Logic is of course a general resource for reasoning at large. But in the first half of the twentieth century, it developed particularity with a view to mathematical applications, and the field of mathematical logic came into being and flourished. In the second half of the century, much the same happened with regard to philosophical applications. Hence philosophical logic. The deliberations of this book cover a varied but interrelated array of key issues in the field. They address the representation of information in linguistic formulation, and modes of cogent demonstration in logic, mathematics, and empirical investigation, as well as the role of logic in philosophical deliberations. Overall, the book seeks to demonstrate and illustrate the utility of logic as a productive resource for rational inquiry at large.

In 1945 Alonzo Church issued a pair of referee reports in which he anonymously conveyed to Frederic Fitch a surprising proof showing that wherever there is (empirical) ignorance there is also logically unknowable truth. Fitch published this and a generalization of the result in 1963. Ever since, philosophers have been attempting to understand the significance and address the counter-intuitiveness of this, the so-called paradox of knowability.
This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox. The contributors include logicians and philosophers from three continents, many of whom have already made important contributions to the discussion of the problem. The volume contains a general introduction to the paradox and the background literature, and is divided into seven sections that roughly mark the central points of debate. The sections include the history of the paradox, Michael Dummett's constructivism, issues of paraconsistency, developments of modal and temporal logics, Cartesian restricted theories of truth, modal and mathematical fictionalism, and reconsiderations about how, and whether, we ought to construe an anti-realist theory of truth.

The content of the volume is divided as follows: after presenting two rival approaches to substantiality and causality: a traditional (ontological) view vs. a transcendental one (Rosiak) there follow two sections: the first presents studies of substance as showing some causal aspects (Buchheim, Keinanen, Kovac, Piwowarczyk), whereas the other contains investigations of causality showing in a way its reference to the category of substance (Kobiela, Meixner, Mitscherling, Wronski). The last, short section contains two studies of extension (Leszczynski and Skowron) which can be regarded as a conceptual background of both substantiality and causality. The book gives a very colourful picture of the discussions connected with substantiality and causality which may be of potential interest for the readers.

For centuries debates about reason and its Other have animated and informed philosophy, art, science and politics throughout Western civilization - but nowhere, arguably as deeply and turbulently as in Germany. Reason, the legacy of the Enlightenment, has been claimed, rejected and redefined by influential German thinkers from Kant to Nietzsche to Habermas. In our own time - more than 200 years after Kant's Critique of Pure Reason - the status of reason and the irrational, what is and what should be excluded from reason, what qualifies as a critique of reason, are all still central philosophical issues in Germany as well as throughout the West.

This collection of papers, published in honour of Hector J. Levesque on the occasion of his 60th birthday, addresses a number of core areas in the field of knowledge representation and reasoning. In a broad sense, the book is about knowledge and belief, tractable reasoning, and reasoning about action and change. More specifically, the book contains contributions to Description Logics, the expressiveness of knowledge representation languages, limited forms of inference, satisfiablity (SAT), the logical foundations of BDI architectures, only-knowing, belief revision, planning, causation, the situation calculus, the action language Golog, and cognitive robotics.

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point of view.

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Vaananen, whose ecumenical approach to logic reflects the unity of the discipline."

Kevin Scharp proposes an original theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. Replacing Truth opens with an overview of work on the nature of truth (e.g., correspondence theories, deflationism), work on the liar and related paradoxes, and a comprehensive scheme for combining these two literatures into a unified study of the concept truth. Scharp argues that truth is best understood as an inconsistent concept, and proposes a detailed theory of inconsistent concepts that can be applied to the case of truth. Truth also happens to be a useful concept, but its inconsistency inhibits its utility; as such, it should be replaced with consistent concepts that can do truth's job without giving rise to paradoxes. To this end, Scharp offers a pair of replacements, which he dubs ascending truth and descending truth, along with an axiomatic theory of them and a new kind of possible-worlds semantics for this theory. As for the nature of truth, he goes on to develop Davidson's idea that it is best understood as the core of a measurement system for rational phenomena (e.g., belief, desire, and meaning). The book finishes with a semantic theory that treats truth predicates as assessment-sensitive (i.e., their extension is relative to a context of assessment), and a demonstration of how this theory solves the problems posed by the liar and other paradoxes.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Tyler Burge presents a collection of his seminal essays on Gottlob Frege (1848-1925), who has a strong claim to be seen as the founder of modern analytic philosophy, and whose work remains at the centre of philosophical debate today. Truth, Thought, Reason gathers some of Burge's most influential work from the last twenty-five years, and also features important new material, including a substantial introduction and postscripts to four of the ten papers. It will be an essential resource for any historian of modern philosophy, and for anyone working on philosophy of language, epistemology, or philosophical logic.

This volume responds to and reassesses the work of Hector-Neri Castaneda (1924-1991). The essays collected here, written by his students, followers, and opponents, examine Castaneda s seminal views on deontic logic, metaethics, indedicality, praticitions, fictions, and metaphysics, utilizing the critical viewpoint afforded by time, as well as new data, to offer insights on his theories and methodology."

The Logical Must is an examination of Ludwig Wittgenstein's philosophy of logic, early and late, undertaken from an austere naturalistic perspective Penelope Maddy has called "Second Philosophy." The Second Philosopher is a humble but tireless inquirer who begins her investigation of the world with ordinary perceptual beliefs, moves from there to empirical generalizations, then to deliberate experimentation, and eventually to theory formation and confirmation. She takes this same approach to logical truth, locating its ground in simple worldly structures and our knowledge of it in our basic cognitive machinery, tuned by evolutionary pressures to detect those structures where they occur.
In his early work Tractatus Logico-Philosophicus, Wittgenstein also links the logical structure of representation with the structure of the world, but he includes one key unnaturalistic assumption: that the sense of our representations must be given prior to-independently of-facts about how the world is. When that assumption is removed, the general outlines of the resulting position come surprisingly close to the Second Philosopher's roughly empirical account. In his later discussions of logic in Philosophical Investigations and Remarks on the Foundations of Mathematics, Wittgenstein also rejects this earlier assumption in favor of a picture that arises in the wake of the famous rule-following considerations. Here Wittgenstein and the Second Philosopher operate in even closer harmony-locating the ground of our logical practices in our interests, our natural inclinations and abilities, and very general features of the world-until the Second Philosopher moves to fill in the account with her empirical investigations of the world and cognition. At this point, Wittgenstein balks, but as a matter of personal animosity rather than philosophical principle.

The present volume has its origin in a meeting of philosophers, linguists and cognitive scientists that was held at Umea University, Sweden, September 24-26, 1993. The meeting was organized by the Department of Philosophy in co-opersation with the Department of Linguistics, and it was called UmLLI-93, the Umea Colloquium on Dynamic Approaches in Logic, Language and Information. The papers included here fall into three broad categories. In the first part of the book, Action, are collected papers that concern the formal theory of action, the logic of norms, and the theory of rational decision. The papers in the second part, Belief Change, concern the theory of belief dynamics in the tradition of Alchourron, Gardenfors and Makinson. The third part, Cognition, concerns abstract questions about knowledge and truth as well as more concrete questions about the usefulness and tractability of various graphic representations of information.

In three comprehensive volumes, Logic of the Future presents a full panorama of Charles S. Peirce's most important late writings. Among the most influential American thinkers, Peirce took his existential graphs to be a significant contribution to human thought. The manuscripts from 1895-1913, with many of them being published here for the first time, testify to the richness and open-endedness of his theory of logic and its applications. They also invite us to reconsider our ordinary conceptions of reasoning as well as the conventional stories concerning the evolution of modern logic. This first volume of Logic of the Future is on the historical development, theory and application of Peirce's graphical method and diagrammatic reasoning. It also illustrates the abundant further developments and applications Peirce envisaged existential graphs to have on the analysis of mathematics, language, meaning and mind.

Instance ontology, or particularism - the doctrine that asserts the individuality of properties and relations - has been a persistent topic in Western philosophy, discussed in works by Plato and Aristotle, by Muslim and Christian scholastics, and by philosophers of both realist and nominalist positions. This book by D. W. Mertz is the first sustained analysis that applies the rules and systems of mathematics and logic to instance ontology in order to argue for its validity and for its problem-solving capacities and to associate it with a version of the realist position that Mertz calls "moderate realism". Mertz surveys the history of instance ontology in writings from Plato and Aristotle through Leibniz, followed by modern philosophers such as Bertrand Russell and D. M. Armstrong, among others. He also includes a thorough critique of the recent work of Keith Campbell and other contemporary nominalists. Building on the insights gained through this historical overview, he delves deeper into the logic of instance ontology and uncovers some of its extraordinary problem-solving features: distinguishing legitimate from illegitimate impredicative reasoning; uniformly diagnosing the self-referential paradoxes; being free from the limitation theorems of Godel and Tarski; providing a basis for the derivation of arithmetic construed intensionally; and formally distinguishing identity and indiscernibility.

This volume opens up stimulating new perspectives on a broad variety of Barcan Marcus's concerns ranging from the systematic foundation and interpretation of quantified modal logic, nature of extensionality, necessity of identity, direct reference theory for proper names, notions of essentialism, second-order modal logic, modal metaphysics, properties and classes, substitutional and objectual quantification, actualism, the Barcan formula, possibilia and possible-world semantics to epistemic and deontic modalities, non-language-centered theories of belief, accounts of rationality, consistency of a moral code, moral dilemmas, and much more. The contributions demonstrate that Barcan Marcus's original and clear ideas have had a formative influence on the direction in which certain themes central to today's philosophical debate have developed. Furthermore, the volume includes an illuminating intellectual autobiography from Barcan Marcus herself as well as an informal interview containing her unfiltered, frank answers. The book brings together contributions by Ruth Barcan Marcus, Timothy Williamson, Dagfinn Follesdal, Joelle Proust, Pascal Engel, Edgar Morscher, Erik J. Olsson, and Michael Frauchiger.

Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfolding-from the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the present-that culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.

Philosophical logic has been, and continues to be, a driving force behind much progress and development in philosophy more broadly. This collection by up-and-coming philosophical logicians deals with a broad range of topics, including, for example, proof-theory, probability, context-sensitivity, dialetheism and dynamic semantics.

A new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are any disjoint syntactic categories. On this new approach, we can at last read Frege's notations in their original form revealing striking new solutions to many of the outstanding problems of interpreting his philosophy.