Every manifold in some way participates unity.

For suppose a manifold in no way participating unity. Neither this manifold as a whole nor any of its several parts will be one ; each part will itself be a manifold of parts, and so to infinity; and of this infinity of parts each, once more, will be infinitely manifold; for a manifold which in no way participates any unity, neither as a whole nor in respect of its parts severally, will be infinite in every way and in respect of every part. For each part of the manifold-take which you will-must be either one or not-one ; and if not-one, then either many or nothing. But if each part be nothing, the whole is nothing ; if many, it is made up of an infinity of infinites. This is impossible: for, on the one hand, nothing which is is made up of an infinity of infinites (since the infinite cannot be exceeded, yet the single part is exceeded by the sum) ; on the other hand, nothing can be made up of parts which are nothing. Every manifold, therefore, in some way participates unity.

Elements of Theology, $1

Objection 1 : Unity does not (need to) participate in unity & per the argument above, that which does not participate in unity is non existent.

Answer : Unity (Godhead) indeed does not participate in unity as it DOES NOT belong essentially to the realm of beings. It is consequently niether non-existent nor one. It is many-one, in contrast to beings which are one-many. Unity is the realm of Gods (shown later in the Elements of Theology), all of whom are beyond being. This objection confuses the ontic & henadic realm.

Objection 2 : A part & whole can be infinite, of same cardinality. Eg, set of even numbers & natural numbers.

Answer : This confuses qualitative (essential) & quantitative (accidental) infinites. For even the set of even & natural numbers must fall under a concept determined in our minds in the very least. An undetermined concept which has its content indefinitely deferred is no concept at all. The limit Proclus aims at here is a conceptual limit, which must obtain in the mind or in reference to that which is external to the mind or both. Deny this & reality becomes unintelligible. But the one who claims reality is unintelligible regards this claim to be intelligible, refuting himself.

Objection 3 : Nothing is some thing or the absence of all things or niether a thing nor no thing, hence a conglomerate of nothings can be some thing.

Answer : If nothing is taken in the sense of being, as things, then it does not undermine Proclus's argument, as his argument targets a different claim. If nothing is taken in the sense of absence of all things, then the claim is ill-defined as it provides us no postive concept. We can treat such person as one who isn't in conversation with us. If nothing is taken in the sense of some intermediary which is niether existent, nor nonexistent, then it amounts to a suspension of LNC, which is just a convenient appeal to the world being unintelligible. But as it's shown in Answer 2, this is self refuting.

Objection 4 : Participation is too vague & of no explanatory value. (Given by our master Aristotle)

Answer : This is indeed the best objection & where the life & death of this wonderful claim depends. It concerns the relation between the henadic (Godly) & ontic (beings). First of all, for X to participate in Y is for X to be determined by Y. And yet, it would be impossible for Y to determine X if they were completely distinct from one another. So both X & Y must exist in a community of ground-consequent, cause-effect etc by sharing some aspect (not all) in common. Finally, there's the question of whether X can influence Y in any respect ? The answer is a definite yes, but only because the henadic isn't limited or restricted by the ontic, so the Gods within us (the divine) cause us to return to them. In truth, this is just a more elaborate form of X being determined by Y, except in this case the determination is internal. All of this implies gradation of beings, with those closest to the henadic realm being more divine. As for HOW this relation works in experience, this can only be grasped via experience & by this we mean noesis.