A recently developed formalism which gives a unified picture of the linear transport of moving frames is extended to include a particular type of transport under the 10-parameter Poincaré group. The frame coordinates are expressed in a 5 × 5 matrix representation which includes the position four-vector plus orthonormal tetrads for the internal coordinates. This provides a general description of the kinematics of physical systems which can be represented by moving frames. Several examples are given, including systems moving with spin (...) and Zitterbewegung along both timelike and null paths. The concept of boost or Poincaré momentum is related to system kinematics. Lagrangians of these systems are also discussed. (shrink)

A theory of the extended classical charged particle is presented. The theory assumes extension along the forward light cone of the particle instead of the usual now-plane. Solutions are given for many of the traditional problems including 4/3, instability, infinite self-energy, and runaway velocity. The Lorentz and Lorentz-Dirac equations are derived from a more general equation of motion.

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.

A model of the extended classical charged particle is developed further to prove that the electron potential can be expressed as a superposition of null waves. The null waves are solutions of the homogeneous wave equation and are related to some recently discovered types of solutions which are localized and propagate without dispersion. Connections with quantum electrodynamics and the fine structure constant are indicated.

An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, (...) and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed. (shrink)

Response to commentaries on keynote article.

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)

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.

Markov, A. A. On constructive mathematics.--Ceĭtin, G. S. Mean value theorems in constructive analysis.--Zaslavskiĭ, I. D. and Ceĭtlin, G. S. On singular coverings and properties of constructive functions connected with them.--Maslov, S. Ju. Certain properties of E. L. Post's apparatus of canonical calculi.--Zaslavskiĭ, I. D. Graph schemes with memory.

In REG 73 and 75 I discussed various points connected with the Peace of Philocrates, a number of which have been assailed by M. M. Markle in CQ N.S. 24 in an article entitled ‘The Strategy of Philip in 346 B.C.’. Time passes, and, although de Ste. Croix in his Origins of the Peloponnesian War , p.105, felt able to declare that ‘a book shortly to be published by M. M. Markle makes a valuable and original contribution to our understanding (...) of the Peace of Philocrates’, and Markle himself confirms that a book is indeed forthcoming, some comment on his preliminary comments may be permitted. (shrink)

Molly Farneth’s Hegel’s Social Ethics hearkens back to the tradition of Josiah Royce, which has continued in the work of Richard Bernstein and Jeffrey Stout. At the same time, it reflects the impact of three decades of interpretive work which has offered an alternative to the 19th and early 20th century reading of Hegel as a metaphysical systematizer. In this new reading he was from the beginning a social critic and political theorist who looked to lay the groundwork for post‐Enlightenment (...) vision of the social world as evolving toward one of social cooperation based on mutual recognition. Farneth has developed this reading of Hegel into one of powerful resources for democratic pluralism. (shrink)

There is frequently an appearance of conflict between medicine and economics. This arises first because the nature of health and health care requires the doctor to make decisions on behalf of the patient and thus serves to explain why medical ethics exist. But secondly it is due to the relative lack of acceptance of the ethics of the common good within medical ethics. As a result while economics in the field of health has as an objective the maximisation of the (...) health of the community, subject to resource constraints, medical ethics pushes individual doctors to try to maximise the health of their patients. There is no reason to believe that the latter will sum to the former. To make the maximisation of health of the community the goal of the medical profession requires institutional changes, particularly with regard to budgeting, which will cajole and if necessary coerce doctors to adopt the good of the community as their objective. (shrink)

Hanoch Ben-Yami has argued that the theory of the semantics of natural kind terms proposed by Kripke and Putnam is false and has proposed an allegedly novel account of the semantics of kind terms. In this article, I critically examine Ben-Yami’s arguments. I will argue that Ben-Yami’s objections do not show that Kripke and Putnam’s theory is false, but at most that the specific versions of it held by Kripke and Putnam have some weaknesses. Moreover, I will argue that Ben-Yami’s (...) account is not a novel account but it is only an unsatisfactory version of Kripke and Putnam’s theory. (shrink)

Dr. Leaf's article in the Journal of Hellenic Studies has recalled our attention to the venerable problem of the Rhesus. I hasten to give my adhesion to his main contention that the play is a pièce d'occasion justifying or sanctifying the foundation of the city of Amphipolis. But, as he remarks, seeing that the oracle ordering the removal of the bones of Theseus from Skyros to Athens preceded the actual removal by some years, so this play may be intended to (...) prepare for the actual removal of the bones of Rhesus from Troy by Hagnon, and may be prior to it by several years. For this official theft—doubtless arranged beforehand—we have only the authority of Polyainos' Strategemata, but it is a story which seems likely in itself, and goes far to explain the previously obscure lament of the Muse at the end of the play. My object is to examine the play afresh and see whether anything prevents our believing that it was written and exhibited somewhere near 440 B.C., in which case of course it is almost certainly the work of Euripides and not far from his Cyclops in date. (shrink)