The Theory of Perception

A perception, is a particular understanding of some whole, corresponding to a form of the singularity.
The conception of substance is the absolute totality of all forms, the singularity itself.

Skolem's paradox is a result of the downward Lowenheim-Skolem theorem, stating that a countable first order theory has a countable model. The theory of set theory has a countable model, though it necessitates the existence of uncountable sets.

Let us take set theory as the domain of discourse and examine the conception of uncountability of which a countable set is a form. We are not saying that a countable set is a form of an uncountable set, but of the idea of uncountability. It serves as a realisation of an uncountable set, a perception. To understand the issue of uncountability one must harness understanding of all forms, accumulating the understanding of a totality of perception. There may be uncountable perceptions in which case this would fully realise the issue at hand. There may be particular aspects of perception uncountable themselves. The understanding of the structure of the singularity-form principle is long and tenuous; one cannot ever hope to fully realise each particular branch but only the sum union of all such branches. In fact isolating a branch is dangerous, the model or perception may be countable, in this case, which serves as no contradiction because the issue of countability does in fact constitute the identity of uncountability which must be treated as a structural extension rather than a propositional negation.
Human perception may 'fail', but it allows us to percieve of that which is a superstructure to the immediate belief. It is in fact possible to conceive of a perception, which would require knowing all such sub-structural perceptions, whether they may be different realisations in different logical system, or to some other context. Such perception can never 'fail'.

I elaborate further on previous discourse by analogy, suppose there is one who sees the shadow of an object and identifies it as a particular essence of the initial object as singularity, though the shadows does not constitute the structure of the object at all. In fact the shadow has nothing to do with the object but that we had a preconception relating the two. The shadow still identifies with the projection of some being of the object in question. Take the shadow to be a countable set and the object to be the understanding of uncountability. They are only related in a priori knowledge to this degree that countable sets can be used to construct uncountable sets. Take away the a priori knowledge and the shadow crumbles, it cannot possibly be recognised as any realisation of uncountability (which incidentally would be unbeknownst to ourselves). After all, can we blade the shadow for providing a false outlook on the subject matter, it was our perception to fault - the shadows professed no more than what it is.