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.