Tuesday, 25 November 2008

A Critique of Pure Luck: Meno & Posterior Analytics

In the Meno, Plato shows how knowledge of the Pythagorean theorem is inherent in an uneducated boy. If this is true, then either Socrates knows how to extract external truths or we are witness to trickery. If the former then Socrates is one of the greatest educators ever; if the latter then he is just another fraudster. If the former then what we need to know is somehow embedded within and the training we need is how Socrates' method works. If the latter then we can dismiss the Socratic method. If the former then Socrates embodies the genuine philosopher and upholds the philosophical ideal in real life. But if the latter then philosophy is louche--a cocktail party joke at best! (See John Flood's "For Joe").

Aristotle was so bothered by the Meno, not sensing Socrates' joke so to speak, that he wrote the Posterior Analytics (PA) trying to explain how "all teaching and all intellectual learning come about from already existing knowledge." [71a, 1] The questions arising from the Meno are interesting (e.g. how should we teach? how should we learn?) but Aristotle's answer in the PA turns out for the most part about different forms of understanding the particular, and deductive demonstrations of the universal and the particular. [84b35, 85a15] In Book I of the PA, he sets out a programme for understanding a thing simply (simpliciter) as distinct from universally. What you know simpliciter is different from what you understand universally. [71a25] What the boy knows simply in the particular is, in other words, different from what one would understand universally.

Although he never really explains how the heck the boy in the Meno can "understand" or "deduce" the Pythagorean theorem, sweeping it away as some kind of con job [71a 30], he
does appear to favour a dull Occam's Razor ("demonstration through the fewer items is better, other things being equal") [86b 5]. Perhaps demonstrations of universals are the easiest types of arguments? Unlikely.

Was the boy's understanding a matter of chance?

Aristotle argues: "There is no understanding through demonstration of what holds by chance. For what holds by chance is neither necessary nor for the most part, but what comes about apart from these; and demonstration is of one or other of these. For every deduction is either through necessary or through for the most part propositions; and if the propositions are necessary, the conclusion is necessary too; and if for the most part, the conclusion too is such. Hence if what happens by chance is neither for the most part nor necesary, there will not be demonstration of it." [87b19-26]

I wonder whether the modern discourses based on uncertainty and risks such as finance, risk management and risk-based regulations are impossible to understand not because we are incapable of understanding but because we happen to describe the phenomena in terms of chance.

Saturday, 1 November 2008

Philosophical Issues of the Credit Crisis

I am amazed that the credit crisis forces us to consider some basic philosophical issues re informal fallacies, e.g.

  • Kantian unprovable apriori synthetical metaphysical premises--"the world is one credit crisis";
  • Ghostly deus ex machina causation--"the credit crisis has made my train late";
  • Circulus in probando by filthy rich bankers-turned-unelected dictatorial ministers--"this is the only alternative (pay bankers with taxpayers' money) because I know it is worse any other way";
  • dicto simpliciter--"this is a credit crisis because I say so".


The media's game is to get under our skin so that as Aristotle put it, "we become what we perceive." Thus, "I think therefore I am part of the credit crisis." For the media, "the credit crisis is, therefore I, the media, make money".

One way we might protect ourselves from the electronic tsunami of rumour, falsehoods, hearsay and outright frauds by the news pundits and "macro-economists" who happen to work for banks or funds is to gain a modicum of financial literacy and to focus on what might be called "a critique of pure luck".

What is financial literacy? It is basically to understand risk in its dimensions through social time and social space. When you think about it, finance as risk is extremely symmetrical. We can get into a very long and fascinating discussion here. [Beyond the basic slogans, for the social theorists, I will only point to two areas of fundamental fecundity: (1) Group Theory--as defined by the mathematical logicians of the 19th century--from Galois on through Lie, Abel, and used to re-write the physics of the 20th & 21st centuries; and (2) Category Theory--an alternative to set theory which is yet to be applied in social science and law but extremely suggestive--the world as arrows and functors.]

Another way to approach financial literacy is to simply "keep some skin in the game". I would suggest that if the maths are just too boring for you, that you can learn finance viscerally by just trading. As preparation for trading, consider some of the best traders I know are: (1) excellent surfers on real oceanic waves; or (2) shark divers. A fine trader's mentality is found in some of the highest levels of abstraction, e.g. note Pascal's God-bet before he entered enlightened quiessence and Hilbert's enlargen programme on the 10 hardest bets on research programmes in the 20th century.

What is a critique of pure luck? It is the belief that all things are alive. Lots of so-called traditional people think this is obvious--what the cultural anthropologists called "animistic". To update this "animistic urge" into the best of Western thinking and to be a bit more precise (but still unpardonably vague), all things that interact as communicating systems are Von Neumann Universal Constructors--that is, these "things" do just that (what is logically required) to replicate themselves in whatever world they find themselves. These nestled systems give the world its form. This form is not invariant. The only necessary invariant is that material of this world hasn't changed at all for billions of years. [Democritus & Leucippus, et Lecretius RIP.] Physicists tell us this--that the planet Earth is composed of the same atoms (give or take some meteroic and cometal accretions and collisions) since the very beginning over 4.5 billion years ago, and for another googleplex years, the atoms will be the same. Although we might wrongly believe that there has been "progress" since way back then. All there has been is really a "re-arrangement" of form. Socrates is even more right now--we as humans are ridiculously insignificant.

As an exercise for the Von Neumann Universal Constructor, we might consider the credit crisis as a good opportunity to think about what laws are conserved through global crisis or anticipating the dark ages (forget the Depression, that's just too small a wave to bother surfing), in case of the BIG ONE, what is the form of laws that are necessary to re-boot civilization?

Answers should be sent to the New York Times and the Financial Times.