Foundations of Mathematics

Foundations and Logic

What were Aristotle’s contributions to logic?

Aristotle contributed syllogisms and propositions to the world of logic—in other words, the verbal versions of the formal deductive rules for logic. Aristotle believed that any logical argument could be explained in these standard forms. Today, we call these ideas Aristotelian logic, whereas Aristotle would have called it “analytics;” he would have referred to the term “logic” as “dialectics.” Although syllogisms are attributed to Aristotle, no doubt others came up with the same ideas with different ways of expressing them. But his teachings were well-known, even in his time. Thus, syllogistic logic would dominate Western cultural thought for more than 2,000 years.

Aristotle’s six books—Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and On Sophistical Refutations—were compiled around 1 B.C.E. Some historians don’t believe all the writings should be totally attributed to Aristotle, but were changed over time by teachers, lecturers, and students who studied his works. It is also thought that the books were used extensively in the school founded by Aristotle at the Lyceum (a form of educational school). The collection of books is often called the Organon, the name given by the followers of Aristotle (often referred to as the Peripatetics).


An example of a syllogism.


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