For you have often heard that the greatest thing to learn is the idea of good by reference to which just things and all the rest become useful and beneficial. And now I am almost sure you know that this is what I am going to speak of and to say further that we have no adequate knowledge of it. And if we do not know it, then, even if without the knowledge of this we should know all other things never so well, you are aware that it would avail us nothing, just as no possession either is of any avail without the possession of the good. Or do you think there is any profit in possessing everything except that which is good, or in understanding all things else apart from the good while understanding and knowing nothing that is fair and good?
The explicit introduction of the Idea of the Good into philosophy by Plato’s Socrates comes in these lines at Republic 505. How do we interpret this pivotal speech? First, we note that Socrates leads off by disclaiming that it introduces anything new, insisting instead that he is simply making a presupposition of ordinary language explicit, even while defamiliarizing it. The shock of the recognition of the familiar under a very unfamiliar description is intended here. (I will argue that we should receive this as the shock of the recognition of metamathematics as ethics. Put that aside for the moment.)
Second, even the articulation of the thesis raises significant difficulties concerning the equivalences or passages implied here. Lacking this (lacking knowledge of this?), everything else (everything else of knowledge? knowledge of everything else?) does not avail us. The most important thing to note immediately, even if only to hold it in reserve for later discussion, is that this speech on the good moves, perhaps analogically, perhaps not, between the levels of concept and object, distinguishing them in general, even while mention of the good moves through them in a nice rhetorical chiasmus: KPPK, knowledge (concept-level) – possession (object-level), (non) possession, (non) knowledge.
Bracketing both of these these important lines of investigation for a moment, two possible ways of schematizing the situation described by the thesis that relates “the good” to “everything” or “everything else” can be distinguished. Take the Good to be a critical point of unity that’s in some tension with the totality indicated by “everything”. In one version – figured, say, by a pyramid or cone, every effort toward wholeness also orients the thinker to the apex of the figure as a distinguished point. The clearer the whole structure, the more one has in view, the more clear the crucial point is, as source, origin, or pinnacle. To see a pyramid (cone) as a pyramid (cone) is to see it in relation to the apex through which it is defined. This is the picture that seems to express the topology of ontotheology: the view of the whole orients us to the One. They may be nonidentical in that the One is transcendent, but they’re deeply compatible. This is a monist picture.
But in another image, also decisive for Greek mathematics, the crucial point is decisively lost when we grid out the “whole”. For this whole is always a false whole, and the grid not its transcendental map but itself an element of the situation it describes/selects. (In fact the being of the grid is our link to a repressed element of the situation: the missing object appears through the materialization of the concept.) In this second schema, when the critical point is seen, the whole is refuted as contradictory, and instead of the ontotheological relation whole -> one (where the arrow separates an asymptotic transcendence to which the whole nevertheless leads) philosophy is charged with thinking the relation all/one (where the bar, the original negation, codes for the inexistence of the whole). But since there is no space in which these two principles could be separated as contraries that does not rather belong to one term or the other, this duality is the source of an unmediated intimacy of contradictories. A second relational apprehension of the one and the multiple is then possible, but only as negating the wholeness it transcends – rather than a pyramid, a tangled hierarchy. In this way the Good as diagonalization complicates any purported decision between arche and an-archy.
Colloquy with d
d: what exactly do you mean by “grid”?
j: the equivalent of Cartesian axes back-projected on the Pythagoreans, so, basically the Cartesian plane, but where we only think of the rational lattice-points as knowable.
d: so i see immediately from what you just said that the grid leaves out all irrationals/incommensurables and so is not “whole” (and never can be, is not just accidentally partial, i.e. not fixable, fillable)
j: intended to, but fails at a certain point either to name it exactly or to leave it out comfortably.
d: ok, that seems important and maybe worth saying explicitly
j: since we can construct this point very easily relative to the grid, the length from the origin to (1,1)
d: ok, i think i see. so it’s something like, neither is the grid able to account in its own terms for the irrational (for fairly obvious reasons) but neither can it claim that that’s just something it’s not supposed to care about, something comfortable other than itself
j: yes
d: which is a different sort of “well we can’t really talk about that” than in the monist/theist picture
j: right, not a whole that refers to the One as its cause and capstone, even if transcendent,
d: where of course we can’t talk directly about god but we can do what we can do, etc
d: so, “and the grid not its transcendental map but itself an element of the situation it describes/selects” so is that an additional observation or a consequence of the former?
j: related but additional.
transcendental ~= transcendent
(sorry)
d: oh i glossed right over that. so wait, is that supposed to be “transcendental” or “transcendent”
j: “transcendental” there is correct. meant in Kant’s sense of transcendental logic, i.e., what determines the form of possible objects without being itself objective. there’s a kind of “transcendence” there in that the categories are not objects, but they’re nothing but the forms of possible objects. so, like in aristotle, a “transcendence” that just takes one step back to re-embrace the object. for Kant, recall, the “transcendental” use of reason is legitimate, but not its transcendent use,
e.g., a proof of the existence of god.
d: right, right (i remember now that you remind me )
j: i’m attacking both. but not in the same way. a transcendent god, i propose, is knowably unreal. while transcendental categories, i propose, are periodized. you create them by putting a certain structure off-limits as content. and eventually you have to pay the debt. in a diagonalization / event / incommensurability -type moment. so there’s an interval, an actual temporal interval and a logical one, where you can put out of play the fact that the map is part of the territory. but that interval has a beginning and an end. (i’m clearly very close to badiou here, and anyone else who understands the consequences of diagonalization)
d: hence “periodized”, ok, interesting. i like this
d: clarifying grammatical question: when you say “you create them by putting a certain structure off-limits as content” do you mean you disqualify something from being structure and call it content? or do you mean you say that a certain structure cannot be content?
j: the latter. it will count as form.
d: ok. so something like, this cannot be the content of any experience (cognition, whatever), because of reasons, and in so doing there is created a certain structure to thinking/being/something. but out of that structure that supposedly excluded “this” comes an experience of that very “this”, i.e. diagonalization. something like that?
j: yes. a good example: the properties of the code as code are not supposed to count as message. (might just be a good example, or might be the paradigm; i’m not sure.)
d: ah, yes, i think i’m starting to see (again). code needs to be “transparent” in order to work, in this sense.
j: yes