This volume comprises nine lively and insightful essays by leading scholars on the philosophy of Ludwig Wittgenstein, focusing mainly on his early work. The essays are written from a range of perspectives and do not belong to any one exegetical school; they approach Wittgenstein's work directly, seeking to understand it in its own terms and by reference to the context in which it was produced. The contributors cover a wide range of aspects of Wittgenstein's early philosophy, but three central themes emerge: the relationship between Wittgenstein's account of representation and Russell's theories of judgment; the role of objects in the tractarian system; and Wittgenstein's philosophical method. Collectively, the essays demonstrate how progress in the understanding of Wittgenstein's work is not to be made by focusing on overarching, ideological issues, but by paying close attention to his engagement with specific philosophical problems.

Reliabilist accounts of knowledge are widely seen as having the resources for blocking sceptical arguments, since these arguments appear to rely on assumptions about the nature of knowledge that are rendered illegitimate by reliabilist accounts. In Scepticism and Reliable Belief Jose L. Zalabardo assesses the main arguments against the possibility of knowledge, and challenges their consensus. He articulates and defends a reliabilist theory of knowledge that belongs firmly in the truth-tracking tradition. Zalabardo's main analytic tool in the account of knowledge he provides is the theory of probability: he analyses both truth tracking and evidence in these terms, and argues that this account of knowledge has the resources for blocking the main standard lines of sceptical reasoning--including the regress argument, arguments based on sceptical hypotheses, and the problem of the criterion. But although Zalabardo's theory can be used to refute the standard lines of sceptical reasoning, there is a sceptical argument against which his account offers no defence, as it does not rely on any assumptions that he renders illegitimate. According to this argument, we might have considerable success in the enterprise of forming true beliefs: if this is so, we have knowledge of the world. However, we cannot know that we are successful, even if we are. Beliefs to this effect cannot be knowledge on Zalabardo's reliabilist account, since these beliefs do not track the truth and we cannot obtain adequate evidence in their support. Zalabardo ends with the suggestion that the problem might have a metaphysical solution: although the sceptical argument may make no illegitimate epistemological assumptions, it does rest on a questionable account of the nature of cognition."

This book provides a rigorous introduction to the basic concepts and results of contemporary logic. It also presents, in two unhurried chapters, the mathematical tools (mainly from set theory) that are needed to master the technical aspects of the subject. Methods of definition and proof are also discussed at length, with special emphasis on induct

This book provides a rigorous introduction to the basic concepts and results of contemporary logic. It also presents, in two unhurried chapters, the mathematical tools (mainly from set theory) that are needed to master the technical aspects of the subject. Methods of definition and proof are also discussed at length, with special emphasis on inductive definitions and proofs and recursive definitions. The book is ideally suited for readers who want to undertake a serious study of logic but lack the mathematical background that other texts at this level presuppose. It can be used as a textbook in graduate and advanced undergraduate courses in logic. Hundreds of exercises are provided. Topics covered include basic set theory, propositional and first-order syntax and semantics, a sequent calculus-style deductive system, the soundness and completeness theorems, cardinality, the expressive limitations of first-order logic, with especial attention to the Loewenheim-Skolem theorems and non-standard models of arithmetic, decidability, complete theories, categoricity and quantifier elimination.

Jose L. Zalabardo puts forward a new interpretation of central ideas in Wittgenstein's Tractatus Logico-Philosophicus concerning the structure of reality and our representations of it in thought and language. He shows the origins of Wittgenstein's picture theory of propositional representation in Russell's theories of judgment, arguing that the picture theory is Wittgenstein's solution to some of the problems that he found in Russell's position. Zalabardo defends the view that, for Wittgenstein, facts in general, and the facts that play the role of propositions in particular, are not composite items, arising from the combination of their constituents. They are ultimate, irreducible units, and what we think of as their constituents are features that facts have in common with one another. These common features have built into them their possibilities of combination with other features into possible situations. This is the source of the Tractarian account of non-actual possibilities. It is also the source of the idea that it is not possible to produce propositions answering to certain descriptions, including those that would give rise to Russell's paradox. Zalabardo then considers Wittgenstein's view that every proposition is a truth function of elementary propositions. He argues that this view is motivated by Wittgenstein's epistemology of logic, according to which we should be able to see logical relations by inspecting the structures of propositions. Finally, Zalabardo considers the problems that we face if we try to extend the application of the picture theory from elementary propositions to truth functions of these.

Jose L. Zalabardo puts forward a new interpretation of central ideas in Wittgenstein's Tractatus Logico-Philosophicus concerning the structure of reality and our representations of it in thought and language. He shows the origins of Wittgenstein's picture theory of propositional representation in Russell's theories of judgment, arguing that the picture theory is Wittgenstein's solution to some of the problems that he found in Russell's position. Zalabardo defends the view that, for Wittgenstein, facts in general, and the facts that play the role of propositions in particular, are not composite items, arising from the combination of their constituents. They are ultimate, irreducible units, and what we think of as their constituents are features that facts have in common with one another. These common features have built into them their possibilities of combination with other features into possible situations. This is the source of the Tractarian account of non-actual possibilities. It is also the source of the idea that it is not possible to produce propositions answering to certain descriptions, including those that would give rise to Russell's paradox. Zalabardo then considers Wittgenstein's view that every proposition is a truth function of elementary propositions. He argues that this view is motivated by Wittgenstein's epistemology of logic, according to which we should be able to see logical relations by inspecting the structures of propositions. Finally, Zalabardo considers the problems that we face if we try to extend the application of the picture theory from elementary propositions to truth functions of these.