Future, Present, & Past:

~~ Giving itself latitude and leisure to take any premise or inquiry to its furthest associative conclusion.
Critical~~ Ready to apply, to itself and its object, the canons of reason, evidence, style, and ethics, up to their limits.
Traditional~~ At home and at large in the ecosystem of practice and memory that radically nourishes the whole person.

Oυδεὶς άμουσος εἰσίτω

Saturday, August 21, 2010

Infinite allusion

In the Meno, Socrates faces this objection from the titular character: if you are seeking anything (say, a definition of knowledge or justice or love), you don’t have it (otherwise you wouldn’t seek it); but in this case, you cannot recognize it if you do find it, since in order to recognize it you must already have it (recognition being the comparison of what one finds with the mental image or concept of what one sought). Socrates of course replies, that's why you do recognize it.

Harman remarks (in his Atlanta speech, and elsewhere) that this paradox of Meno’s is also a correlationist dodge (or rather, that the correlationist move can be mapped onto Meno’s): you can only find what you already have. He opines that it's a sophistic excuse for laziness.

It's notable, I think, that in this dialogue, Socrates never actually refutes the paradox. Moreover, he responds with the myth of anamnesis: a "likely story" that makes all knowledge into a sort of memory and all learning into recollection, which in a certain measure grants the critique, but tries to turn it on itself. This is really remarkably close in spirit to the famous remark from Pascal's Pensees which I quoted recently: "You could not seek me if you had not found me, and you would not have found me had I not drawn you," God says to the seeker. Harman suggests that referring to what one does not know directly is perfectly possible; we do this all the time, he says, by way of allusion. We allude to what is nor present and perhaps what cannot be present. This does not cause it to be present, but it elides the distance (even the insurmountable distance) in question.

Such ontologies as this are inevitably "likely stories." They are more or less compelling--and clearly, many of us are finding them more so, of late--but they do not amount to a refutation of correlationism any more than does Socrates' myth of anamnesis. They are, rather, alternatives to correlationism.

Meillassoux's effort to push correlationism to a radical inversion of itself, via mathematizing the in-itself, is a different alternative, and may seem closer to being an actual refutation. But its force depends upon granting the status of trump-card to the mathematical move against the interpretive one. As I read him, Meillassoux follows Badiou in rejecting hermeneutics. For Badiou, hermeneutics is the last stage of romanticism, which is in turn the last refuge of religion. The decision for the ostensible pure rigor of mathematics, and against the blur of interpretation, is thus a move with a polemical impetus. Meillassoux in likewise opting for the purely mathematizable "primary qualities" as the in-itself is seeking to make philosophy inhospitable for fideism, since the latter colludes, willy-nilly, with the worst forms of superstition.

Now, Socrates' recourse in the Meno to mathematics does not stop with the doubling of the square. He goes on to argue that this ability of Meno's slave boy to reach this mathematical conclusion, guided only by Socrates' questions, points to the reality of anamnesis. But this is, very clearly, an interpretation, not just of a particular mathematical problem but as it were of mathematics itself: of the fact that we can access truth in this way, can see it as undeniably true, even if our explanation of how we know has to stop somewhere (just as Wittgenstein says).

Harman says someplace (I've lost the reference, sorry) that although he doesn't agree with Meillassoux, he doesn't want to push his critique too far, because he likes what Meillassoux is coming up with anyway and doesn't want him to stop. Likewise, I feel about object-oriented approaches that while I don't see these as watertight arguments with irrefutable QED's at the bottom, they are gorgeous ways of thinking, with many beautiful and exotic ramifications, every bit as perplexing and provoking as the notion that all learning is an accessing of knowledge we had already. Does this myth on the Meno skirt an infinite regression? Yes; if all learning is remembering what we “already knew,” then when did we learn it? (And this already resonates with Meillassoux's invocation of Badiou's laicization of infinity.) But this infinitude is what compels us to have recourse to something other than pure mathematics: to a praxis that is more ad hoc, whether this be language, or some other manner of negotiating the obdurate realities with which our thought must deal. Such an improvisation can be very extensive and intricate, and such (I suggest) is speculation on the life of objects via allusion, which likewise flirts with infinite regress.

Allusion, moreover, is precisely the meaning of the trope metalepsis. "In a metalepsis," Harold Bloom clarifies (if it is a clarification), "a word is substituted metonymically for a word in a previous trope, so that a metalepsis can be called, maddeningly but accurately, a metonymy of a metonymy." That is, the previous trope is only alluded to. (Wikipedia usefully offers the example: “I’ve got to catch the worm tomorrow.”) But metalepsis in the philosophical sense alludes, as it were, to a trope that was never given. It is as if one listened to an opera in a foreign language, with no sense of the meaning of the words. One senses, one assumes, that there is a context in which the words are meaningful; one might say that they are given as meaningful; but this context evades one. Mikhail Emelianov a while ago snarked that the notion of the withdrawn object was like the claim that “my toy soldiers come alive at night.” I've mentioned before that I sort of like this comment--minus the snark, it is not too far from my own take: one cannot know this infinite depth within the thing, but one can evoke it.

One can in fact sometimes evoke it quite exactly. The well-known Cantorian diagonal proof, that elegant gesture of numerical self-surpassing, is a study in miniature (if one can use this term for something infinite) of how to do this. A list of all the whole numbers is paired one-to-one with “all” the irrational decimals. Then one uses the diagonal procedure to generate a new number that is, by definition, not on the list: one takes the first digit of the first number and changes it, the second digit of the second number and changes it, and so on. The resultant number thus differs from the first number on the list in at least the first digit, from the second number in at least its second digit, and so on, and thus is different from every number on the list. In this way one has encountered the first transfinite quantity, an uncountable quantity (whereas the whole numbers are, precisely, countable). The mind thus encounters an infinity that obviously exceeds its algorithmic procedures; which is not surprising, since infinity itself already exceeds “one, two, three…” in the same way.
As I mentioned to Timothy Morton a bit ago, a propos his application of Gödelian strange loops to ontology, the withdrawal/availability "split" of OOO seems to me closely analogous to the diagonal proof, in the way one infinity veers off from another.

Now, what are the ethics of this metalepsis?

It is quite striking that while Levinas figures in After Finitude as a paragon of irrational fideism for Meillassoux--precisely the sort of philosophy that must be overcome--he, too, recurs to a thinking of infinity. Indeed, the difference between Badiou and Levinas can be summarized in saying that for Badiou, infinity will be the object of technique, whereas for Levinas, it is always what is intimated through technique. (Using "technique" in the sense I did in the post linked to above, on faith.) The Cantorian procedure would be, for Badiou, a technique that finally shows the infinite as a completely mundane quantity, inexhaustible but wholly of this world, the only world there is; a natural infinity, since there is no alternative to the natural. This is why Badiou also wants to have done with interpretation; interpretation is the trope by which one would reinstate the supernatural, because interpretation is always contestable. To the endless improvisation of various stances of availability to the open which hermeneutics strikes (and Levinas is not so far in some respects from this), Badiou wants to respond with a different directive; that of truth. The infinity of the face, for Levinas, comes before any interpretation. It immediately involves us in being (in an obviously loaded figure of speech) beholden. Thus Levinas often cites Dostoevsky: "we are all guilty before everyone, and I more than the others."

In my rant on the BP oil spill, I had occasion to cite this, and also Solzhenitsyn's similar remark that "the line between good and evil runs through every human heart." But there is a problem with this sort of line, often noted: the claim that we "are all guilty," very easily colludes with ideology and the status quo. From the assertion that we are all tainted, it's but a short step to the suggestion that there's nothing one can do to make it better--so why not just throw one's hands up and go buy something else-- or even better, click here on this box to "give" to a charity, to "make a difference" in a way that is precisely like everything else you do that makes no difference at all.

The comparison arises: isn't Solzhenitsyn's (Dostoevsky's) universalization of guilt, easily used to occasion complacency, like the sophistic paradox of Meno? I.e.: we can't escape the hermeneutic circle, so then, go ahead and get into it. This is more or less the move Harman decries in ontology, and it is even worse in ethics: to try to re-cast the problem as the solution--isn't this the height (or nadir) of being co-opted?

But of course, this is not the only way to respond to the dilemma. Levinas is right-- the face does make us beholden. But this should not paralyze us, it should galvanize us. Kierkegaard says in Purity of Heart is to Will One Thing: "The Eternal with its 'obey at once' must not become a sudden shock which merely confuses the temporal. It should, on the contrary, be of assistance to the temporal." This is quite a lot, coming from Kierkegaard, who after all did not go out of his way to make things easy; but above all, he knew that merely being confused was precisely to make things easy on oneself. (Think of Skimpole in Bleak House, who affects to find anything complex--i.e., anything that would make demands upon him--over his head, thus justifying his dependence on the charity of his friends because he cannot be bothered to keep track of things like money; "I am a child," he protests over and over, a kind of nasty parody of the Christian call to "become as one of these little ones," while his own children and wife must fend for themselves.)

Socrates, in the Meno, is compared to a stingray, and the shock he gives is indeed one that could either merely stun or confuse, or "be of assistance." In every single moment, there is an encounter with the infinite that calls on one to respond anyway. One cannot evade philosophy just by turning to "practical" matters; one can only do it badly. Philosophy is the coming-up-short of every technique. But this does not excuse us from having to discern, again and again, which flawed technique to use this time. I think the best ethical abbreviation of this is the Kantian rule of thumb that "ought implies can;" with the proviso, however, that this "implies" is precisely by metalepsis: an allusion, every bit as compelling, and every bit as problematic, as Socrates' story of knowledge as recollection.


  1. It shouldn't come as a surprise that I find any dependence upon a notion of 'allusion' suspect, but there's an additional point to make about the Meno argument, which has struck me a number of times. The whole paradox of being unable to inquire unless one already knows what one is inquiring into depends upon a misunderstanding of what it is to 'know' or 'understand' something. This is because it doesn't accept that there is anything other than *complete* knowledge/understanding.

    Many thinkers (including Heidegger at the beginning of B&T) recognise that one cannot inquire after something unless one has some understanding of it, i.e., that one must at least be able to individuate the object of one's questioning. For instance, if I ask where my mother is currently, I must have some understanding of who my mother is, which picks her out, or if I ask whether uranium is the most common fuel in nuclear reactors, I must have some understandings both of what uranium is and what nuclear reactors are. However, in neither case does this understanding need to be complete, and thus in neither case must it contain the information which I am inquiring after. I have some grasp of who my mother is (in terms of both her appearance, her temperament, her relations to myself and others, etc.) but I have no knowledge of her present location and little of her youth. I have some knowledge of uranium (e.g., that it is a metal, and its place on the periodic table), but I have little to no knowledge of the details of its common use, or the potential uses for it that have yet to be discovered.

    The notion of a partial grasp of something is perfectly licit, and once recognised it dissolves the paradox without any appeals to allusion.

  2. Still the Platonic view is influential as in theories of education and the propaduetic. We find in the koan and the teaching stories of the Sufis the mystery of how one gets to a new level. Can you teach abduction?

    Just to say that the unknown object is a defeater of the correlationist view leaves one waiting for the other shoe to drop - what sort of ontological system can contain it?

  3. "seeking to make philosophy inhospitable for fideism, thus colluding, willy-nilly, with the worst forms of superstition."

    I'm not sure I follow you here. Would you elaborate a little?

    I followed your links and upon reading your link to "Ecology without Nature" I amused myself by wondering if the Henkin sentence was defined by Leon Henkin the logician or Dr. William Henkin the proponent of Consenual Sadomasichism. Google creates all sorts of interesting connections, no?

  4. dy0~~

    sigh. what would I do without my readers to catch my typos? This is what comes of editing too much or not enough. Of course I meant that Meillassoux thinks it is fideism which thus colludes. Amended the post; thanks.

    I don't know if the Henkins are the same; but Consensual Sadomasochism rather sounds like a strange loop all on its own.

  5. Ombh~~

    Just to say that the unknown object is a defeater of the correlationist view leaves one waiting for the other shoe to drop - what sort of ontological system can contain it?

    Indeed, and I think it's clear that I do not regard it as a clear defeater. But I like it all the same. The ontological system, as would be articulated in one or another descriptive account of the sorts of things that are and can be, runs against some fundamental questions when it comes to the in-itself; either, "on what grounds/with what evidence do you assert these unknowable objects?" or, put otherwise, "what is the point of this extra flourish, since once you have said these unknowable objects exist, that is literally all you can say about them?" As I have said elsewhere, I think all ontological systems (and even asystematic ones) encounter such snags; it's inherent in the project of representing the whole. So I do not count these as objections; what matters is not whether there will be such limits but to what effect one will turn them. As you point out, thee have been many traditional applications of just such limits; the koan is a good example.

  6. Pete~~ thanks much for the comment.

    Something similar to what (I take it) you are saying has often struck me w/ regard to the deconstructive critique of phenomenology and its lingo of "pure and complete presence." Husserl for instance does argue that the eidos of anything is completely before me: when I see my cat I see only one side at a time, but I intend my cat, not just one side of her.

    In the case of the natural numbers, it is easy to see that we do have a "complete" grasp even of their infinitude, in the sense that we can be completely certain of this. This utter certitude is actually quite baffling when one considers that such infinitude exceeds-- I was about to write "vastly" exceeds, but it has nothing to do with vastness-- the number of electrons in the universe. And yet, we can also establish (again, with certitude) that the all the even numbers may be matched one-to-one with all the natural numbers. Harman or Bryant might hazard that one has complete grasp on this denumerable list of qualities and relations of any given thing, but the thing itself evades one. (And indeed, evades everything else).

    If i were to run with the notion of partial, as I take you to be using it, it would be in the spirit of "unpacking" (or "cashing out," as they say in Analytic-speak) the Socratic allusion, more than of rejecting it outright. I have some hesitations about the limits of what such cashing-out entails, but I very much like the general approach of trying to resolve a paradox by making distinctions: we know X insofar as we grasp certain parameters, or with respect to these parameters, but not outside these. One argument would respond that this "pushes the question back a stage;" if I know uranium quametal but not quacommon uses thereof, I am completely informed as to the former, and as regards what I don't know, completely ignorant. This strikes some folks as a sophistry-- I might even say, rightly so-- but at some point, if one tracks knowing down to some kernel (e.g., Russell's knowledge 'by acquaintance') and everything else that tends from it (e.g., knowing 'by description'), one has to make do with a practical, not theoretical, distinction.

    I might be getting you wrong. But I think I am going to be better-disposed towards some sort of just-so story ("allusion") than you at the end of the day in any case.