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.
Danielle Macbeth is Associate Professor of Philosophy at Haverford College.
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