Language was at the heart of philosophical inquiry for Plato and Aristotle, and in contemporary discussion it is no less central. In addition to the history of philosophy's extensive investigations of language, analytic and continental philosophy too have focused intensively on the matter. But since most inquiries into language remain enclosed in their own methodology, terminology, and tradition, the multiplicity of approaches is often accompanied by their mutual isolation. This book shows that these traditions can, however, speak meaningfully to each other on language: rather than preventing dialogue, their differences provide opportunities for fruitful inquiry. The essays in this volume each treat a central topic in the contemporary study of language. Part One addresses how expression determines thought according to Humboldt, the use of paraphrase in Quine's semantic ascent, and the non-ambiguity of the Frege-Russell senses of ‘is.’ Part Two includes treatments of the possibility and impossibility of promising in Nietzsche, and Derrida's re-working of Saussure's distinction between language and world. Topics in Part Three include the origin and end of language for Heidegger and Foucault, and the mutual sharpening of logic and ordinary speech in Anselm. This book fills a gap in current scholarship by bringing together nine essays that, through rejecting the debilitating yet often unquestioned divisions between disciplines, are able to illuminate the fundamental nature of language.

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Thomas C. Vinci aims to reveal and assess the structure of Kant's argument in the Critique of Pure Reason called the "Transcendental Deduction of the Categories." At the end of the first part of the Deduction in the B-edition Kant states that his purpose is achieved: to show that all intuitions in general are subject to the categories. On the standard reading, this means that all of our mental representations, including those originating in sense-experience, are structured by conceptualization. But this reading encounters an exegetical problem: Kant states in the second part of the Deduction that a major part of what remains to be shown is that empirical intuitions are subject to the categories. How can this be if it has already been shown that intuitions in general are subject to the categories? Vinci calls this the Triviality Problem, and he argues that solving it requires denying the standard reading. In its place he proposes that intuitions in general and empirical intuitions constitute disjoint classes and that, while all intuitions for Kant are unified, there are two kinds of unification: logical unification vs. aesthetic unification. Only the former is due to the categories. A second major theme of the book is that Kant's Idealism comes in two versions-for laws of nature and for objects of empirical intuition-and that demonstrating these versions is the ultimate goal of the Deduction of the Categories and the similarly structured Deduction of the Concepts of Space, respectively. Vinci shows that the Deductions have the argument structure of an inference to the best explanation for correlated domains of explananda, each arrived at by independent applications of Kantian epistemic and geometrical methods.