Sentential Logic for Psychologists Richard Grandy Daniel Osherson Rice University1 Princeton University2 September 28, 2010
[email protected] [email protected] ii Copyright This work is copyrighted by Richard Grandy and Daniel Osherson. Use of the text is authorized, in part or its entirety, for non-commercial non-profit purposes. Electronic or paper copies may not be sold except at the cost of copy- ing. Appropriate citation to the original should be included in all copies of any portion. iii Preface Students often study logic on the assumption that it provides a normative guide to reasoning in English. In particular, they are taught to associate con- nectives like “and” with counterparts in Sentential Logic. English conditionals go over to formulas with ! as principal connective. The well-known difficul- ties that arise from such translation are not emphasized. The result is the conviction that ordinary reasoning is faulty when discordant with the usual representation in standard logic. Psychologists are particularly susceptible to this attitude. The present book is an introduction to Sentential Logic that attempts to situate the formalism within the larger theory of rational inference carried out in natural language. After presentation of Sentential Logic, we consider its mapping onto English, notably, constructions involving “if . then . .” Our goal is to deepen appreciation of the issues surrounding such constructions. Errors, obscurity, or other defects can be brought to our attention via elec- tronic mail (
[email protected],
[email protected]). The provenance of revisions will be gratefully acknowledged as new versions are produced. Richard Grandy Daniel Osherson iv Note to students So .