London: Williams and Norgate, 1880. 1st Edition. FIRST EDITION OF THE JOINT FIRST PUBLICATION OF VENN DIAGRAMS (see below for clarification of concurrent publication). Venn diagrams provide an easy and better way of visualizing elements, information, sets, concepts, logical relationships, and even simply ideas. Essentially, they are illustrations that utilize circles (which can be overlapping or non-overlapping) in order to depict a relationship between finite groups of things such as mathematical or logical sets. 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 was a critic of Euler circles (diagrams), arguing that Euler’s system failed in its efforts to depict consistent pieces of information in one diagram; as well, Venn believed Euler’s circles did not well-depict non-empty sets. Venn’s goal in devising a new system was to overcome these “expressive limitations so that partial information can be represented. The solution was his idea of ‘primary diagrams’. A primary diagram represents all the possible set-theoretic relations between a number of sets, without making any existential commitments about them” (Stanford Philosophy Portal).
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.
“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” (Pickover, The Math Book, 272).
This volume also includes papers by Francis Galton, Alexander Bain, Leslie Stephen, William James and John Watson who, with the influential paper published here, “The Method of Kant”, led a Kantian Revival of sorts in the English speaking world. Item #1586
CONDITION & DETAILS: London: Williams and Norgate. Complete volume. 8vo. 8.5 by 6 inches (213 x 150mm). , viii, , 4. Ex-libris bearing small circular stamps on the front and rear pastedown and flyleaves; there are no markings on the spine whatsoever. Tightly bound in half contemporary calf and buckram, rubbed and scuffed a bit at the edge tips. Five raised bands at the spine with each compartment gilt-tooled. Gilt-lettered burgundy morocco spine label. The interior is bright and clean throughout. Very good condition.