The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

This volume examines the role of logic in cognitive psychology in light of recent developments. Gonzalo Reyes's new semantic theory has brought the fields of cognitive psychology and logic closer together, and has shed light on how children master proper names and count nouns, and thus acquire knowledge. The chapters highlight the inadequacies of classical logic in its handling of ordinary language and reveal the prospects of applying these new theories to cognitive psychology, cognitive science, linguistics, the philosophy of language and logic.

This important book presents seminal contributions to the emerging synthesis of logic and cognitive psychology. Logicians, who typically concern themselves with ideal reasoning processes, have rarely crossed paths with cognitive psychologists and their more empirical endeavors. With the introduction of a landmark semantic theory by Gonzalo E. Reyes, however, the fields have somewhat reconciled and together have been fruitful in shedding new light on several issues--for example, on how children may master proper names and count nouns, and thus acquire knowledge. Authored by an outstanding collection of leading theorists and researchers across disciplines, this book details the inadequacies of classical logic in its handling of ordinary language and reveals the prospects for applying a symbiosis of logic and psychology to cognitive psychology, cognitive science, linguistics, the philosophy of language, and logic itself. Both scholarly and engaging, The Logical Foundations of Cognition will be of interest to psychologists, philosophers, linguists, and computer scientists alike.