The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is (...) countably infinite. In particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H). (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Given the sordid history of injustices linking genetics to race and ethnicity, considerations of justice are central to ensuring the responsible development of precision medicine programmes around the world. While considerations of justice may be in tension with other areas of concern, such as scientific value or privacy, there are also tensions between different aspects of justice. This paper focuses on three particular aspects of justice relevant to this precision medicine: social justice, distributive justice and human rights. We describe the (...) implications of each for the use of race and ethnicity in precision medicine, and also how they intersect and potentially conflict with each another. By attending to these intersections, we aim to enrich and add nuance to debates over how best to proceed with precision medicine initiatives. (shrink)

G. E. R. Lloyd explores the amazing diversity of views that humans have held on being, humanity, and understanding. In a cross-cultural study that ranges from ancient to modern times, he asks how far we are bound by the conceptual systems to which we belong, and explores topics such as ontology, morality, philosophy of language, and communication.

Taking a set of central issues from ancient Greek medicine and biology, this book studies firstly, the interaction between scientific theorising and folklore or popular assumptions; secondly, the ideological character of scientific inquiry. Topics of interest in the philosphy and sociology of science illuminated here include the relationship between primitive thought and early science, the roles of the consensus on the scientific community, tradition and the authority of the written text, in the development of science.

In this paper I shall venture into an area with which I am not very familiar and in which I feel far from confident; namely into phenomenology. My main motive is not to get away from standard, boring, methodological questions like those of induction and demarcation; but the conviction that a phenomenological account of the empirical basis forms a necessary complement to Popper's falsificationism. According to the latter, a scientific theory is a synthetic and universal, hence unverifiable proposition. In fact, (...) in order to be technologically useful, a scientific hypothesis must refer to future states-of-affairs; it ought therefore to remain unverified. But in order to be empirical, a theory must bear some kind of relation to factual statements. According to Popper, such a relation can only be one of potential conflict. Thus a theory T will be termed scientific if and only if T is logically incompatible with a so-called basic statement b, where b is both empirically verifiable and empirically falsifiable. In other words: T is scientific if it entails ¬b; where b, hence also ¬b, is an empirically decidable proposition. (shrink)

ABSTRACTThis article, which summarises some of the main arguments of Analogical Investigations [Lloyd 2015], undertakes a comparative cross-cultural critique of the dominant Western view that downgrades analogy especially when that is contrasted unfavourably with a notion of axiomatic-deductive demonstration aiming to secure incontrovertible conclusions. It draws on materials from ancient Greece, ancient China and modern social anthropology and philosophy of science to explore the problems of translation and mutual intelligibility. It develops the idea of semantic stretch to qualify the literal/metaphorical (...) dichotomy and the notion of the multidimensionality of reality to clarify aspects of the controversy between realism and relativism. (shrink)

This article presents evidence supporting the claim that ethical reasoning is a skill that can be taught and assessed. We propose a working definition of ethical reasoning as 1) the ability to identify, analyze, and weigh moral aspects of a particular situation, and 2) to make decisions that are informed and warranted by the moral investigation. The evidence consists of a description of an ethical reasoning education program—Ethical Reasoning in Action —designed to increase ethical reasoning skills in a variety of (...) situations and areas of life. ERiA is housed at a public, major comprehensive U.S. university—James Madison University—and assessment of the program focuses on interventions delivered prior to and during orientation for incoming first-year students. Findings indicate that the interventions measurably enhance the ability of undergraduate students to reason ethically. ERiA’s competency-targeted program and positive student learning outcomes offers a promising model for higher education ethics programs seeking to connect classroom learning in ethics to decision-making in everyday life. (shrink)

We tend to assume that our map of the intellectual disciplines is valid cross-culturally. G. E. R. Lloyd challenges this in relation to eight main areas of human endeavour, namely philosophy, mathematics, history, medicine, art, law, religion, and science, by examining how the disciplines were conceived and developed in different times and places.

Dr Lloyd writes for those who want to discover and explore Aristotle's work for themselves. He acts as mediator between Aristotle and the modern reader. The book is divided into two parts. The first tells the story of Aristotle's intellectual development as far as it can be reconstructed; the second presents the fundamentals of his thought in the main fields of inquiry which interested him: logic and metaphysics, physics, psychology, ethics, politics, and literary criticism. The final chapter considers the unity (...) and coherence of Aristotle's philosophy, and records briefly his later influence on European thought. This is a concise and lucid account of the work of a difficult and profound thinker. Dr Lloyd's business is only with the essentials; but he does not shirk the difficulties which arise in their interpretation, nor does he invest Aristotle with a spurious modernity. (shrink)

This book explores the universe and its subsystems from the three lenses of evolutionary (diversifying), developmental (converging), and complex (adaptive) processes at all scales. It draws from prolific experts within the academic disciplines of complexity science, physical science, information and computer science, theoretical and evo-devo biology, cosmology, astrobiology, evolutionary theory, developmental theory, and philosophy. The chapters come from a Satellite Meeting, "Evolution, Development and Complexity" (EDC) hosted at the Conference on Complex Systems, in Cancun, 2017. The contributions will be peer-reviewed (...) and contributors from outside the conference will be invited to submit chapters to ensure full coverage of the topics. This book explores many issues within the field of EDC such as the interaction of evolutionary stochasticity and developmental determinism in biological systems and what they might teach us about these twin processes in other complex systems. This text will appeal to students and researchers within the complex systems and EDC fields.. (shrink)

Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defence of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.

A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals, defined by a direct elementary technique, turn out to be the computable elements of the hereditary continuous partial objects; moreover, there is a commutative system of enumerations of any given type by any type below (relative numberings). By this and by results in [1] and [2], the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) (...) are easily characterized. (shrink)

The question of determining the genuine works of Hippocrates, a topic already much discussed by the ancient commentators, still continues to be actively debated, although the disagreements among scholars remain, it seems, almost as wide as ever. In comparatively recent times, Edelstein's IIEPI AEPQN and two subsequent studies of his written in the 1930s and marked a turning-point in that they presented a particularly clear and comprehensive statement of the sceptical view, according to which Hippocrates is, as Wilamowitz put it (...) long ago, ‘ein beriihmter Name ohne den Hintergrund irgend einer Schrift’. (shrink)

This article, in the example of the subject of shukr (gratitude), proposes a ‘perspective’ for the instructor who determines the processes of bringing a subject into the learning environment. This perspective is related to the encounter with the knowledge of the subject to be taught. It points to the approach of the instructor to the information he/she will refer to about the subject he/she will teach while preparing in the mental plan. The content of the subject, the objectives, the methods, (...) techniques, and resources to be used to present the subject, and how the output will be measured and evaluated are largely determined by this perspective. In a way, the proposed perspective involves monitoring the change and transformation of life and the contextualization of religious knowledge by paying attention to the methodological functioning. Thus, the way the subject of gratitude presented in the Qur’an and hadith narrations aims to provide the teacher with a ‘perspective’ on what kind of content to prepare. This is a suggestion for the instructor to reveal that while managing the process of religiously understanding/interpreting life as it flows by, the instructor should not ignore the ways in which knowledge appears in the Qur’an and hadith narrations. For example, the first meaning of the word shukr (gratitude) in the Qur’an is “faith in Allah.” However, traditionally, shukr (gratitude) is not taught within the subject area of faith. In this context, the article follows the suggestion that referring to the method and source of the knowledge to be taught can provide the instructor with a holistic and in-depth ‘perspective.’. (shrink)

The Term ‘liberty’ invokes such universal respect that most modern political economists and moralists endeavour to find a conspicuous place for it somewhere in their systems or prescriptions. But in view of the innumerable senses of this term an insistence on some kind of definition prior to any discussion seems to be justified. For our present purposes attention to two particularly conflicting interpretations will be sufficient. These are sometimes called the ‘negative’ and the ‘positive’ notions of Liberty. According to the (...) ‘negative’ notion, my own liberty implies the reduction to a minimum of the deliberate interference of other human beings within the area in which I wish to act. Conversely the absence of liberty, or coercion, is regarded as undesirable because it amounts to the prevention by other persons of my doing what I want. On the other hand, the ‘positive’ sense of the word ‘liberty’ consists in the attainment of self-mastery, or, in other words, the release from the domination of ‘adverse’ influences. This ‘slavery’ from which men ‘liberate’ themselves is variously described to include slavery to ‘nature’, to ‘unbridled passions’, to ‘irrational impulses’, or simply slavery to one's ‘lower nature’. ‘Positive’ liberty is then identified with ‘self-realisation’ or an awakening into a conscious state of rationality. The fact that it is contended that such a state can often be attained only by the interference of other ‘rational’ persons who ‘liberate’ their fellow beings from their ‘irrationality’, brings this interpretation of liberty into open and striking conflict with liberty in the ‘negative’ sense. (shrink)