contemporary notion in jurisprudence and ecclesiology. Cameron's analysis (...) and documentation is rich, thoughtful, and encompassing. This may have made the lectures too serious and dense, but it makes the book satisfying and thought-provoking, and deserving of a much larger audience than could have filled the lecture hall.—W. G. E. (shrink)

Classical French spirituality, ornate and delicate, rich and stylized, like the Louis Quatorze furniture of the same period, is perhaps not to everyone's taste. Jacques Bénigne Bossuet, the great "Eagle of Meaux," was the most eloquent and elegant sacred orator of the period of the great Louis, and his prose has remained ever since a model of that style. This is the first translation of his Méditations sur l'Evangile, perhaps more elegant and certainly more personally intense than the great state (...) sermons. The translation, however, is too close to the French style; it would have been better to match the elegance of the French with comparably elegant English.--W. G. E. (shrink)

Joining his monumental erudition in the phenomenology of religion with affinity and skill in the arts, Gerardus van der Leeuw has produced a really beautiful work. Tracing the genesis of the various arts from an original unity in expressive religious dance, through their assertions of independence as distinctive secular forms marked by the individualism of their practioners, he tries to show that each art form structurally expresses an aspect of the holy. His concern is to prepare for the reunification of (...) the arts based on a religious esthetics. The writing is somewhat diffuse but graceful, the presentation descriptive rather than argumentative. Throughout, one senses the quality of the author's cultivation and concern. The posthumous translation and publication of this work gives his many admirers in the English-speaking world a fitting memorial of a beloved master.—W. G. E. (shrink)

In its original form this was Bonhoeffer's first work, presented as a theological dissertation when the author was only twenty-one. It has been very influential on proponents of "religionless Christianity" among the Continental theologians. The argument is compressed and often elliptical, exceedingly difficult to grasp. Bonhoeffer follows Tonnies' distinction between society and community, holding that the religious community is a community of will which admits no end outside itself, but whose telos, God, is its boundary. It is a structure of (...) meaning rather than a structure of purpose, uniting persons in an I-Thou relationship in which they assume the relative independence of a Leibnitzian monad. The book is magnificent; the translation unobtrusive and long overdue.—W. G. E. (shrink)

This book is the result of a series of discussions among Cambridge theologians on the general topic of the relevance of established religion and theology to the problems and values of the mid-twentieth century. A wide range of problems is treated: the methodology and importance of natural theology, the effect of recent philosophies of science on theology, the analogical use of the notion of the transcendent, Freudian analysis, and moral theology, the authority of scriptures and the church, prayer, the grounds (...) of moral judgments and the role of the established church in society. The essays reflect the varied interests and capabilities of the writers and should be of interest to a quite varied audience. Most of the essays reveal fresh viewpoints, perspicuous analysis, and rigorous thought.--W. G. E. (shrink)

This recent publication by professor Kai Nielsen may be best seen as a logical progression of thought that follows from his 1991 study, After the Demise of the Tradition: Rorty, Critical Theory, and the Fate of Philosophy, and from several articles since this publication. Described by Nielsen as a "metaphilosophical study", On Transforming Philosophy is his on-going treatment of how the aims of the traditional philosophical project have failed and how a transformed conception of philosophy should now focus on the (...) "problems of life." Although many philosophers may doubt that an inquiry of this nature is possible, Nielsen nonetheless sets out to dispel various traditional conceptions of the central task of philosophy. In its place he seeks to establish what he believes to be a more "humanly important" view of philosophy. (shrink)