The Psychology of Proof

Lance J. Rips is Professor of Psychology at Northwestern University.

Part 1 Preliminaries: psychological approaches to deduction - some examples of deductive reasoning, the centrality of deductive reasoning, main trends in reasoning research, conclusions and prospects; reasoning and logic - formal proof, the CPL (classical predicate logic) system, the place of logic in a theory of reasoning; reasoning and computation - problems of search in deduction, non-resolution methods and revisions to the, natural-deduction rules, solving problem by proving theorem. Part 2 A psychological theory of deduction: mental proofs and their formal properties - overview of the core theory, core assumptions, formal properties, appendix - proofs of the major propositions; mental proofs and their empirical consequences - some tests of the proof model, consistency with prior findings; variables in reasoning - extending the core system to variables, formal properties, appendix - proofs of the major propositions; reasoning with variables - empirical predictions for sentences with a single variable, predictions for multi-variable contexts, summary, appendix - syllogism results. Part 3 Implications and extensions: the role of deduction in thought - deduction as a cognitive architecture, frames, schemas, theories, and deduction, natural deduction, nonmonotonic logic, and truth maintenance, open questions; alternative psychological theories - rule-based systems - alternative theories based on natural deduction, pragmatic schemas, social contracts, summary; alternative psychological theories - ruleless systems - heuristic-based theories and "Content" effects, reasoning by diagrams and models, how plausible are mental diagrams and models as, explanations of reasoning?; perspectives on reasoning ability - aren't you making people out to be more logical or, rational than they really are?, aren't you making people out to be more illogical or, irrational than they really are?, summary.