On the Diagrammatic and Mechanical Representation of Propositions and Reasonings in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Volume X, Fifth Series, July-December 1880, pp. 1-18. J. Venn, John.

On the Diagrammatic and Mechanical Representation of Propositions and Reasonings in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Volume X, Fifth Series, July-December 1880, pp. 1-18

London: Taylor & Francis, 1880. 1st Edition. FIRST EDITION OF OF THE JOINT FIRST PUBLICATION OF VENN DIAGRAMS (see below for clarification of concurrent publication). Devised by the British philosopher and cleric John Venn and presented in this paper, Venn diagrams provided an easy and better way of visualizing elements, information, sets, concepts, logical relationships, and even simply ideas. Venn diagrams became an important part of the 1960s new math movement based on set theory and are still widely used today.

John Venn was a British philosopher and cleric in the Anglican Church. Unusually, when he was ready announce his discovery, he did so by publishing two separate papers in two separate journals — each appearing in the July issues of their respective journals. 'On the diagrammatic and mechanical representation of propositions and reasonings' in the Philosophical Magazine, and 'On the forms of logical proposition' in Mind. There is scholastic disagreement as to whether one or the other publication truly constitutes the ‘first’ announcement. Many scholars cite the Phil Mag paper; others, including the Stanford Encyclopedia of Philosophy, cite the Mind paper. Regardless, each was published at exactly the same time. Note that we also offer the Phil Mag volume separately.

Venn diagrams are constructed of a collection of simple closed curves drawn within a plane. “The principle of these diagrams is that classes or similar sets of information may be represented by regions within the curves, such that in relation to one another all the possible logical relations of these classes or sets of information can be indicated in the same diagram. Venn diagrams normally comprise overlapping circles, the simplest being two circles. The interior of the circle symbolically represents the elements or sets of information, while the exterior represents elements that are not members of the set” (US Navy Museum portal).

For example, let us say that “region [circle] H represents humans, region W winged creatures, and region A angels” (Pickover, The Math Book, 272). A Venn diagram containing the given circles, would then “reveal (1) All angels are winged creatures (region A lies entirely within region W; (2) No humans are winged creatures (regions H and W are nonintersecting); and (3) No humans are angels (regions H and A are nonintersecting).

“The uses of these kinds of diagrams in logic were used before Venn – for example, by mathematician Gottfried Leibniz and Leonhard Euler – but Venn was the first to comprehensively study them and formalize and generalize their usage (ibid). Item #732

CONDITION & DETAILS: London: Taylor & Francis. (8.5 x 5.5 inches; 213 x 138mm). Complete. [4], vii, [456], 4. Nine plates and in-text illustrations throughout. Ex-libris but bearing only a perforated library stamp on the title page; there are no spine or other interior or exterior markings whatsoever. Handsomely, solidly, and tightly bound in three quarter brown calf over marbled paper boards. Five gilt-ruled raised bands at the spine; gilt armorial devices in the compartments. Gilt-lettered red and black morocco spine labels. Bright and clean inside and out. Near fine condition.

Price: $1,025.00