Understanding: Deductive reasoning
This article begins with an account of logic, and of how logicians formulate formal rules of inference for the sentential calculus, which hinges on analogs of negation and the connectives if, or, and and. It considers the various ways in which computer scientists have written programs to prove the validity of inferences in this and other domains. Finally, it outlines the principal psychological theories of how human reasoners carry out deductions.
Introduction (Via Laird)
Deductive reasoning is the mental process of making inferences that are logical. It is just one sort of reasoning. But, it is a central cognitive process and a major component of intelligence, and so tests of intelligence include problems in deductive reasoning. Individuals of higher intelligence are more accurate in making deductions,1 which are at the core of rationality. You know, for instance, that if your printer is to work then it has to have ink in its cartridges, and suppose that you discover that that there is no ink in its cartridges. You infer that the printer would not work. This inference has the important property of logical validity: if its premises are true then its conclusion must be true too. Logicians define a valid deduction as one whose conclusion is true in every possibility in which all its premises are true (Ref 2, p. 1). All able-minded individuals recognize that certain inferences are valid because there are no counterexamples to them, that is, no possibilities in which the premises hold but the conclusion does not. This idea underlies deductive reasoning. And deductive reasoning in turn underlies the development of all intellectual disciplines and our ability to cope with daily life. The topic is studied in logic, in artificial intelligence, and in cognitive science. Hence, the aim of this interdisciplinary review is to survey what these different disciplines have to say about deduction, and to try to solve the mystery of how individuals who know nothing of logic are nevertheless able to reason deductively.