Frege’s Notations: What They Are and How They Mean (History of Analytic Philosophy)

A New Approach To Reading Frege's Notations That Adheres To The Modern View That Terms And Well-formed Formulas Are Any Disjoint Syntactic Categories. On This New Approach, We Can At Last Read Frege's Notations In Their Original Form Revealing Striking New Solutions To Many Of The Outstanding Problems Of Interpreting His Philosophy. By Gregory Landini. A faithful reading of Frege's ideographic notations makes terms and well-formed formulas disjoint categories. Where i! is a function term, a"ui! is a well-formed formula. We can at last read Frege in the original. And when we do, new solutions to the many problems of interpreting his philosophy are revealed. Frege's Grundgesetze (1893) hoped to provide a foundation for arithmetic in logic. The book offers a new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are disjoint syntactic categories. Where i! is any function term (open or closed), Frege's a"ui! is a well-formed formula. On this new approach, we can at last read Frege's notations in their original form. And when we do, striking new solutions to many of the outstanding problems of interpreting his philosophy are revealed. The book argues that Frege's wertverlaufe are function-correlates. Function correlation must be given by an identity. Its import is lost in its translation as biconditional, but it is the conceptual linchpin of Frege's philosophy of arithmetic. When faced with Russell's 1901 paradox of the class of all classes not members of themselves, Frege proposed a way out and published it in an appendix to Grungesetze's second Volume. The proposal has bewildered readers ever since, and it seems incompatible with the notion of a class in the logical sense (as an extension). The book argues that the bewilderment is produced by unfaithful translations of the logic of Frege's conceptual-notation. Though Frege's way out fails, his theory of function-correlation is not a theory of classes, and logical restrictions on correlation can be found. Function-correlation, though it has been lost and forgotten in modern translations of Frege's work, is the key to unraveling the many outstanding problems of interpreting Frege's philosophy of arithmetic Cover Title Copyright Dedication Contents Preface Author’s Note on the Use of Modern Logical Notations 1 Introduction 2 Frege’s Basic Logics (without Wertverläufe) 2.1 Quantification theory versus CPLogic 2.2 Sentences are not names 2.3 Judgeable contents 2.4 Basic Law IV 2.5 Begriffsschrift and Grundlagen 2.6 Grundgesetze 2.7 Derivations of some theorems in the basic logic of the Grundgesetze 3 The Ancestral 3.1 The ancestral for objects 3.2 Proof of induction within CPLogic 3.3 Cardinality as a second-level concept 3.4 The problem of infinity 4 Wertverläufe 4.1 Numbers as objects 4.2 Grundlagen and Hume’s principle 4.3 Missing IV in the Grundlagen 4.4 I believe that for ‘extension of the concept’ we could write simply ‘concept’ 5 Analysis and Recomposition 5.1 Free variables and the turnstile 5.2 Parts of senses and the informativity of logic 5.3 Oratio Obliqua 5.4 Russell’s paradox of Sinn 6 Engaging Problems 6.1 Urelements 6.2 The Ins and Outs of Frege’s Way Out 6.3 The argument for referentiality 6.4 Whence the contradiction? 6.5 Frege’s Academy Notes Bibliography Index "A new approach to reading Frege's notations that adheres to the modern view that terms and well-formed formulas are any disjoint syntactic categories. On this new approach, we can at last read Frege's notations in their original form revealing striking new solutions to many of the outstanding problems of interpreting his philosophy."--Amazon.com This systematic and historical treatment of Russell's contributions to analytic philosophy, from his embrace of analysis in 1898 to his landmark theory of descriptions in 1905, draws important connections between his philosophically motivated conception of analysis and the technical apparatus he devised to facilitate analyses in mathematics
Gregory Landini offers a detailed historical account of Frege's notations and the philosophical views that led Frege from Begriffssscrhrift to his mature work Grundgesetze, addressing controversial issues that surround the notations. Are the reasons for which we act the causes of our actions? In the nine essays collected here (including a major historical overview by the editors), experts in the field re-evaluate the history and current state of the reasons/causes debate.