Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning and expression. (...) It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

Originally published in 1958. A study in the logical foundations of modern theoretical semantics, this book is concerned with notions of designation and consistency as well as denotation and truth. It presents several semantical theories, each of which with what were new concepts or treatments from the author. Talking at a time when semantical theory was gained great ground, this book also looks at the methodology of the sciences and the semantics of scientific language alongside analysis of meaning and expression. (...) It is influenced by the writings of Carnap, Church, Frege, Goodman, Quine, Russell and Tarski. (shrink)

Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

The method of Ramsey sentences has been proposed for handling theoretical constructs within a scientific system. Essentially it consists of constructing a certain "monolithic" sentence for an entire theory. In this present paper several improvements are suggested which help to overcome some of the awkward features of the method. In particular we have here many Ramsey sentences rather than just one, each erstwhile primitive theoretical term giving rise to a Ramsey sentence. Such a sentence in effect defines what we call (...) a Ramsey constant. Using Ramsey constants, we attempt to improve the method in important logical and semantical respects. It is suggested also that such constants are of interest for the philosophy of mathematics. (shrink)

The philosophical papers comprising this volume range from process metaphysics and theology, through the phenomenological study of intentionality, to the foundations of geometry and of the system of real numbers. New light, it is thought, is shed on all these topics, some of them being of the highest interest and under intensive investigation in contemporary philosophical discussion. Metaphysi cians, process theologians, semanticists, theorists of knowledge, phenomenologists, and philosophers of mathematics will thus find in this book, it is hoped, helpful materials (...) and methods. The categoreal scheme of Whitehead's Process and Reality is discussed rather fully from a logical point of view in the first paper [I] in the light of the author's previous work on the logico-metaphysical theory of events. The clarification that results is thought to provide a new depth and precision to the problem of interpreting one of the most difficult books in the recent history of metaphysics and cosmol ogy. A detailed examination of some aspects of Hartshorne's recent Creative Synthesis and Philosophic Method is given in II. This book is perhaps the most significant work on process philosophy since Process and Reality itself, and its logical underpinnings thus merit a full critical discussion. (shrink)

Richard Martin's aim in this paper is to present a critical method of making ethical decisions in a medical context. He feels that such a reflective method provides the best means of making the appropriate decisions in given situations. It is based on Dr Martin's experience in applying ethical theory while collaborating with physicians in the daily course of clinical practice. Through his giving of a functional definition of medical ethics, his descriptions of an analytical model, the significance of values (...) for clinical decision-making and the advocacy role of medical ethicists and their relationships with clinicians, Richard Martin sets out his own value-intention as regards an ideal decision process. He stresses that his argument is of particular importance to his fellow ethicists who should continuously and vigorously examine the creative interaction of faith and fact in their own inquiry and action. Dr Martin concludes by stating that physicians and ethicists can work together to accomplish their common aim, which is, of course, the health and well-being of the patient. (shrink)

The ontological argument of Saint Anselm, one of the most famous in the entire history of philosophy, has fascinated men’s minds for centuries. And yet, as Hartshorne makes abundantly clear, much of its subtlety has been missed by some of the keenest commentators. Although it has been discussed again and again, little work seems to have been done, even up to the moment, in exploring the logical forms or deep structures needed for an exact statement. Part of this is due (...) no doubt to the subtlety of the argument itself, but part of it is due to that fact that the key ideas involved are not of the kind that easily lend themselves to being handled within the standard kinds of logic. (shrink)

The issue on which I intend to focus is whether there is anything else, anything more than ontological economy, which, in Russell's mature account of the constituents of propositions, is gained by his rejection of denoting concepts. I will argue that in order to answer this question, it is necessary to appreciate that by the time of "On Denoting," Russell was not merely advancing a claim of philosophical logic or a theory of the logical form of the descriptive phrases of (...) English. (edited). (shrink)

Current UK legislation is impacting upon the feasibility and cost-effectiveness of medical record-based research aimed at benefiting the NHS and the public heath. Whereas previous commentators have focused on the Data Protection Act 1998, the Health and Social Care Act 2001 is the key legislation for public health researchers wishing to access medical records without written consent. The Act requires researchers to apply to the Patient Information Advisory Group for permission to access medical records without written permission. We present a (...) case study of the work required to obtain the necessary permissions from PIAG in order to conduct a large scale public health research project. In our experience it took eight months to receive permission to access basic identifying information on individuals registered at general practices, and a decision on whether we could access clinical information in medical records without consent took 18 months. Such delays pose near insurmountable difficulties to grant funded research, and in our case £560 000 of public and charitable money was spent on research staff while a large part of their work was prohibited until the third year of a three year grant. We conclude by arguing that many of the current problems could be avoided by returning PIAG’s responsibilities to research ethics committees, and by allowing “opt-out” consent for many public health research projects. (shrink)