Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

Elaborating on the substantial parallels between Molina’s and Kant’s attempts to reconcile human freedom with divine foreknowledge and natural causal determinism respectively, my aim is to establish a proper historical connection as well. Leibniz is shown to be the crucial mediator in two respects: (i) Kant knew Molina’s account of divine knowledge in general in its Leibnizian version through Baumgarten’s Metaphysica. In this work, scientia media plays no role in the explication as to how God knows absolute future contingents. (ii) (...) In the Critique of Practical Reason Kant resorted to doctrines similar to Molina’s in his criticism of Leibniz’s alternative explication which drew on complete concepts of monads. (shrink)

Truth is a stable, epistemically unconstrained property of propositions, and the concept of truth admits of a non-reductive explanation: that, in a nutshell, is the view for which I argued in Conceptions of Truth. In this paper I try to explain that explanation in a more detailed and, hopefully, more perspicuous way than I did in Ch. 6.2 of the book and to defend its use of sentential quantification against some of the criticisms it has has come in for.

The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations. It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its (...) central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function. The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism. (shrink)

This paper deals with Hans Reichenbach's common cause principle. It was propounded by him in, and has been developed and widely applied by Wesley Salmon, e.g. in and. Thus, it has become one of the focal points of the continuing discussion of causation. The paper addresses five questions. Section 1 asks: What does the principle say? And section 2 asks: What is its philosophical significance? The most important question, of course, is this: Is the principle true? To answer that question, (...) however, one must first consider how one might one argue about it at all. One can do so by way of examples, the subject of section 3, or more theoretically, which is the goal of section 4. Based on an explication of probabilistic causation proposed by me in,, and, section 4 shows that a variant of the principle is provable within a classical framework. The question naturally arises whether the proved variant is adequate, or too weak. This is pursued in section 5. My main conclusion will be that some version of Reichenbach's principle is provably true, and others may be. This may seem overly ambitious, but it is not. The paper does not make any progress on essential worries about the common cause principle arising in the quantum domain; it only establishes more rigorously what has been thought to be plausible at least within a classical framework. (shrink)

I argue that the project of naturalizing intentionality is misconceived. Intentionality should not be considered as a challenge to our naturalistic world-view, but rather as something which gives rise to a logical problem: how to save the principle of indiscernibility of identicals from apparent counterexamples arising from intensional discourse.

ls it possible to understand not only linguistic expressions and actions but also persons? According to common sense it surely is. Here it is argued that to understand a person a fourfold knowledge is required, although this knowledge is not identical with the understanding of a person. The understanding of a person is cognitive, but neither complete nor scientific.