Frege's Logic

For many philosophers, modern philosophy begins in 1879 with the publication of Gottlob Frege's Begriffsschrift, in which Frege presents the first truly modern logic in his symbolic language, Begriffsschrift, or concept-script. Danielle 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. Setting out to explain the nature of Frege's logical notation, Macbeth brings clarity not only to Frege's symbolism and its motivation, but also to many other topics central to his philosophy. She develops a uniquely compelling account of Frege's Sinn/Bedeutung distinction, a distinction central to an adequate logical language; and she articulates a novel understanding of concepts, both of what they are and of how their contents are expressed in properly logical language. In her reading, Frege's Begriffsschrift emerges as a powerful and deeply illuminating alternative to the quantificational logic it would later inspire. The most enlightening examination to date of the developments of Frege's thinking about his logic, this book introduces a new kind of logical language, one that promises surprising insight into a range of issues in metaphysics and epistemology, as well as in the philosophy of logic.

Table of Contents:
Preface Introduction 1. THE STARTING POINT 1.1 The Fundamental Idea of Frege's Conceptual Notation 1.2 Generality and the Expression of Laws 1.3 Understanding Logical Generality: Two Strategies 1.4 Our Starting Point 2. LOGICAL GENERALITY 2.1 Reading Begriffsschrift 2.2 The Logical Justification for a Two-Dimensional Notation 2.3 Begriffsschrift Latin Italic Letters 2.4 The Diversity of Logical Relations 3. A MORE SOPHISTICATED INSTRUMENT 3.1 The Advance from Level to Level 3.2 What Is a Function? 3.3 The Expressive Role of the Concavity with German Letter 3.4 The Formality of Logic 3.5 Mastering the Instrument 4. THE WORK BROUGHT TO MATURITY 4.1 The Shape of Frege's Discovery 4.2 The Formula Language of Arithmetic 4.3 The Formula Language of Pure Thought 4.4 The Striving for Truth 4.5 The Science of Logic 5. COURSES OF VALUES AND BASIC LAW V 5.1 Frege's Grundlagen Definition of Number 5.2 A Further Difficulty 5.3 Russell's Paradox 5.4 A Final Reckoning Epilogue Notes Abbreviations Index

About the Author :
Danielle Macbeth is Associate Professor of Philosophy at Haverford College.

Review :
Macbeth's careful attention to the continuous development of Frege's thought, and the several successive changes in his understanding of his notation, should suffice to exorcise the phantom two-period Frege of other exegetes. The clear and concise prose style is also in refreshing contrast to the not infrequent obscurity and still more frequent longueurs of some of the other literature in this area. This is an excellent book, well-conceived, nicely organized and beautifully written. It will be essential reading for anyone interested in Frege's logic and the history of analytic philosophy. More specifically, it can be recommended to undergraduates who have done a first course in logic and philosophical logic/philosophy of language, and to postgraduates interested in, and all those responsible for teaching, Frege's logic and early analytic philosophy. The book was a delight to read, lucid and instructive, with many insights into complex issues formulated with clarity and precision. This is an engaging, controversial, and refreshingly well-written book about Frege's logic...Danielle Macbeth explains Frege's complicated two-dimensional logical notation more patiently, accurately, and with a greater variety of examples than I have previously seen.