This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography. ong Copy

This collection brings together recent scholarship on Frege, including new translations of German material which is made available to Anglophone scholars for the first time.

This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference.

Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfolding—from the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the present—that culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.

This volume collects nine essays that investigate the work of Gottlob Frege. The contributors address Frege’s work in relation to literature and fiction (Dichtung), the humanities (Geisteswissenschaften), and science (Wissenschaft). Overall, the essays consider internal connections between different aspects of Frege’s work while acknowledging the importance of its philosophical context. There are also further common strands between the papers, such as the relation between Frege’s and Wittgenstein’s approaches to philosophical investigations, the relation between Frege and Kant, and the place of Frege’s work in the philosophical landscape more generally. The volume is therefore of direct relevance to several current debates in philosophy in general, in addition to Frege and Wittgenstein research in particular. Even though Frege’s great significance for contemporary philosophy is not disputed, the question of how we are to understand the character and aims of his project is debated. The debate has a starting point in Frege’s specific conception of logic. The volume elucidates this conception as well as the relation between natural language and the Begriffsschrift. It will help philosophers, researchers, and students better understand the nuances of this great thinker. By extension, it will also help readers seeking to understand Wittgenstein’s approach to philosophical difficulties and his struggle to find an apt form of presentation for his philosophical investigations.

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

First published in 1989, this book considers Bertrand Russell’s philosophy through his correspondence with others. Indeed, his exchanges with his elders in philosophy, with his contemporaries, and with one of his most outstanding pupils are brought to life in this judicious exposition: meticulously documented before being judged with insight and sympathy, as well as impartiality. Elizabeth Ramsden Eames here explores the issues that emerged from Russell’s exchanges with certain other philosophers, and interprets the resulting reciprocal influences and reactions. The conversations presented cover subjects such as: the nature of relations; pluralism versus monism; the relation of the subject and object in knowledge; the analysis of experience; the definition of truth; the analysis of belief; and the theory of meaning. These have been in the forefront of philosophical discussion in our time, and Russell’s dialogue with his contemporaries promises to illumine them.

Lois Lane knows that Superman can fly, but she does not know that Clark Kent can fly. How can that be, given that Superman and Clark are one and the same? To answer this question, Frege famously distinguished the reference of a name (the thing it is a name of) from what he called its 'sense' or 'mode of presentation'. The sense was meant to capture our (necessarily limited) perspective on reference and to explain the difference in 'cognitive value' between "Superman can fly" and "Clark can fly". Frege's distinction has been widely discussed in the last century, but much about it remains unclear. In this collection, Richard Kimberly Heck, one of the world's foremost experts on Frege's philosophy, distinguishes three aspects of Frege's famous 'puzzle' and explores the connections between them. Their wide-ranging discussion touches on issues in philosophy of mind, philosophy of language, philosophy of logic, the history of analytic philosophy, and meta-philosophy. Heck argues that, while many of the details of Frege's position cannot be defended, his famous puzzle still has much to teach us both about the foundations of cognition and about the nature of linguistic communication. Modes of Presentation presents eight previously published papers, two of which are significantly expanded. There are also three new chapters, three new postscripts responding to criticisms, and a substantial overview that introduces the issues and traces connections between the chapters.