Classic Papers #1: On the diagram, by John Venn

Title: “On the diagrammatic and mechanical representation of propositions and reasonings

Author: John Venn

Journal: Philosophical Magazine

Date published: July 1880

Builds upon: Euler diagrams

Citations (Google Scholar): 336

Citations Since 2010: 152

Best figure: Not satisfied with two sets, he jumped right to the symmetry-preserving extreme of his system and drew out a four set intersection with a place for labels:

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This would hardly be out of place in a genomics article published today.

Best sentence: “The fact is, as I have explained at length in the article above referred to, that the five distinct relations of classes to one another (viz. the inclusion of X in Y, their coextension, the inclusion of Y in X, their intersection, and their mutual exclusion), which are thus pictured by these circular diagrams, rest upon a totally distinct view as to the import of a proposition from that which underlies the statements of common life and common logic.”

Oddest moment: “I have no high estimate myself of the interest or importance of what are sometimes called logical machines, and this on two grounds. In the first place, it is very seldom that intricate logical calculations are practically forced upon us; it is rather we who look about for complicated examples in order to illustrate our rules and methods. In this respect logical calculations stand in marked contrast with those of mathematics, where economical devices of any kind may subserve a really valuable purpose by enabling us to avoid otherwise inevitable labour. Moreover, in the second place, it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines. It is but a very small part of the entire process which goes to form a piece of reasoning which they are capable of performing.”

(No wonder Turing proposed his test of whether something was a “true” AI.)

(Runner up: Venn’s use of the word “especial” instead of “special.”)

Lasting impact: This paper is a classic that jumps directly to the tough questions of how to visualize sets and set differences and even directly addresses the utility of a sort of artificial intelligence, or as Venn calls it, a “logical machine.” And of course, it introduced what we now know as the Venn diagram.


Editorial note: This is the first entry in what will hopefully be a series of classic papers cutting across disciplines that I’m interested in. For some reason, papers don’t seem to be discussed as commonly as books in my circles, which is strange because they’re shorter, usually more novel, and more information dense. This series is an attempt to write the blog posts I want to see in the world.

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