or it may be a class of entities (objects,
houses, cities, men, animals). The predi-
cateis the property or mode of existence
that does or does not exist with a given
subject. For example, a singular plant
(subject) may or may not be blooming
(predicate); all houses (subject) may or
may not have two stories (predicate).Who invented a way of analyzing
syllogisms?
In 1880 English logician John Venn
(1834–1923) presented a method to ana-
lyze syllogisms, now known as Venn dia-
grams. Venn initially criticized such
diagrams in works by his contempo-
raries, especially those of English math-
ematicians 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 Sym-
bolic 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 Got-
tfried Wilhelm Leibniz (1646–1716) used such graphic representations in his work.
And even Swiss mathematician Leonhard Euler (1707–1783) is known to have pre-
sented diagrams that had a definite “Venn-ish” look a century before John Venn.What are some examplesof Venn diagrams?
Venn diagrams are schematic illustrations used in logic theory to show collections of
sets and the relationship between them. Overlapping circles represent the sets (or the
subjects and predicates in syllogistic logic); the standard way of presenting such dia-
grams include the intersection of two (order-two diagram) to three (order-three dia-
gram) circles. Based on what circles intersect and the areas shaded, a conclusion about
the sets may then be read directly from the diagram. Such illustrations can include the
union of two sets, the intersection of two sets, the complement of a set, and the com-
106 plement of the union of two sets. (For more information about sets, see p. 122).
In these examples of Venn diagrams, the top illustra-
tion represents an order-two diagram, and the bot-
tom is an order-three diagram.