The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. (...) I argue that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” (see [4]). The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. (...) Both procedures taken together were successfully verified by using so-called AGM (see [5]), postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson (e.g. [1]). Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: (1) non-formal examples for nonmonotonicity and (2) formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point (1) and almost none belonging to (2) satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them. (shrink)

In this paper, I outline a pragmatist epistemology of logic inspired by later work of Charles S. Peirce that shares many features with an anti-exceptionalism about logic but, I argue, can better respond to a key problem that plagues the anti-exceptionalist. I first lay out what I take to be the tenets of anti-exceptionalism, discussing some difficulties in formulating the position that make it difficult to definitively label the position discussed here. I then analyze a key (...) class='Hi'>problem for the anti-exceptionalist, the background logic problem, and suggest that when framed as a problem for certain types of inquiry, it shares a presupposition about the priority of logic with other problems in the epistemology of logic. Turning to a discussion of Peirce from the 1903 Lowell Lectures, I then outline a pragmatism about logic that rejects the priority claims underlying the problems for inquiry in logic and, I argue, can resolve the background logic problem. (shrink)

The problem of Galileo's logical methodology has long interested scholars. In this volume William A. Wallace offers a solution that is completely unexpected, yet backed by convincing documentary evidence. His analysis starts with an early notebook Galileo wrote at Pisa, appropriating a Jesuit professor's exposition of the Posterior Analystics of Aristotle, and ends with one of the last letters Galileo wrote, stating that in logic he has been a Peripatetic all his life. Wallace's detective work unearths the complete (...) logic course from which the notebook was excerpted, then proceeds to show how its terminology and methodology continue to surface in Galileo's later writings in which he founds his new sciences of the heavens and of local motion. The result is a tour de force that commends itself not only to Galileo's scholars and to logicians, philosophers, and historians, but to anyone interested in the epistemic roots of modern science. (shrink)

Logical rationalism asserts that we can acquire immediate, non-inferential justification for beliefs in basic logical principles. The intuitions that arise when we consider particular cases of validity can offer justification for our foundational logical beliefs about rules of inference. I motivate rationalism through an argument from the indispensability of intuitions. This argument shows that rationalism is the theory best equipped to solve the problem of background logic. This is the challenge of explaining how we gain justified beliefs (...) in rules of inference without using those rules in a viciously circular way to arrive at the beliefs. As rationalism is the best epistemology which solves this important challenge, it is our best account of logical knowledge. In addition, I argue that a second major motivation for logical rationalism arises from work on logical practice. Recently, it has been claimed that we should attend to the practices of logicians when selecting an epistemology of logic. I argue that these considerations from logical practice also favour the adoption of logical rationalism. (shrink)

This paper examines al-Fārābī's logical thought within its Arabico-Islamic historical background and attempts to conceptualize what this background contributes to his logic. After a brief exposition of al-Fārābī's main problems and goals, I shall attempt to reformulate the formal structure of Arabic linguistics (AL) in terms of the ontological and formal characteristics that Arabic logic is built upon. Having discussed the competence of al-Fārābī in the history of AL, I will further propose three interrelated theses about (...) al-Fārābī's logic, in terms of which I will attempt to redefine it: the logico-linguistic conception, the project of logicization, and nuclear logic. The final question that will arise is how Aristotle's logic could be built upon AL, which has a nature contrary to logic. The present paper also contributes to examining our traditional research habits in Arabic studies. (shrink)

After introducing the adoption problem (AP) as the claim that certain basic logical principles cannot be adopted, I offer a characterization of this notion as a two-phase process consisting in (1) the acceptance of a basic logical principle, and (2) the development, in virtue of Phase 1, of a practice of inferring in accordance with that principle. The case of a subject who does not infer in accordance with universal instantiation is considered in detail. I argue that the AP (...) has deep and wide implications for the epistemology of logic, extending well beyond Kripke’s original target, viz. Putnam’s proposal for the empirical revision of logic and its background Quinean epistemology. In particular, the AP questions whether basic logical principles could have a fundamental role in our inferential practices, drawing our attention to the nature of basic inferences and the need to have a clearer conception of them before taking a stand on the matter of the epistemic justification of the logical principles. (shrink)

Theodore the Studite resolved the logical problem posed by the second Iconoclasm in an explicitly paraconsistent way, when he applied to Jesus the definition of the human hypostasis while stating that there is no human hypostasis in Jesus. Methodologically he was following, albeit without knowing, Eulogius of Alexandria. He, in turn, was apparently followed by Photius, but in a confused manner.

Schurz draws on modern alethic- deontic predicate logic to address the venerable yet enduring problem of whether what ought to be can be derived from what is. After two extensive introductory chapters supplying the background in philosophy and logic to readers unfamiliar with it, he examines such dimensions as the logical explication of Hume's thesis, the special Hume thesis, weakened versions of it, generalizations, some applications to ethical arguments, problems of identity and existence, whether there are (...) analytic bridge principles, and whether they are scientifically justifiable. The inquiry is expanded from Part II of his 1989 Relevant Deduction in Science and Ethics with a Case Study of the Is-Ought Problem. No index. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

In 1913 Pierre Duhem published a lecture in which he summarized his then startling discovery that Galileo owed a great deal to medieval scholastic natural philosophers. The result of this discovery was not only to establish the history of medieval science as an autonomous scholarly discipline, but also to initiate intensive research into the background and sources of Galileo's work. No scholar has contributed more in recent years to this research than William Wallace. His Prelude to Galileo and his (...) Galileo and His Sources have gone a long way toward solving a number of problems concerning Galileo's connection to the medieval tradition. In two important new books, Wallace takes this research another step forward by documenting Galileo's participation in the commentary tradition on Aristotle's Posterior Analytics. (shrink)

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.

To understand logic is, first and foremost, to understand logical consequence. This Element provides an in-depth, accessible, up-to-date account of and philosophical insight into the semantic, model-theoretic conception of logical consequence, its Tarskian roots, and its ideas, grounding, and challenges. The topics discussed include: the passage from Tarski's definition of truth to his definition of logical consequence, the need for a non-proof-theoretic definition, the idea of a semantic definition, the adequacy conditions of preservation of truth, formality, and necessity, the (...) nature, structure, and totality of models, the logicality problem that threatens the definition of logical consequence, a general solution to the logicality, formality, and necessity problems/challenges, based on the isomorphism-invariance criterion of logicality, philosophical background and justification of the isomorphism-invariance criterion, and major criticisms of the semantic definition and the isomorphism-invariance criterion. (shrink)

In this paper we consider whether the background logic problem actually presents a serious challenge for anti-exceptionalists about logic. We argue that logical theorizing does not depend upon a background logic to get started, but merely on the defeasible assumption that the specific arguments offered are good ones. These assumptions are compatible with multiple explanations of the goodness of these arguments, including accounts on which they are not formally valid but materially justified. Furthermore, as (...) in other areas of science, the success of the general research program is compatible with the rejection of initial characterizations of the data—in this case initial claims about the goodness of specific arguments—as well as rejections of initial hypotheses about both the logical form of those specific arguments and the explanation of their goodness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Religious Background of Seventeenth-Century Philosophy RICHARD H. POPKIN IT IS AN EXCEEDINGLY GREAT PLEASURE tO participate in the twenty-fifth anniversary issue of the Journal of the Historyof Philosophy.The editor, Professor Makkreel, offered me the opportunity to discuss the rationale for my present research, which I hope has some relevance for future research in the history of philosophy. At a symposium at the American Philosophical Association meeting in (...) Washington in December x985, I argued for taking the historyof philosophy seriously, that is, understanding thinkers and ideas in their actual historical contexts, instead of detaching them into some ahistorical ethereal realm. I argued that one could not make sense of a philosopher's thought detached from his time and circumstances. His ideas could not be understood unless one took account of the language, the usages, the issues and the concerns of the thinker and his time. The all too frequent "reconstruction" of philosophers ' thoughts sees them instead as logical machines, simply moving from clearly stated premises to their logical consequences. As many of us have sought to show, this often grossly distorts what Descartes, Spinoza, Locke, Leibniz and others might have actually thought, and misses much of what they were probably thinking about. I should like to carry this theme further by examining the need to take seriously the religious aspect of philosophizing. I will center on the intellectual scene of the seventeenth century, which I am currently working on though I believe many of the same points could be made about any period in the history of philosophy. Among historians of science there is an ongoing debate about whether the history of the subject should be studied internally or externally. The [:35] 36 JOURNAL OF THE HISTORY OF PHILOSOPHY internalists examine a set of ideas presented by scientist A, and trace their use or development by scientist B. The study that results is primarily the tracing of the course of a set of ideas through a time period. Background data about the scientists, their problems, and their place in society are regarded as of little relevance. The externalists insist that one cannot understand why various questions became important, why various individuals tried to solve them, why they used certain kinds of possible solutions instead of others, etc., unless one knows the external conditions of the time. This has spawned a lot of interesting research into the way scientific studies went on, who supported them, who did them, how they got accepted, and so on. The sociology and even anthropology of science is now a thriving research area, yielding many amazing studies about the scientific world and how it functioned. In so doing, scholars have not just examined the great successful scientists, the Keplers, Galileos, Harveys, and Newtons, but also the small fry, the mediocre, the poor scientists, and even the incompetent ones. They have examined why wrong-headed theories were supported, and accepted, while evidence supporting other theories was readily available. Their concern with the actual course of scientific development as an ongoing part of intellectual history is vital to understanding the scientific world of today, which plays such an overwhelming role in our society. So, some people study the education of the good, the mediocre, the bad scientists; their relative social statuses, incomes, and so on. The religious concerns are, of course, an obvious part of the story from Copernicus to Kepler to Newton to Darwin to Freud to Einstein. The scientists were involved in an ongoing religious world that influenced the role of science. The above named scientists had their religious or irreligious views that were involved with their scientific concerns. And, as we know too well, the impact of their work on religion has been of great importance to the broader intellectual world, and the impact of religion on the acceptance of their science has been and is part of the ongoing intellectual world. This interest amongst historians of science in the sociology, psychology, and anthropology of science has hardly rubbed off on the historians of philosophy. Most of the leading scholars of the last few decades in this work are hardly known and rarely cited in studies in the history of philosophy. We... (shrink)

Socio-cultural and political transformations that are taking place in the modern world under the influence of globalization, predetermine the growth of scientific interest in the history and the theory of shaping the group unity.The coverage of various aspects of this problem is found in the works of foreign philosophers (M. Gibernau, S. Huntington, E. Hiddens, B. Yak, et al.), which focus their primary attention on studying the factors, contributing to the emergence of communities in the modern world, while distancing (...) from the development of universal explanatory schemes for the process of forming the collective unity at various stages of the historical development of society.Some Ukrainian researchers (Y. Hrytsak, V. Kravchenko, H. Kasyanov, et al.), who, in contrast to foreign scholars, pay more attention to studying the various aspects of Ukrainian nation-building, are approaching the above problems from a bit different angle of view to solve them. Undoubtedly, the work of these researchers thoroughly and fully covers the history of the formation of the Ukrainian nation, explains the reasons or factors that contributed to its appearance. Meanwhile, they do not have sufficient potential to explain the causes of the cultural fragmentation of modern Ukrainian society, which, in our opinion, has become a logical consequence of the undivided domination in the Ukrainian intellectual discourse of the paradigm of perennialism, within which the cultural identity of the community appears to be a kind of “entity or reality.” Proponents of this position believe that the cultural diversity of nations emerged in the early stages of social development. Within this outlook, Ukrainians, as a mentally and culturally distinct community, have always existed. Of course, their culture has been developing and enriching in the process of historical development and intercultural communication, while its original spiritual and symbolic core remaining unchanged.Despite the fact, that renaissance has a rational grain and can become themethodological basis for very effective national consolidation strategies, one should not ignore its failure to explain the causes of the cultural and civilizational fragmentation of modern Ukrainian society. In our opinion, the solution of this issue requires a comprehensive understanding of the origins, mechanisms and factors, and the formation of a culturally homogeneous Ukrainian cultural space. In view of this, the purpose of our work is to uncover the theoretical preconditions and mechanisms for shaping the cultural identity of Ukrainians in the XIX and early XX centuries. Instead, the task of the work is to highlight the ideological foundations of the growth of scientific interest in folk culture in foreign and Ukrainian intellectual discourse and to reveal their significance in the process of thematizing the modern Ukrainian identity.Methods.The interdisciplinary approach and the principle of unity of the historical and logical have become a methodological basis of scientific research. Methods of historical and philosophical reconstruction, cultural analysis, and extrapolation have been also widely used in the process of research, as well as the fundamental principles of hermeneutics, which have been taken into account.Results. The dominance of the educational enlightenment-cognitive paradigm has contributed to the growth of scientific interest in the cultural identity of peoples, which, according to the prevailing beliefs, has been most clearly preserved in folk poetry and ancient literature. The study of the latter has resulted in the outbreak of ethnographic and linguistic exploration, which facilitated the gradual introduction of the Ukrainian language to literary use, thereby contributing to the thematization of modern Ukrainian identity. (shrink)

Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic, focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, (...) and it balances the philosophical and technical aspects of the subject.The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading.Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis. (shrink)

The aim of this article is to apply Józef M. Bocheński’s logic of authority to a key interpersonal relation of philosophical interest: the master–disciple relation. The present research addresses the problem of philosophical authority in terms of the assumptions of the logic of authority and its consequences for philosophical historiographical research and verifies the claims of the logic of authority in this respect. The analyses show that, in the field of philosophy, the axiological authority of the (...) master plays a fundamental role and is not limited solely to epistemic or deontic authority. (shrink)

Is deduction of use in application to our everyday problems? Aristotle said that in practical matters we cannot use a strictly deductive attitude: "we must be content...in speaking about things which are only for the most part true, with premises of the same kind, to reach conclusions that are no better" (Nic.Eth.I,4 - my underlining). We may content ourselves with conclusions which - according to the usual views - are not true; but what happens when we realize that such conclusions (...) bring us into contradiction with some of our deepest beliefs? We have to pursue our search of rationality in the most compelling manner, and this effort forces us to express our background beliefs in order to check what may be wrong with that. In this paper I will give two classical examples, one form the history of cinema and another from the history of artificial intelligence: in comparing these two examples I claim that logical compulsion - the deep need for convention - is highly valuable where feelings are not enough. (shrink)

Scientific discourse leaves implicit a vast amount of knowledge, assumes that this background knowledge is taken into account – even taken for granted – and treated as undisputed. In particular, the terminology in the empirical sciences is treated as antecedently understood. The background knowledge surrounding a theory is usually assumed to be true or approximately true. This is in sharp contrast with logic, which explicitly ignores underlying presuppositions and assumes uninterpreted languages. We discuss the problems that (...) class='Hi'>background knowledge may cause for the formalization of scientific theories. In particular, we will show how some of these problems can be addressed in the context of the computational representation of scientific theories. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume and the Lockean Background: Induction and the Uniformity Principle David Owen Introduction What has come to be called Hume's problem of induction is special in many ways. It is arguably his most important and influential argument, especially when seen in its overall context of the more general argument about causaUty. It has come to be one of the great "standard problems" ofphilosophyandyetis,by most accounts, almost unique (...) in having no ancient precursor. Interestingly, the argument is frequently presented in terms that the author never used. Itis difficult for us not to think of the problem in terms of the contrast between deductive vs. inductive reasoning (or logic, or whatever). But this is a contrast nowhere to be found in Hume: he talks of demonstrative vs. probable (or moral) reasoning. Hume uses the word "induction" only twice in the Treatise1 and in neither case is it clear that the word is used toreportapieceofprobablereasoning.2One ofthefewoccurrences of"deduce" or "deducing" occurs in the second Enquiry, where he talks about "following the experimental method, and deducing general maximsfrom acomparisonofparticularinstances,"3hardlyaparadigm of what we would call deductive reasoning.4 Many modern studies of Hume that make a real attempt to understand what Hume meant by demonstration and probability, in the context of his argument about induction, tend towards the ahistorical,6 treating Hume's writings as contemporary texts. But failure to take into account some of the background concerning the nature of demonstrative and probable reason makes it unlikely, I think, that we can understand Hume's argument. Part ofthe problem is the failure to identify Hume's targets in that famous negative argument about induction (vague reference is sometimes made to the "rationalists") and part of the problem is identifying the role the uniformity principle plays in Hume's famous argumentand thelightitsheds on the conception ofprobablereasoning Hume was attacking. In this paper I want to argue that a careful look at Locke solves some ofthese problems: he has a well developed view ofdemonstrative and probable reasoning, his confidence in conformity as a ground of probability is a Ukely target of Hume's attack and his Volume XVIII Number 2 179 DAVID OWEN accountshedsmuchlightonwhatrole the principleofuniformitymight play in Hume's account.6 Of course, at a certain level of philosophical abstraction it is irrelevant whether we have understood what Hume "really meant." Theproblemofinductionhas emergedas a central onein epistemology, philosophical logic, and philosophy of science. It would be an interesting question in philosophical historiography to trace the development ofthe "problem" from Hume's time to our own but that is not my task here. I trust one needs no justification for taking an historical look at a famous problem rather than tackling the problem head-on in one's own terms. But if one is needed, here is mine: sometimes, by looking at a problem from a different, historical perspective, one sees a different problem or afamiliar problem in a new light. One's philosophical horizons are broadened. Furthermore, one may make an interesting historical discovery, or at least draw some interesting historical connections. I take it as uncontroversial that Locke, following Descartes, rejected a formal, logical account of demonstrative reasoning. Instead ofusing a formal, syllogistic account ofhow two propositions can entail a third, Locke concentrated on the relation two ideas bear one to another.7 Thus a demonstration, for Locke, getsits force, notfrom what we would call a deductive relation between one set of propositions (.the premises) and anotherproposition (the conclusion), butrather from the relation one idea bears to another, either directly, or via a chain of intermediate ideas. It is true that Locke frequently talks of inferring one proposition from another, but this is always cashed out in terms of relations ofideas via a chain ofintermediate ideas.8 It is also true that Locke occasionally uses the terms "deduce" and "deduction." But these are never used in our sense that has to do with formal deductive validity. Rather, they are simply used loosely in the informal sense of "argue" or "infer," and "argument" or "inference."9 In the rest of this paper, all uses ofthe word"deduction" andits cognates shouldbe taken as having the modern sense, unless flagged as having "Locke... (shrink)

Argumentation theory is a distinctly multidisciplinary field of inquiry. It draws its data, assumptions, and methods from disciplines as disparate as formal logic and discourse analysis, linguistics and forensic science, philosophy and psychology, political science and education, sociology and law, and rhetoric and artificial intelligence. This presents the growing group of interested scholars and students with a problem of access, since it is even for those active in the field not common to have acquired a familiarity with relevant (...) aspects of each discipline that enters into this multidisciplinary matrix. This book offers its readers a unique comprehensive survey of the various theoretical contributions which have been made to the study of argumentation. It discusses the historical works that provide the background to the field and all major approaches and trends in contemporary research. Argument has been the subject of systematic inquiry for twenty-five hundred years. It has been graced with theories, such as formal logic or the legal theory of evidence, that have acquired a more or less settled provenance with regard to specific issues. But there has been nothing to date that qualifies as a unified general theory of argumentation, in all its richness and complexity. This being so, the argumentation theorist must have access to materials and methods that lie beyond his or her "home" subject. It is precisely on this account that this volume is offered to all the constituent research communities and their students. Apart from the historical sections, each chapter provides an economical introduction to the problems and methods that characterize a given part of the contemporary research program. Because the chapters are self-contained, they can be consulted in the order of a reader's interests or research requirements. But there is value in reading the work in its entirety. Jointly authored by the very people whose research has done much to define the current state of argumentation theory and to point the way toward more general and unified future treatments, this book is an impressively authoritative contribution to the field. (shrink)

In the paper we present a technique for eliminating quantifiers of arbitrary order, in particular of first-order. Such a uniform treatment of the elimination problem has been problematic up to now, since techniques for eliminating first-order quantifiers do not scale up to higher-order contexts and those for eliminating higher-order quantifiers are usually based on a form of monotonicity w.r.t implication (set inclusion) and are not applicable to the first-order case. We make a shift to arbitrary relations “ordering” the underlying (...) universe. This allows us to incorporate background theories into higher-order quantifier elimination methods which, up to now, has not been achieved. The technique we propose subsumes many other results, including the Ackermann's lemma and various forms of fixpoint approaches when the “ordering” relations are interpreted as implication and reveals the common principle behind these approaches. (shrink)

It is hard to imagine our life without questions. They facilitate orientation in our environment, enable interpersonal communication and make the acquisition of knowledge possible. Questions direct scientific research, are used as research tools and are an important medium of transferring knowledge in teaching. The book is intended as a par excellence philosophical monograph of the theory of questions, presenting the most important erotetic problems, their general background and selected practical applications. It is prepared in all fairness to results (...) acquired in the framework of the logical theories of questions but goes beyond this framework. (shrink)

Perfect for students with no background in logic or philosophy, Simple Formal Logic provides a full system of logic adequate to handle everyday and philosophical reasoning. By keeping out artificial techniques that aren’t natural to our everyday thinking process, Simple Formal Logic trains students to think through formal logical arguments for themselves, ingraining in them the habits of sound reasoning. Simple Formal Logic features: a companion website with abundant exercise worksheets, study supplements (including flashcards (...) for symbolizations and for deduction rules), and instructor’s manual two levels of exercises for beginning and more advanced students a glossary of terms, abbreviations and symbols. This book arose out of a popular course that the author has taught to all types of undergraduate students at Loyola University Chicago. He teaches formal logic without the artificial methods–methods that often seek to solve farfetched logical problems without any connection to everyday and philosophical argumentation. The result is a book that teaches easy and more intuitive ways of grappling with formal logic–and is intended as a rigorous yet easy-to-follow first course in logical thinking for philosophy majors and non-philosophy majors alike. (shrink)

John Searle''s hypothesis of the Background seems to conflict with his initial representationalism according to which each Intentional state contains a particular content that determines its conditions of satisfaction. In Section I of this essay I expose Searle''s initial theory of Intentionality and relate it to Edmund Husserl''s earlier phenomenology. In Section II I make it clear that Searle''s introduction of the notion of Network, though indispensable, does not, by itself, force us to modify that initial theory. However, a (...) comparison of this notion to the notion of horizon from Husserl''s later phenomenology and an interpretation of Husserl''s conception of the determinable X as providing a solution to the problem of perceptual misidentification lead me to conclude that in his discussion of ''twin examples'' Searle had better modified his initial theory. Finally, I critically examine Searle''s claim that anyone who tries seriously to follow out the threads in the Network will eventually reach a bedrock of non-Intentional capacities. In Section III I show in detail, partly in a rather Husserlian vein, that Searle''s four official arguments for the Background thesis, though containing some very valuable contributions to a theory of linguistic skills, are not convincing at all if they are to be understood as going beyond the scope of Searle''s ''content-cum-Network'' picture of Intentionality. The upshot of these considerations is that the Background thesis should be read as a thesis concerning the causal neurophysiological preconditions of human Intentionality rather than concerning the logical properties of Intentional states in general. Recently Searle himself has come to the same result, but he does not say for which reasons. The present essay makes it clear why Searle just had to arrive at this important result. (shrink)

Zachar's commentary can be read as a sophisticated theoretical extension of the target article, and I am very pleased to see support for a relationalist turn in understanding mental disorders. Indeed, underlying causal properties are only an ingredient of essentialism and a more elaborate discussion of this issue brings us readily to the discourse on kinds and ontology. Zachar is an advocate for thinking of psychiatric constructs as practical kinds. This logically leads him to think that the problem with (...) categorical classification systems like the Diagnostic and Statistical Manual of Mental Disorders and the International Classification of Diseases are practical problems (lack of... (shrink)

The paper deals with the problem of representation on the background of J. Rancière’s political philosophy, in which he rejects the concept of the unrepresentable. The resolution of the problem follows from the confronting of two conceptions of the unrepresentable: that of the esthetics of the sublime in Kant and Lyotard and of the politics of prohibition in Foucault on one hand and Rancière’s understanding of sharing the perceptible on the other hand. This discussion leads the author (...) to the problem of visuality conceived as a set of visual representations, which in a historically given period are legitimately visible. This definition of visuality returns the representation and the unrepresentable back into the political conception of image. (shrink)

In this paper I argue that Kant’s doctrine of definitions, as it is developed in theTranscendental Doctrine of Method(TDM) and in the lectures on logic, lays down the semantic background of the problem of the objective reality of the categories and of the solution Kant provides for it in theTranscendental Analytic. The distinction between nominal and real definitions introduces a two-dimensional element in Kant’s theory of concepts, and this, I argue, provides a compelling explanation for the assumption (...) Kant makes in §13 that it is possible to possess a concept without knowing the conditions of its legitimate application. This view is supported by the parallels between Kant’s discussion of empirical, mathematical, and philosophical concepts in §13 and in theTDM. And, it allows clarifying the sense in which the arguments that prove the objective reality of the categories are, at the same time, counterfactual reflections that give us (incomplete) insight into their real definitions. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

Traditional logical empiricist and more recent historicist positions on the logic of discovery are briefly reviewed and both are found wanting. None have examined the historical detail now available from recent research on Darwin, from which there is evidence for gradual transition in descriptive and explanatory concepts. This episode also shows that revolutionary research can be directed by borrowed metascientific objectives and heuristics from other disciplines. Darwin's own revolutionary research took place within an ontological context borrowed from non evolutionary (...) predecessors with methodological objectives borrowed from and justified by their success in Newton's physics. The logic of discovery is not a special form of inference from observation to theory, but rather a theory of the rationality of research, including principles bearing upon the rational choice of problems, or epistemic objectives, and heuristic, or means to solving the problems. Such choices can be justified only locally in the context of a relatively stable background ontology and substantive epistemology, not globally for all science. (shrink)

Specific historical and linguistic circumstances gave way to a Swiss original concept of a multilingual state as the nation of the will. The discussion concerns problems inherent to the unity-in-diversity philosophy and the proportional representation of national languages within the framework of the Swiss constitution, including the legislation protecting language and the language principles obtaining in Switzerland. Drawing on the language ideology studies, this paper shows how the linguistic diversity is designed on the administrative level and what provisions have been (...) made to maintain multilingualism. The discussion also addresses and concludes on the ever timely questions of diversity, pluralism and intergroup cooperation fostered by the Swiss political and social culture. (shrink)

Aristotle was the first and one of the greatest logicians. He not only devised the first system of formal logic, but also raised many fundamental problems in the philosophy of logic. In this book, Dr Lear shows how Aristotle's discussion of logical consequence, validity and proof can contribute to contemporary debates in the philosophy of logic. No background knowledge of Aristotle is assumed.

Fuzzy logic is finding increased application in the control of real-world processes and in the work with and the manipulation of inexact knowledge. Two of the major attractions of fuzzy logic are: it permits one to express problems in (familiar) linguistic terms and it can be applied where the numerical mathematical model of a system may be too complex or impossible to build using conventional techniques. This book, written in an easily accessible style, assumes that students have a (...) solid background in embedded systems including basic logic design and C/C programming. (shrink)

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks... it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven (...) optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. (shrink)

The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam's claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the `true' logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to (...) clarify the possible misunderstandings surrounding the more radical claims about the revision of logic, assessing them in particular both in the context of more general quantum-like theories (in the framework of von Neumann algebras), and against the background of the current state of play in the philosophy and interpretation of quantum mechanics. Characteristically, the conclusions that might be drawn depend crucially on which of the currently proposed solutions to the measurement problem is adopted. (shrink)

Sortal concepts are at the center of certain logical discussions and have played a significant role in solutions to particular problems in philosophy. Apart from logic and philosophy, the study of sortal concepts has found its place in specific fields of psychology, such as the theory of infant cognitive development and the theory of human perception. In this monograph, different formal logics for sortal concepts and sortal-related logical notions are characterized. Most of these logics are intensional in nature and (...) possess, in addition, a bidimensional character. That is, they simultaneously represent two different logical dimensions. In most cases, the dimensions are those of time and natural necessity, and, in other cases, those of time and epistemic necessity. Another feature of the logics in question concerns second-order quantification over sortal concepts, a logical notion that is also represented in the logics. Some of the logics adopt a constant domain interpretation, others a varying domain interpretation of such quantification. Two of the above bidimensional logics are philosophically grounded on predication sortalism, that is, on the philosophical view that predication necessarily requires sortal concepts. Another bidimensional logic constitutes a logic for complex sortal predicates. These three sorts of logics are among the important novelties of this work since logics with similar features have not been developed up to now, and they might be instrumental for the solution of philosophically significant problems regarding sortal predicates. The book assumes a modern variant of conceptualism as a philosophical background. For this reason, the approach to sortal predicates is in terms of sortal concepts. Concepts, in general, are here understood as intersubjective realizable cognitive capacities. The proper features of sortal concepts are determined by an analysis of the main features of sortal predicates. Posterior to this analysis, the sortal-related logical notions represented in the above logics are discussed. There is also a discussion on the extent to which the set-theoretic formal semantic systems of the book capture different aspects of the conceptualist approach to sortals. These different semantic frameworks are also related to realist and nominalist approaches to sortal predicates, and possible modifications to them are considered that might represent those alternative approaches. (shrink)

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

This book was completed by the early 1960s and published in 1984 but it has not lost its topicality, for it contains an important re-assessment of the relations of two main streams of contemporary philosophy - the Analytical and the Dialectic. Adherents and critics of these traditions tend to assurnethat they are diametrically opposed, that their roots, concerns and approaches contradict each other, and that no reconciliation is possible. In contradistinction Russell derives both traditions from the common root of the (...) dissatisfaction with the arguments against speculative philosophy. These according to the author leave a lacuna - certain elementsof our Weltanschaaung have been removed, but they cannot be removed without replacement lest we have an incomplete world view, so incomplete in fact that it cannot be viable. According to Russell part of this vacuum is taken up by the analytical tradition but this tradition is not capable of taking up the remainder of it. That portion of the vacant space is however taken up by the dialectical tradi tion, which in turn cannot itself handle the whole of the problem. Thus the two reactions to the demise of speculative philosophy appear to be complementary in at least this sense. But the author goes further, for according to hirn the analytical arguments themselves clearly point to the emergence of dialectical problems, and the dialectical problems themselves need some such background to arise. (shrink)

The central focus of this article is the epistemological assumption that knowledge could be generated based on human beings’ experiences and over their conceptions of the world. Logical characterisation of human inductive learning over their produced conceptions within terminological systems and providing a logical background for theorising over the Human Concept Learning Problem (HCLP) in terminological systems are the main contributions of this research. In order to make a linkage between ‘Logic’ and ‘Cognition’, Description Logics (DLs) will (...) be employed to provide a logical description and analysis of actual human inductive reasoning (and learning). This research connects with the topics ‘logic & learning’, ‘cognitive modelling’, and ‘terminological knowledge representation’. (shrink)

Implicit definitions have been much discussed in the history and philosophy of science in relation to logical positivism. Not only have the logical positivists been influential in establishing this notion, but they have addressed the main problems connected with the use of such definitions, in particular the question whether there can be such definitions, and the problem of delimiting their scope. This paper aims to draw further insights on implicit definitions from the development of this notion from its first (...) occurrence in German language in Enriques’s “Principles of Geometry” (1907) to Schlick’s General Theory of Knowledge (1918). Enriques was one of the first to acknowledge that implicit definitions in mathematics are possible only for higher-order entities or structures, which can have infinitely many interpretations in terms of physical objects. While Schlick introduced coordinating principles to account for the scientific interpretations of implicit definitions, Enriques addressed the problem of bridging the gap between abstract and concrete terms in a different way: He identified, within mathematics, structural patterns that provide a clarification of conceptual relations, and so also serve (indirectly) the purposes of applied mathematics. My suggestion is that Enriques’s analysis of these patterns deserves deeper consideration also from a contemporary perspective on mathematical concept formation. (shrink)

This article is dedicated to the philosophy ofscience which was developed by the outstanding Soviet physicist and leader of a powerful scientificcommunity, L. I. Mandelstam. It is shown that thisphilosophy can be summed up under the heading operationalism. A comparison with the paradigmaticoperationalism of Percy Bridgman is undertaken andthe German positivist roots of Mandelstam's philosophyare indicated. The final section reconstructs the principle ofexpedient idealization, the principle which was putforward by Mandelstam's disciples in the spirit of hisoperationalism to solve problems of (...) the theory ofnon-linear oscillations. (shrink)

The Synoptic Problem is a puzzle that scholars have desired to solve since the 18th century. The discussion has a religious background, because it is about the first three canonical Gospels of the Church, namely Matthew, Mark and Luke, which came to be called the Synoptic Gospels. The discussion, in the most basic context, concentrates on the point that there is a possible relationship or connection between the Synoptic Gospels and that each one is substantially similar to another (...) but at the same time includes different aspects. This theoretical discussion separates the Gospel of John from the Synoptic Gospels and does not see it as a main source for the history of Jesus. The method of discussion is based on the reading of the Synoptic Gospels from a birds-eye-view, as seen together, and as comparatively in relation to each other. The aim of the discussion is to reach accurate historical information about Jesus and the birth of Christianity by analyzing the possible relationship between the Synoptic Gospels through their sources. Several hypotheses have been proposed for the solution of the Synoptic Problem. However, all the modern studies in the context of the problem are carried out by Western scholars. In other words, Synoptic Problem is a relatively unknown subject in the Turkish academic circles. So in this paper the aim is to draw the attention of the Turkish academy to the substance and framework of the Synoptic Problem through an introductory survey. In addition, some results that can be reached in this context will be exemplified by getting help from the redaction criticism. Summary: The Synoptic Problem is a puzzle that scholars have been trying to solve since the 18th century. The discussion has a religious background, for it is about the first three canonical Gospels of the Church (namely Matthew, Mark, and Luke, which are called the Synoptic Gospels). The discussion, in the most basic context, concentrates on a possible relationship or connection between the Synoptic Gospels and that each one is substantially similar to another one, but at the same time including different aspects. This theoretical discussion separates the Gospel of John from the Synoptic Gospels, and does not see it as a main source for the history of Jesus. The method of this discussion is based on the broad reading of the Synoptic Gospels as well as a comparison in relation to each other. The aim of the discussion is to reach accurate historical information about Jesus and the birth of Christianity by analyzing the possible relationship between the Synoptic Gospels through their sources.The traditional four Gospels have been debated since ancient times. There have been many dimensions of these discussions. However, whether the Gospels contain contradictory information or not has always been at the forefront. Pagan writers, such as Celsus or Porphyry, criticized the Gospels in this respect. Christian writers, such as Marcion or Tatian who lived in the second century when the Gospels were not seen as canon yet, raised some suggestions based on the doubts that the Gospels were incompatible with the Jewish scriptures and contained contradictions among themselves. Marcion included a single Gospel that was close to the Gospel of Luke in his New Testament canon. Tatian made a mixed version of the four Gospels. In the next stage, the contradictions in the Gospels were explained by the Christian writers, such as Origenes or Augustine. However, the four Gospels were more prominent in this new era and they were regarded as canons by the Church. Therefore, the Christian writers’ approach to the Gospels also began to change. Origen emphasized allegorical interpretation which had been known since the Jewish philosopher Philo (d. 50) in Alexandria. Thus, he wanted to protect the contradictory texts from being seen as the source of the problem. He argued that the problem was the human mind that could not grasp the allegorical mystery of the text or the narrative in the text. Augustine had a similar approach with the suggestion that the Gospels should be read by a faithful heart. According to Augustine, it is natural that the Gospels reflect different characters because the Gospel writers describe Christ differently. In order to be able to comprehend the divine meaning in these texts, the Gospels must be read in a spiritual mood. After all, all these Christian writers aimed to respond to the criticism by the pagan writers regarding the Gospels, as well as the current suspicions in the minds of Christians.Origen was the first Christian thinker to devote an effort to solve the debates on the Gospels in a logical and systematic way. As for Augustine, he was the starting point of the Synoptic Problem since Augustine was the first to mention the links between the Gospels texts, namely the idea that the authors of the Gospels may have used each other as sources. However, in the modern sense, the Synoptic Problem has been transformed into an academic discipline by the intellectuals who followed the path of Enlightenment thinkers, such as Reimarus (1684-1768), Lessing (1729-1781), Griesbach (1745-1812), and Eichhorn (1752-1827). Because modern researchers differ from old writers based on Church ideologies, they began to demolish traditional beliefs about the Gospels. Thus, the effort to harmonize incompatible narratives in the Gospels is left aside. Indeed, the ancient writers put a lot of effort into it. Now, in the places where indirect relations can be established between the Gospels, the idea of finding the common hypothetical sources of these Gospels is prominent. The claim that the Gospels were directly connected to Jesus as a historical figure has been gradually faded away. The basis of the Synoptic Problem is the comparative reading of the Synoptic Gospels. In the modern sense, this comparison and its interpretation was made by J. J. Griesbach (1745-1812) for the first time. Griesbach was the first scholar to compare Matthew, Mark, and Luke in a way to create a synopsis. His comparison is based on a reading done by placing several passages or narratives from the Gospels side by side.Many hypotheses have been put forward for the solution of the Synoptic Problem. Two-Source Hypotheses, Four-Source Hypotheses, and Farrer Theory are the most popular ones among researchers. These views are based on Marcan Priority. In this context, independently from each other, Matthew and Luke used Mark’s text as their sources. Also, according to the Two-Sources and Four-Source Hypotheses, the authors of Matthew and Luke used another written document as their sources. This document is named the “Q” which derives from the German word “Quellen.” In this way, it is assumed that the Q-document and the Gospel of Mark are the sources of the Gospels of Matthew and Luke.The writers of the Gospels wrote their own texts by using written and oral sources. One of the scholarly methods is the redaction criticism that explores how the Gospel writers shaped the old literary documents by arranging, re-shaping, and revising them. This theory looks at whether the source used by an author is known and available today in order to understand whether how the author used his sources would provide important clues about his tendencies or ideologies. In this regard, the theory of the Marcan priority can be rendered functional along with the redaction criticism. In doing so, it is possible to reach important conclusions about Jesus and the birth of Christianity, as well as the theological and ideological ideas of the unknown authors of the Gospels of Matthew and Luke. First of all, the authors of Matthew and Luke used Mark’s text as their sources. Secondly, we have these three Gospels today. And finally, the ways in which the writers of Matthew and Luke shaped the text, phrases, or expressions of Mark reveal important results about their thoughts. The analysis shows that the authors of Matthew and Luke sometimes made additons that could be called interpolation to Mark’s text; sometimes they wanted to censor some statements in Mark; sometimes they tried to explain or clarify some statements in the Mark, or sometimes they tried to blur clear expressions and expositions in Mark's text. These authors did not do such things without a reason. They wanted to reshape Mark’s text in accordance with their theological understanding of Jesus as Christ. In this context, according to some expressions in Mark, Jesus' power had a limit. The authors of Matthew and Luke did not find these statements appropriate, because they changed Mark’s some statements to create an impression that Jesus’ power was not limited. This proves that the authors of Matthew and Luke re-arranged their resources to present Jesus as a superhuman being. Similarly, in Mark, there are lines in which Jesus declares his loyalty and servitude to the God of Israel. In such passages, he presented his personality in a low Christology context against God. However, the authors of Matthew and Luke were disturbed by such statements, because they intervened in these statements in Mark. They wanted to change some of the meanings and contexts in Mark’s text through such interventions and presented Jesus as Christ in a high Christological context to their readers. In the end, all these researches also responded to the question of to what extent the Gospels provide reliable information on a historical basis. (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)

I give a revision (“reload”) of an earlier paper on logico-empiricism’s philosophy of biology by checking its central theses against the background of the international conferences of Prague (1934), Paris (1935), and Copenhagen (1936), so important for the development of logical empiricism and its spread in the western world. My theses are that logical empiricism did not contribute in the same way to the development of philosophy of biology, as it did e.g. to the development of philosophy of mathematics (...) or physics. The reasons for this failure were: (1) logical empiricists were unexperienced in biological science. (2) They concentrated on an unproductive ('ideological') framework (anti-vitalism, reduction) that they took to be philosophy of biology. (3) This prevented them from dealing with actual problems of biological science. Between the various sections of the paper, I insert “intermezzos” that present several conference participants in a wider historical context (Great War, persecution, language). (shrink)

A Border Disputeintegrates the latest work in logic and semantics into a theory of language learning and presents six worked examples of how that theory revolutionizes cognitive psychology. Macnamara's thesis is set against the background of a fresh analysis of the psychologism debate of the 19th-century, which led to the current standoff between logic and psychology. The book presents psychologism through the writings of John Stuart Mill and Immanuel Kant, and its rejection by Gottlob Frege and Edmund (...) Husserl. It then works out the general thesis that logic ideally presents a competence theory for part of human reasoning and explains how logical intuition is grounded in properties of the mind. The next six chapters present examples that illustrate the relevance of logic to psychology. These problems are all in the semantics of child language (the learning of proper names, personal pronouns, sortals or common nouns, quantifiers, and the truth-functional connectives) and reflect Macnamara's rich background in developmental psychology, particularly child language - a field, he points out, that embraces all of cognition. Technical problems raised by but not included in the examples in the main part of the text are dealt with in a separate chapter. The book concludes by describing laws in cognitive psychology, or the type of science made possible by Macnamara's new theory. John Macnamara is Professor of Psychology and Director of the Program in the History and Philosophy of Science, McGill University. A Bradford Book. (shrink)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning (...) points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (shrink)

Discussion of Wittgenstein's Tractatus is currently dominated by two opposing interpretations of the work: a metaphysical or realist reading and the 'resolute' reading of Diamond and Conant. Marie McGinn's principal aim in this book is to develop an alternative interpretative line, which rejects the idea, central to the metaphysical reading, that Wittgenstein sets out to ground the logic of our language in features of an independently constituted reality, but which allows that he aims to provide positive philosophical insights into (...) how language functions. McGinn takes as a guiding principle the idea that we should see Wittgenstein's early work as an attempt to eschew philosophical theory and to allow language itself to reveal how it functions. By this account, the aim of the work is to elucidate what language itself makes clear, namely, what is essential to its capacity to express thoughts that are true or false. However, the early Wittgenstein undertakes this descriptive project in the grip of a set of preconceptions concerning the essence of language that determine both how he conceives the problem and the approach he takes to the task of clarification. Nevertheless, the Tractatus contains philosophical insights, achieved despite his early preconceptions, that form the foundation of his later philosophy. -/- The anti-metaphysical interpretation that is presented includes a novel reading of the problematic opening sections of the Tractatus, in which the apparently metaphysical status of Wittgenstein's remarks is shown to be an illusion. The book includes a discussion of the philosophical background to the Tractatus, a comprehensive interpretation of Wittgenstein's early views of logic and language, and an interpretation of the remarks on solipsism. The final chapter is a discussion of the relation between the early and the later philosophy that articulates the fundamental shift in Wittgenstein's approach to the task of understanding how language functions and reveal the still more fundamental continuity in his conception of his philosophical task. (shrink)

Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us (...) to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics. (shrink)

Available from UMI in association with The British Library. Requires signed TDF. ;This thesis investigates the nature of Dr. Johnson's arguments in four main areas: religion, morality, literature and politics. The investigation proceeds by analysing the forms of the arguments and the coherence of their logic, establishing the premises of the arguments, and indicating which of a number of sanctions govern these premises. The sanctions looked at are reason, revelation, experience, testimony, authority and universality, with an attempt to establish (...) whether or not there is a hierarchy of these sanctions and, if so, which Johnson regards as the most important in each area. The thesis is organised in four parts which correspond to the subject areas. Each part has two sections: the first analyses the sanction applied to that subject, and the second takes from Johnson's writings examples of specific issues, showing how the sanctions are applied to them. ;Part I deals with Johnson's arguments on religion. The sanctions considered in this part are reason, revelation, testimony, authority, universality and experience. Attention is drawn to the antecedents of Johnson's arguments in order to indicate the background to Johnson's arguments. The specific issues looked at are the immateriality and immortality of the soul, ghosts and second sight, and the problem of evil. ;Part II deals with Johnson's moral arguments. Here the sanctions are reason, revelation, universality and experience. Again, the antecedents are identified, notably Samuel Clarke, Richard Cumberland, Mandeville and Shaftesbury. The specific issues highlighted are the duties of charity, retirement and idleness. ;In Part III Johnson's literary arguments come under scrutiny, and here the sanctions dealt with are rather different. Revelation is not involved here . Its place is taken by morality, which, having been examined in the preceding part, itself becomes a sanction, and is considered along with reason, experience, authority and universality. These sanctions are then applied to biography and pastorals. ;The final part deals with Johnson's political arguments based on the sanctions of authority, universality, reason and experience, and shows how these are applied to the American problem. (shrink)