Aristotle's logical system

Aristotle recognised four 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.

The Organon was used in the school founded by Aristotle at the Lyceum, and some parts of the works seem to be a scheme of a lecture on logic. So much so that after Aristotle's death, his publishers (e.g. Andronicus of Rhodes in 50 BC) collected these works.

In these works we can find the first ontological category theory (relevant in some branches of intensional logic), the first development of formal logic, the first known serious scientific inquisitions on the theory of (formal and informal) reasoning, the foundations of modal logic, and some antecedents of methodology of sciences.

The Organon was not always popular during the Hellenistic era. Stoic logic was predominant, particularly the work of Chrysippus (none of whose work has survived).

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 Albertus Magnus (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.

Immanuel Kant thought that there was nothing else to invent after the work of Aristotle, and a famous logic historian called Carl Prantl claimed that any logician who said anything new about logic was "confused, stupid or perverse." These examples illustrate the general tendency during the period between the 13th century and the 19th century to accept without question the work of Aristotle. He had already become known by the Scholastics (medieval Christian scholars) as "The Philosopher." The dogmatism created by the Scholastics in favor of Aristotle took a long time to disappear.

Aristotelian logic has lost most of its reputation as the one only correct logic. Gottlob Frege and Bertrand Russell criticized the work of Aristotle and showed its many limitations. They helped remove the positive prejudice associated with the work of Aristotle. Today logicians who study modern logic respect the Aristotelian logic in the sense of its great early accomplishment.

Bibliography

Texts of Aristotle's logical works are available from the article on the Organon.

• Bocheński, I. M.: Ancient Formal Logic. North-Holland Publishing Company, Amsterdam, 1951.
  
• Couturat, Louis: La Logique de Leibniz. Georg Olms Verlagsbuchhandlung, Hildesheim, 1961.
  
• Lukasiewicz, Jan: Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic. Clarendon Press. Oxford, 1951.
  
• Parry, William T., Hacker, Edward A.: Aristotelian Logic. State University of New York Press. Albany, 1991.
  
• Rose, Lynn E.: Aristotle's Syllogistic. Charles C Thomas Publisher, Springfield, 1968.
  
  
  

Links

This article incorporates material from Aristotle on PlanetMath, which is licensed under the GFDL.