Aristotelian logic

Aristotelian logic, also known as syllogistic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. It later developed into what became known as traditional logic or Term Logic.

Aristotle recognised 4 kinds of quantified sentences, each of which contain a subject and a predicate:

  • Universal affirmative: Every S is a P.
  • Universal negative: No S is a P.
  • Particular affirmative: Some S is a P.
  • Particular negative: Not every S is a P.

There are various ways to combine such sentences into syllogisms, both valid and invalid. In Mediaeval times, students of Aristotelian logic classified every possibility and gave them a name. For example, the Barbara syllogism is as follows:

  • Every X is a Y.
  • Every Y is a Z.
  • Therefore, every X is a Z.

Aristotle also recognised the various immediate entailments that each type of sentence has. For example, the truth of a universal affirmative entails the truth of the corresponding particular affirmative, and the falsity of the corresponding universal negative and particular negative. The square of opposition lists all these logical entailments.

Famously, Aristotelian logic runs into trouble when one or more of the terms involved is empty (has no members). For example, under Aristotelian logic, "all trespassers will be prosecuted" implies the existence of at least one trespasser.

The influence of the Organon

Aristotle's works on logic, (collectively called the Organon), are the only significant works of Aristotle that were never "lost"; all his other books were "lost" from his death, until rediscovered in the 11th Century.

In the 8th Century the Scholastics, in non-Arab Europe, studied and promoted the study of logic based on the Organon. One of the greatest Scholastics was Dominican monk Albert the Great (1206 - 1280), the teacher of Thomas Aquinas (1226 - 1274).

The books of Aristotle were available in the Arab Empire and were studied by Islamic and Jewish scholars, including Rabbi Moses Maimonides (1135 - 1204) and Muslim Judge Ibn Rushd (1126 - 1198); both lived in Cordoba, Spain. Cordoba had 70 libraries, one of them with over 40,000 volumes; the two largest libraries in non-Arab Europe each had only 2,000 volumes. Thomas Aquinas used the writings and comments of Aristotle ("the philosopher"), Albert, Maimonides ("the Rabbi") and Ibn Rushd ("the commentator") and many others.

See also: logic

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