How do people make deductions? The orthodox answer to the question is that deductive reasoning depends on a mental logic containing formal rules of inference. The authors of this book have spent several years investigating the process. They repudiate the orthodox theory. They argue instead that people reason by imagining the relevant state of affairs, i.e. building an internal model of it, formulating a tentative conclusion based on this model, and then searching for alternative models that might refute the conclusion. Formal rules work syntactically; mental rules work semantically. The two theories therefore make different predictions about the difficulty of deductions. The book reports the results of experiments that compared these predictions in the three main domains of deduction: propositional reasoning based on connectives such as "if" and "or"; relational reasoning based on spatial descriptions; and complex reasoning based on quantifiers such as "all" and "none". In each domain, the results corroborated the model theory and ran counter to the use of formal rules.
The authors relate their findings to problems in artificial intelligence, linguistics and anthropology. They describe various computer programs based on the model theory, including one that solves a major problem in the design of electronic circuits. Finally, they show how the theory resolves a long standing controversy about the nature of rationality and whether there are cognitive universals common to all human cultures.
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