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.

ABSTRACT Our discussion of Niccolò Tornioli's The Astronomers questions some of the traditional identifications of its characters, although we cannot claim to have solved these figures’ identities and several remain a mystery. We do present new iconographic interpretations of particular scientific instruments, diagrams, and natural phenomena in the canvas. These novel readings occasionally remain conjectural in part because Tornioli represents these entities in a way that makes it clear that he did not fully comprehend them. The errors and obscurities in (...) Tornioli’s painting lead us to two conclusions. First, that his erudite patron Virgilio Spada was unlikely to have been involved in the definition of the painting’s iconographies, as he would have objected to Tornioli’s crass mistakes and obscure imagery. Second, that these errors and indistinct details should be taken at face value, insofar as they accentuate the difficulties of astronomical observation. Beyond highlighting these challenges, we argue that the painting also visualizes techniques for countering them. Specifically, the canvas would have focused early modern observers’ attention on the edifying powers of civil conversations and communal observations with scientific instruments as well as images—including diagrams, celestial maps, and paintings. (shrink)

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.

Inspection of surviving mirrors and related objects shows that they were too crude to offer the early Renaissance painter an optical short-cut to a naturalistic image of his subject. The craftsmanship of mirror makers was independent of and inferior to the quality of theories of image formation of the day.

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.

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...) argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

Drawing on case studies from around the world - including Iran, Guatemala, USA and Mexico - this collection documents how transnational human rights discourses and legal institutions are materialised, imposed, resisted and transformed in a variety of contexts.

Discusses the moral and ethical aspects of euthanasia and related topics.

Written by a former student of Heidegger, this book examines the relationship between the philosophy and the politics of a celebrated teacher and the allure that Nazism held out for scholars committed to revolutionary nihilism.

In this study, Worsley argues that it is rational to believe in a loving God in the face of evil. Beginning with a critique of Alvin Plantinga, he shows that human freedom is highly complex, and so depends upon complex structures in nature. These are both necessary for freedom but also sufficient for natural evil. He offers close analysis of the evolution of the human brain. The book develops a parallel argument that human evil stems from the evolution of personality.

. History of the concept of economic efficiency . INTRODUCTION James Buchanan won the Nobel Prize by proving that the process by which elected officials ...

Philosophers are increasingly coming to recognize the importance of Freudian theory for the understanding of the mind. The picture Freud presents of the mind's growth and organization holds implications not just for such perennial questions as the relation of mind and body, the nature of memory and personal identity, the interplay of cognitive and affective processes in reasoning and acting, but also for the very way in which these questions are conceived and an interpretation of the mind is sought. This (...) volume of essays, by some of today's leading philosophers, explores all these topics, as well as the methods, results and status of the theory itself, while two 'classical' discussions by Wittgenstein and Sartre are also included. A number of the contributions – those by Donald Davidson, W. D. Hart, Jim Hopkins, Adam Morton, David Pears and Richard Wollheim – have not been published before, and a very useful bibliography is provided. It is an anthology that will be vital to anyone interested in Freudian theory and, more generally, in philosophical psychology. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

In line with the British Psychological Society's recent recommendations for teaching the history of psychology, this comprehensive undergraduate textbook emphasizes the philosophical, cultural and social elements that influenced psychology's development. The authors demonstrate that psychology is both a human (e.g. psychoanalytic or phenomenological) and natural (e.g. cognitive) science, exploring broad social-historical and philosophical themes such as the role of diverse cultures and women in psychology and the complex relationship between objectivity and subjectivity in the development of psychological knowledge. The result (...) is a fresh and balanced perspective on what has traditionally been viewed as the collected achievements of a few 'great men'. With a variety of learning features, including case studies, study questions, thought experiments and a glossary, this new textbook encourages students to critically engage with chapter material and analyze themes and topics within a social, historical and philosophical framework. (shrink)