At the 46th gathering of the Philosophical Foundations of Law and Finance, on Friday 26 March 2010, from 6.00 to 8.00pm, in room 5.16, 309 Regent Street (University of Westminster) we will explore the concept of the groupoid and Descartes.
For those who hate vague thoughts, the groupoid allows for the specification and intra-convertibility of the singular general principle and the plural instantiation of things. The groupoid is the concept that sits between the generality of the Set and the symmetric specification of the Group, and provides us a way to think systematically without having to bother with every little detail. The groupoid is a form of strategic thinking par excellence. Even if you hate generalities, you might fall in love with the groupoid.
Joe will present a brief talk on "Risk as Non-Invertibility for 7 Year Olds" which is part of a project on "A Group Theory of Law: A Logico-Empirical Philosophical Investigation of Laws". He will introduce a cyclic-hierarchic conceptual structure and by analogy, pay homage to Plotinus, 2nd century neo-Platonist, who attempted to synthesize Platonic static ideals with the dynamic potentiality-actuality of Aristotle. We will review some concepts that help us to think (and calculate) symmetrically, i.e. groupoid, list of elements, property, binary operation, associative operation, identity, invertibility, subgroup, coset, simple group. These infantile concepts amazingly give us a way to "count" the symmetry of things and to speak precisely like aliens from physics departments in other universes – just kidding, of course. This abstraction should take us about half an hour.
The rest of the time we will read together and comment on passages of the greatest methodological work of the modern period: Descartes’ Discourse on Method (http://records.viu.ca/~johnstoi/descartes/descartes1.htm). Descartes' Discourse links algebra to geometry explicitly thereby linking two different functions of the brain together for the first time! Some neuro-physiologists theorize that the brain is a "futures simulator". This vision is not possible without Descartes Method and after the Method, we start to see answers to particular problems as specific pathways in coordinate systems.
If the Discourse gets too heavy, we will reflect in the "baker's oven" with Descartes incomparably beautiful and moving Meditations (http://www.wright.edu/cola/descartes/mede.html).
After so much fluffy abstract structure, we will need the sustenance of real food and drink at Vapiano (19-21 Great Portland Street, W1W 8QB) from 8.00pm onwards.
See you on Friday!
Joe and Laura