Frege's Notations

This book offers 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. 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. Frege's Grundgesetze (1893) hoped to provide a foundation for arithmetic in logic. 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 Grundgesetze'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). This 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.