The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic developments. Extracting central philosophical ideas from Tarski's early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic exemplified in numerous recent mathematical and linguistic writings. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her development of the notion of logicality for quantifiers of many variables and her work on branching are of great importance, for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinnings of logic. She proposes a "constructive" definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications.

The book addresses two main areas of Kant’s theoretical philosophy: the doctrine of transcendental idealism and various central aspects of the arguments from the Metaphysical and Transcendental Deductions, as well as the relation between the deduction argument and idealism. Among the topics covered are the nature of objective validity, the role and function of transcendental logic in relation to general or formal logic, the possibility of contradictory thoughts, the meaning of the Leitfaden at A79 and the unity of cognition, the two-steps-in-one-proof interpretation and categorial instantiation, categorial illusion, Strawson’s transcendental argument, the persistently perplexing question of the derivation of the categories, and the relation between apperception, objectivity, judgement, and idealism. With regard to idealism in particular, the focus is on the metaphysical two-aspect interpretation and its problems, on the merits and demerits of the controversial phenomenalist reading of Kant’s idealism, and on the topic of subjectivism and epistemic humility. In all of the aforementioned topics, the book presents wholly novel interpretations compared to the standard or mainstream interpretations

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.

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.

This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Game theory is central to understanding human behavior and relevant to all of the behavioral sciences—from biology and economics, to anthropology and political science. However, as The Bounds of Reason demonstrates, game theory alone cannot fully explain human behavior and should instead complement other key concepts championed by the behavioral disciplines. Herbert Gintis shows that just as game theory without broader social theory is merely technical bravado, so social theory without game theory is a handicapped enterprise. This edition has been thoroughly revised and updated. Reinvigorating game theory, The Bounds of Reason offers innovative thinking for the behavioral sciences.

In Philosophy Within Its Proper Bounds, Edouard Machery argues that resolving many traditional and contemporary philosophical issues is beyond our epistemic reach and that philosophy should re-orient itself toward more humble, but ultimately more important intellectual endeavors. Any resolution to many of these contemporary issues would require an epistemic access to metaphysical possibilities and necessities, which, Machery argues, we do not have. In effect, then, Philosophy Within Its Proper Bounds defends a form of modal skepticism. The book assesses the main philosophical method for acquiring the modal knowledge that the resolution of modally immodest philosophical issues turns on: the method of cases, that is, the consideration of actual or hypothetical situations (which cases or thought experiments describe) in order to determine what facts hold in these situations. Canvassing the extensive work done by experimental philosophers over the last 15 years, Edouard Machery shows that the method of cases is unreliable and should be rejected. Importantly, the dismissal of modally immodest philosophical issues is no cause for despair - many important philosophical issues remain within our epistemic reach. In particular, reorienting the course of philosophy would free time and resources for bringing back to prominence a once-central intellectual endeavor: conceptual analysis.