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)

Using payment to recruit research subjects is a common practice, but it raises ethical concerns that coercion or undue inducement could potentially compromise participants’ informed consent. This is the first national study to explore the attitudes of IRB members and other human subjects protection professionals concerning whether payment of research participants constitutes coercion or undue influence, and if so, why. The majority of respondents expressed concern that payment of any amount might influence a participant’s decisions or behaviors regarding research participation. (...) Respondents expressed greater acceptance of payment as reimbursement or compensation than as an incentive to participate in research, and most agreed that subjects are coerced if the offer of payment makes them participate when they otherwise would not or when the offer of payment causes them to feel that they have no reasonable alternative but to participate . Views about undue influence were similar. We conclude that human subjects protection professionals hold expansive and inconsistent views about coercion and undue influence that may interfere with the recruitment of research participants and impede valuable research. (shrink)

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)

Originally published in 1965. This is a textbook of modern deductive logic, designed for beginners but leading further into the heart of the subject than most other books of the kind. The fields covered are the Propositional Calculus, the more elementary parts of the Predicate Calculus, and Syllogistic Logic treated from a modern point of view. In each of the systems discussed the main emphases are on Decision Procedures and Axiomatisation, and the material is presented with as much formal rigour (...) as is compatible with clarity of exposition. The techniques used are not only described but given a theoretical justification. Proofs of Consistency, Completeness and Independence are set out in detail. The fundamental characteristics of the various systems studies, and their relations to each other are established by meta-logical proofs, which are used freely in all sections of the book. Exercises are appended to most of the chapters, and answers are provided. (shrink)

Despite the periodic table having been discovered by chemists half a century before the discovery of electronic structure, modern designs are invariably based on physicists’ definition of periods. This table is a chemists’ table, reverting to the phenomenal periods that led to the table’s discovery. In doing so, the position of hydrogen is clarified.

The Symposia Aristotelica were inaugurated at Oxford in 1957. They are conferences of select groups of Aristotelian scholars from the UK, USA and Europe, and are held every three years. In 1975 the meeting was held in Cambridge and was devoted to Aristotle's psychological treatises, the De anima and the Parva uaturalia. The members of the conference discussed some of the much debated problems of Aristotle's psychology and broached important new topics such as his ideas on imagination. Dr Lloyd and (...) Professor Owen have collected and edited the papers presented to the Symposium and provided an analytical index. (shrink)