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David Roden, Philosophy, The Open University UK
Oh by 'sigma (x)' please read 'phi (x)' in my post! I was referring to the property that comprehends Omega not the diagonalizer. ;)
I very much enjoyed this post, Jeffrey, and will no doubt be re-reading it in days to come. My worry about the application of Priest's schema is that Derrida's arguments tend to undermine the first premise of the inclosure argument: namely, that there exists a totality comprehended by a property like 'meaningful', 'thinkable' etc. For the first premise to be true, the predicate Sigma(x) needs to have some determinate extension or intension. It needs to be satisfiable in such a way that any candidate for inclusion in Omega either has it or it doesn't. If we are doing formal logic, we can assume that the semantics takes care of itself. But for the Humean reasons you give here, I don't think that assumption is available to Derrida. For example, the iterability argument implies that there can be no conditions associated with meaningfulness that apply to all signifying states. This doesn't entail that all language is without signification, merely that there need be no property or disjunction of properties in virtue of which a given mark is a signifier. So the thrust of deconstruction is detotalizing. The inclosure schema just doesn't get started.
Catarina's point is very well made (I said much the same thing in my introduction to the Sage Derrida Boxed set). Deconstructive undecidability is supposedly general, not local. While a sentence that is formally undecidable in a given object language can be informally supported in its metalanguage (as in the case of GS's). Différance and iterability supposedly afflict every system. For example, the logic of "supplementary" that Derrida discusses in his reading of Rousseau in Of Grammatology involves cases where the Supplement is both a contingent addition to an Origin & where the existence of the Origin necessitates that something with the characteristics of the Supplement already exists (namely the divided Origin itself). Thus Rousseau's thinking about the relationship between nature, culture and language requires that culture is distinct from nature (something that comes from the outside to screw it up) even though Rousseau also describes the natural condition in ways that show that it must harbor the possibility of writing, imagination, amour-propre, etc. If this were a simple contradiction, which applied in, a system-relative way, to Rousseau's philosophy it would be of some exegetical interest to any Rousseau scholars but it would have none of the dizzying consequences that Derrida claims of it. The interest of Derrida's reading rests on a more or less implicit metaphilosophical claim to the effect that any attempt to describe a self-sufficient origin or totality is self-undermining and Rousseau's double bind exemplifies this general predicament. We can agree or disagree about whether Derrida's is right to claim this, but, for the most part, I think, none of his arguments depend on an analog of the Diagonalization Theorem. It's easy to get confused about this because Derrida's arguments are reflective in their implications. If he is right, then, for sure, there are principled limits on conceptual analysis and the axiomatization of thought which can be exemplified in terms like "differance" or "hymen" which then can be used to mark or figure this limit. Although it is formally a noun or categorematic expression with an independent meaning "Hymen" in Mallarme's poem is semantically empty because its effect depends on its relation to "entre". Thus (effectively) it is a syncategorematic expression. But while Derrida's reading is insightful it does not have the force of an argument. It has the force of an illustration of a more general principle of iterability that Paul discusses on p. 10 of his article. However, the iterability argument does not assume that language is a closed rule-governed system or hinge on the possibility of self-reference. It claims that you cannot have a system of rules R governing a symbol S if R is constitutive of S. That is, it is always possible to use S without observing all of R. The iterability argument is a claim about the conditions of anything being a signifying state. It can be marked or illustrated with cases of quotation and self-reference (as Derrida does, extensively in Limited Inc) but these exemplify his point they do not establish it.
Jon, I like your characterization of Priest as a "speculative realist" avant la lettre - must be a paper in there somewhere. I suspect that what Priest may share with most other speculative realists is that inclosure arguments require an initial totalizing move in their dialectic. You can't have a transcendence without a totality such as the set of sets that are not members of themselves. Similarly, you can't have the kind of radical transcendence that both Harman and Meillassoux want to elicit without having some totality of conditions on "finitude" that (somehow) fail to apply to the real. In Meillassoux's case the totality seems to be a Correlation defined by some some or other set of constraints on thought. The fact that the contingency of the Correlation is not a correlate (a pole of a thought-object correlation) then is taken to entail that thought can also grasp an absolute, namely the thought of contingency itself. Like Pete, I worry about the conflations between different kinds of modality that seem to occur here. Meillassoux, to be fair, acknowledges this when he points up the difference between facticity and contingency, but I don't get how he avoid it. Suppose that we accept that Correlations are absolutely contingent in some sense. Well, any facts which supervene on the Correlation will be similarly contingent. If there is a Correlation involving s a Kantian transcendental subject, then facts about appearances will be contingent. But these don't seem be the kind of absolute facts (facts about the coming into being of correlations, or whatever) that Meillassoux wishes to account for. There may be an argument for a kind of absolute contingency here, but it just doesn't seem to be the right kind. But I think we can also resist Meillassoux's starting point. Are there good grounds for thinking that there are such things as Correlations: conditions on objective thought as such? I think most of the phenomenological arguments for a priori structures are looking tired these days: we don't have the insight into phenomenological necessity needed to make them run. Maybe, arguments which start from conditions for semantic content can cut the mustard, as Pete seems to be implying (I'm skeptical) but then it is even less clear that they are the right kind of facts to get us Meillassoux's hyperchaos.
Thanks for two fascinating posts, Jon. Hope this response isn't too orthagonal to your concerns: Meillassoux must get from an epistemological statement about the "facticity" or non-necessity of a given correlation to an ontological claim about absolute contingency (AF, 54). He seems to assume that a given thought-world correlation delimits the class of thinkable propositions. This is implied by your verificationist formula P --> <>KP given the contrapositive of the "obvious fact" <>KP --><>TP. I.e. P --> <>TP. Meillassoux's characterization of the strong correlationist as an "agnostic" in the debate between the believer and atheist thus seems odd if the set of P's "belong" to a given correlation. But how else could be verificationism be a consequence of correlationism? If there are propositions that don't belong to the correlation (could be true but unthinkable) then their truth cannot entail their knowability. The correlationist would be inconsistent to assert agnosticism but would be justified in adopting the logical positivist line and saying that atheist and the theist are talking nonsense. However, not much follows from this. The lack of necessity of the correlation entails that unthinkable propositions are possibly true only if (pace verificationism) there are unthinkable propositions.
David Roden added a favorite at Jon Cogburn's Blog
Jan 19, 2012
It's nice to see a mention of Samuel Wheeler, whose writings on Derrida and Davidson are exemplary and really deserve to be revisited. My piece in Ratio, 'Radical Quotation and Real Repetition', is a kind of Davidsonian gloss on Wheeler's reading of Derrida (if that isn't too convoluted already!). Regarding Auebarch's post: There are lots of ropy passages in Speech and Phenomena and I suspect that Derrida's analysis of the phenomenological voice is one of the most dispensable parts of his philosophy. However, Derrida does have a response to the semantic holist that is germinal in S&P and which only becomes fully explicit, I think, in 'Signature Event Context'. This goes via the 'iterabilty thesis' which holds that a condition of signification is the differential repeatability of the vehicles of content. This undermines holism if iteration must be possible beyond the systems that confer semantic or syntactic identity. That is, iteration is real and not scheme-relative repetition. If the iterability thesis holds then no definite conditions can determine the semantic essence of the sign, whether these are holistic, molecular or atomistic. I argue this at some length in the Radical Quotation article but there's a more recent post responding to Graham and Levi here.
Toggle Commented Dec 6, 2011 on David Auerbach on Derrida at Jon Cogburn's Blog
Thanks for linking to review of Corballis' book (still on my shelf of shame, but hope to get round to it soon). I wonder if we can make the link between counterfactual reasoning, recursion and intentional attribution in the following way. It's plausible to hold that being a believer involves having a concept of belief because believing p is a matter of holding p true. We cannot hold p true unless we understand this is a commitment that we or others might not have. If we don't understand that belief in p is a commitment, then we cannot withdraw belief in p, for example. But it is not clear that it makes sense to say that we can have a commitment to anything if we could not conceive of circumstances in which the commitment could be withdrawn or not initially made. So believing that p entails also believing certain counterfactuals such as that others might believe p false or or that we might not have committed ourselves to its truth. So having beliefs minimally involves counterfactual reasoning about doxastic commitments. But, of course, this also requires that we be able to make belief states the objects of other belief states. Davidson and (as I understand it) Brandom have argued that doxastic commitments must be discursive or linguistic. While this may be the case in many instances of human belief, I'm not sure that it has to be.
David Roden added a favorite at Jon Cogburn's Blog
Oct 30, 2011
Mitchell: The article doesn't explicitly cite trauma as grounds for the Extended Mind Thesis. However, if external objects and processes are parts of mental states and processes, then damage to them is on a par morally with damage to the mind/brain. Thus EMT is in a position to explain why some environmental destruction is bad for people. This is hardly a decisive reason for adopting EMT, but it could be a reason for strengthened commitment to it. David
This dramatizes the ways in which cognition depends on natural and artificial affordances that are inherently fragile and contingent. Thanks for posting, David
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