Graduate studies at Western
|Abstract||The consideration of careful reasoning can be traced to Aristotle and earlier authors. The possibility of rigorous rules for drawing conclusions can certainly be traced to the Middle Ages when types o f syllogism were studied. Shortly after the introduction of computers, the audacious scientist naturally envisioned the automation of sound reasoning—reasoning in which conclusions that are drawn follow l ogically and inevitably from the given hypotheses. Did the idea spring from the intent to emulate s Sherlock Holmes and Mr. Spock (of Star Trek) in ﬁction and Hilbert and Tarski and other great mind i n nonﬁction? Each of them applied logical reasoning to answer questions, solve problems, and ﬁnd e proofs. But can such logical reasoning be fully automated? Can a single computer program b d esigned to offer sufﬁcient power in the cited contexts? Indeed, while the use of computers was quickly accepted for numerical calculations and data processing, intense skepticism persisted—even in the early 1960s—regarding the ability of computers to a pply effective reasoning. The following simple (but perhaps deceptive) example provides a taste of the type of argument that might have been used to support this skepticism.|
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