The author states in his preface that he has not undertaken a history of aesthetic thought during the French Enlightenment, nor an intellectual history of French aesthetics, nor a synthesis of eighteenth-century French thought on aesthetics, nor a history of eighteenth-century French art. What he has attempted to do is to outline doctrines of French aesthetic thought during the eighteenth century. The term doctrine is perhaps not too strong here because some of these writers were rather doctrinaire in their approach. (...) Following an outline of their respective positions, the author then subjects their works to a logical analysis. More than two-thirds of the authors cited are relatively unknown: André, d'Argens, Batteux, Bonnet, Briseux, Chaussard, Crousaz, Mme. Dacier, Estère, de Jaucourt, de La Motte, di Marcenay de Ghuy, de Piles, Rollin, Taillason, Trublet. One should not be surprised to learn that few of these were professional philosophers. Others cited by Coleman are well-known eighteenth-century figures: d'Alembert, Condillac, Diderot, Dubos, Montesquieu and St. Evremond. The author explains that he undertook the book in order to fill a gap in the literature on the subject. It is an excellent beginning and the style in which it is written is often as witty and elegant as that of many of the authors he considers.—P. N. (shrink)
This is the collection of essays presented to Bochenski on his 60th birthday, and it contains, as a mirror of Bochenski's own work, a broad spectrum of studies ranging from formal logic and history of logic, to the philosophy of logic and language, and to the methodology of explanation in Greek philosophy. Of the seventeen articles, these are some of the more important to the reviewer: "Betrachtungen zum Sequenzen Kalkül" by Paul Bernays, which is an extensive study of Gentzen-type formulations (...) of logic; "Remarks on Formal Deduction," H. B. Curry, a further discussion of sequenzen-logics; "Marginalia on Gentzen's Sequenzen Kalkül" by Hughes Leblanc; "Method and Logic in Presocratic Explanation," Jerry Stannard; "On the Logic of Preference and Choice," H. S. Houthakker, a suggestive presentation of decision and utility theory in logical form; "Leibniz's Law in Belief Contexts," Chisholm; "On Ontology and the Province of Logic," R. M. Martin; and "N. A. Vasilev and the Development of Many-valued Logics," G. L. Kline, an important addition to the history of logic. Other contributors are: Storrs McCall, Albert Menne, E. W. Beth, Benson Mates, Ivo Thomas, J. F. Staal, F. R. Barbò, A.-T. Tymieniecka, and N. M. Luyten. There is a bibliography of Bochenski's writings through 1962.—P. J. M. (shrink)
We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this (...) theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed. (shrink)
We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Z p n or the Witt ring W 2 (F 4 ) (which is the characteristic four analogue of the Galois field with four elements).
In the article we are trying to answer the question why people make mistakes in their reasoning. According to the theory proposed by P. N. Johnson-Laird, reasoning is a semantic process based on mental models. Reasoners build models of the situations described in premises and then check which conclusion holds in all the models. Unfortunately, our working memory has a limited processing capacity, and so we often fail to represent all possibilities necessary to draw a valid conclusion. The more models (...) we have to build, the higher the chance of making a mistake. Due to limitations of our working memory, we tend to represent in the models only what is true, but not what is false. One of the consequences of this fact is the occurrence of certain illusions: inferences that are compelling but invalid. The existence of such illusionary inferences have been corroborated by numerous experiments. (shrink)