Historical Remarks on Nonmonotonic Reasoning, Especially Circumscription

John McCarthy

Humanshave always done nonmonotonic reasoning, but rigorous monotonic reasoning in reaching given conclusions has been deservedly more respected and admired. Euclid contains the first extended monotonically reasoned text available to a large public. I suspect that even Euclid did nonmonotonic reasoning in arguing for the postulates. It is unfortunate that the rigorous monotonic reasoning of Euclid has been deemphasized in education, because Euclid generates in people who are not mathematically minded a respect for rigor. Conclusions derived by monotonic logical reasoning from precisely stated premises have always been the ideal. When people jump to conclusions, they are criticized for the gaps in their reasoning, because the conclusions are not guaranteed to follow from the premises. Worse yet, the premises are often unstated. The inability to base all conclusions on logical reasoning from precise and agreed premises has been long noted. There are two main reactions. One is to try to develop other principles of reasoning, and the other is to abandon logic — a big mistake.

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