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.

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.

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)

Written in the 1960s, TRUTH AND METHOD is Gadamer's magnum opus.

George Berkeley (1685-1753) is the superstar of Irish Philosophy. He entered Trinity College, Dublin, in 1700 and became a fellow in 1707. In 1724 he resigned his Fellowship to become Dean of Derry, and in 1734 he was made Bishop of Cloyne. He settled in Oxford in 1752 and died the following year. The work of George Berkeley is marked by its diversity and range. His writings take in such topics as mathematics, psychology, politics, health, economics, deism and (...) education, as well as that with which he is most associated - philosophy. Whatever topic he dealt with, his grasp of the subject matter was always impressive and his criticisms of his contemporaries often acute. Among the most noteable of the British Empiricists, he took his starting point from Locke's new 'way of ideas', but he rejected abstract ideas and the possibility of real existence outside perception. It is for this doctrine that he is most known - that there is no such thing as matter, and that things are collections of ideas which can exist only in our minds and only for so long as they are perceived. This philosophy, summed up in his phrase 'to be is to be perceived', he termed 'immaterialism'. A.C. Fraser's collection includes a series of what were previously unpublished notes by Berkeley on all the main topics of his philosophy. This, the 1901 edition, was the first complete edition of his works. (shrink)

A brilliant and comprehensive history of the creation of the modern Western mind. Soul Machine takes us back to the origins of modernity, a time when a crisis in religious authority and the scientific revolution led to searching questions about the nature of human inner life. This is the story of how a new concept—the mind—emerged as a potential solution, one that was part soul and part machine, but fully neither. In this groundbreaking work, award-winning historian George Makari shows (...) how writers, philosophers, physicians, and anatomists worked to construct notions of the mind as not an ethereal thing, but a natural one. From the ascent of Oliver Cromwell to the fall of Napoleon, seminal thinkers like Hobbes, Locke, Diderot, and Kant worked alongside often-forgotten brain specialists, physiologists, and alienists in the hopes of mapping the inner world. Conducted in a cauldron of political turmoil, these frequently shocking, always embattled efforts would give rise to psychiatry, mind sciences such as phrenology, and radically new visions of the self. Further, they would be crucial to the establishment of secular ethics and political liberalism. Boldly original, wide-ranging, and brilliantly synthetic, Soul Machine gives us a masterful, new account of the making of the modern Western mind. (shrink)

Throughout The Blessed and Boundless God, he proves his doctrine by demonstrating God's incomparableness in His being, attributes, works, and words. Swinnock is a pastor-theologian who views theology as the means by which we grow in acquaintance with God and, consequently, in godliness.

George Herbert Mead (1863-1931) had a powerful influence on the development of American pragmatism in the twentieth century. He also had a strong impact on the social sciences. This classic book represents Mead's philosophy of experience, so central to his outlook. The present as unique experience is the focus of this deep analysis of the basic structure of temporality and consciousness. Mead emphasizes the novel character of both the present and the past. Though science is predicated on the assumption (...) that the present is predictable based on a thorough knowledge of the past, the experience of the present, says Mead, is an utterly unique moment comparable to no other, and when it is past the novel character of that unique experience is irrevocable. The emergence of novelty within the perceived rational order of reality is the crux of the problem that Mead explores. The present, in his words, is "the emergent event . . . something which is more than the processes that have led up to it and which by its change, continuance, or disappearance, adds to later passages a content they would not otherwise have possessed." The present as "the seat of reality" heavily conditions our retrospective view of the past as much as it helps to shape the future. The novelty of every present experience causes us to reconstruct our preceding experiences to make sense of the past, which is naturally assumed to be the main cause of what we presently experience. Our perspective on reality is thus relative to the conditioning of each new event and it changes continuously as the effects of the present shift our view of the past and future. This emphasis on the integrative, holistic nature of reality, in which everything past, present, and future is a condition of everything else, makes Mead's philosophy highly relevant to today's scientific picture of a quantum universe, where chance and probability play a role in the emergence of reality. Also of great interest is the way in which he extends his basic analysis of temporal-spatial reality to the emergence of mind and consciousness as a natural development of the evolutionary process. This stimulating and provocative work attests to John Dewey's praise of Mead as "the most original mind in philosophy in America" of his generation. (shrink)

touch 27 Thirrdly, the straining of the eye 28 The occasions which suggest distance have in their own nature no relation to it 29 A difficult case proposed by Dr. Barrow as repugnant to all the known theories 30 This case contradicts a ...

The Oxford Philosophical Texts series consists of authoritative teaching editions of canonical texts in the history of philosophy from the ancient world down to modern times. Each volume provides a clear, well laid out text together with a comprehensive introduction by a leading specialist,giving the student detailed critical guidance on the intellectual context of the work and the structure and philosophical importance of the main arguments. Endnotes are supplied which provide further commentary on the arguments and explain unfamiliar references and (...) terminology, and a fullbibliography and index are also included.The series aims to build up a definitive corpus of key texts in the Western philosophical tradition, which will form a reliable and enduring resource for students and teachers alike.In his Principles of Human Knowledge Berkeley makes the striking claim that physical things consist of nothing but ideas, and so do not exist outside the mind. This establishes Berkeley as the founder of the idealist tradition in philosophy. Berkeley argues vigorously that once we correct ourunderstanding of the physical, we can find a new proof of the existence of God, refute sceptical attacks on human knowledge, and resolve many difficulties and paradoxes raised by the advance of science.The text printed in this volume is the 1734 edition of the Principles which is generally agreed to represent Berkeley's mature thought. Also included are the four important letters between George Berkeley and Samuel Johnson, written in 1729-30. The text is supplemented by a comprehensiveintroduction which looks at the structure and main arguments of the text, as well as discussing Berkeley's life, influences, and general philosophy. In addition the volume includes an analysis of the text, a glossary, detailed notes, and a full bibliography with guidance on further reading.This new edition of Berkeley's most famous work, published alongside his other masterpiece, the Three Dialogues (also edited by Jonathan Dancy) provides the student with a thorough introduction to the central ideas of one of the world's greatest philosophers. (shrink)

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos (...) does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency. (shrink)

First published in 1713, this work was designed as a vivid and persuasive presentation of the remarkable picture of reality that Berkeley had first presented two years earlier in his Principles of Human Knowledge. His central claim there, as here, was that physical things consist of nothing but ideas in minds--that the world is not material but mental. Berkeley uses this thesis as the ground for a new argument for the existence of God, and the dialogue form enables him to (...) raise and respond to many of the natural objections to his position. The text printed in this volume is that of the 1734 edition of the Dialogues. (shrink)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

bk. 1. 1868-1909 -- bk. 2. 1910-1920 -- bk. 3. 1921-1927 -- bk. 4. 1928-1932 -- bk. 5. 1933-1936 -- bk. 6. 1937-1940 -- bk. 7. 1941-1947 -- v. 8. 1948-1952.

The paper begins with a clarification of the notions of intuition (and, in particular, modal intuition), modal error, conceivability, metaphysical possibility, and epistemic possibility. It is argued that two-dimensionalism is the wrong framework for modal epistemology and that a certain nonreductionist approach to the theory of concepts and propositions is required instead. Finally, there is an examination of moderate rationalism’s impact on modal arguments in the philosophy of mind -- for example, Yablo’s disembodiment argument and Chalmers’s zombie argument. A less (...) vulnerable style of modal argument is defended, which nevertheless wins the same anti-materialist conclusions sought by these other arguments. (shrink)

This is the first study of business ethics to take into consideration the plethora of issues raised by the Information Age. The first study of business ethics to take into consideration the plethora of issues raised by the Information Age. Explores a wide range of topics including marketing, privacy, and the protection of personal information; employees and communication privacy; intellectual property issues; the ethical issues of e-business; Internet-related business ethics problems; and the ethical dimension of information technology on society. Uncovers (...) previous ignored ethical issues. Underlines the need for public discussion of the issues. Argues that computers and information technology have not necessarily developed in the most ethical manner possible. (shrink)

The topic of a priori knowledge is approached through the theory of evidence. A shortcoming in traditional formulations of moderate rationalism and moderate empiricism is that they fail to explain why rational intuition and phenomenal experience count as basic sources of evidence. This explanatory gap is filled by modal reliabilism -- the theory that there is a qualified modal tie between basic sources of evidence and the truth. This tie to the truth is then explained by the theory of concept (...) possession: this tie is a consequence of what, by definition, it is to possess (i.e., to understand) one’s concepts. A corollary of the overall account is that the a priori disciplines (logic, mathematics, philosophy) can be largely autonomous from the empirical sciences. (shrink)

George tackles the issues at the heart of the contemporary conflict of worldviews and shows that traditional beliefs may still be the best course of action.

Most of the major schools of contemporary philosophy, from Marxism to Existentialism, are reactions to Hegelianism and all, if they are to be understood, require some understanding of Hegel's Logic. From its first appearance in 1812, this work has been recognized by both admirers and detractors alike as being the absolute foundation of Hegel's system.

This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

A modern, highly readable translation of a primary text in Western philosophy. Complete translation in English with introduction, notes and glossary. The glossary is keyed to the primary occurrences of important terms in the text and provides insights into the concepts beyond the translation, especially useful pedagogical device for students coming to Hegel for the first time. Focus Philosophical Library translations are close to and are non-interpretative of the original text, with the notes and a glossary intending to provide the (...) reader with some sense of the terms and the concepts as they were understood by Hegel’s immediate audience. (shrink)

Global Economy, Global Justice explores a vital question that is suppressed in most economics texts: "what makes for a good economic outcome?" Neoclassical theory embraces the normative perspective of "welfarism" to assess economic outcomes. This volume demonstrates the fatal flaws of this perspective--flaws that stem from objectionable assumptions about human nature, society and science. Exposing these failures, the book obliterates the ethical foundations of global neoliberalism. George DeMartino probes heterodox economic traditions and philosophy in search of an ethically viable (...) alternative to welfarism. Drawing on the work of Amartya Sen, DeMartino proposes the egalitarian principle of the "global harmonization of capabilities" to guide economics. This principle provides a basis for resisting oppression the world over while nevertheless demanding respect for cultural diversity. DeMartino puts this principle to work adjudicating contemporary debates over global policy regimes, and completes thebook with a set of deeply egalitarian global policies for the year 2025. Global Economy, Global Justice 's engaging prose will appeal to those seeking to understand the intersection between economics and political philosophy. Its focus on the normative foundations of contemporary policy disputes makes it unique in the literature on globalization. (shrink)

Radical empiricism is the view that a person's experiences (sensory and introspective), or a person's observations, constitute the person's evidence. This view leads to epistemic self-defeat. There are three arguments, concerning respectively: (1) epistemic starting points; (2) epistemic norms; (3) terms of epistemic appraisal. The source of self-defeat is traced to the fact that empiricism does not count a priori intuition as evidence (where a priori intuition is not a form of belief but rather a form of seeming, specifically intellectual (...) as opposed to sensory). Moderate rationalism, by contrast, avoids self-defeat. (shrink)

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, (...) but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer. (shrink)

This new translation of The Science of Logic (also known as 'Greater Logic') includes the revised Book I (1832), Book II (1813), and Book III (1816). Recent research has given us a detailed picture of the process that led Hegel to his final conception of the System and of the place of the Logic within it. We now understand how and why Hegel distanced himself from Schelling, how radical this break with his early mentor was, and to what extent it (...) entailed a return (but with a difference) to Fichte and Kant. In the introduction to the volume, George di Giovanni presents in synoptic form the results of recent scholarship on the subject, and, while recognizing the fault lines in Hegel's System that allow opposite interpretations, argues that the Logic marks the end of classical metaphysics. The translation is accompanied by a full apparatus of historical and explanatory notes. (shrink)

Taking Carnap’s classic exposition as a starting point, this paper develops a pragmatic account of the method of explication, defends it against a range of challenges and proposes a detailed recipe for the practice of explicating. It is then argued that confusions are involved in characterizing explications as definitions, and in advocating precising definitions as an alternative to explications. Explication is better characterized as conceptual re-engineering for theoretical purposes, in contrast to conceptual re-engineering for other purposes and improving exactness for (...) purely practical reasons. Finally, three limitations which call for further development of the method of explication are discussed. (shrink)

But the charged personal encounter between master and disciple is precisely what interests George Steiner in this book, a sustained reflection on the infinitely ...

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

This is the first comprehensive and systematic analytical study of the major philosophical concepts of classical yoga. The book consists of a series of detailed discussions of the key concepts used by Pata-jali in his Yoga-Sutra to describe and explain the enigma of human existence and to point a way beyond the perpetual motion of the wheel of becoming. Feuerstein's study differs from previous ones in that it seeks to free Pata-jali's aphoristic statements from the accretions of later interpretations; instead, (...) the author places the Sutra in its original context and sees it as the source of the whole edifice of classical yoga and not just as a summary of previous developments. This book will be of interest to comparative reliogionists, Indologists, and practitioners of yoga who wish to deepen their understanding of its philosophical basis._. (shrink)