Frege's Notations - What They are and How They Mean (Electronic book text)

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.