Transcendental Knowledge?

[Neo-Scholastic]

…I'm not quite sure what to make of Idealism, of which I still have not seen a convincing rebuttal…

Just because we only know the world by means of the senses does not mean that you cannot reason about the parts of reality that exist apart from the senses. Form this process someone can know of real things that exist apart from particular knowing subjects. For example, the truthes of mathematics are discovered, not invented. They are necessary truths that do not depend on a knowing subject for their validity. Secondly, perceptions are contingent upon the existence of an independent perceiver. The perceiver must exist prior to its perceptions, unless you posit a perfectly self-perceptive preciever ;-) or a real unifying and insensate principle that binds experiences into identifiable knowing subjects.

"The function of the understanding... constitutes the basis of empirical reality."

“The realist forgets that the Object ceases to be Object apart from its reference to the Subject, and that if we take away that reference, or think it away, we at once do away with all objective existence.”

Is it true that the object of consciousness ceases to exist apart from a knowing subject? Again I would refer to the truths of mathematics whose objects are immaterial and thus can be known by the intellect apart from any particular sensible form.

With respect to the "Objects in themselves", the fact that we are limited in our understanding and do not observe objects in their fullness all at once doesn't mean we don't know about the objects. Why must we think that since we do not have god-like omniscience of something that the something remains ineffable. I say it just means there are things about it that you don't yet know. That notion is hardly problematic.