Wednesday, January 26, 2011

The Medium of Contingency

“The medium of contingency”(shortly available in volume 22 of pli) clarifies many points that remained implicit in “The Blank Swan”, it particularly precises the divergence that exists between Elie Ayache’s (EA in the following) and Quentin Meillassoux’s (QM) thought. In that, it does answer my earlier comment, somehow confirming it, but also, strangely, I came to disagree with this one to the extent of now holding the contrary belief that EA’s and QM’s thought do merge into a seeming compatibility.


The following passage (on page 2) from “The medium of contingency” seems to assume a certain conception of thought, or at least of its placement in order to think speculatively, in QM’s sense:

“If a speculation like Meillassoux's must bring our thought flat against the matter of absolute contingency, with a flattening of the depth where we would have searched for the reason why things are what they are and not otherwise and with the flipping of ontology from the side on which things are to the side on which things can be and if, correlatively, contingency has to be thought independently of any division of underlying states in which the contingent thing possibly can be something or other, then the step back from contingency - for only by stepping back from its absolute strike are we able to make sense of it and unfold the expanse where it can be thought speculatively - should take place in a direction and through a medium that maintain the absence of reason and the absence of states.”

I am not sure there is any depth to be flattened in the way thought relates to any of its object, and in the way thought is really, since I can’t conceive of a thought severed from its object (in the way I can conceive of an objectless desire, for instance). On the contrary, I tend to believe that thought is flat, what does have depth is its manifestation via language, but thought is largely independent of it, and it is independent naturally “of any division of underlying states”, which are just tools used to express itself (i.e. its object).
As such, thought can easily criticize these divisions, these states, while it may lose itself in it every now and then, it always retains the capacity of freeing itself from their influence, of turning against them, of staring at them in an inquisitive manner. Language can even help thought in its rebellion against language, as any natural language contains its own meta-level. In that, thought can easily turn itself (and its object) upside down.
So I am not convinced that “a medium that maintain the absence of reason and the absence of states” is all that necessary, provided that states are not taken too seriously, too heavily so as to place us in “a world that is repelled by gravity”(The Blank Swan-p.152, Après la finitude-p.149). As long as the totalization of states in not given too much credit, the philosophical debt can easily, and instantly be repaid.
That being said, “a medium that maintain the absence of reason and the absence of states” may not be necessary, but it may be useful, but more on this later.

The condition for thought to stay in control of its fate, and thereby, be speculative, is doubt, which may just be the historical root of QM’s factuality, as just like facticity cannot be said to be factitious (Après la finitude-p.107), doubt itself cannot be submitted to doubt.
Doubt seems therefore to appear as the psychological form of facticity (see Après la finitude-p.101), or to go further, as the subjective face of it, and to extrapolate a bit more, one may wish to consider the equivalence between the necessity of facticity and the necessity of doubt, wherein the former does imply the object (principle of factuality) and the latter, the subject. I will not follow this line of thought now however, and I genuinely don’t know whether it leads anywhere.

Doubt is nonetheless dated, and often distorted beyond recognition by a mundane usage, whereas axiomatics propose a modern mathematical formalization of doubt. It may then be through axiomatics, and mathematics (and maybe indeed topology, to follow Jeff Malpas along with EA, The Medium of Contingency-p.18) that speculative thought can progress. Mathematics, in their axiomatized form, also present the great advantage to be a very flat language, containing its own meta-language, and providing an unmatched clarity to the extent of being tautological (as it is fully explicit).


While I don’t think the market is the only available medium for factual speculation to develop, I wholly follow EA’s analysis of the market as being a genuinely “contingent and immanent place”. As such, it is therefore useful, but not only because of what it has done, but more because of what it promises to do.
Looking at the market, not as the medium for factual speculation but as just one of many such media, we should expect all these media to communicate with each others, to exchange and nourish their respective speculation.
Clearly for instance, and some works may already have started on this matter, that I still have to get acquainted with, the derivatives market should be a fruitful domain for the factual speculation on probability axiomatics, which itself could lead to topological and therefore ontological results.
It may also be that a speculative resolution of Hume’s problem (as stated by QM in Après la Finitude-p.176) could draw some insights from the material un-totalization of contingent claims by the endless complexification of exotics contracts.

Furthermore, the market may not be the only one, but it appears, in some important regard, to be the purer, the most devoid of faux-semblants, it will therefore act as a useful reference for the other places of factual speculation. Not unique but central, it may play the role of a singularity, a repelling or an attracting one, it does not matter but it will be instrumental in the development of factual speculation, and it may even be more than that, as I believe it also has a political and ethical relevance which is not foreign to its immanence, but that is another matter.

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.