** Title **: De Morgan and the Syllogism

**Abstract** (prepared by Richard Kaye)

De Morgan worked on logic and the syllogism over an extended period of time (with publications between 1848 and 1868). We will present the ideas of some of this work, focusing particularly on the 1860 paper "Syllabus of a proposed system of logic". This resume gives some outline of the talk with no details. The actual details will be in the presentation.

De Morgan works with eight separate relations between classes, one of
which being essentially the "subclass of" relation. His relations are
built using a complicated system of brackets and dot, and care is
certainly needed to interpret the brackets and dot correctly. This will
be explained. De Morgan's brackets are related to the idea of
quantification of the predicate (an idea associated particularly with
William Hamilton ) and the
way the system fits together and works is in some sense a generalisation
and vindication of this idea. For De Morgan, the copula (i.e. the word
"is" or "are" in the middle of a statement) is essentially symmetric,
the required asymmetry in logic being introduced by different
quantification of subject and predicate. Interestingly, the dot is
** not ** negation (i.e. "is not" or "are not") but is in fact logical dual.
De Morgan doesn't have any direct way of representing the negation of a
relation. Thus the familiar De Morgan laws are built into the notation,
but the reasons for the way it all works become clear with the
computation of the complement of a class and how it is quantified.
De Morgan's notation and its use has an uncanny resemblance to the Dirac
bra-ket notation, though I have as yet been unable to see any formal
connection.

If this all sounds mysterious to you, you will not be alone. To me, the truly amazing thing is how beautifully simple the final system is to use and how well it actually works. Of course this will be demonstrated properly in the seminar.

To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).

School of Mathematics

University of Birmingham

http://web.mat.bham.ac.uk/R.W.Kaye/

Dr Walter Dean

Department of Philosophy

University of Warwick

http://go.warwick.ac.uk/whdean