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Thinking and Being
Opposing a long-standing orthodoxy of the Western philosophical tradition running from ancient Greek thought until the late nineteenth century, Frege argued that psychological laws of thought—those that explicate how we in fact think—must be distinguished from logical laws of thought—those that formulate and impose rational requirements on thinking. Logic does not describe how we actually think, but only how we should. Yet by thus sundering the logical from the psychological, Frege was unable to explain certain fundamental logical truths, most notably the psychological version of the law of non-contradiction—that one cannot think a thought and its negation simultaneously. Irad Kimhi...
Quine in Dialogue
Quine was one of the 20th century’s great philosophers. This volume begins with a number of interviews Quine gave about his perspectives on 20th-century logic, science and philosophy, the ideas of others, and philosophy generally. Also included are his most important articles, reviews, and comments on other philosophers, from Carnap to Strawson.
Philosophy of Logic, 2nd Edition
With his customary incisiveness, W. V. Quine presents logic as the product of two factors, truth and grammar--but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.
Self-Consciousness and Objectivity
Sebastian Rödl undermines a foundational dogma of contemporary philosophy: that knowledge, in order to be objective, must be knowledge of something that is as it is, independent of being known to be so. This profound work revives the thought that knowledge, precisely on account of being objective, is self-knowledge: knowledge knowing itself.
Frege's Logic
For many philosophers, modern philosophy begins in 1879 with the publication of Frege's Begriffsschrift, in which Frege presents the first truly modern logic in his symbolic language, Begriffsschrift, or concept-script. Macbeth's book, the first full-length study of this language, offers a highly original new reading of Frege's logic based directly on Frege's own two-dimensional notation and his various writings about logic.
Set Theory and Its Logic, Revised Edition
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Frege's Philosophy of Mathematics
Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's philosophy of mathematics: the emerging interest in the intellectual background to his logicism; the rediscovery of Frege's theorem; and the reevaluation of the mathematical content of The Basic Laws of Arithmetic. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of Frege's theory of arithmetic. Together they form an accessible and authoritative introduction to aspects of Frege's thought that have, until now, been largely missed by the philosophical community.
After Parmenides
Engages with one of the oldest philosophical problems—the relationship between thought and being—and offers a fresh perspective with which to approach the long history of this puzzle. In After Parmenides, Tom Rockmore takes us all the way back to the beginning of Western philosophy, when Parmenides asserted that thought and being are the same. This idea created a division between what the mind constructs as knowable entities and the idea that there is also a mind-independent real, which we can know or fail to know. Rockmore argues that we need to give up on the idea of knowing the real as it is, and instead focus on the objects of cognition that our mind constructs. Though we cannot know mind-independent objects as they “really” are, we can and do know objects as they appear to us. After Parmenides charts the continual engagement with these ideas of the real and the knowable throughout philosophical history from Plato and Aristotle to Descartes, Kant, Fichte, Hegel, Schopenhauer, Marx, and others. This ambitious book shows how new connections can be made in the history of philosophy when it is reread through a new lens.
Understanding the Infinite
An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common se...
