The generalized Liouville equation is studied in a new light using the Lie derivative of a differential form with respect to a vector field.

Various aspects of the integrability of dynamical systems are discussed with the help of the singular point analysis. In particular the connection with the Painlevé property is described. Several examples will serve as illustrations.

The analysis of interacting relativistic many-particle systems provides a theoretical basis for further work in many diverse fields of physics. After a discussion of the nonrelativisticN-particle systems we describe two approaches for obtaining the canonical equations of the corresponding relativistic forms. A further aspect of our approach is the consideration of the constants of the motion.

Few major philosophers show evidence of having studied the works of their predecessors with special care, even in cases where they were subject to particular influences which they were ready to acknowledge. Hume knew that he was working in the tradition of ‘some late philosophers in England, who have begun to put the science of man on a new footing’—‘Mr Locke, my Lord Shaftsbury, Dr Mandeville, Mr Hutchinson, Dr Butler, &c.’ But there is not much sign in the Treatise or (...) elsewhere in Hume's writings of any close acquaintance with the works of these authors; the presumption must be that he had read them at some time and extracted the main ideas, but was not in the habit of returning to their texts. He had something more important to do, namely to work at philosophical problems of his own. Similarly Kant, though he said that the Critique of Pure Reason was not meant to be ‘a critique of books and systems, but of the faculty of reason in general’, had clearly felt the impact of the thought of some important past philosophers, but equally had never spent much time in finding out just what these philosophers had to say. Plato, Aristotle, Descartes, Locke, Leibniz and Hume all get fairly frequent mention in his pages. But Kant takes his knowledge of Plato and Aristotle from J. J. Brucker's Historia critica philosophiae, a six-volume compilation which first appeared in 1742, or from doubtful sources such as Mendelssohn's doctored translation of the Phaedo, and though he doubtless knew the more recent authors at first hand clearly felt no need to study them in any depth. This was true even of writers to whom he attributed a particular importance, such as Leibniz and Hume. The references to Hume in the Critique and Prolegomena are all disappointingly general, and though the summary of Leibniz's philosophy in the section called ‘The Amphiboly of Concepts of Reflection’ has a certain force, it is not documented with references to Leibnizian texts. Kant knows that there is a difference between the views of the historical Leibniz and those which constituted the ‘Leibnizian-Wolffian system’ of his successors. But he is not very curious about the difference, or inclined to explore it. (shrink)

It is a widely held doctrine at the moment that metaphysical propositions are meaningless, are, in fact, not genuine propositions at all. This doctrine is supported by the contention that only propositions which are verifiable are significant: and it is held that metaphysical propositions do not fulfil this condition, and are consequently pseudo-propositions. Those who hold this view divide propositions into three classes: Tautologies; which are analytic, certain, and are guaranteed by the principle of contradiction. Factually significant propositions; which are (...) synthetic, hypothetical, and are capable of empirical verification. Pseudopropositions, which only appear to be propositions and are, in reality, meaningless nonsense. (shrink)

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First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.