The question of the relationship of the making of value judgments in a typically ethical sense to the methods and procedures of science has been discussed in the literature at least to that point which e. e. cummings somewhere refers to as “The Mystical Moment of Dullness.” Nevertheless, albeit with some trepidation, I feel that something more may fruitfully be said on the subject.

I wish, for the sake of the vivacity of any discussion which might ensue, that I could find myself more in disagreement with Dr. Brodbeck than I do. As a matter of fact, however, I find myself in substantial agreement with her on practically all of the points upon which she takes issue with Hayek. There are, to be sure a few questions of relatively minor import that I should like to ask Dr. Brodbeck, but in the main I have (...) confined my own discussion to an elaboration and supplementation of some of the points considered in her paper, and some related considerations raised in Hayek's book but which Dr. Brodbeck did not have the time, perhaps, to treat. (shrink)

IN a recent article Dr. Paul D. Wienpahl proposes an explication for Frege's notion of sense that, he believes, "fits the data of Frege's discussion and does not make sense a subsistent entity" (p. 483). Wienpahl's proposal is that "the sense of a sign is the combination of its physical properties" (p. 488). But in the face of the requirements which he has set himself, there seem to be three considerations which lead to the conclusion that his proposal is defective.

In some ways, I think, the analytic method in philosophy and science suffers from an embarrassment of riches. It has too many distinctions—in the sense that any distinction which is infirm, but which is yet carted about along with the necessary apparatus of a method, is superfluous. In these pages I propose to examine one such distinction.A principle which is subscribed to by almost all of the “analysers” with whose work I am acquainted is that which is constituted by a (...) certain kind of dichotomization between what we may for the present loosely characterize as the “formal” and the “non-formal.” Sometimes this distinction is presented as one existing between the “formal sciences” and the “non-formal sciences”; more frequently, perhaps, it is taken as a distinction holding between certain kinds of expressions, i.e., analytic and synthetic statements. It will be the thesis of this paper that there are good reasons for believing that this distinction in either of its forms is not a cogent one. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

This study reconstructs the relationship between philosophy and politics in the way in which Heidegger's failure as a politician influenced the redevelopment of philosophy in the 1930s. The author also explains how Heidegger's failure influenced the content and direction of his later work.

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

The ancient Taoist text that forms the central part of this book was discovered by Wilhelm, who recognized it as essentially a practical guide to the integration of personality. Foreword and Appendix by Carl Jung; illustrations. Translated by Cary F. Baynes.A Helen and Kurt Wolff Book.

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

"This is an excellent textbook on Neoplatonism which gives the reader a very concise and lucid overview of the basic doctrines and leading thinkers of the last great philosophy to emerge before the Christianization of the Roman Empire. I’ve no doubt that my students next semester will benefit from the analyses contained in the book. The contents of the chapters are very informative and adequately place developments in their socio-cultural context." --Michael B. Simmons, Auburn University at Montgomery.

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)

Despite their differences in origin, the three influential schools of twentieth-century continental cultural criticism--the Frankfurt School, existentialism, and poststructuralism--have long been treated as an ensemble and with critical hesitancy. Examining these schools as responses to the apparent collapse of Western civilization in the twentieth-century and as formidable intellectual challenges to the cultural legacies of the Enlightenment, this book provides a productive base for criticism and broadens our understanding of their histories and reception.

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.