Vrije Universiteit Brussel
Review of Bennett, Deborah Drawing logical conclusions.
Larvor, Brendan Philip
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Mathematical Reviews
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2016
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Citation for published version (APA):
Larvor, B. P. (2016). Review of Bennett, Deborah Drawing logical conclusions. Mathematical Reviews.
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MR3313806 (Review) 01A45 01A50 01A55 03-03
Bennett, Deborah [Bennett, Deborah J.] (1-NJCU-M)
Drawing logical conclusions.
Math Horiz. 22 (2015), no. 3, 12–15.
This article recounts the history of Venn-type diagrams, which (so far as is known) were
first used to illustrate syllogistic arguments. As Bennett explains, it is well known that
L. Euler used such diagrams in the 1760s as a teaching aid in his [Letters of Euler on
different subjects in physics and philosophy. Addressed to a German princess, Murray
and Highley, London, 1802]. However, it is certain that he was not the first. The principal
finding of this paper is that Leibniz, in a fragment that was not published until 1903, had
diagrams that are identical to Euler’s aside from the labeling. Bennett notes that letters
were a semi-public medium in Leibniz’s day, and it is possible that Euler learned of
this diagrammatic technique from Leibniz, perhaps through an intermediary such as the
Bernoullis. By Venn’s time, it had become commonplace in logic textbooks. Bennett’s
article describes the advantages of Venn’s version over its predecessors. The chief of
these is that Venn represented all three propositions of a syllogism on one diagram
rather than drawing a separate diagram for each. She concludes with illustrations of
diagrams that can represent five, six and eleven categorical propositions.
Leibniz is not the only candidate for the distinction of having invented these diagrams.
Sir William Hamilton [Lectures on metaphysics and logic, William Blackwood and Sons,
Edinburgh, 1860 (p. 180)] refers to a work by Christian Weise (1642–1708), published
posthumously in 1712. Since both Leibniz’s and Weise’s diagrams were unpublished in
their lifetimes, it may not be possible to establish priority.
It may be of interest to readers of this article that S.-J. Shin [The logical status
of diagrams, Cambridge Univ. Press, Cambridge, 1994; MR1312613] presents Venntype diagrams as a formal system, specifies rules of transformation and shows that the
resulting system is sound and complete. For a review, see [B. Larvor, Int. Stud. Philos.
Sci. 10 (1996), no. 2, 177–179, doi:10.1080/02698599608573537].
Brendan Philip Larvor
c Copyright American Mathematical Society 2016