80th Session of the Philosophical Foundations of Law and Finance (24 June, 6-8pm, room 516, University of Westminster, 309 Regent St, London)

Dear all, 

1. This is the third lecture by Joe to re-characterise and translate Hohfeld's analytical jurisprudence into an n-Categorical algebra.

2.  There are many symmetries embedded in Hohfeld's octonic discrete projective mapping which are really dual quatronic. In a previous lecture we showed how Hohfeld himself perhaps unconsciously missed perfecting his beautiful gem, indicating that he was not fully aware of the deep symmetries of his model.

3.  Is it not obvious that Hohfeld's 8 legal relations constitute a set? But sets tell us nothing of dynamic structures; they order but do not inform.

4. In the lecture, we explain how the 8 legal relations as jural opposites and jural correlatives relate to category theory. We dig even deeper and ask why this must be so.

5.  We show how the 8 legal relations are idempotent endomaps in the framework of jural opposites of a single human being, ie, in the monadic.

6. To map jural correlatives, however, we must use functors which are defined as morphisms which preserve in a one-for-one correspondence the objects and morphisms of two categories. Or, simply, a functor is a morphism between categories.

7.  One big result is that jural correlatives are not idempotent endomaps but rather isomorphic free and forgetful functors between categories of individuals (monads).

8. Not lazily resting on this discovery, we hypothesize (1) that systemic risk and the great cycles of default are left and right adjoints of pre- and post-default subsystems and together form a Dun Scotus-like fourfold cyclic symmetry; and (2) that short cuts through the great cycles of default via tinkering financial regulation only accelerates the centrifugal forces against the good.

See you soon, 

Rezi & Joe

80th Session of the Philosophical Foundations of Law and Finance (24 June, 6-8pm, room 516, University of Westminster, 309 Regent St, London)

79th Session of the Philosophical Foundations of Law and Finance

Dear all,


For the 79th session of the Philosophical Foundations of Law and Finance (Friday, June 17 · 6:00pm - 8:00pm, Room 516, 309 Regent Street, University of Westminster), we will apply the concepts of a Categorical Algebra of Law and Finance announced in the 78th session [see notes thereto in the Facebook group] to Hohfeldian analytical jurisprudence with special reference to: (1) political phenomena and (2) categorical theory and financial instrument patents. 

Under (1), we will examine the concept of executive vision as per Ron Paul [see the YouTube video: (3) http://www.zerohedge.com/article/complete-ron-paul-highlights-last-nights-new-hampshire-debate] and note how his vision differs from Obama's in categorical Hohfeldian terms.

With regard to (2), see (4) http://www.google.co.uk/patents?id=_kKnAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q&f=false and and (5) http://www.google.co.uk/patents/about?id=7C3kAAAAEBAJ.

Sometimes, I'm asked what is the point of all this formalism, ie Categorical Algebra of Law and Finance? I guess there's a hopeful answer that goes along the path of formalism post Newton and Leibniz, where the conception of a coordinate system allowed the calculation of movement of objects, and that these systems of simultaneous equations got us amazing answers to many problems facing the development of the human species. With the quantum mechanics of the 20th century, something broke in our general view of physical calculations and ultimately, about our sense of having a genuine mathesis universalis. The great symmetrists, Herman Weyl and Eugene Wigner, the former tried but failed to pin-down quantum mechanics to a totally symmetric view with group theory and the latter, elegantly showed us how to calculate with group theory sub-atomic phenomena using Heisinberg's "ugly random symmetric matrices," could not come up with a wide enough view of nature including consciousness because basically, in my view, they placed bets on the wrong type of formalism! If only category theory had been invented in 1900 rather than 1947! [Sigh!]. Then Einstein and Poincare would have come quickly to the same conclusions! And even Hohfeld, the well-trained chemistry major, would have been able to erect a much more direct superstructure. Here's the trick I've learned in formal logic way back when I was a teenager studying under Prof Hart at the University of Hawaii, who at one time, edited Copi's standard textbook on Logic, that the more fundamental premise, the wider the applicability, but without instantiation, the framework is too wooly to be of any real use. So I've been on a long search for just the right set of premises (the Goldilocks premises) which can unlock and link. So far, category theory comes closest to the ideal. It's very useful. Instead of checking for and arguing logical fallacies, you can sketch a few straw and ball diagrams and get to the essence of quantum mechanics, special relativity, Hohfeldan analytics, Plato's Laws, Aristotle's Metaphysics, all with a bit of gracefulness and light humour.

As always, after the intensity of philosophical discussion, we can most deservedly unwind at the Galleria Restaurant at 17 New Cavendis St, from 8:30pm onwards.

Ciao
Joe

79th Session of the Philosophical Foundations of Law and Finance

57th Session of the Philosophical Foundations of Law and Finance Updated

Dear All,

We are happy to announce that the fifty-seventh session of the Philosophical Foundations of Law and Finance will be held at the Latimer Conference Centre (for directions, see http://www.devere.co.uk/our-locations/latimer-place), with Joe leading a discussion from 6 to 7pm on "The Philosophical Foundations of Bounty-Hunting under the Dodd-Frank Act" followed by a dinner from 7 to 8pm.  In attendance will be about thirty candidates of the LLM Corporate Finance Law and two PhDs candidates.  You are welcome to attend the lecture and please RSVP to Rezi at rezartavukatana@gmail.com for the dinner, which for guests will be a nominal charge of £15.  Please also note that there is an alumni networking lunch on Oct 9th at 1 to 2:30pm where former LLM students now working in banking and finance will join us.

The topic of discussion will be a continuation of Hohfeldian 'analytical jurisprudence' and Category Theory (see Conceptual Mathematics by Lawvere and Schanuel, 2009, 2ed) with application of such theories to the Whistleblower Incentives and Protection provisions (mainly sections 748 and 921-924) of the US Dodd-Frank Act 2010, also known as the "Bounty Hunting" provisions. You can access the US Dodd-Frank Act text by clicking here http://frwebgate.access.gpo.gov/cgi-bin/getdoc.cgi?dbname=111_cong_bills&docid=f:h4173enr.txt.pdf.

We will investigate the structural features of bounty-hunting in regulatory gaming space in terms of the isomorphism of time, space, greed and fear. We will also ask whether the fundamental psychological unit of risk is non-invertible (and thus, implying an invariance) across a universal regulatory space amongst gaming agents pro se. This move in the development of theory is in response to James Waters' query in the 56th session as to whether Category Theory in social science and specifically, in its applications to financial economic phenomena could be improved with the addition of "combinatorics" and "numerics". Joe's initial response in the last session was to agree with Waters' suggestion that it was in "the combination of categories" that we can see the worth of category theory in terms of practical applications of the predictive sort to legal and financial phenomena. But this practical move would merely be an implementation of a much more fundamental and general position which still needs proof and justification. The prime motivation of Category Theory as applied to law and finance generally is to hunt down structures which are not simply analogous but literally in a rigorous sense, fundamentally the same across specialist discourses.  Our hunt is Parmenidean in the sense of recovering by force of simple structures arguments in favour of the One. In the simplest terms, we wish to find the structures of law and finance, since neither discourse is equipped or motivated to do this job for us, and our suspicion is that bounty-hunting not only offers radical rewards to particular whistleblowers but that it establishes a market nucleus that has the same structural properties that make investment banking so successful.

This fifty-seventh session of the Philosophical Foundations of Law and Finance is the capstone of the introductory set of lectures for the LLM Corporate Finance Law programme, and the beginning of the Corporate Finance Law Executive Weekend which will include 18 hours of intensive instruction led by Professor Mark Watson-Gandy, module leader of Legal Aspects of Corporate Finance,  Florin Coseraru, Director of Barclays Capital & Fellow and Module Leader of Investment Banking, Dr. Dmitry Gololobov, Fellow of Corporate Criminal Law & Module Leader of Money Laundering and Corporate Fraud, Viktoria Baklanova, PhD Candidate in Law and Senior Director of Fitch, New York.

If you can't make it to the Friday session, you are most welcome to join us for the networking lunch on Saturday.

See you there!

Rezi and Joe

57th Session of the Philosophical Foundations of Law and Finance Updated

Philosophical Foundations of Law and Finance - 56th Weekly Meeting

Dear all

We are keen and delighted to announce that the 56th session of the Philosophical Foundations of Law and Finance will take place on Friday 1 October 2010, from 6.00 to 8.00pm, in room 5.16, 309 Regent Street (University of Westminster).

To get us back in the mood of philosophizing about the nature of laws we will read something classical (Plato's Laws or Aristotle's Rhetoric) and develop quite independently what might be called "A Hierarchy of Algebras for Legal Analysis". Joe will set out how Hohfeld's schema of legal relations, i.e., jural opposites and jural correlatives of rights, privileges, power and immunity, can be more simply understood in terms of Category Theory.

Category Theory, born about 60 years ago is now firmly embedded in the way we think about modern algebras – it is an extremely superficial theory that can be applied to practically anything –computing networks, quarks, boxing, dish stacking menus, flights of birds, and now, hopefully, legal theory and applications.

Hohfeld in the early part of the 20th century purported to have established an "analytical jurisprudence" that could be used to unravel the mysteries of any legal problem by showing how genuinely complex any legal relation is in terms of jural opposites and correlatives. This schema has always been quite difficult to apply, but with a bit of practice, can be used to resolve many so-called problems in the interpretation of laws – or, in the so-called "practice of law".

Joe will propose to simplify Hohfeld's "field equations" into a much more compact framework, making use of monoids and the articles of faith of Category Theory. The hypothesis is that if we can show how Hohfeld's legal relations are a category, then wherever Hohfeld's analysis applies, we also have a category. Thus, this sort of legal analysis would get everything else that Category Theory has to offer for free! Further, we would have a precise way of speaking about the structure of laws as fundamental conceptions of mathematics. This sounds like a conceptual breakthrough... At this level of abstraction, fundamental conceptions of law (which is the very title and aim of Hohfeld's work) are equivalent to fundamental conceptions of mathematics – which is the title to high school level text on Category Theory. How weird and wonderful if the implied isomorphism is actually the case!

We shall consequently test the application of Category Theory to our traditional banqueting session at Vapiano (19-21 Great Portland Street, W1W 8QB), from 8pm onwards.

See you on Friday!
Joe, Rezarte and Laura

Philosophical Foundations of Law and Finance - 56th Weekly Meeting