We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

Ackermann’s function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive formulation—and therefore its totality—has a simple proof in Isabelle/HOL. This is a small example of formalising mathematics using a proof assistant, with a focus on the treatment of difficult recursions.

Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references (...) to more advanced reading. Part II provides enough detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach. (shrink)

We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical logics. We report some experiments using the higher-order automated theorem prover LEO-II.

within-field task as testing proceeded. (In any case, the two-field task is presumably a more difficult one than the one-field task. ...

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very (...) notion of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

ETHICS: A PLURALISTIC APPROACH TO MORAL THEORY, FIFTH EDITION provides a comprehensive yet clear introduction to the main traditions in ethical thought, including virtue ethics, utilitarianism, and deontology. Additionally, the book presents a conceptual framework of ethical pluralism to help students understand the relationship among various theories. Lawrence Hinman, one of today's most respected and accomplished educators in ethics and philosophy education, presents a text that gives students plentiful opportunities to explore ethical theory and their own responses to them, (...) using fascinating features such as the Ethical Inventory sections that appear at the beginning and the end of the text. End-of-chapter discussion questions, and the use of current issues and movies help students retain what they've learned and truly comprehend the subject matter. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very (...) notion of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

The work of French philosopher Maurice Merleau-Ponty touches on some of the most essential and vital concerns of the world today, yet his ideas are difficult and not widely understood. Lawrence Hass redresses this problem by offering an exceptionally clear, carefully argued, critical appreciation of Merleau-Ponty's philosophy. Hass provides insight into the philosophical methods and major concepts that characterize Merleau-Ponty's thought. Questions concerning the nature of phenomenology, perceptual experience, embodiment, intersubjectivity, expression, and philosophy of language are fully and systematically (...) discussed with reference to main currents and discussions in contemporary philosophy. The result is a refreshingly jargon-free invitation into Merleau-Ponty's important and transformational way of understanding human experience. (shrink)

Skeptics have cast doubt on the idea that scientific theories give us a true picture of an objective world. Lawrence Sklar examines three kinds of skeptical arguments about scientific truth, and explores the important role they play within foundational science itself. Sklar demonstrates that these kinds of philosophical critique are employed within science, and reveals the clear difference between how they operate in a scientific context and more abstract philosophical contexts. The underlying theme of Theory and Truth is that (...) science and philosophy are essential to one another. Sklar advances the claim that one cannot understand the methods of science without a comprehension of philosophy, and one cannot fruitfully pursue philosophy of science without understanding fundamental science as well. (shrink)

In this book, Lawrence Hatab provides an accessible and provocative exploration of one of the best-known and still most puzzling aspects of Nietzsche's thought: eternal recurrence, the claim that life endlessly repeats itself identically in every detail. Hatab argues that eternal recurrence can and should be read literally, in just the way Nietzsche described it in the texts. The book offers a readable treatment of most of the core topics in Nietzsche's philosophy, all discussed in the light of the (...) consummating effect of eternal recurrence. Although Nietzsche called eternal recurrence his most fundamental idea, most interpreters have found it problematic or needful of redescription in other terms. For this reason, Hatab's book is an important and challenging contribution to Nietzsche scholarship. (shrink)

How is it that sounds from the mouth or marks on a page—which by themselves are nothing like things or events in the world—can be world-disclosive in an automatic manner? In this fascinating and important book, Lawrence J. Hatab presents a new vocabulary for Heidegger’s early phenomenology of being-in-the-world and applies it to the question of language. He takes language to be a mode of dwelling, in which there is an immediate, direct disclosure of meanings, and sketches an extensive (...) picture of proto-phenomenology, how it revises the posture of philosophy, and how this posture applies to the nature of language. Representational theories are not rejected but subordinated to a presentational account of immediate disclosure in concrete embodied life. The book critically addresses standard theories of language, such that typical questions in the philosophy of language are revised in a manner that avoids binary separations of language and world, speech and cognition, theory and practise, realism and idealism, internalism and externalism. (shrink)

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as$\bar{x}$and$\bar{y}$), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. (...) There are efficient algorithms for proof search and model construction. (shrink)

Although now replaced by more modern theories, classical mechanics remains a core foundational element of physical theory. From its inception, the theory of dynamics has been riddled with conceptual issues and differing philosophical interpretations and throughout its long historical development, it has shown subtle conceptual refinement. The interpretive program for the theory has also shown deep evolutionary change over time. Lawrence Sklar discusses crucial issues in the central theory from which contemporary foundational theories are derived and shows how some (...) core issues have nevertheless remained deep puzzles despite the increasingly sophisticated understanding of the theory which has been acquired over time. His book will be of great interest to philosophers of science, philosophers in general and physicists concerned with foundational interpretive issues in their field. (shrink)

ABSTRACTMany social scientific studies have shown the positive effects of self-awareness and reflexivity in shaping individuals’ career paths. However, using life- and work-history interviews conducted with salespersons in Toronto, Canada, I find that high levels of self-awareness – as demonstrated by active deliberation over one’s career – has both positive and negative results in terms of career outcomes. Respondents whose careers initially progressed as they expected tended to benefit from reflexively managing their careers. However, the benefits of reflexivity were mixed (...) for respondents whose careers did not begin as planned. This group of respondents sometimes benefited from thinking about alternatives; but also, sometimes, cast themselves outside of careers that they deemed to be ‘normal’. Observing the way that some respondents formed new career plans based on unmet expectations, and began to pursue those emergent plans, I argue that scholarly uses of reflexivity should incorporate its function as a potential career trajectory anchor. (shrink)

The spate of popular books attacking religion can be seen as a manifestation of the recoil against the idea of multiculturalism. Religious identities are also cultural identities, and no meaningful form of multiculturalism is possible that leaves religion outside the sphere of public recognition. This paper argues that ‘aggressive atheism’ undermines its appeal to reason by refusing to see anything of value in religion. It also risks exacerbating cultural differences at a time when reconciliation is needed. The critique focuses on (...) the contribution of Richard Dawkins and examines a number of tensions within the aggressive atheism of his best-selling book The God Delusion. The second part of the paper introduces an alternative, a framework of reconciliatory dialogues, between atheism and religion and within religious communities, operating not just at a formal or institutional level but also in cultural expressions and in the practices of everyday life. (shrink)

My One Fallacy theory says there is only one fallacy: equivocation, or playing on an ambiguity. In this paper I explain how this theory arose from rnetaphilosophical concerns. And I contrast this theory with purely logical, dialectical, and psychological notions of fallacy.

Through his innovative study of language, noted Heidegger scholar Lawrence Hatab offers a proto-phenomenological account of the lived world, the “first” world of factical life, where pre-reflective, immediate disclosiveness precedes and makes possible representational models of language. Common distinctions between mind and world, fact and value, cognition and affect miss the meaning-laden dimension of embodied, practical existence, where language and life are a matter of “dwelling in speech.” In this second volume, Hatab supplements and fortifies his initial analysis by (...) offering a detailed treatment of child development and language acquisition, which exhibit a proto-phenomenological world in the making. He then takes up an in-depth study of the differences between oral and written language (particularly in the ancient Greek world) and how the history of alphabetic literacy shows why Western philosophy came to emphasize objective, representational models of cognition and language, which conceal and pass over the presentational domain of dwelling in speech. Such a study offers significant new angles on the nature of philosophy and language. (shrink)

ABSTRACT McGowan’s notion of norm ‘enactment’ is the linchpin of her practical project, designed to provide an objective standard that circumvents the need to assess actual subjective uptake of discriminatory norms proposed by racist utterances in public spaces. However, the essential role of uptake to potential norm-imposing utterances—and responses like dismissing, countermanding, and ignoring—cannot be waved away. Contributions to conversations, and even more so to other social interactions, do not exert the normative compulsion upon participants that McGowan’s theory needs. People’s (...) words, even their ugly words, are not invariably norm ‘enactments’ that ‘constitute harm’—sometimes they are just words. (shrink)

If racism is a matter of possessing racist beliefs, then it would seem that its cure involves purging one’s mind of all racist beliefs. But the truth is more complicated, and does not permit such a straightforward strategy. Racist beliefs are resistant to subjective repudiation, and even those that are so repudiated are resistant to lasting expulsion from one’s belief system. Moreover, those that remain available for use in cognition can shape thought and behavior even in the event that one (...) has recognized their falsehood. Yet if one is intent upon combating the racism within one’s mind, one is not without effective cognitive countermeasures that can render one’s racist beliefs ineffectual. (shrink)

In Can We Live Together? Alain Touraine combines a consummate analysis of crucial social tensions in contemporary societies with a strong normative appeal for a new emancipatory 'Subject' capable of overcoming the twin threats of atomisation or authoritarianism. He calls for a move from 'politics to ethics' and then from ethics back to politics to enable the new Subject to make a reality out of the goals of democracy and solidarity. However, he has little to say about the nature of (...) such an ethics. This article argues that this lacuna could usefully be filled by adopting a form of radical humanism found in the work of Erich Fromm. It defies convention in the social sciences by operating from an explicit view of the 'is' and the 'ought' of common human nature, specifying reason, love and productive work as the qualities to be realised if we are to move closer to human solidarity. Although there remain significant philosophical and political differences between the two positions, particularly on the role to be played by 'the nation', their juxtaposition opens new lines of inquiry in the field of cosmopolitan ethics. (shrink)

During his years as a member of the Frankfurt School, Erich Fromm developed a strong interest in the idea that there were distinctive male and female character orientations. Drawing on the positive evaluation of matriarchy made in the nineteenth century by the Swiss anthropologist J. J. Bachofen, Fromm argued that a “matricentric” psychic structure was more conducive to socialism than the patricentric structure which had predominated in capitalism. His interest in maternalism and his opposition to patriarchy played an important part (...) in his rejection of Freud's theory of drives and in the development of a humanistic ethics in which love plays a central part. The idea of a gendered humanism is central to Fromm's social thought, although there is a danger that the over‐emphasis of sex‐based character differences unintentionally re‐opens the danger of the kind of sexual stereotyping which he resolutely opposed. (shrink)

Departing from the sociological dual process model that divides thoughts into automatic and unconscious, or deliberate and conscious occurrences, this book draws on empirical cases to demonstrate the existence of 'automatic deliberation'. Through research into the ways in which people address difficult subjects, such as death and dying, paedophilia, and career decision-making, the author sheds light on a mode of thinking which is both habitual and effortful, displaying a combination of habituated understandings and conscious deliberation. Advancing a blended view of (...) cognition by which individuals draw on schemas and frames to think through complex topics, this volume will appeal to sociologists and psychologists with interests in cognition and the ways in which we make decisions. (shrink)

T. H. Marshall, a British sociologist, gave a series of lectures in 1949 under the title “Citizenship and Social Class.” To many American intellectuals, his analysis still offers a persuasive account of the origins of the welfare state in the West. But Marshall spoke in the early postwar era, when the case for expanded social benefits seemed unassailable. Today's politics are more conservative. In every Western country the welfare state is under review. Yet Marshall's conception can still help define the (...) issues in social policy and the way forward. (shrink)

This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty's work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty's system internalized the monotonicity/polarity markings by generating strings using a categorial grammar whose categories already contain the markings that the earlier (...) system would obtain by separate steps working on an already-derived string. Despite the linguistic advantages of the internalized system, no soundness proof has yet been given for it. This paper offers an account. The leading mathematical idea is to interpret categorial types as preorders (in order to talk about monotonicity in the first place), and then to add a primitive operation to the type hierarchy of taking the opposite of a preorder (in order to capture monotone decreasing functions). At the same time, the use of internalized categories also raises issues. Although these will not be addressed in full, the paper points out possible approaches to them. (shrink)

The difference between Poe's and [Paul] Valéry's theory of notes—between a theory that emphasizes the nonsensical unpredictability of notes and a theory that discovers in notes the essential logic not only of all reading but of the mind itself—cannot be resolved. To some extent, perhaps, it derives from a conflict between two genres: marginalia, and the marginal gloss. Marginalia—traces left in a book—are wayward in their very nature; they spring up spontaneously around a text unaware of their presence. Nor could (...) they have been considered publishable until the Romantic period had encouraged a taste for fragments and impulses, the suggestive part rather than the ordered whole. Significantly the term was introduced by Coleridge, that great master of the fragment; and Poe himself was the first author ever to publish his marginalia. The charm of such notes depends on their being on the edge: the borders of intelligibility or consciousness . The reader catches an author off his guard, intercepting a thought that may scarcely have risen to formulation. At their best, marginalia can haunt us like a few passing words overheard in the street; all the more precious because the context remains unknown. Lawrence Lipking, professor of English and comparative literature at Princeton University, is the author of The Ordering of the Arts in Eighteenth-Century England and coeditor of Modern Literary Criticism 1900-1970. Some of the material in this article is drawn from a book currently in progress, The Poet-Critics, a study of the relations between poetry and criticism in the work of authors who have excelled in both. "Arguing with Shelly" appeared in the Winter 1979 issue of Critical Inquiry. (shrink)

The Clash of Economic Ideas interweaves the economic history of the last hundred years with the history of economic doctrines to understand how contrasting economic ideas have originated and developed over time to take their present forms. It traces the connections running from historical events to debates among economists, and from the ideas of academic writers to major experiments in economic policy. The treatment offers fresh perspectives on laissez faire, socialism and fascism; the Roaring Twenties, business cycle theories and the (...) Great Depression; Institutionalism and the New Deal; the Keynesian Revolution; and war, nationalization and central planning. After 1945, the work explores the postwar revival of invisible-hand ideas; economic development and growth, with special attention to contrasting policies and thought in Germany and India; the gold standard, the interwar gold-exchange standard, the postwar Bretton Woods system and the Great Inflation; public goods and public choice; free trade versus protectionism; and finally fiscal policy and public debt. (shrink)