the four principal theses of the 'metalogical plato' project (insomniac version)

1. The elenchos, grounded in the duality of the ti esti and peri tinos questions,* traces a disjunction of consistency and completeness.

2. By default, reflexivity aims to synthesize the answers to the two questions, but the only true reflexivity is virtual and negative.

3. Incommensurability raised to the level of the concept, yields incompleteness. (This matters exegetically because incommensurability is obviously accessible to Plato.)

4. The form of the Good is - well, you know what I think it is! Diagonalization!

*(ti esti: what is X? peri tinos: X about what?)

Colloquy with a friend

g: What sense of ‘virtuality’ are you invoking when you claim that reflexivity is virtual? Is this to say that true reflexivity cannot be actual(ized)? Does this have as a consequence that, as real but impossible (to actualize), true (i.e., complete-consistent) reflexivity constitute a kind of transcendental condition for incomplete-inconsistent subjectivity? Does desire play a role here with respect to reflexivity and diagonalization (form of the good)?

j: First pass: 1. I concede upfront that “virtual” may not be the best term for my purposes. I haven’t found one that works better, but in the event, I’d jettison it happily.

2. For me, in this context, “virtual” belongs to the triple of alternatives actual/virtual/nonexistent. The contrast is among the theses O: “Self-reference is actual (in at least some cases notably pertaining to perfection and completeness)”, C: “There is no self-reference,” and G: “Self-reference is virtual.” I borrow the term, “virtual”, as you know, from Deleuze’s contrast of the virtual with a potential that stands in correlation with the actual, but, as you would expect (given the differences in ontologies and projects, not to mention assessments of Plato), without conforming to the specifics of Deleuze’s usage. In fact, I’m a lot closer to using it in places Badiou uses “generic”. (With my choice of letters above, I underline that there’s a straightforward translation between the position I reserve for virtual self-reference and Badiou’s generic orientation – viz. by pairing actual-self-reference with the ontotheological orientation, and no-self-reference with the constructivist orientation. This is a special case of the heuristic that propositions “about” the infinite can generally be intertranslated with propositions “about” self-reference, but a change of vocabulary is often perspicuous – it wouldn’t seem very illuminating to try to call an instance of reflexivity “generic”, at least it wouldn’t strike me as helpful.)

3. I take it to be the most radical lesson of the Meno that there is no sense to the third (vitualist, generic) thesis that can be specified in advance of a formal experimentum/experience like that of diagonalization. This, because a concept of meaning does not function neutrally in the discussion of whether there is a third position to be had. To take the perspective of meaning, is, in a sense, to become systematically blind to what takes place and is shown in/at diagonalization. The latter is not something that has a systematically preassigned place in meaning, but rather something that happens to meaning. (Here, of course, we’re close to early Derrida.)

4. Self-reference is virtual, when true, because, in the only instance of self-reference that we have that’s definitely referential (true about something), a new form arises which can be described as self-referential in a way, but which can also be said, rightly, to lack self-reference. “There’s no self-reference in the Godel sentence,” is true, even if often misleading. And that’s important! At a certain point the “self” of self-reference has to either preserve itself and become imaginary or else yield to truth, which is always contamination by an Other. (Cf. early Derrida again.) We recapture in this way the rational part of the dialectic of self-certainty and truth in Hegel, while diverging, at the right point, from the imaginary recapture of truth by Spirit.

5. Ultimately, I think that what I’m presenting as “virtual self-reference” gives a resolute interpretation of the epekeina tes ousias.

6. "Is this to say that true reflexivity cannot be actual(ized)?" Yes. Maybe with some caveats about conceivable fancy quantum phenomena, the guess is that self-reference, at least general self-reference (self-reference in an open referential context), is constitutively excluded from being, as much as (and on pain of) contradiction.

7. Not quite, I don’t think, and I’d like to hear what you have to say about this. I find that when working at this level of abstraction what order of precedence, what order of rank, we assign to the different terms of art and their associated conceptual operations on each other matters a great deal. (It’s also possible that this is just a philosophers’ conceit.) This is illustrated above, in the reversal of the priority between meaning and diagonalization. I’d be inclined to say the same thing about any horizonal or asymptotic notions, viz. that diagonalization is something that happens to a horizon, and after what ought to have been a transcendental limit, in passing through it (negatively, of course).

8. I intend “true” in a perhaps stronger and more partisan way than you were reading it at first. So, as you know, I take it that the synthesis of consistency and completeness is *false*, even though it is what is prereflectively desired and posited as the regulative pole of meaning. (Desire and meaning are part of the same process here, or at least on the same level relative to repetition and event). So when I speak of *true* reflexivity, by contrast, it’s not intended to indicate the desired consistent-complete reflection, since the latter, as transcendental condition and object of desire is precisely false, but rather to indicate what makes truth – the experience of incompleteness, including that of inconsistency as one of its moments – out of the ambivalent relation between foreground consistency and background completeness in ordinary subjectivity, which is also to say, what brings the experience of the subject into a temporarily less false relation to “its” being, (“its” necessarily in brackets or a stronger form of erasure, since the price of this experience of truth is a sort of death, the displacement of own-being, which, however, is not, I think the same jouissance as that of the death drive. (What we say about the Good as diagonalization here seems to meet Bataille’s criterion for a rational relation to the unsurpassably negative in self-consciousness, Bataille being, with Sartre and Levinas, one of the few figures to lay down criteria for a rational metaethics.)

9. Running out of steam. The essential thing is what I’ve said in 8. Textually, my gambit is to link Sartrean conversion (the distance fleetingly taken from the ideal of being, the in-itself-for-itself) with Platonic conversion, contra everyone’s intentions (except now, as it will appear, following Badiou).

Forgive the jargony prose. 

g: Sorry for my lateness in response. Thanks for your detailed reply!

So, we have the triplet O-C-G: the ontotheological assertion of the actuality of reflexivity, the constructivist denial of the possibility of reflexivity, and the generic assertion that reflexivity is virtual. I’m not well-versed enough in Badiou’s terminology to really be able to draw out the implications of the language of ‘generic’ here, although I would venture a guess that it has to do with the diagonal movement that draws a transversal line across the actual and the impossible; this feels like Hegel, but for the fact that the fact that this line is precisely not actual, and, following Deleuze, what we understand to be virtual does not even resemble its actualization: as you say, the lesson of Meno is crucial here – no virtual or diagonal line results in something which can be predicted based on what is actual. When I was pushing in the direction of an explicitly transcendental program here it was in more in the vein of Maimon than Kant, i.e. reflexivity as a genetic principle of what we understand to be real subjectivity, rather than a condition for its mere possibility.

The difficulty then seems to be, and here we’re back on metamathematical terrain, whether it is possible to formalize this structure of unpredictability, given that the very way in which you rightly point out that meaning is tied to its emergence and yet refers to the context that determines it, yielding a double structure that precludes its being (actually) grasped in advance. But your reversal makes this feel all too Hegelian again, namely: if diagonalization isn’t conditioned by the horizon, but rather what turns out to be called the ‘horizon’ is conditioned by this movement of escape, then I’m waiting to hear more about what ‘secures’ the contingent status of such a movement, on pain of discovering again that this apparent surpassing is already contained within the very structure of what is surpassed – dialectics all over again (and again and again, as always). That is, can there really be a meta-formulation of this movement if it is precisely intended to capture evasion or elusion, the diagonal?

Perhaps it’s not a new thought for you, but it’s new to me – I’m fascinated by your coordination of background and completeness, foreground and consistency. I want to hear more about that. And I’m rather sympathetic to the idea that what would be the convergence thereof, complete-consistency or the actually reflexive, provides us with a name for death – even if I’m not convinced yet that this is its privileged name. But a question that’s actually worth asking here (by which a question which might actually be answered) is, what about the present conditions are such that prereflectively we desire such actual death? Why is it, in other words, that this is the sense of ‘true’ reflexivity that we’re left with?