Without attempting to cover all the philosophical questions posed by modern mathematics, provides a glimpse of a broad vision of the subject. Covering general philosophical perspectives, foundational approaches, the applicability of mathematics, and history, treats selected topics from a variety of perspectives to demonstrate the range of practices in the discipline. Among them are moderate mathematical fictionism, categorical foundations of the protean character of mathematics, the mathematical overdetermination of physics, and Hungarian traditions and the philosophy of non-classical logic. The 21 (...) papers were presented at a meeting of the International Academy of Philosophy of Science, held in Budapest in May 1993. No index. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

Attemts to explain causal paradoxes of Quantum Mechanics (QM) have tried to solve the problems within the framework of Quantum Electrodynamics (QED). We will show, that this is impossible. The original theory of QED by Dirac (Proc Roy Soc A117:610, 1928) formulated in its preamble four preliminary requirements that the new theory should meet. The first of these requirements was that the theory must be causal. Causality is not to be derived as a consequence of the theory since it was (...) a precondition for the formulation of the theory; it has been constructed so that it be causal. Therefore, causal paradoxes logically cannot be explained within the framework of QED. To transcend this problem we should consider the following points: Dirac himself stated in his original paper (1928) that his theory was only an approximation. When he returned to improve the theory later (Proc Roy Soc A209, 1951), he noted that the new theory “involves only the ratio e / m , not e and m separately”. This is a sign that although the electromagnetic effects (whose source is e ) are magnitudes stronger than the gravitational effects (whose source is m ), the two are coupled. Already in 1919, Einstein noted that “the elementary formations which go to make up the atom” are influenced by gravitational forces. Although in that form the statement proved not to be exactly correct, the effects of gravitation on QM phenomena have been established. The conclusion is that we should seek a resolution for the causal paradoxes in the framework of the General Theory of Relativity (GTR)—in contrast to QED, which involves only the Special Theory of Relativity (STR). We show that causality is necessarily violated in GTR. This follows from the curvature of the space-time. Although those effects are very small, one cannot ignore their influence in the case of the so-called “paradox phenomena”. (shrink)