Negation in natural language
David Woodford Ripley · Carolina Digital Repository (University of North Carolina at Chapel Hill) · 2019
Negation is ubiquitous in natural language, and philosophers have developed plenty of different theories of the semantics of negation. Despite this, linguistic theorizing about negation typically assumes that classical logic's semantics for negation---a simple truth-functional toggle---is adequate to negation in natural language, and philosophical discussions of negation typically ignore vital linguistic data. The present document is thus something of an attempt to fill a gap, to show that careful attention to linguistic data actually militates {\\em against} using a classical semantics for negation, and to demonstrate the philosophical payoff that comes from a nonclassical semantics for natural-language negation. I present a compositional semantics for natural language in which these questions can be posed and addressed, and argue that propositional attitudes fit into this semantics best when we use a nonclassical semantics for negation. I go on to explore several options that have been proposed by logicians of various stripes for the semantics of negation, providing a general framework in which the options can be evaluated. Finally, I show how taking non-classical negations seriously opens new doors in the philosophy of vagueness.