Foundations of Mathematics

Foundations and Logic

Who invented a way of analyzing syllogisms?

In 1880, English logician John Venn (1834–1923) presented a method to analyze syllogisms, now known as Venn diagrams. Venn initially criticized such diagrams in works by his contemporaries, especially those of English mathematicians George Boole (1815–1864) and Augustus De Morgan (1806–1871). But in 1880, Venn introduced his own, now famous, version of the diagrams in his paper On the Diagrammatic and Mechanical Representation of Prepositions and Reasonings. By 1881, along with correcting Boole’s work, Venn further elaborated on the diagrams in his book, Symbolic Logic. Today we are most familiar with Venn diagrams in connection with understanding sets.

Although Venn is credited with the diagrams, he was not the first person to use such geometric methods to represent syllogistic logic. German mathematician Gottfried Wilhelm Leibniz (1646–1716) used such graphic representations in his work. And even Swiss mathematician Leonhard Euler (1707–1783) is known to have presented diagrams that had a definite “Venn-ish” look a century before John Venn.


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