Tuesday, January 25, 2011

The Blank Swan

I already have published a review of “The Blank Swan” on Amazon site, I will not repeat it here, rather, I wish to further an analysis (which I outlined on Amazon’s review, but in very vague terms) of some of its thesis in relation with those of Quentin Meillassoux in “After Finitude: An Essay on the Necessity of Contingency”(the original version of this book being in French: Apres la Finitude).


1. Hume’s problem and its probabilistic inference
In “After Finitude”, Quentin Meillassoux takes on Hume’s problem which investigates the possibility of grounding rationally the observed stability of natural laws, or, in Meillassoux’words, our capacity to demonstrate the necessity of causal connections. Meillassoux lists three types of answers to this problem: a metaphysical, a skeptic and a transcendental one.
I am only interested in the latter here, I leave to the interested readers to check on the others in Meillassoux’ book.
The transcendental solution to Hume’s problem is typically the one proposed by Kant. Kant’s argument is a reductio ad absurdum, starting from assuming that there is no necessity in the causal connections, it results, according to Kant, in the complete destruction of the possibility of representation, as the very categories of representation would lost all meaning in a world where causal connection would keep changing. From there, Kant infers that therefore, since we have representation and consciousness of phenomenon, causal connections are necessary.
However, Meillassoux notices that Kant’s argument hinges on a probabilistic assumption, the one according to which if causal laws could change, they would change often, to the point where all representation would become impossible. It is this assumption that Meillassoux does criticize, by proposing the concept of untotalization, inspired by Cantor’s work on transfinite numbers.

2. Cantor’s transfinite and the concept of untotalization
Cantor’s theorem establishes that the power set of any set A (finite and infinite alike) has a cardinality superior the the original set A, in other words, the set of all subsets of A has more elements that A itself. That leads Cantor to introduce transfinite numbers to account for the cardinality of various infinite sets: aleph-null is then the cardinality of the natural number, while aleph-one is the cardinality of the set of all countable ordinal numbers.
From the work of Alain Badiou, who interpreted Cantor’s theory in ontological terms, Meillassoux argues that such a concept of the transfinite invalidates Kant’s argument, as probabilities are valid, in their frequentist interpretation only insofar that a totalization of the cases is not problematic. In Meillassoux’words:
“We are completely ignorant of the legitimacy there is in totalizing the possible, as we totalized the faces of a die. Such an ignorance is sufficient to demonstrate the illegitimacy of extending an argument about uncertainty outside of a totality given by experience.”
The possible, because of Cantor’s theorem, may therefore escape, according to Meillassoux, a totalization compatible with its treatment by probabilistic means, and that is enough to invalidate Kant’s argument. Meillassoux does not provide however a positive demonstration of how Cantor’s theorem, applied to the possible, makes probabilities invalid, he simply raises the question, and concludes, rightfully in my view and for the problematic he’s looking at, that this is enough to reject Kant’s argument.


Elie Ayache’s book is subtitled “the end of probability”, and its central thesis is indeed, following the trail opened up by Meillassoux, to assert that probability theory is unable to account for the reality taking place in Finance.
It would be presumptuous to summarize here all that there is in “The Blank Swan”, just as the previous section can in no way be taken as a summary of Meillassoux’ work, I just wish to precise a few concepts, in order to point out an ambiguity which, in my opinion, is left unresolved by Ayache.

What Ayache proposes to do, in his book, is to apply Meillassoux’ conclusions about the physical world and our relations to it, to the world of derivatives trading. For that, he asserts, in convincing terms, that the market (of derivatives) is a medium of contingency. Therefore, the market is untotalized, in the very same way that Meillassoux says possibilities in the material world are, and in the market, this untotalization can be derived from the non-redundancy of derivatives contracts, as indeed, if a contract is redundant, its market would simply vanish; or in the words of Ayache:

“If there were an established law, then some derivatives would never be exchanged.”(p.167)

This is indeed true, if valuation were exact, there would be no room to exchange a contract at variance with this valuation, and therefore no market. The existence of a market clearly points out to the inadequacy of the valuation process, and therefore to an untotalization of possibilities.
All this is still very much in line with the thesis from Meillassoux, however, Ayache goes a step further when he writes:

”In ‘thinking’ contingency as absolute with regard to the material world, Meillassoux is thrown into the exchange. His speculation is untenable in ‘pure’ thought and the corresponding detachment or transcendence.
All I am trying to do is to carve out the space that is adapted to speculative factual thought.”

Here I see a divergence between Ayache’s and Meillassoux’thought. Elsewhere, Ayache wrote:

“Speculation thus recovers its absolute meaning. It surpasses even thought itself.”(p.175)

Such a stance seems to assert speculation (which, in Ayache’s terms, means the act of inverting the model, whatever it is, for valuating an option and engaging into “the trading of the derivatives at variance with its replication plan”, i.e. the writing of the market), as a process that exceeds thoughts, that reaches to a point beyond thought. But then, one of the main point of Meillassoux being the re-appropriation of the domain of the absolute by thought, isn’t Ayache positing a new absolute which he again places beyond thought?
Another way to put it is: Isn’t Ayache falling into a new kind of Fideism, which is properly a target of Meillassoux’work?
By proposing such a radical criticism of probability, positing not the end of some interpretation or axiomatization of probability but of probability itself, Ayache may have hypostatized a reality beyond thought, only accessible through speculation. What then differentiate speculation from a magical ritual, that one must perform in order to access to a higher level of reality? Aren’t we driven into a fideistic way of relating to the world (be it the world of the market) and to give up any illusion of grasping it with an analytical apparatus?
That matter doesn’t find any treatment in “The Blank Swan”, and it is, in my opinion, its major defect. Because of it, an atmosphere of ambiguity does linger over the pages, becoming more and more persistent.

I shall stop here for now, not that I’ve said it all, and I will likely come back to comment on some other ideas from the book, such as the logic of place, that I wish to analyse further, in relation to Nishida Kitaro’s ideas of the logic of basho, for instance, though I still have some study to do before that.


numbersix said...

Hi Jean-Philippe,

Thank you for this very penetrating comment. I intended to comment your post on Amazon, however, I will start doing it briefly here.

It is true that the problem that Meillassoux poses -- i.e. finding the right 'medium' for his factual speculation, i.e. a 'medium' where absolute contingency is no longer bothered by possibilities, totalized or nor -- has challenged me into working out my idea of the market of contingent claims as an answer to Meillassou's quest, pending a proper generalization of the 'market' beyond the purely, or vulgar, financial acceptation.

It is true that my whole book hinges on the idea that the necessity to exchange is what produces non-totalization in the market, therefore the hope, is that the necessity to exchange would somehow be the 'material' that Meillassoux's sought medium is made of.

To me, exchanging and writing are the same thing (ch. 4); and writing is indeed an experience that constantly surpasses thought and representation and even beats it is 'speculation speed'. I agree with you, there is some kind of mystical move or leap of faith here, i.e. I am really looking for something, I call it a 'capacity' that exceeds thought; maybe it lodges in the body, for all we know.

In a word, one should no longer think metaphysics with the faculty of thought alone, once one has reached Meillassoux' speed or Meillassoux's brand of speculation, i.e. factual and the necessity of contingency, but think metaphyscis with, well, writing. Perhaps my mundane conclusion is that one always writes metaphysical books.

Please have a look at my paper:
The Medium of Contingency, written after the book:

Jean-Philippe said...

Hi Elie,

Thank you for this prompt reply.

I am now reading your article "The medium of contingency", it indeed clarifies a lot with regard to your differences with Quentin Meillassoux.
I hope to finish it by today, and I will post a detailed commentary on my blog as soon as I can.

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