A Linguistic Turn: New Directions in Logic

• Published in: Studies in Logic and the Foundations of Mathematics Vol. 114; pp. 205 - 240
• Main Author: Benthem, Johanvan
• Format: Book Chapter
• Language: English
• Published: 1986
• ISBN: 9780444876560; 0444876561
• ISSN: 0049-237X
• DOI: 10.1016/S0049-237X(09)70694-9

Modern logic has derived its main inspiration from the science of mathematics, with important and well-known results. Some new directions in logical research on the common border with modern linguistics are presented. Generalized quantifiers and logical quantifiers are discussed. The chapter describes patterns of inference. Instead of giving the logical constants, and determining their valid inferences, one is giving the inference patterns and asking for the range of constants validating them. This new type of “inverse logic” may be explored quite systematically, for all possible inferential theories. The two most important variations from a linguistic point of view concern the postulates of extension and quantity. The chapter presents an old direction in logic. The traditional subject matter of logic has been the systematic description of valid inference.