I'm a bit confused when trying to understand second hand accounts of Kant's thesis of transcendental idealism, that debate the ontological and epistemological status of the noumena, since I'm unable to grasp how Kants conception of cognition arrives at such a thing.

I ought to read CPR, but I suspect I might be none the wiser afterwards.

Suppose I accept kants basic thesis, including the transcendental deduction of the categories and identification of space and time as a priori forms of intuition, and their role in the synthesis of my perceptions and cognitive judgements. In other words as I roughly understand it, I accept that the process of cognitive judgement grammatically presupposes the use of certain concepts , which marks such concepts a priori and exempt from the possibility of doubt, with doubt itself being a posteriori in the sense of being a consequence OF cognitive judgement. Then how do I leap from this fairly uncontroversial position to a concept of noumena?

Is the noumena deduced? I can't see how, because by definition, it would then have to be either an empirical deduction and hence empirical, or a transcendental deduction and hence a category of understanding , and hence either way, not noumenal by definition.

Is the noumena inferred through logical induction as a necessary but unknowable transcendental cause? I can't see how, because I understand that for Kant, causation is a category of understanding for relating empirical observations. And to my understanding, kant never discussed a third possibility of transcendental induction, which would seem nonsensical.

The only way I can therefore arrive at a concept of the noumena, is through a thought experiment that involves me to fictitiously conceive of transcending the bounds of my own cognition and to then conclude that the world in itself is distinct from my understanding of the world. But Kant has surely already ruled out that possibility as being utterly nonsensical in being in violation of the bounds of cognitive closure as delimited by the a priori conditions of understanding.

It seems therefore to me, that transcendental idealism only makes sense when considered in terms of the conditional assertion "IF it were meaningful to talk of transcending the bounds of cognition, the world would be conceptually divisible into appearances and things in themselves." - to which it responds in the negative by rejecting the premise.

In other words, the conclusion of transcendental idealism given its stated premises, seems to be neither ontological nor epistemological. The conclusion cannot be a positive assertion of mind-dependent knowledge and phenomena on an empirical level of appearances on the one hand, and of an unknowable reality of "things as they are in themselves" on some 'transcendental' level. Neither can the conclusion be merely epistemological in still accepting the conceivability of noumena but denying knowledge of its nature or existence.

The conclusion of kants premises can only amount to an outright denial of the conceivability of noumena, and in turn, a denial of the conceptual dichotomy of realism and idealism.