Negation: A theory of its meaning, representation, and use

Abstract

This article presents a model-based theory of what negation means, how it is mentally represented, and how it is understood. The theory postulates that negation takes a single argument that refers to a set of possibilities and returns the complement of that set. Individuals therefore tend to assign a small scope to negation in order to minimize the number of models of possibilities that they have to consider. Individuals untrained in logic do not know the possibilities corresponding to the negation of compound assertions formed with if, or, and and, and have to infer the possibilities one by one. It follows that negations are easier to understand, and to formulate, when individuals already have in mind the possibilities to be negated. The paper shows that the evidence, including the results of recent studies, corroborates the theory.

Keywords:

• Negation
• Falsity
• Mental models
• Comprehension
• Representation
• Reasoning
• Pragmatics

Acknowledgments

This research was supported by a National Science Foundation Graduate Research Fellowship to the first author, and by National Science Foundation Grant No. SES 0844851 to the third author to study deductive and probabilistic reasoning. We thank Jay Atlas, Jeremy Boyd, Herb Clark, Alan Garnham, Sam Glucksberg, Adele Goldberg, Geoff Goodwin, Jennifer Heil, Olivia Kang, Philipp Koralus, Mark Liberman, Max Lotstein, Anna Liu, Paula Rubio, Carlos Santamaría, and Elizabeth Sucuyan for their helpful suggestions and criticisms.