This volume contains six new and fifteen previously published essays -- plus a new introduction -- by Storrs McCall. Some of the essays were written in collaboration with E. J. Lowe of Durham University. The essays discuss controversial topics in logic, action theory, determinism and indeterminism, and the nature of human choice and decision. Some construct a modern up-to-date version of Aristotle's bouleusis, practical deliberation. This process of practical deliberation is shown to be indeterministic but highly controlled and the antithesis of chance. Others deal with the concept of branching four-dimensional space-time, explain non-local influences in quantum mechanics, or reconcile God's omniscience with human free will. The eponymous first essay contains the proof of a fact that in 1931 Kurt Godel had claimed to be unprovable, namely that the set of arithmetic truths forms a consistent system."

Although the study of reasons plays an important role in both epistemology and moral philosophy, little attention has been devoted to the question of how, exactly, reasons interact to support the actions or conclusions they do. In this book, John F. Horty attempts to answer this question by providing a precise, concrete account of reasons and their interaction, based on the logic of default reasoning. The book begins with an intuitive, accessible introduction to default logic itself, and then argues that this logic can be adapted to serve as a foundation for a concrete theory of reasons. Horty then shows that the resulting theory helps to explain how the interplay among reasons can determine what we ought to do by developing two different deontic logics, capturing two different intuitions about moral conflicts. In the central part of the book, Horty elaborates the basic theory to account for reasoning about the strength of our own reasons, and also about the related concepts of undercutting defeaters and exclusionary reasons. The theory is illustrated with an application to particularist arguments concerning the role of principles in moral theory. The book concludes by introducing a pair of issues new to the philosophical literature: the problem of determining the epistemic status of conclusions supported by separate but conflicting reasons, and the problem of drawing conclusions from sets of reasons that can vary arbitrarily in strength, or importance.

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

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer's biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincare, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.

Saul Kripke's Naming and Necessity was one of the most influential philosophical works of the twentieth century. In this collection of essays leading specialists explore issues arising from this and other works of Kripke's.

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

The book presents the state of the art of research into the legacy of interwar Polish analytic philosophy and exemplifies different approaches to the history of philosophy. It contains discussions and reconstructions of aspects of Polish philosophy and logic as well as reactions to and developments of this tradition.

William G. Lycan offers a fresh original approach to the long-running debate among philosophers and logicians about the best way to analyse and understand conditional sentences. Lycan attends not just to the semantics of such sentences, but equally to their syntax, making use of insights from linguistic theory. Real Conditionals is the definitive presentation of Lycan's view, written in his characteristically lively style.

Though the subject of this work, "nominalism and contemporary nom inalism," is philosophical, it cannot be fully treated without relating it to data gathered from a great variety of domains, such as biology and more especially ethology, psychology, linguistics and neurobiology. The source of inspiration has been an academic work I wrote in order to obtain a postdoctoral degree, which is called in Belgium an "Aggregaat voor het Hoger Onderwijs" comparable to a "Habilitation" in Germany. I want to thank the National Fund of Scientific Research, which accorded me several grants and thereby enabled me to write the academic work in the first place and thereafter this book. I also want to thank Prof. SJ. Doorman (Technical University of Delft) and Prof. G. Nuchelmans (University of Leiden), who were members of the jury of the "Aggre gaatsthesis," presented to the Free University of Brussels in 1981 and who by their criticisms and suggestions encouraged me to write the present book, the core of which is constituted by the general ideas then formulated. I am further obliged to Mr. X, the referee who was asked by Jaakko Hintikka to read my work and who made a series of constructive remarks and recom mendations. My colleague Marc De Mey (University of Ghent) helped me greatly with the more formal aspects of my work and spent too much of his valuable time and energy to enable me to deliver a presentable copy. All remaining shortcomings are entirely my responsibility. I asked Prof."

This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.

by the question in its being an answer, if only in a circumstantial (i. e. inessential) manner. One indeed must question oneself in order to remember, says Plato, but the dialectic, which would be scientific, must be something else even if it remains a play of question and answer. This contradiction did not escape Aristotle: he split the scientific from the dialectic and logic from argumentation whose respective theories he was led to conceive in order to clearly define their boundaries and specificities. As for Plato, he found in the famous theory of Ideas what he sought in order to justify knowledge as that which is supposed to hold its truth only from itself. What do Ideas mean within the framework of our approach? In what consists the passage from rhetoric to ontology which leads to the denaturation of argumentation? When Socrates asked, for example, "What is virtue?," he thought one could not answer such a question because the answer refers to a single proposition, a single truth, whereas the formulation of the question itself does not indicate this unicity. For any answer, another can be given and thus continuously, if necessary, until eventually one will come across an incompatibility. Now, to a question as to what X, Y, or Z is, one can answer in many ways and nothing in the question itself prohibits multiplicity. Virtue is courage, is justice, and so on.

It is the aim of the present study to introduce the reader to the ways of thinking of those contemporary philosophers who apply the tools of symbolic logic to classical philosophical problems. Unlike the "conti nental" reader for whom this work was originally written, the English speaking reader will be more familiar with most of the philosophers dis cussed in this book, and he will in general not be tempted to dismiss them indiscriminately as "positivists" and "nominalists." But the English version of this study may help to redress the balance in another respect. In view of the present emphasis on ordinary language and the wide spread tendency to leave the mathematical logicians alone with their technicalities, it seems not without merit to revive the interest in formal ontology and the construction of formal systems. A closer look at the historical account which will be given here, may convince the reader that there are several points in the historical develop ment whose consequences have not yet been fully assessed: I mention, e. g., the shift from the traditional three-level semantics of sense and deno tation to the contemporary two-level semantics of representation; the relation of extensional structure and intensional content in the extensional systems of Wittgenstein and Carnap; the confusing changes in labelling the different kinds of analytic and apriori true sentences; etc. Among the philosophically interesting tools of symbolic logic Lesniewski's calculus of names deserves special attention."

This book explains the first published consistency proof of PA. It contains the original Gentzen's proof, but it uses modern terminology and examples to illustrate the essential notions. The author comments on Gentzen's steps which are supplemented with exact calculations and parts of formal derivations. A notable aspect of the proof is the representation of ordinal numbers that was developed by Gentzen. This representation is analysed and connection to set-theoretical representation is found, namely an algorithm for translating Gentzen's notation into Cantor normal form. The topic should interest researchers and students who work on proof theory, history of proof theory or Hilbert's program and who do not mind reading mathematical texts. "

Normal adults do not have any difficulty in recognizing their homes. But can artificial systems do in the same way as humans? This book collects interdisciplinary evidences and presents an answer from the perspective of computing, namely, the theory of cognitive prism. To recognize an environment, an intelligent system only needs to classify objects, structures them based on the connection relation (not through measuring!), subjectively orders the objects, and compares with the target environment, whose knowledge is similarly structured. The intelligent system works, therefore, like a prism: when a beam of light (a scene) reaches (is perceived) to an optical prism (by an intelligent system), some light (objects) is reflected (are neglected), those passed through (the recognized objects) are distorted (are ordered differently). So comes the term 'cognitive prism'! Two fundamental propositions used in the theory can be informally stated as follow: an orientation relation is a kind of distance comparison relation -- you being in front of me means you being nearer to my face than to my other sides; a pair of objects being connected means any object, precisely the space occupied by the object, can be moved to a place where it connects with the pair.

Thinking about reasoning suffers from a failure of vision. Philosophers, social scientists, and others who discuss and analyze reasoning have a particular activity in view: reasoning to figure things out, solve problems, and reach judgments. But there is a different activity we engage in that we call reasoning. We reason in the course of living together, when we are responsive to those with whom we live and neither commanding nor deferring to them, neither manipulating nor ignoring them. Analysis of this second kind of activity has relied on the tools and frameworks developed to make sense of the first kind of activity. In this book, Anthony Simon Laden invites his readers to approach this activity of reasoning on its own terms. He claims that if we are to truly see and appreciate the role and value of reasoning in living together, we need a new, social picture of the activity of reasoning. According to the social picture of reasoning developed here, reasoning is a species of conversation, and like casual conversation is social and ongoing. It is neither defined nor determined by its end, although it is governed by a set of characteristic norms. It consists of inviting others to accept that our words can speak for them as well. Reasoning: A Social Picture proposes an attractive new approach to thinking about how to live together, reasonably.

This book provides a new, linguistic approach to Argumentation Theory. Its main goal is to integrate the logical, dialectical and rhetorical dimensions of argumentation in a model providing a unitary treatment of its justificatory and persuasive powers. This model takes as its basis Speech Acts Theory in order to characterize argumentation as a second-order speech act complex. The result is a systematic and comprehensive theory of the interpretation, analysis and evaluation of arguments. This theory sheds light on the many faces of argumentative communication: verbal and non-verbal, monological and dialogical, literal and non-literal, ordinary and specialized.
The book takes into consideration the major current comprehensive accounts of good argumentation (Perelman's New Rhetoric, Pragma-dialectics, the ARG model, the Epistemic Approach) and shows that these accounts have fundamental weaknesses rooted in their instrumentalist conception of argumentation as an activity oriented to a goal external to itself. Furthermore, the author addresses some challenging meta-theoretical questions such as the justification problem for Argumentation Theory models and the relationship between reasoning and arguing.

1. Main assumptions, objectives and conditionings 1.1. The present book is concerned with certain problems in the logical philosophy of language . It is written in the the Polish logical, philosophical, and semiotic spirit of syntax of tradition, and shows two conceptions of the categorial languages : the theory of simple languages, i.e ., languages which do not include variables nor the operators that bind them (for instance, large fragments of natural languages, calculi, the language of languages of well-known sentential Aristotle's traditional syllogistic, languages of equationally definable algebras), and the theory of w-languages, i.e., languages which include operators and variables bound by the latter

"Topical Themes in Argumentation Theory" brings together twenty exploratory studies on important subjects of research in contemporary argumentation theory. The essays are based on papers that were presented at the 7th Conference of the International Society for the Study of Argumentation (ISSA) in Amsterdam in June 2010. They give an impression of the nature and the variety of the kind of research that has recently been carried out in the study of argumentation.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse.

The volume starts with three essays that provide stimulating theoretical perspectives on argumentation. Subsequently, some views are explained on the intriguing topics of 'dissensus' and 'deep disagreement'. After a discussion of three different approaches to the treatment of types of argumentation some classical themes from antique argumentation theory are revisited. The new research area of visual argumentation is explored in the next part. The volume concludes with three reports of experimental studies concerning argumentative discourse."

This comprehensive account of the concept and practices of deduction is the first to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice. Catarina Dutilh Novaes draws on all of these perspectives to argue for an overarching conceptualization of deduction as a dialogical practice: deduction has dialogical roots, and these dialogical roots are still largely present both in theories and in practices of deduction. Dutilh Novaes' account also highlights the deeply human and in fact social nature of deduction, as embedded in actual human practices; as such, it presents a highly innovative account of deduction. The book will be of interest to a wide range of readers, from advanced students to senior scholars, and from philosophers to mathematicians and cognitive scientists.

The topic to which this book is devoted is reductionism, and not reduction. The difference in the adoption of these two denominations is not, contrary to what might appear at first sight, just a matter of preference between a more abstract (reductionism) or a more concrete (reduction) terminology for indicating the same sUbject matter. In fact, the difference is that between a philosophical doctrine (or, perhaps, simply a philosophical tenet or claim) and a scientific procedure. Of course, this does not mean that these two fields are separated; they are only distinct, and this already means that they are also likely to be interrelated. However it is useful to consider them separately, if at least to better understand how and why they are interconnected. Just to give a first example of difference, we can remark that a philosophical doctrine is something which makes a claim and, as such, invites controversy and should, in a way, be challenged. A scientific procedure, on the other hand, is something which concretely exists, and as such must be first of all described, interpreted, understood, defined precisely and analyzed critically; this work may well lead to uncovering limitations of this procedure, or of certain ways of conceiving or defining it, but it does not lead to really challenging it.

The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo- gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t'Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J.Luka- siewicz's seminar on mathematicallogi

In this book, Veikko Rantala makes a systematic attempt to understand cognitive characteristics of translation by bringing its logical, pragmatic and hermeneutic features together and examining a number of scientific, logical, and philosophical applications. The notion of translation investigated here is called explanatory, but it is not a translation in the standard sense of the word since it admits of conceptual change. Such translations can take various degrees of precision, and therefore they can occur in contexts of different kinds: from everyday discourse to literary texts to scientific change. The book generalizes some earlier approaches to translation, especially the one presented in David Pearce's monograph Roads to Commensurability. Rantala argues that the notion has something in common with Thomas Kuhn's earlier conception of scientific change and his views of language learning, but it can be used to go beyond Kuhn's well-known ideas and challenge his criticism concerning the import of the correspondence relation.

Christopher Phillips has devoted his life to carrying the torch of Socrates and his quest to "Know Thyself." Yet upon the death of his beloved father and mentor, the originator of the burgeoning global Socrates Cafe movement had little choice but to confront the inescapable truth: that there are some things we cannot know for sure. This moving, insightful and ultimately hopeful and helpful blend of memoir and philosophical exploration begins in Phillips' native stomping grounds of the tiny volcanic island of Nisyros, Greece and unfurls through space and time as the author explores the connections between his immediate circumstances and the eternal wisdom of popular philosophers. - In this personal and probing book, the acclaimed 'philosopher for the people' shares lessons gleaned from his intimate and often unexpected encounters with uncommonly perceptive human beings both living and long deceased, in the form of weary travelers and some of history's greatest thinkers, from Heraclitus to Dr. Cornel West. Along the way, he charts a pathway for sculpting what Shakespeare describes as a "soul of goodness," which meshes with Plato's paradigm-shattering conception of the "healthiness of soul." For those struggling to overcome the hopelessness that can result from grievous loss, setback, or betrayal - what Phillips' touchstone Percy Blythe Shelley calls life circumstances "darker than death or night" - the author spotlights, with philosophical prescriptions both timely and timeless, how to cultivate a 'Socratic spirit' that leads to renewed love, forbearance, and hope at the other end of the tunnel.

This book presents a constitutive approach to controversy based on a discourse analysis of news texts, focusing on the role of journalists as participants who shape public controversy for readers. Drawing data from the Reuters Corpus, the project identifies formulas that journalists use in reporting controversy and draws conclusions about how these serve professional and textual functions and how they shape public controversy as a natural, historical, and pragmatic event. While the traditions of dialectic and rhetoric have focused on the prescriptive aim of training participants to resolve controversies in philosophical dialogue or public debate settings, this orientation has tended to preempt questions about where controversy is located and how it is shaped. This project contributes to descriptive, ethnographic research about controversy, using discourse analysis to address a problem in argumentation.