The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

Statman and Orevkov independently proved that cut-elimination is of nonelementary complexity. Although their worst-case sequences are mathematically different the syntax of the corresponding cut formulas is of striking similarity. This leads to the main question of this paper: to what extent is it possible to restrict the syntax of formulas and — at the same time—keep their power as cut formulas in a proof? We give a detailed analysis of this problem for negation normal form , prenex normal form and (...) monotone formulas. We show that proof reduction to NNF is quadratic, while PNF behaves differently: although there exists a quadratic transformation into a proof in PNF too, additional cuts are needed; the elimination of these cuts requires nonelementary expense in general. By restricting the logical operators to {,,,}, we obtain the type of monotone formulas. We prove that the elimination of monotone cuts can be of nonelementary complexity . On the other hand, we define a large class of problems where cut-elimination of monotone cuts is only exponential and show that this bound is tight. This implies that the elimination of monotone cuts in equational theories is at most exponential. Particularly, there are no short proofs of Statman's sequence with monotone cuts. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...) logic of linear discrete time with gaps follows. (shrink)

We define a generalization of the first-order cut-elimination method CERES to higher-order logic. At the core of lies the computation of an set of sequents from a proof π of a sequent S. A refutation of in a higher-order resolution calculus can be used to transform cut-free parts of π into a cut-free proof of S. An example illustrates the method and shows that can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.

The length of resolution proofs is investigated, relative to the model-theoretic measure of Herband complexity. A concept of resolution deduction is introduced which is somewhat more general than the classical concepts. It is shown that proof complexity is exponential in terms of Herband complexity and that this bound is tight. The concept of R-deduction is extended to FR-deduction, where, besides resolution, a function introduction rule is allowed. As an example, consider the clause P Q: conclude P) Q, where a, f (...) are new function symbols extending Herbrand's universe. P ()Q from Q) and Skolemization). By modification of a construction of Statman it is shown that FR-deductions may be nonelementarily shorter than R-deductions . Finally it is proved that FR-deduction has weaker effects only if clausal logic is restricted to Horn logic. (shrink)

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure (...) cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our under- standing of a molecule in isolation, as well as of chemistry’s relation to quantum physics. (shrink)

While it might seem prima facie plausible that divine foreknowledge is all that is needed for prophecy, this seems incorrect. To issue a prophecy, God hasto know not just how someone will act, but how someone would act were the prophecy issued. This makes some think that Middle Knowledge is required.I argue that Thomas Flint’s two Middle Knowledge based accounts of prophecy are unsatisfactory, but one of them can be repaired. However the resources needed for repair also yield a sketch (...) of a foreknowledge-only account of prophecy. (shrink)

Discussion of the relevance of grounding to substantiveness, theory-choice, and “location problems” in metaphysics.

Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent. A natural idea is that there are requirements of "structural rationality" that forbid us from being in these incoherent states. Yet a number of surprisingly difficult challenges arise for this idea. These challenges have recently led many philosophers to attempt to minimize or eliminate structural rationality, arguing that it is just a "shadow" of "substantive rationality"--that is, correctly responding to one's (...) reasons. -/- In *Fitting Things Together*, Alex Worsnip pushes back against this trend--defending the view that structural rationality is a genuine kind of rationality, distinct from and irreducible to substantive rationality, and tackling the most important challenges for this view. In so doing, he gives an original positive theory of the nature of coherence and structural rationality that explains how the diverse range of instances of incoherence can be unified under a general account, and how facts about coherence are normatively significant. He also shows how a failure to focus on coherence requirements as a distinctive phenomenon and distinguish them adequately from requirements of substantive rationality has led to confusion and mistakes in several substantive debates in epistemology and ethics. -/- Taken as a whole, Fitting Things Together provides the first sustained defense of the view that structural rationality is a genuine, autonomous, unified, and normatively significant phenomenon. (shrink)

Professional philosophers and advanced students working in metaphysics and the philosophy of science will find this book both provocative and stimulating.

The present study investigated whether individual differences between psychologists in thinking styles are associated with accuracy in diagnostic classification. We asked novice and experienced clinicians to classify two clinical cases of clients with two co-occurring psychological disorders. No significant difference in diagnostic accuracy was found between the two groups, but when combining the data from novices and experienced psychologists accuracy was found to be negatively associated with certain decision making strategies and with a higher self-assessed ability and preference for a (...) rational thinking style. Our results underscore the idea that it might be fruitful to look for explanations of differences in the accuracy of diagnostic judgments in individual differences between psychologists (such as in thinking styles or decision making strategies used), rather than in experience level. (shrink)

The purpose of this study was to gain a better understanding of the impact of moral issues on the moral decision-making process within the field of accounting. In particular, the study examined differences in the perceptions of the underlying characteristics of moral issues on the specific steps of the moral decision-making process of four different accounting situations.The research results suggested that student's perception of the components of moral intensity as well as the various stages of the moral decision-making process was (...) influenced by the type and intensity of the moral issue. In general, accounting student's perceptions of the importance of these variables varied between less unethical and more unethical accounting issues. The differences in perceptions of four moral intensity components: magnitude of consequences, concentration of effect, probability of effect and proximity stood out more in the accounting issues analyzed. (shrink)

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist (...) can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume. (shrink)

Thomas Samuel Kuhn (1922–1996) is one of the most influential philosophers of science of the twentieth century, perhaps the most influential. His 1962 book The Structure of Scientific Revolutions is one of the most cited academic books of all time. Kuhn’s contribution to the philosophy of science marked not only a break with several key positivist doctrines, but also inaugurated a new style of philosophy of science that brought it closer to the history of science. His account of the development (...) of science held that science enjoys periods of stable growth punctuated by revisionary revolutions. To this thesis, Kuhn added the controversial ‘incommensurability thesis’, that theories from differing periods suffer from certain deep kinds of failure of comparability. (shrink)

This Is A New Release Of The Original 1868 Edition.

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.

Philosophical discussions often involve appeals to verdicts about particular cases, sometimes actual, more often hypothetical, and usually with little or no substantive argument in their defense. Philosophers — on both sides of debates over the standing of this practice — have often called the basis for such appeals ‘intuitions’. But, what might such ‘intuitions’ be, such that they could legitimately serve these purposes? Answers vary, ranging from ‘thin’ conceptions that identify intuitions as merely instances of some fairly generic and epistemologically (...) uncontroversial category of mental states or episodes to ‘thick’ conceptions that add to this thin base certain semantic, phenomenological, etiological, or methodological conditions. As this chapter discusses, thick conceptions turn out to have their own methodological problems; some may even leave philosophers in the methodologically untenable position of being unable to determine when anyone is doing philosophy correctly. (shrink)

Thomas Kuhn transformed the philosophy of science. His seminal 1962 work "The Structure of Scientific Revolutions" introduced the term 'paradigm shift' into the vernacular and remains a fundamental text in the study of the history and philosophy of science. This introduction to Kuhn's ideas covers the breadth of his philosophical work, situating "The Structure of Scientific Revolutions" within Kuhn's wider thought and drawing attention to the development of his ideas over time. Kuhn's work is assessed within the context of other (...) philosophies of science notably logical empiricism and recent developments in naturalized epistemology. The author argues that Kuhn's thinking betrays a residual commitment to many theses characteristic of the empiricists he set out to challenge. Kuhn's influence on the history and philosophy of science is assessed and where the field may be heading in the wake of Kuhn's ideas is explored. (shrink)

This volume contains the Arabic translations of a lost treatise by Alexander of Aphrodisias "On the Principles of the Universe" with English translation, introduction and commentary. It also includes an Arabic and Syriac glossary. The introduction and commentary deal in detail with the manuscripts, the translators and the exegetical tendencies of the text, as well as with its reception in Arabic philosophy. The main theme of the work is the motion of the heavenly bodies and their influence on the (...) physical world. (shrink)

Common errors on the mind.--Errors of suppressed correlatives.--The civil service examinations.--The classical controversy.--Metaphysics and debating societies.--The university ideal, past and present.--The art of study.--Religious tests and subscriptions.--Procedure of deliberative bodies.

In this paper we first give a survey of reductive cut-elimination methods in classical logic. In particular we describe the methods of Gentzen and Schütte-Tait from the abstract point of view of proof reduction. We also present the method CERES which we classify as a semi-semantic method. In a further section we describe the so-called semantic methods. In the second part of the paper we carry the proof analysis further by generalizing the CERES method to CERESD . In the generalized (...) version CERESD we admit general elimination rules which are based on the mere semantical truth of sentences. We construct complete cut-free LK-derivations originating from derivations potentially containing unproven lemmas. Finally we give a comparison of reductive methods and CERESD by presenting a general simulation result. (shrink)

' But, although such a being (a purely intellectual being) might perhaps be conceived to exist, and although, in studying our internal frame, ...

I propose an approach to liar and Curry paradoxes inspired by the work of Roger Swyneshed in his treatise on insolubles (1330-1335). The keystone of the account is the idea that liar sentences and their ilk are false (and only false) and that the so-called ''capture'' direction of the T-schema should be restricted. The proposed account retains what I take to be the attractive features of Swyneshed's approach without leading to some worrying consequences Swyneshed accepts. The approach and the resulting (...) logic (called ''Swynish Logic'') are non-classical, but are consistent and compatible with many elements of the classical picture including modus ponens, modus tollens, and double-negation elimination and introduction. It is also compatible with bivalence and contravalence. My approach to these paradoxes is also immune to an important kind of revenge challenge that plagues some of its rivals. (shrink)

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

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)

In the late Middle Ages the philosopher and mystic Meister Eckhart preached that to know the truth you must be the truth. But how to be the truth? Eckhart's answer comes in the form of an imperative: release yourself, let be. Only then will you be able to understand that the deepest meaning of being is releasement. Only then will you become who you truly are. This book interprets Eckhart's Latin and Middle High German writings under the banner of an (...) imperative of releasement, and then shows how the twentieth-century thinker Martin Heidegger creatively appropriates this idea at several stages of his career. Heidegger had a lifelong fascination with Eckhart, referring to him as "the old master of letters and life." Drawing on archival material and Heidegger's marginalia in his personal copies of Eckhart's writings, Moore argues that Eckhart was one of the most important figures in Heidegger's philosophy. This book also contains previously unpublished documents by Heidegger on Eckhart, as well as the first English translation of Nishitani Keiji's essay "Nietzsche's Zarathustra and Meister Eckhart," which he initially gave as a presentation in one of Heidegger's classes in 1938. (shrink)

Hate speech law can be found throughout the world. But it is also the subject of numerous principled arguments, both for and against. These principles invoke a host of morally relevant features and practical considerations . The book develops and then critically examines these various principled arguments. It also attempts to de-homogenize hate speech law into different clusters of laws/regulations/codes that constrain uses of hate speech, so as to facilitate a more nuanced examination of the principled arguments. Finally, it argues (...) that it is morally fitting for judicial and legislative judgments about the overall warrant of hate speech law to reflect principled compromise. Principled compromise is characterized not merely by compromise over matters of principled concern but also by compromise which is itself governed by ideals of moral duty or civic virtue. (shrink)

Many introductions to this field start with the problem of justifying scientific knowledge but Alexander Bird begins by examining the subject matter, or metaphysics, of science. Using topical scientific debates he vividly elucidates what it is for the world to be governed by laws of nature. This idea provides the basis for explanations and causes and leads to a discussion of natural kinds and theoretical entities. With this foundation in place he goes on to consider the epistemological issues of (...) how science arrives at knowledge, favouring a treatment of scientific reasoning based on inference to the best explanation. Drawing on contemporary work in epistemology, Bird argues that scepticism about induction should not be a problem for science and examines the consequences of this position for controversies surrounding the ideas of scientific progress and scientific revolution. Bird's insightful treatment makes Philosophy of Science an ideal text for undergraduate courses. The guides to further reading provided in each chapter help the reader pursue interesting topics and facilitate the use of the book in conjunction with primary sources. (shrink)

Achieving space situational awareness requires, at a minimum, the identification, characterization, and tracking of space objects. Leveraging the resultant space object data for purposes such as hostile threat assessment, object identification, and conjunction assessment presents major challenges. This is in part because in characterizing space objects we reference a variety of identifiers, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, operational processes, operational statuses, and so forth, which tend to be defined in highly heterogeneous and sometimes inconsistent (...) ways. The Space Domain Ontologies are designed to provide a consensus-based realist framework for formulating such characterizations in a way that is both consistent and computable. Space object data are aligned with classes and relations in a suite of ontologies built around the existing Space Object Ontology. They are stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space situational awareness and the needs of spacecraft operators and analysts. This paper provides an overview of the Space Domain Ontologies and their development and use. It presents the motivation for and advantages of the Space Domain Ontologies, including the benefits they provide for enhancing and maintaining long-term space situational awareness. (shrink)

Scotland has played an immense role in European high culture through the centuries, and among its cultural links none have been greater than those with France. This book shows that the links with France stretch back deep into the Middle Ages, and continue without a break into the 18th century, the Age of Enlightenment.

Any serious student attempting to better understand the nature, methods, and justification of science will value Alex Rosenberg's and Lee McIntyre's updated and substantially revised Fourth Edition of Philosophy of Science: A Contemporary Introduction. Weaving lucid explanations with clear analyses, the volume is as a much-used, thematically-oriented introduction to the field.

'A wonderfully assured and utterly riveting biography that captures not only the much-maligned Machiavelli, but also the spirit of his time and place. A monumental achievement.' - Jessie Childs, author of God's Traitors. 'A notorious fiend', 'generally odious', 'he seems hideous, and so he is.' Thanks to the invidious reputation of his most famous work, The Prince, Niccolò Machiavelli exerts a unique hold over the popular imagination. But was Machiavelli as sinister as he is often thought to be? Might he (...) not have been an infinitely more sympathetic figure, prone to political missteps, professional failures and personal dramas? Alexander Lee reveals the man behind the myth, following him from cradle to grave, from his father's penury and the abuse he suffered at a teacher's hands, to his marriage and his many affairs (with both men and women), to his political triumphs and, ultimately, his fall from grace and exile. In doing so, Lee uncovers hitherto unobserved connections between Machiavelli's life and thought. He also reveals the world through which Machiavelli moved: from the great halls of Renaissance Florence to the court of the Borgia pope, Alexander VI, from the dungeons of the Stinche prison to the Rucellai gardens, where he would begin work on some of his last great works. As much a portrait of an age as of a uniquely engaging man, Lee's gripping and definitive biography takes the reader into Machiavelli's world - and his work - more completely than ever before. (shrink)

A collection of essays by Alexander Rosenberg, the distinguished philosopher of science. The essays cover three broad areas related to Darwinian thought and naturalism: the first deals with the solution of philosophical problems such as reductionism, the second with the development of social theories, and the third with the intersection of evolutionary biology with economics, political philosophy, and public policy. Specific papers deal with naturalistic epistemology, the limits of reductionism, the biological justification of ethics, the so-called 'trolley problem' in (...) moral philosophy, the political philosophy of biological endowments, and the Human Genome Project and its implications for policy. Rosenberg's important writings on a variety of issues are here organized into a coherent philosophical framework which promises to be a significant and controversial contribution to scholarship in many areas. (shrink)