3 Comments

1. Noah

   Hello,

   Thank you for sharing this paper.

   I like how you emphasize that Goedel has two proofs with two aspects– incompleteness and inconsistency. Interestingly enough, I think it was really Lacan that taught us how these two proofs things are equivalent and inextricably linked (via his graphs of sexuation and the logical equivalence of the two sides). Many people miss this and think that only one of the two implications hold. For instance, Meillassoux seems to think that only a pure inconsistency is the implication of the transfinite and its paradoxes (which are of course directly related to Goedel’s work).

   Another thing people miss is that Goedel’s second most important work is on the GCH and that (along with Cohen) showed how undecidability is at work there (again something Meillassoux seems to miss, and I think that is due to inattention to the work of Derrida and what that name conceptually represents) and how his work on this topic is the other side of Cohen’s (I’m not clear that Badiou also grasps this as I cannot think of a reference that would imply that).

   I also liked that you refer to the work of Martin Davis and Gregory Chaitin as they, as far as I can tell, were the first to document how the digital revolution was the result of crises within the field of pure axiomatics (if you know of another reference I would be interested to hear). I get the impression you are most influenced by those two names (even though you have the Wolfram diagram on your blog). If so, I highly recommend Chaitin’s new book on Darwin (which he was kind of enough to send me–although that gifting means I feel obligated to incorporate it into a manuscript).

   I hope you will post your Liverpool address in this manner also if possible.

   Noah

   Posted on 05-Jun-12 at 8:04 am | Permalink
2. parallax00

   Hey Noah,

   Thanks for the generous comments – makes a change to read a generous one, rather than ungenerous on other blogs. I think Levi has also said something about Godel/Lacan to this effect. But Paul Livingston is the guy who has taken this incompleteness/inconsistency dyad to its conclusion in his critique of Badiou in The Politics of Logic (cannot recommend it highly), by emphasising the paradoxical elements of a complete but inconsistent method of formal engagement (as opposed to Badiou’s incomplete by consistent generic approach). I will be uploading my paper for Liverpool at some point definitely.

   I’m not entirely sure about you’re claim as to whether Meillassoux misses the Godel link in GCH. He’s talked a lot about a signless sign though. He has promised some sort of mathematical proof of The Principle of Unreason though.

   I am influenced by Davis and Chaitin – but not nearly as much as Turing and to some extent Wolfram, both of whom are NEVER discussed in depth in Continental Circles. It’s time that this should be addressed – and I’m starting with taking Badiou down with computability theory. But my larger engagement with Turing is in my thesis (which I really should let other people see to be honest, it’s gone past 100,000 words).

   best
   Rob

   Posted on 06-Jun-12 at 1:43 pm | Permalink
3. Noah

   Hi Rob,

   I do not know about other blogs really. Sometimes the most generous thing one can do philosophically is to criticize or attack another. For instance, I would be happy to read a criticism of RNG–even one with an axe to grind.

   I know that Levi Bryant in his book discusses Lacan’s graph. I offer a critique of that rendering in RNG, but also in the manuscript I shared with you on Darwinism. Bryant’s work would be a good example of thinking that the 2 Goedelian proofs can be separated from each other (that is, only a “feminine” ontology is true). Goedel and even Cohen also even seemed to be realist in the sense that they thought ultimately it will be shown that CH is either true or false. But I oppose that form of realism and support the idea that the undecidability of CH is a fundamental aspect of the real itself. If one wants to argue that CH is actually really true or false, I think you need a logic and metaphysics then no one (not even those engaged in work on large cardinals) has been able to dream up yet (if it is possible).

   I looked at some of the free chapters of Livingston’s book, but it seemed to be more so an explanation of familiar ideas rather than offering any form of critique. Based on what you say, I would say rather that the paradox is that both approaches work and have a hold on the real.

   Now, that I think about things I am guessing that one could say that Badiou does account for Goedel’s work on the Continuum Hypothesis with his (Badiou’s) whole notion of the state and state of the situation. In this way, and I do not know what Livingston says, but the issue would be if Badiou attempts to say the state option is somehow ‘less real’ or derivative.

   I know Meillassoux gave a lecture on the nature of the sign, but I have not seen it or heard it. If you know of a video of that lecture, I would be interested to know. Meillassoux seems to think that characterizing things as transfinite means anything goes and anything can happen. But Goedel’s work on CH is one way of showing why that at the same time that is not the case. I do not know of any place Meillassoux sees that or refers to Goedel. He simply wants to say the hyperchaos makes possible everything, but then you would have to show how it shows both models are possible.

   If Meillassoux wants a mathematical proof of such a thing, I would recommend he turn to Chaitin. Since it is only going to be by arguing that being itself is characterizable by Chaitin’s constant and infinite incompressiblity, that one might have a hope of showing it. In particular, if one is advocating ‘hyper-chaos.’ But I offer my first critique of such a notion in that anti-Darwin manuscript as well (I do not know if you glanced at it).

   I know what you mean when you say Turing and Wolfram are never discussed. I am hoping my own work might change that. I am less interested in Turing than in Chaitin, Wolfram, von Neuman, etc. But if you are looking for a reader though of your work on Badiou or otherwise, feel free to email me it.

   Regards,

   Noah

   Posted on 06-Jun-12 at 2:33 pm | Permalink

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