In addition, this book contains tools that, in principle, can search a set of algorithms to see whether a problem is solvable, or more specifically, if it can be solved by an algorithm whose computations are efficient.

Reference [12] introduced a novel formula to formula translation tool that enables syntactic metatheoretical investigations of first-order modallogics, bypassing a need to convert them first into Gentzen style logics in order torely on cut elimination and the subformula property. In fact, the formulator tool,as was already demonstrated in loc. cit., is applicable even to the metatheoreticalstudy of logics such as QGL, where cut elimination is unavailable. This paper applies the formulator approach to show the independence of the axiom schema ☐A (...) → ☐∀ A of the logics M3and ML3 of [17, 18, 11, 13]. This leads to the conclusion that the two logics obtained by removing this axiom are incomplete, both with respect to their natural Kripke structures and to arithmetical interpretations. In particular, the so modified ML3 is, similarly to QGL, an arithmetically incomplete first-order extension of GL, but, unlike QGL, all its theorems have cut free proofs. We also establish here, via formulators, a stronger version of the disjunction property for GL and QGL without going through Gentzen versions of these logics. (shrink)

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so (...) that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing. (shrink)

We refine the definition of II-computability of [12] so that oracles have a “consistent”, but natural, behaviour. We prove a Kleene Normal Form Theorem and closure of semi-recursive relations under ∃1. We also show that in this more inclusive computation theory Post's theorem in the arithmetical hierarchy still holds.

This paper investigates a first-order extension of GL called \. We outline briefly the history that led to \, its key properties and some of its toolbox: the \emph{conservation theorem}, its cut-free Gentzenisation, the ``formulators'' tool. Its semantic completeness is fully stated in the current paper and the proof is retold here. Applying the Solovay technique to those models the present paper establishes its main result, namely, that \ is arithmetically complete. As expanded below, \ is a first-order modal logic (...) that along with its built-in ability to simulate general classical first-order provability―"\" simulating the the informal classical "\"―is also arithmetically complete in the Solovay sense. (shrink)

A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer the metatheoretical results to the original logic (e.g., [1, 6, 8, 18, 10, 12]). In the first-order modal case, on one hand we know that the Gentzenisation of the straightforward first-order extension of GL, the logic QGL, admits no cut elimination (if the rule is included as primitive; (...) or, if not included, then the rule is not admissible [1]). On the other hand the (cut-free) Gentzenisations of the first-order modal logics M3 and ML3 of [10, 12] do have cut as an admissible rule. The syntactic cut admissibility proof given in [18] for the Gentzenisation of the propositional provability logic GL is extremely complex, and it was the basis of the proofs of cut admissibility of the Gentzenisations of M3 and ML3, where the presence of quantifiers and quantifier rules added to the complexity and length of the proof. A recent proof of cut admissibility in a cut-free Gentzenisation of GL is given in [5] and is quite short and easy to read. We adapt it here to revisit the proofs for the cases of M3 and ML3, resulting to similarly short and easy to read proofs, only slightly complicated by the presence of quantification and its relevant rules. (shrink)

We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.

We introduce a first order extension of GL, called ML 3 , and develop its proof theory via a proxy cut-free sequent calculus GLTS. We prove the highly nontrivial result that cut is a derived rule in GLTS, a result that is unavailable in other known first-order extensions of GL. This leads to proofs of weak reflection and the related conservation result for ML 3 , as well as proofs for Craig’s interpolation theorem for GLTS. Turning to semantics we prove (...) that ML 3 is sound with respect to arithmetical interpretations and that it is also sound and complete with respect to converse well-founded and transitive finite Kripke models. This leads us to expect that a Solovay-like proof of arithmetical completeness of ML 3 is possible. (shrink)

Idealist philosopher Georg Hegel defied the traditional epistemological distinction of objective from subjective and developed his own dialectical alternative. Remarkable for its breadth and profundity, this work combines aspects of psychology, logic, moral philosophy, and history to form a comprehensive view that encompasses all forms of civilization. Its three divisions consist of the subjective mind (dealing with anthropology and psychology), the objective mind (concerning philosophical issues of law and morals), and the absolute mind (covering fine arts, religion, and philosophy). Wide-ranging (...) in its influence, this survey of the evolution of consciousness is essential reading for all students of philosophy and history. (shrink)

TRANSLATORS PREFACE THE PRESENT TRANSLATION OF GEORG SIMMEL'S Schopen- hauer und Nietzsche: Ein Vortragszyklus (1907), ...

The description for this book, Desert, will be forthcoming.

The idea of nature in medical theory and practice -- Diseases -- Health: popular concept and philosophical question -- Is a pedagogy of healing possible? -- The problem of regulation in the organism and in society.

Berkeley's Idealism both advances Berkeley scholarship and serves as a useful guide for teachers and students.

What drives much of the current philosophical interest in the idea of group cognition is its appeal to the manifestation of psychological properties—understood broadly to include states, processes, and dispositions—that are in some important yet elusive sense emergent with respect to the minds of individual group members. Our goal in this paper is to address a set of related, conditional questions: If human mentality is real yet emergent in a modest metaphysical sense only, then: (i) What would it mean for (...) a group to have emergent cognitive states? (ii) Is this even a metaphysically coherent view? (iii) Relative to which notion of emergence do we have reason to believe that certain groups in fact have emergent cognitive states? We shall argue that evidence from a wide variety of social science domains makes it plausible that there are group cognitive states and processes no less metaphysically emergent than human cognitive (and other special science) states and processes. (shrink)

Georges Sorel's Study on Vico is a revelatory document of the depths and stakes of French social thought at the end of the 19th century. What brought Sorel to the 18th century Neapolitan theorist of history? Acute awareness of the limitations of Marxist thought in his day, a profound concern with the material underpinnings of language, law, and culture, and the imperative to understand the possibilities of revolutionary change. We find here a different Sorel, one who speaks in surprising ways (...) to the 21st century. The translation is accompanied by an introduction and by a set of notes which situate the text both in Sorel's overall intellectual trajectory and in the fin de siècle debates from which it emerged. (shrink)

In the light of two unpublished letters from Carnap to Kuhn, this essay examines the relationship between Kuhn's The Structure of Scientific Revolutions and Carnap's philosophical views. Contrary to the common wisdom that Kuhn's book refuted logical empiricism, it argues that Carnap's views of revolutionary scientific change are rather similar to those detailed by Kuhn. This serves both to explain Carnap's appreciation of The Structure of Scientific Revolutions and to suggest that logical empiricism, insofar as that program rested on Carnap's (...) shoulders, was not substantially upstaged by Kuhn's book. (shrink)

Darwin the writer -- Learning to see : Darwin's prophetic apprenticeship on the Beagle voyage -- The prose of On the origin of species -- Surprise and paradox : Darwin's artful legacy -- Darwinian mind and Wildean paradox -- Hardy's Woodlanders and the Darwinian grotesque -- Coda : the comic Darwin.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Stolen Legacy by George G.M. James refutes the Euro-centric myth that the origin of Western philosophy is Greek. First published in 1954, this book was seminal in leading to a radical reappraisal of a philosophical system long thought to be of European origin. It is an essential work in the syllabus for the study of Western philosophy.

This edited volume draws upon Lacanian psychoanalytic theory to examine the conscious and unconscious forces underlying race as a social formation, conceptualizing race, racial identity, and racism in ways that go beyond traditional modes of psychoanalytic thought Featuring contributions from Lacanian scholars from diverse geographical and disciplinary contexts, chapters span a wide breadth of topics including white nationalism and contemporary debates over confederate monuments; emergent theories of race rooted in Afropessimism and postcolonialism; Latinx and other racialized groups; apartheid and American (...) slavery; and applications of Lacan's concepts of the lamella, drive and sexuation to processes of racialization. The collection both reorients readers' understandings of race through its deployment of Lacanian theory and redefines the Lacanian subject through its theorizing of subjectivity in relation to race, racism and racial identification. Lacan and Race will be a definitive text for psychoanalytic theorists and contemporary scholars of race and appeal to readers across the fields of psychology, cultural studies, humanities, politics, and sociology. (shrink)

Many epistemologists have been interested in justification because of its presumed close relationship to knowledge. This relationship is intended to be ...

How do we evaluate the power and utility of language when it has been made to articulate falsehoods in certain totalitarian regimes or has been charged with vulgarity and imprecision in a mass-consumer democracy? How will language react to the increasingly urgent claims of more exact speech such as mathematics and symbolic notation? These are some of the questions Steiner addresses in this elegantly written book, first published in 1967 to international acclaim.

This book introduces the reader to the philosophy of early Christianity in the 2nd-4th centuries AD, and contextualizes the philosophical contributions of early Christians in the framework of the ancient philosophical debates. It examines the first attempts of Christian thinkers to engage with issues such as questions of cosmogony and first principles, freedom of choice, concept formation, and the body-soul relation, as well as later questions like the status of the divine persons of the Trinity. It also aims to show (...) that the philosophy of early Christianity is part of ancient philosophy as a distinct school of thought, being in constant dialogue with the ancient philosophical schools, such as Platonism, Aristotelianism, Stoicism, and even Epicureanism and Scepticism. This book examines in detail the philosophical views of Christian thinkers such as Justin Martyr, Clement of Alexandria, Irenaeus, Tertullian, Origen, Basil and Gregory of Nyssa and sheds light in the distinct ways they conceptualized traditional philosophical issues and made some intriguing contributions. The book's core chapters survey the central philosophical concerns of the early Christian thinkers and examines their contributions. These range across natural philosophy, metaphysics, logic and epistemology, psychology and ethics, and include such questions as how the world came into being, how God relates to the world, what is the status of matter, how we can gain knowledge, in what sense humans have freedom of choice, what the nature of soul is and how it relates to the body, and how we can attain happiness and salvation. The Philosophy of Early Christianity is intended for undergraduate and postgraduate students of ancient philosophy and early Christianity, from across the disciplines of classics, history and theology. (shrink)

Benjamin Franklin famously wrote that “the good [that] men do separately is small compared with what they may do collectively” (Isaacson 2004). The ability to join with others in groups to accomplish goals collectively that would hopelessly overwhelm the time, energy, and resources of individuals is indeed one of the greatest assets of our species. In the history of humankind, groups have been among the greatest workers, builders, producers, protectors, entertainers, explorers, discoverers, planners, problem-solvers, and decision-makers. During the late 19th (...) and early 20th century, many social scientists employed the notorious “group mind” idiom to express the sensible idea that groups can function as the seats of cognition, intelligence, and agency in their own right (Allport 1968; Wilson 2004). In their quest to stress (rightly) that group phenomena are something “over and above” the sum of individual contributions, a fondness for vitalist metaphors led them to believe (wrongly) that genuine group cognition must be the result of tapping into individualistically inaccessible, “holistic” forces. Today, inspired in part by historically unparalleled forms of mass collaboration enabled by the internet, it has once again become popular to speak of collective intelligence, group agency, or even the emergence of a “global brain” (cf. the wiki-edited MIT Handbook of Collective Intelligence). -/- In this chapter, I review some contemporary developments of the idea of group cognition, defined broadly as the collaborative performance of cognitive tasks such as remembering, problem-solving, decision-making, or verbal creativity for the purpose of producing a group-level outcome. My discussion serves a two-fold purpose. First, by discussing how the idea of group cognition can be operationalized, I seek to show that we can retain some central theoretical insights of the “group mind” thesis without succumbing to its eccentric metaphysical overtones. Second, by providing a useful array of generalizable taxonomic resources, I hope to foster greater degrees of mutual awareness among insufficiently integrated areas of research on group performance. (shrink)

Since its publication in 1935, Kenneth Burke's Permanence and Change, a text that can serve as an introduction to all of Burke's theories, has become a landmark of rhetorical study. Using new archival sources and by contextualizing the theory in the past and present, Ann George offers the first sustained exploration of Burke's work and seeks to clarify the notoriously difficult book for both amateurs and scholars of rhetoric in Kenneth Burke's Permanence and Change: A Critical Companion.

De récents travaux ont éclairé sans équivoque aucune l'adhésion de Martin Heidegger au totalitarisme hitlérien. Georges-Arthur Goldschmidt, traducteur de Kafka et de Nietzsche, reprend la question par un biais plus personnel, dans les pas de Victor Klemeperer, l'auteur de la Lingua Tertii Imperrii (1947). "Gefolgschaft", "Einsatz", "Ereignis" : autant de termes appartenant à la fois au vocabulaire nazi et au système philosophique heideggerien. L'appropriation d'un tel langage n'a rien d'opportuniste ou d'occasionnel, mais marque un engagement profond. Cet ouvrage rare et (...) décisif restitue au lecteur français le champ lexical allemand contemporain d'Heidegger. Il dévoile les implications politiques d'une terminologie qui, en passant dans la traduction d'une langue à l'autre, lui échappent souvent. Une telle contamination constitue symboliquement l'un des événements les plus importants du XXe siècle philosophique, dont on ne finira pas de mesurer la portée et les conséquences. (shrink)

The ‘extended mind’ thesis asserts that cognitive processes are not bound by the skull or even skin of biological individuals, but actively incorporate environmental structures such as symbols, tools, artifacts, media, cultural practices, norms, groups, or institutions. By distributing cognition across space, time, and people in canny ways, we circumvent or overcome the biological limitations of our brains. Human beings are creative, albeit opportunistic experts in cognitive ‘self-transcendence.’ This entry surveys discussions of EM in philosophy of mind and cognitive science (...) which point to this overarching theme. (shrink)

George GrantÑphilosopher, conservative, Canadian nationalist, ChristianÑwas one of Canada’s most significant thinkers, and the author of Lament for a Nation, Technology and Empire, and English-Speaking Justice. Admirers and critics of the author will welcome these compelling essays about society’s traditional values in a technological age.

Reflections by leading Latin American and African American philosophers on their identity within the field of philosophy.

In der Philosophiegeschichte findet sich keine detailliert ausformulierte Philosophie des Abschieds. Die Publikation liefert hierzu die Spur des Abschieds, die als ein abwesend anwesendes Phänomen nachzuzeichnen ist. Neben der Rekonstruktion der relevanten philosophischen Thanatologien von der Antike bis ins 20. Jahrhundert, der Phänomenologie von Leiden und Schmerz, des Trostes und der Trauer werden vorrangig über Nietzsches Philosophie der tragischen Bejahungpraxis philosophische Orientierungen für ein souveränes Verhaltengegenüber dem existentiellen Phänomen des Abschieds präsentiert"--Page 4 of cover.

Consent theory -- The principle of fair play -- Multiple principle theory -- Limits of political obligation.

This book will examine paradoxes in diverse areas of thought: philosophy, mathematics, physics, economics, political science, psychology, computer science, logic, statistics, linguistics, law, etc. Though the treatment of each paradox is rigorous, the book will be written accessibly with a lighthearted and humorous tone so as to keep the reader engaged. Each chapter will focus on a single paradox, structured roughly like so: 1. A question is asked in the context of a story. As an answer, the paradox is presented (...) (which often results in an aha moment). The historical background of the paradox is recounted. 2. The dénouement explains how the paradox is resolved or why there is no resolution. 3. The chapter ends with further remarks, usually contemporary real-world examples or applications of said paradox. Some examples of the paradoxes covered are the Axiom of Choice (Mathematics), Monty Hall Problem (Statistics), Morgenbesser's Paradox (Linguistics), Tea Leaves Paradox (Physics), The Ultimatum Game (Economics), and The Chicken or Egg Question (Evolution). (shrink)