Mind the Gap

The distinction is actually very simple, and I’m sure you will grasp its ‘essence’ immediately once you see it. Roughly, the difference (and gap) here between the countable and the uncountable infinities is that between the effable and ineffable quantitative aspects of the absolute. “Time-order” here does not mean time itself. We have to break time down into its deeper-level (polar in this case) elements. And this naturally corresponds to the distinction between transitive and immanent forms of time, respectively. So, a time-ordered or step-wise process is essentially a linear one–a trajectory, regardless of whether it traces a nonlinear form–and hence it is transitive (as well as classical, as we can see here the solid/particle bias in the abstracted trajectory found in classical mechanics, and also in the wave-function in STILL-CLASSICAL quantum mechanics…classical in the Prigoginian sense). Zeno, tracing the proto-ontological form of fundamental mathematics and the continuum, is essentially dealing with the interface between the finite and the infinite as well as the transitive and immanent/transcendent axes. And where that resolves with exhaustion is always the indefinite…e.g. the arrow never reaches its mark, and time has (only apparently) come to a stop in the regressive immanence of emptiness and NOW.

This is the negative or deconstruction phase, but we must resolve to the positive correlate in reintegration through and through. What Zeno demonstrates is that a time-ordered sequence of division (or demarcation) cannot exhaust (or construct) continuity. Continuity, as infinitely divisible and infinitely “divided” (folded or differentiated through and through, always and already) must exist prior to any regressive step-wise process. This is where the principle of nondual rationality must resolve, which points ultimately beyond the rational numbers (identities) themselves, and into the “irrational” or transrational numbers which unfold at deeper levels on the axis (emptiness or freedom) opened up initially with the ratio, namely that of immanence and transcendence, which is only transitively explored through any step-wise process.

Simply put, as with Spinoza’s escape from modal (structural) thinking, the route out of the labyrinth of the continuum must take the form of an escape from the (transitive) regress. We must come to see our role in abstracting out *aspects* of deep infinity in tracing our trajectories through time in our interfacing with the absolute. And in this Zenonian sense of always already, infinite divisibility (through and through) equals indivisibility, or Zeno’s Parmenidean Being-now. This is not outside of process, but simply an emphasis on the the stasis aspect of the absolute. Because, of course, time doesn’t stop merely because (in time) we fall into a transitive regression into immanence.

So, we are effing the ineffable through the lens of the Zenonian core paradox of plurality (which we’ll get to a bit later), and this traces the structure of the modern mathematical continuum, which has resolved Zeno’s paradox only operationally, syntactically, unconsciously. The paradox, to this point in orthodoxy, has not been resolved semantically or meta-mathematically, simply because the immanent-transendent axis remains un-integrated, or implicit. So Verelst shows that Zeno’s structure in the paradox of plurality (the form which they all share) is divided “through and through”, or as we’d say, “always already”. This is already outside any step-wise or time-ordered process or algorithm, and points to infinite immanence and multiplicity. As opposed to tracing a single trajectory, we move into radical plurality, and this is the key step in understanding the move into real complexity (immanent and post-classical causation) still on the horizon in the sciences, as well as to understanding why the attempts at refutation of Zeno’s paradox have all failed. These attempts have injected non-Zenonian premises (namely transitive time, or time-ordering) into the argument and ended up as straw-men.

What then exists in the gaps of the incompleteness of effing the ineffable? The ineffable real. It’s effing ineffitable!