p.434-435. It is the category of organism as indivisible then, which when implicitly misapplied causes this dichotomy of not quite right conclusions we perceive as a paradox. The intrinsic precision of the actuality cannot be reached by the imprecision of the extrinsic boundaries of the category, and so we oscillate between the two closest approximations:
Paradoxes, then, are errors of intrinsic incompatibility in a compartmentalised, categorical and dualistic logically descriptive system. … From a different vantage point, then – e.g. from a more detailed system of categories -we will see that the paradoxes can, and often do indeed disappear. … by explicitly modelling the pivotal detail inaccessible by the categorical framework rendering and generating the paradox.
The category, then, serves a transcendent and transitive (trans-biased) representational function of power over the territory beneath the category – this territory being namely emergent “meaning” and sub-representation. Language or syntax in this sense is thus transcendent to and emergent from semantics or embodied meaning. Yet syntax, in turn, symbiotically modulates semantics from above, serving as a medium or lens through which embodied meaning can be manipulated and further elevated.
So, the way we communicate concepts effects the way the concepts are represented, and those representations in language then also condition the manner in which the communication takes place, as well as the conceptual structure itself?
p.439. This is the simplest “answer” to the paradox, which was honed in the nondual traditions themselves. Opposites, such as the opposing conclusions or categories of the paradox, are simply acknowledged as intrinsic elements of each other. Like yin in yang, and vice versa, they are “identical opposites”. Nondual traditions embrace the paradox because they know that the problem is not one merely of representation (illusion or Maya), in a dualistic and oppositional set of categories. The problem sometimes happens then, that in the embrace of the paradox, they can often tend to hold onto it as essential to reality or nondual philosophy itself. The paradox must be remembered as a dualistic function of illusion and perspective, and it must be conceived free from dualistic attachment in order to retain the possibility of seeing it as one, from a different categorical perspective.
p.441. Can reason itself, through the acategorical imperative, reach into the categorical fissures of common-sense – the paradoxes – and find their common-ground in some kind of deeper level of fluidity and emergence – some nondual form of rationality that resolves paradoxes naturally?
p.447. The Infinite has no internal conceptual relation or multiplicity which can be abstracted free from the derivative relation of the aspect infinite or its modal interfaces, which are its conceptual modalities – its senses. Abstraction into relation is this interface.
p.460 … polarity is the most general function of the world of conceptual relation, which of necessity includes the world of logic. In his [Zeno's] paradoxes of motion, we will see plurality expressed through the infinite divisibility of change, and through the same underlying form the simultaneously infinite division of time is demonstrated to be the equivalent of the indivisibility of eternity manifesting in the Zenonian instant. Motion, then, is not so much denied, as demonstrated to be indivisible, continuous and ultimately ONE eternal and instantaneous Unity – the Parmenedian Being-now. And this is naturally in conjunction with our PNDR “infinite division equals indivisibility”, and its Ariadnian resonance into the chord of “infinite determinism equals indeterminism” and its eternal-NOW.
p.463 If we “pulverise” the category of “thing” upon the exoteric ambiguity hidden within it, we can divide it into two categories; individuals and dividuals (e.g. a-tomoi and holons) Zeno’s argument merely demonstrates, and purposefully so, the impossibility of the absolute individual (a-tom), with respect to the concept of size, and thus indirectly for the implicit holonic logic of sets, with its implicit unity in the ONE-ALL.
p.469. Verelst demonstrates that all of Zeno’s paradoxes of motion (PM) – including even the stadium paradox – can be subsumed under the timeless and instantaneous form of the general paradox of plurality (PP), rendered into mathematical rigor, above, and explained in her paper in the formal language of domain theory.
It is the uncountable infinite of the ignored PP which already exists as the actual infinite underlying all of the PM. And further, it is divisible movement that takes on the time-ordered, stepwise function of the potentially infinite, never able to reach the immanent pole of the actually existing omni-axis within which motion acts.
p.476. As we have seen throughout mathematics and the conceptual embriogenesis itself, immanence breaks the trans-bias to effect a transcendence into new operations and identities. Likewise Zeno’s naked paradox radicalizes immanence to break the transcendent bias of dualistic representation – i.e. diction – shocking us, generation after generation into various and sundry attempts to refute him. All the while, in this very interface – in this refutational dance with Zeno himself – we move closer and closer to operationalizing and vindicating the polarity and truth hiding in the naked core of his ubiquitous paradox.
It strikes me here, that with enough of a stretch of the mind, the resolution of these paradoxes will occur spontaneously. It makes me think of the sages saying that when we realize the real, the actual, in its simplicity, we will tilt our heads back and laugh at the sky! I believe we will begin giggling soon…..