[FOM] Boole on Aristotle on Euclid
John Corcoran
corcoran at buffalo.edu
Sun Apr 11 11:00:35 EDT 2004
BOOLEAN GEOMETRY: [I]t becomes possible to present the entire procedure
of the Science [of Geometry] in the forms of consecutive Syllogisms. ...
Geometry is no more than an application...of the Logic of the Schools. 
Boole 1997, 178.
This bizarre passage, which virtually contradicts several passages in
Boole's published writings of 1847, 1848 and 1854 on logic, is found in
Boole's previously unpublished manuscripts dated "Probably after 1855"
by I.GrattanGuinness and G.Bornet, editors of GEORGE BOOLE: SELECTED
MANUSCRIPTS ON LOGIC AND ITS PHILOSOPHY, Basel: Birkhauser 1997.
More specifically, this passage is from the last page 178 of Chapter XV
of Boole 1997. If this passage could be dated before 1847, it would help
to provide dramatic evidence of a radical development of Boole's
thinking and of the strength of Boole's character and intellectual
independence. On the other hand, if it could be dated after 1854, it
might tend to suggest weakness of Boole's grasp of his own
accomplishments, blindness to the logical character of geometrical
reasoning and a strong grip he was held in by indoctrination into
traditional renderings of Aristotelian logic. By the way, I assume that
we all know that Aristotle himself never made any such CLAIMS for his
system of syllogistic logic, but of course he virtually espoused
founding of a field one of whose ultimate goals was a complete
description of geometrical demonstration.
Q1 Is there any literature on the dating of the Boole manuscripts?
Q2 Does anyone know of previous discussion, whether before or after
1997, of Boole's view of the formalization of any branch of mathematics
(geometry, number theory, analysis, or any other)?
Q3 Is there anything in print or on the web about this book of Boole
manuscripts?

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