## Week 4, 21 October 2014 (16:00-18:00 Arts LR2)

### Matthew Robey

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.

The Midlands Logic Seminar was founded in 2011 and aims to cover all areas of mathematical logic, as well as related areas of theoretical computer science and philosophy of mathematics.

#### Study group

Our topic for Term 1 of 2014-2015 is the use of induction and heuristics in mathematical problem solving. We will be working through George Polya's book Induction and Analogy in Mathematics .

#### Logistics

All meetings for Term 1 2014-15 will be Tuesday from 16:00-18:00 (study group 16:00-17:00, research talks 17:00-18:00) in room 310 of Watson Building (TBC) on the campus of the University of Birmingham.
• campus map
To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).

#### Organizers

Dr Richard Kaye
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