During the Middle Ages many Greek mathematical and astronomical texts were translated from Greek into Arabic and from Arabic into Latin. There were many factors complicating the study of them, such as translation from or into other languages, redactions, multiple translations, and independently transmitted scholia. A literal translation risks less in loss of meaning, but can be clumsy. This article includes lists of translations and a large bibliography, divided into sections.

Theodosius Sphaerica: Arabic and Medieval Latin Translations. Edited by Paul Kunitzsch and Richard Lorch. Boethius, vol. 62. Stuttgart: Franz Steiner, 2010. Pp. vii + 431. €64.

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)

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.

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 Curry-Howard isomorphism is a proof-theoretic result that establishes a connection between derivations in natural deduction and terms in typed lambda calculus. It is an important proof-theoretic result, but also underlies the development of type systems for programming languages. This fact suggests a potential importance of the result for a philosophy of code.

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)

This classic, provocative introduction to classical metaphysical questions focuses on appreciating the problems, rather than attempting to proffer answers.

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.

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)

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)

Das Ziel des Bandes besteht darin, einen Überblick über die Grundfragen, Kernthemen und Handlungsfelder der praktischen Wirtschaftsphilosophie zu geben. Zu diesem Zweck befasst sich Teil I einführend mit dem Verhältnis von Ökonomie und Ethik, der Verbindung zwischen Wirtschaft, Gesellschaft und Politik sowie dem Zusammenhang von Globalisierung, Transnationalisierung und Interkulturalität. Teil II setzt sich mit den Kernthemen der praktischen Wirtschaftsphilosophie auseinander. Es werden Begriffe und Themen vorgestellt, die sowohl für die ökonomische Wissenschaft als auch für die Realökonomie relevant sind. Hierzu zählen (...) systematische und normative Begriffe wie Präferenzen, Rationalität oder Regeln, Grundlagenthemen wie Freiheit, Verantwortung oder Gerechtigkeit und operative Themenfelder wie Handel, Markt, Kooperation oder Digitalisierung. Teil III beschäftigt sich abschließend aus wirtschaftsphilosophischer Perspektive mit zentralen Praxisfeldern der Ökonomie. Dazu gehören das Verhältnis von Unternehmens- und Konsumentenverantwortung, die Rolle von Stakeholder-Beziehungen, Shared Value-Ansätze, die Verbindung von Governance und Institutionen sowie alternative Wirtschaftsformen und die Wirtschaftspolitik. Das Handbuch Wirtschaftsphilosophie verbindet in interdisziplinärer Perspektive philosophische Grundlagenreflexion mit theoretischer und praktischer Erschließung des ökonomischen Handelns. Methodisch werden dabei wissenschaftstheoretische, normative, kulturbezogene und historische Aspekte miteinander verbunden. (shrink)

This book gives a descriptive analysis of specific Madhyamika texts. It compares the ideology of Kumarajiva (a translator of the four Madhyamika treatises 400 A.D.) with the ideologies of the three Chinese contemporaries - HuiYuan, Seng-Jui and Seng-Chao. It envisages an intercultural transmission of religious and philosophical ideas from India to China.

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.

Early in the first volume of his Ideen zu einer reinen Phiinomeno logie und phiinomenologischen Philosophie, Edmund Husserl stated concisely the significance and scope of the problem with which this present study is concerned. When we reflect on how it is that consciousness, which is itself absolute in relation to the world, can yet take on the character of transcendence, how it can become mundanized, We see straightaway that it can do that only by means of a certain participation in (...) transcendence in the first, originary sense, which is manifestly the transcendence of material Nature. Only by means of the experiential relation to the animate organism does consciousness become really human and animal (tierischen), and only thereby does it achieve a place in the space and in the time of Nature. l Consciousness can become "worldly" only by being embodied within the world as part of it. In so far as the world is material Nature, consciousness must partake of the transcendence of material Nature. That is to say, its transcendence is manifestly an embodiment in a material, corporeal body. Consciousness, thus, takes on the characteristic of being "here and now" (ecceity) by means of experiential (or, more accurately, its intentive) relation to that corporeal being which embodies it. Accordingly, that there is a world for consciousness is a conse quence in the first instance of its embodiment by 2 that corporeal body which is for it its own animate organism. (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.

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

The standard adaptationist explanation of the presence of a sensory mechanism in an organism—that it detects properties useful to the organism—cannot be given for color vision. This is because colors do not exist. After arguing for this latter claim, I consider, but reject, nonadaptationist explanations. I conclude by proposing an explanation of how color vision could have adaptive value even though it does not detect properties in the environment.

Part I The Imperative Mood 'Virtue, then, is a disposition governing our choices '. ARISTOTLE, Eth. Nic. 36 Prescriptive Language. ...

Should particularists about ethics claim that moral principles are never true? Or should they rather claim that any finite set of principles will not be sufficient to capture ethics? This paper explores and defends the possibility of embracing the second of these claims whilst rejecting the first, a position termed 'principled particularism'. The main argument that particularists present for their position-the argument that holds that any moral conclusion can be superseded by further considerations-is quite compatible with principled particularism; indeed, it (...) is compatible with the idea that every true moral conclusion can be shown to follow deductively from a finite set of premises. Whilst it is true that these premises must contain implicit ceteris paribus clauses, this does not render the arguments trivial. On the contrary, they can do important work in justifying moral conclusions. Finally the approach is briefly applied to the related field of jurisprudence. (shrink)

This essay examines the first stage of the positive part of the Socratic education in Xenophon’s Memorabilia, whose subject is moderation concerning the gods. This stage of the Socratic education investigates whether providential gods exist and whether it ismoderate to be pious. Socrates does not accept either one of the two teleological sarguments in favour of the existence of providential gods that he advances in the Memorabilia. Instead, he holds that human beings cannot know whether or not the gods exist, (...) and moderation refers to the manner in which Socrates deems it reasonable to proceed in light of this uncertainty. Socrates suggests that the smoderate alternative to piety is justice, and this essay concludes by considering why justice is moderate but piety is not. (shrink)