John Venn

Portrait of John Venn

Who Drew The Empty Compartments · Logician & Clergyman · 1834–1923

The Cambridge logician whose 1880 paper insisted a diagram show every combination of classes — including the empty ones and the region outside them all — and shade what a proposition denies.

Who was Venn?

John Venn was born at Hull in 1834 into a well-known family of Evangelical clergymen. He was ordained, served briefly in parishes, and then returned to Cambridge as a fellow of Gonville and Caius, lecturing in the moral sciences. He later resigned his orders, having concluded he could no longer hold the Thirty-Nine Articles, but remained at the college for the rest of his long life. His first book, The Logic of Chance (1866), argues that a probability is not a degree of belief but the proportion with which an event occurs in a long run of similar cases — a position that shaped the subject for a century. In 1880 he published in the Philosophical Magazine a paper on the diagrammatic and mechanical representation of propositions, and in it the figure that carries his name. The overlapping circles were not new; Euler had used them, and others before him. What is Venn's is the requirement that the diagram show every possible combination of the classes, whether or not anything falls into any given one: two classes give four compartments, three give eight, and the compartment belonging to neither — the region outside the circles but inside the frame — is one of them and must be drawn. You then SHADE the compartments that a proposition declares empty. Euler's diagrams drew only what was occupied, which is precisely why they cannot represent a statement that merely denies something. The distinction matters more than it sounds. A logic diagram in Venn's hands is a statement about what can exist, not a tally of how many things do. He built a machine to represent propositions mechanically, and — being a Cambridge man of his period — a machine to bowl at cricketers; it is reported to have bowled out a visiting Australian batsman four times. In old age he compiled, with his son, the Alumni Cantabrigienses, a register of every known member of the University from its foundation.

Major achievements

Life in brief

Explore the life of Venn — five chapters

  1. Four Generations of Clergymen — A family with a settled plan for him
  2. The Logic of Chance — A probability is a proportion, not a feeling
  3. The 1880 Paper — Every compartment, including the empty ones
  4. Two Machines — A logical engine, and a bowling machine that took four wickets
  5. Resigning Orders, and Counting a University — An honest exit and a very long index

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