Philosophical Foundations of Law and Finance - 46th Weekly Meeting

Dear All

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

Philosophical Foundations of Law and Finance - 46th Weekly Meeting

Proceedings from the 44th meeting (5 March) of the Philiosophical Foundaitons of Law and Finance

Dear all

Follow the proceedings from the 44th meeting of the Philosophical Foundations of Law and Finance seminar:

1. In the first part of the class Joe introduced his groundbreaking work-in-progress on the application of Group Theory (GT) to law and finance.

2. Philosophy, the LOVE of wisdom, from ancient times has hunted the goose with truth, symmetria and beauty. (Plato's Philebus.) The model of truth for Plato came from the perfect forms of geometry which he tried very hard to apply to social issues. Understanding the 'perfect state' (The Republic) and 'God given laws' (The Laws) was built on tiny precise arguments--always hunting the elusive goose.

3. Modernly, since the early 19th century, symmetria have become Group Theory (GT). GT is the algebraic form of ALL geometric symmetries. That is, with GT you can calculate the quantity (measure the degree) of symmetry. This is a vast improvement over Plato's Euclidean machinery and the proof is in the pudding since GT now underpins most of physics, chemistry, biology and many of the arts, architecture, design, etc. But GT has not touched the theories of law at all. Not one article has been published which even tries to establish the link between GT and the law.

4. GT is extraordinarily simple. It starts with a definition of a group as a set (collection or system) of elements, where any two elements combined form another element of the group. This definition is sometimes called the Axiom of Closure, which can be written as {G, m}, G stands for the elements of the group and m stands for the binary operation. The concept of the group is further constrained by three other Axioms (Associativity, Identity and Vertibility [http://en.wikipedia.org/wiki/Group_%28mathematics%29]) which act as conditions to the qualification of a group. So, for something (anything at all) to be a group, we need to find the appropriate elements and appropriate binary operator. This is what Joe is trying to do in his paper, "Group Theory of Law and Finance--Chasing the Goose".

5. Is all the effort worth the trouble? What is clear is that if GT can be applied to law then we would have a precise view of the entirety of laws, their "structure" would have objective meaning and instead of moanfully bleating about the "complexity" of laws (which many legal theorists do), we would have some means of calculating and predicting "its" (in the most general sense) and "their" (in the most particuliarized sense) order. So much could be imported from GT for free!

6. Hopefully the technology of GT may help us get beyond Platonic aporia.

7. In the second part of the class we continued reading Kierkegaard’s “Fear and Tremble”. This time we dived in chapter one, the Panegyric Upon Abraham. K. announces his intention to ‘recall’ the binding of Isaac by Abraham in order to uphold the memory of this profoundly religious episode which presents human despair and the consolation – and predicament – of faith.

8. One controversial interpretation of the text was that the torrential ode to faith is in fact parodistic. There is almost sarcasm in K’s pious declamation – in presenting devoted elegies the narrator is instead caught by doubts. “No, not one shall be forgotten who was great in the world. But each was great in his own way, and each in proportion to the greatness of that which he loved. For he who loved himself became great by himself, and he who loved other men became great by his selfless devotion, but he who loved God became greater than all… It is human to lament, human to weep with them that weep, but it is greater to believe, more blessed to contemplate the believer”. Really? The narrator is full of wonder for the appalling proof of faith demanded by God to Abraham. In the end the narrator, frenzied, seems to question its very questions and declares himself and his purpose belittled by the impenetrability of the very events he aimed at upholding: “Venerable Father Abraham! In marching home from Mount Moriah thou hadst no need of a panegyric which might console thee for thy loss; for thou didst gain all and didst retain Isaac… Thousands of years have run their course since those days, but thou hast need of no tardy lover to snatch the memorial of thee from the power of oblivion, for every language calls thee to remembrance”. It can be also recalled that in the prelude K. provides four alternative accounts of the binding of Isaac (and, for example, in tale no. 2 Abraham… “offered that and returned home. . . . From that time on Abraham became old, he could not forget that God had required this of him. Isaac throve as before, but Abraham’s eyes were darkened, and he knew joy no more”), or that he writes “Fear and Trembling” under pseudonym, or that the thesis was about Socrates’ irony, which he emulated throughout the same thesis…

8. Again, honour to our brave group this time starring Alex, Roman, Francisco, Cameron, Laura, Daniela, Angelina and Gavin.

9. Unfortunately, we can anticipate that Joe is travelling to Istanbul so there will be no class next Friday. The meetings will resume on Friday 19 March.

Kind regards, Joe and Laura

Proceedings from the 44th meeting (5 March) of the Philiosophical Foundaitons of Law and Finance

Philosophical Foundations of Law and Finance - 44th Weekly Meeting

Dear all

Joe has an astoundingly structured agenda for the 44th gathering of the Philosophical Foundations of Law and Finance, on Friday 5 March 2010, from 6.00 to 8.00pm, in room 5.16, 309 Regent Street (University of Westminster):

1. One of the ambitions of First Series of Philosophical Foundations of Law and Finance, Sessions 1 - 40, was to provide a sufficient treatment of the philosophical toolkit consisting of infinity, symmetry and uncertainty. We found that snippets of Plato's Laws, Timaeus, Apology, Republic, and Aristotle's Metaphysics and Rhetoric could be re-jigged according to the following distinctions: (1) divergent versus convergent infinities (Knopp); (2) bilateral, translational and rotational symmetries (Weyl) and (3) risk (Pascal). These then gave us an apparatus to examine the sacredly unsayable (such as "justice" and "truth")) found in the works of Plotinus, Nargarjuna, Blake, Rumi, etc and the meaning of faith translated in the discourse and processes of the global financial system--which is homomorphic (maybe) to Durkheim's vision (1905) of a global religion.
Whew!

2. In Series 2, the ambition is in the same general direction as in Series 1, but our methodology will be sharpened. Instead of using the naïve but beautiful visual symmetries (as if we knew them--sigh), we will look underneath the hood so to speak, at the assumptions that compose the language of symmetry--which is Group Theory.

3. Group Theory (GT) is the algebra (precise calculation) of symmetry. I'd say even more strongly like Descartes in the Discourse of Method relating linear algebra to the two dimensional plane, that Group Theory and Symmetry are the same. Thankfully and mercifully, there are only four GT Axioms: closure, associativity, identity and invertibility. [http://en.wikipedia.org/wiki/Group_theory]

4. By the way, mathematicians think of Group Theory as a form of philosophy rather than maths--it's that easy!

5. Following from Session 41, I will attempt to demonstrate how metrology (scales of knowledge--the nominal, interval, ordinal and rational) is a deep question inside the Axiom of Closure. We can see how the divide between social science and "hard" science occurs in there. For those who love graphics, our questioning turns on the meaning of the abstract symbolism of {G, •}. This notation will be explained.

6. Why such an investigation? Is it worth the trouble? Well, GT gives us a way of talking about the entirety of law and finance, allowing us to make better than best-guess predictions about their structure. That's the hope and promised miraculous snake-oil cure of GT!

7. In the first hour (6 to 7pm), I'll explain point 5 above by reading and commenting on parts of a paper I'm working on.

8. From 7 to 8pm, we will continue reading Kierkegaard's Fear and Trembling.

9. Maybe we'll find an irrational relation between the two hours.

From 8.00pm onwards you can propose topics and jokes at Vapiano (19-21 Great Portland Street, W1W 8QB) where we reconvene for drinks and meal.

See you on Friday!

Best,
Joe and Laura

PS If you have problems in getting into the building please text or call me at 07910 305957 and I’ll try to help. Laura

Philosophical Foundations of Law and Finance - 44th Weekly Meeting