Russell's Paradox And Resolving Credit Crisis Contradictions

I wish to draw an analogy to the crisis of confidence caused by Bertrand Russell to the foundations of set theory in 1901 and the crisis of market and regulatory credibility of 2007-2008. This is not the normal route to draft parallels. Usually, for financial market academics, the analogy is drawn to historical periods of extreme market volatility and morbidity, e.g., Tulipmania, South Sea bubbles, other "extraordinary popular delusions and the madness of crowds" (Mackay 1841) with the extreme conclusion that bubbles are translationally symmetric over time. Such is the nature of our reality that we must accept the eternal recapitulation of stupid-stupid errors of judgment.

But the lack of confidence is not necessarily a stasis. The analogy is drawn to Russell's Paradox and its solution as a matter of generalization, freely floating over any one of a number of historical episodes. It may be the lack of confidence in both Bertie's time and our time spur solutions which may save the foundations of a non-contradictory epistemology and results in an accommodation that preserves our way of life.

The sketch of the argument (rather than the whole thing which is too technical for a blog) is that Russell's Paradox which appeared to destroy set theory with its innocent "R is a set whereby x is not an member of itself" leads to contradictions, and in a single swipe, Frege's attempt to define number and arithmetic based on set theory was utterly devastated. Wow! This was a crisis of confidence because the entire foundation of simple arithmetic was now contradictory. The Russell Paradox motivated Neuman then Bernays and Godel (NBG) to construct a solution based on a two-level classification of "proper classes" (really big collections) and "sets" (which are parts of classes). Now the Russell Paradox is resolved because it becomes a Russell class where x is a set and x is not a member of itself. Around 1908 Zermelo and then later Fraenkel developed another fix called ZF which allowed for only one concept of set and some simple operations like intersection, union and complementation. The ZF solution legislated sets via the simple operations and didn't allow for any proper classes. Sounds like Luhman to the Luhman lovers. A bit later when the dust settled, it was realized in ZF and NBG that no set is an element of itself and that ZF and NBG are equivalent solutions.

How does this little story of maths-logic relate to the credit crisis of 2007-08?

Camera One: the crisis of confidence set out by the Russell Paradox is that Bertie discovered that the foundations of a particular professional discourse were rotten to the core. In market terms, the players (both major market participants and regulators) were conflicted by wearing different hats as it suited them. The Goldman Sachs strategy is simply to buy government influence by having its fraternity occupy seats of power. The credit crisis which is said to be a breakdown of trust and confidence came when we could not swallow any more contradiction--we froze in terrorem when the investment banker wrote the regulations which no one understood (remember Hank Paulson, former CEO of Goldman Sachs, contradicting himself everytime he appeared on TV around Sep through Nov 2008? Lehman went bust on Sept 15, 2008).

Camera Two: to solve the credit crisis, we might take the ZBG route or the ZF route. The ZBG route is to metaphysicalize the market and say, "We (the government) are going to protect a much larger swath of the general public--whatever we say or do will be very very big--much bigger than that little set of troublesome subprime mortgage-backed securities. And in the name of saving the proper class of the entire world, we give you our radical solutions." Of course, these solutions are no different from the past since they can all be lumped into the category of "dictatorial discretion". The ZF route is to say, "We (the market) will continue to operationalize and stick to our simple chores of executing trades on behalf of governments, because all trades will now be part of the governments' debt."

Camera Three: the two "fixes" as it were under Camera Two result in the same (equivalent) reality because in a very strong sense the government and the market continue to game each other.

In the end, Bertie's Paradox resulted in an effloressence of logics. Could it be that the result of the credit crisis, contrary to the predicted constraints of economists, will be even more of the same market-government gamesmanship? This is not a quiet universe.


Reference: Goldblatt, R. (1984, 2006) Topoi, The Categorial Analysis of Logic, pp. 9-12.

Russell's Paradox And Resolving Credit Crisis Contradictions