John Venn

Philosopher, logician, mathematician

• Born: August 4, 1834
• Place of Birth: Place of birth: Hull, England
• Died: April 4, 1923
• Place of Death: Place of death: Cambridge, England

Education: University of Cambridge

Significance: John Venn was a philosopher, logician, and mathematician best known for devising a way of comparing sets of objects to determine their relationship to each other. His method is most often depicted with overlapping curved or rounded shapes in what is known as a Venn diagram.

Background

John Venn was born in Hull, England, on August 4, 1834, to the Reverend Henry Venn and Martha Sykes Venn. His mother died when Venn was about three, and he was raised by his father, an Anglican priest who was serving as a rector in a nearby town. Venn’s grandfather was also an Anglican clergyman, and both his father and grandfather were active advocates for the abolition of slavery, prison reform, and foreign missionary work. Following in the footsteps of his father and grandfather, Venn was also ordained in the Anglican church, first as a deacon in 1858 and then as a priest in 1860. He served as a curate, or assistant to the rector, at two parishes.

During his time in private school and later at Cambridge University, from which he graduated in 1857, Venn had shown great interest and aptitude for mathematics. After spending two years as a curate, Venn returned to Cambridge University in 1862 to serve as a teacher. He taught logic and probability theory and was said to be well liked by both his colleagues and students.

Venn continued to work at Cambridge for most of his career. He also remained a priest until 1883, when he found his personal beliefs at odds with those of the church and resigned from the priesthood, although he maintained his religious convictions for the rest of his life.

Life’s Work

During his time as professor at Cambridge, Venn spent a great deal of time both studying and teaching probabilities, logic, philosophy, and metaphysics. Indulging his interest and aptitude for mathematics, he read the works of George Boole, a mathematician who applied the concepts of symbolic algebra to logic, and Augustus De Morgan, who played a major role in establishing the interconnectedness of mathematics and logic.

Venn would build on the work of these men and further integrate logic into mathematical applications. He took the system for diagramming sets associated with Swiss mathematician Leonhard Euler and enhanced it to make the diagrams more inclusive and detailed. Venn’s system allowed for the diagramming of items that fell outside of a set of objects and also for the representation of empty sets, or sets that did not contain any items.

Venn’s concept used overlapping curved shapes (which may or may not be circular) to show how two or more mathematical sets were related to each other. For example, to diagram how many objects in a room are wooden chairs, one would take three separate curved shapes: one representing all the pieces of furniture in the room, one representing the wooden pieces of furniture, and one representing the chairs. These shapes would be overlapped; the place where they intersect would represent the wooden chairs in the room. The other non-overlapping sections of the diagram could help determine and illustrate which portion of wooden objects in the room are not chairs, which pieces of furniture in the room are not chairs, which of the room’s furniture is not wooden, and other relationships, based on how the diagrams are prepared.

Venn’s findings were shared publicly in one of several works he published during his lifetime. His essay "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings," which put forth his diagramming system, was published in the July 1880 edition of Philosophical Magazine and the Journal of Science. The illustrations of the way sets are combined or relate to each other are called Venn diagrams, a name they were given in 1919 by Clarence Irving Lewis in his book A Survey of Symbolic Logic.

While the concepts behind these diagrams are Venn’s most well-known work, he also published several other papers dealing with the applications of logic and mathematics. These include "Symbolic Logic," published in 1881, and "The Principles of Empirical Logic," published in 1889.

Venn died on April 4, 1923, and was buried in the cemetery at St. Peter’s Church in Hereford, England, one of the parishes where he served as a curate.

Impact

Venn’s work in creating a structure for diagramming sets has had implications in mathematics and beyond. While it was originally developed to help scholarly mathematicians in their work, his technique has been adapted by teachers of other subjects and by industry to provide an easy-to-understand graphic representation of how groups of things relate to each other.

Venn diagrams have also expanded into something used on social media and the Internet to convey a wide array of information. While many of these take liberties with the concept and are not true Venn diagrams, they do indicate the relevancy of Venn’s work into the twenty-first century.

Personal Life

Venn married in 1887 to Susan Carnegie, and they had one son, John Archibald Venn, who sometimes collaborated with his father in his work. Venn was also a philanthropist. He established the Hereford Society for Aiding the Industrious in 1833 and helped to provide bathhouses, soup kitchens, and other services to assist the working poor.

Bibliography

"Dr. Venn of Caius." New York Times. New York Times Company, April 1923. Web. 24 May 2016.

Freeman, David. "John Venn’s Birthday Celebrated in Clever Google Doodle." Huffington Post. TheHuffingtonPost.com, Inc., 4 Aug. 2014. Web. 24 May 2016.

"John Venn." School of Mathematics and Statistics, University of St Andrews, Scotland. Web. 24 May 2016.

"John Venn’s 180th Birthday." Google. Google, 4 Aug. 2014. Web. 24 May 2016.

Rogers, Paul. "Bid by Hereford Group to Restore John Venn’s Vandalised Grave." Hereford Times. Newsquest Ltd., 26 May 2010. Web. 24 May 2016.

Verburgt, Lukas M. John Venn: A Life in Logic. U of Chicago P, 2022.