}∅{ The Full Set

The Full-ness of a Body

This is not what I intend to write on the Subject of Infinity, but it is a projective chain of thoughts. It is a tracing of a yet un-consolidated line of interpretation.

Fido the Yak presents a symbol/concept which – and I’m not sure of its origin or complete meaning – is quite intriguing in the light of my recent readings on Spinoza, the Infinite and mathematics. What I would like to call the Full Set. This is how Fido describes his imagination of it

}∅{ is like an in-cept, yet it emerges discursively as a response to the arche. How does it originate? Autopoietically? Or do we acknowledge that it is a con-cept with the arche? (Like its withness with the empty set.) I talk about }∅{ extemporaneously because the extemporaneous describes it. If you can be in a state of consciousness that includes nothing while excluding nothing then }∅{ can describe such a state of consciousness, or a goal of thinking, a guideline, better. Maybe you’d want it to represent an empty concept, I don’t know. I say now the }∅{ expresses the acknowledgment that the explanation never exceeds its explained, which is a way of saying it never accomplishes what it sets out to do, and that “foundation” is a metaphor—you may see why I call it “the breach.”

We are running in similar directions, but I prefer in my own thinking to not think of it as a breach, so much as a whole plenitude, close to Deleuze’s Full Body, the Body without Organs. (Here my thoughts proceed from his in-spiration, in perhaps an appropriation.) It is closely related to Spinoza’s notion of the Infinite as something that cannot be broken. So, in my hands, it would describe the infinite proximity between any two limits.

It emerges from Spinoza’s diagram of bound infinities, which proclaims that within any bounds there are an infinity of magnitudes which are themselves divisible:

It is important to see that for Spinoza these are magnitudes(and not simply points on an imaginary line, which are at best ab-stractions). As magnitudes, they are FULL. Now, if we are to play with symbols, the requisite symbol for Spinoza’s point about bound infinities would be something like }∞{, which is to say, between any imposed limits, there are an infinity of magnitudes buried. Also importantly, and somewhat divergent from Badiou’s concept of Count-as-one, the symbol should not be {∞}, because for Spinoza any (abstract) internal bounds already, already refers to, or references to some degree a determination that lies outside of it, as in his Letter 12 diagram…

The sub-section between AB and CD {}, already includes comprehension of the circle circumstance itself, }{. Or, the internal count-as-one (set), really is composed, determined by the bordering edges of something beyond it, as a mode of comprehension, consciousness itself.

Playing With Symbols

So, while Spinoza in Letter 12 seems to be presenting something of a }∞{ determination, what would be the intuition of the full set }∅{, which is our subject here mean? It is not that between any two abstract limits there is some sort of nothing, or emptiness (for Spinoza denies the ontological consistency of the void). It is rather that the act of distinction and limitation itself drives itself toward the impossibility of separation: as we enter into the infinity of magnitudes (let us start with Badiou’s count-as-one teeming/erupting with multiplicities) {∞}, we are pre-positedly forced both outward…}∞{…but also inward to the full set itself…}∅{…the way in which what lies between simply cannot be divided at all and remains unbroken. It is not the sheer multiplicity that lies between any borders (inside, or outside), but rather the implicition that there is no “gap”, the very fullness of Being, from which mathematics, figure drawing and set-making composes only an abstraction, an imaginary class. It is for this reason that for Spinoza rational thought leads ultimately to an Intuition of immanent wholes and a speed of thought. 

Or, if put another way, any conception of emptiness, or lack, or nothing {∅} (whether it be mere psychological wanting, or mathematical 0), diverges upon the fullness of being, showing itself to be a figment.