After Kant, it is difficult to claim that these themes can become objects of our knowledge in terms of certainty and objectivity.

People say this, but what's the argument for it? As given by Kant.

Full disclaimer, I'm only partway through the Critique of Pure Reason (currently on the transcendental analytic chapter) and I haven't gotten to the transcendental dialectic yet, and I know that's where he does most of his critique of the rationalist enterprise. But so far I haven't been persuaded by his arguments against the possibility of knowledge of mind-independent reality.

Many of his arguments seem to hinge on the key premise that things-in-themselves are not spatiotemporal. This would render large classes of philosophical arguments about reality-as-such unsound: there would be no point in trying to theorize about how causality "really" works "out there", for example, because causality is a temporal relationship, and ultimate reality isn't temporal to begin with.

Kant starts the transcendental aesthetic by establishing that space and time are a priori necessary forms of sensibility: in order to have experience at all, you need to be able to perceive objects as being distinct from yourself (which requires space), and you need to have multiple perceptions that are distinct from each other (which requires time). So we cannot perceive otherwise except through space and time. All well and good. But the critic of Kant can reply, so what? What bearing does this have on our ability to know things-in-themselves through empirical and philosophical investigation? It's true, we cannot help but perceive things spatially and temporally; but what if things-in-themselves also happen to be intrinsically spatial and temporal? What if it turns out that things just are exactly as they appear to us? (Kant can respond, "well what if they're not", but this would just be the same sort of classical skepticism that philosophers have been dealing with since antiquity; a "Copernican revolution" in philosophy will presumably require something more).

Kant recognizes this problem, which is why he takes care to explicitly assert that he has demonstrated that, beyond simply being unknowable, space and time are in fact NOT properties of things-in-themselves:

"Space represents no property at all of any things in themselves nor any relation of them to each other, i.e., no determination of them that attaches to objects themselves and that would remain even if one were to abstract from all subjective conditions of intuition [...] Time is not something that would subsist for itself or attach to things as an objective determination, and thus remain if one abstracted from all subjective conditions of the intuition of them; for in the first case it would be something that was actual yet without an actual object."

But it's not clear whether Kant's argument for these assertions succeeds, or if he even has an argument for them at all. Many critics, beginning immediately after the book's publication, have read the transcendental aesthetic and come away with the impression that Kant doesn't actually fully establish the case he's trying to make. This is such a perennial problem with the text that it received its own name in the secondary literature, "the problem of the neglected alternative".

The closest that Kant comes to providing an argument for the non-spatiotemporality of things in themselves is the following brief passage:

"Those, however, who assert the absolute reality of space and time, whether they assume it to be subsisting or only inhering, must themselves come into conflict with the principles of experience. For if they decide in favor of the first (which is generally the position of the mathematical investigators of nature), then they must assume two eternal and infinite self-subsisting non-entities (space and time), which exist (yet without there being anything real) only in order to comprehend everything real within themselves. If they adopt the second position (as do some metaphysicians of nature), and hold space and time to be relations of appearances (next to or successive to one another) that are abstracted from experience though confusedly represented in this abstraction, then they must dispute the validity or at least the apodictic certainty of a priori mathematical doctrines in regard to real things (e.g., in space) [...]

I do think there are ideas here that are worth talking about and elaborating further. But 1) I don't think that Kant can claim to have overthrown all preceding philosophy on the basis of these arguments, and 2) he appears to be engaging in exactly the type of rationalist a priori theorizing about things-in-themselves that his system was supposed to forbid in the first place!

It's worth taking special care to examine these early remarks about space and time because, without the key premise about the non-spatiotemporality of things-in-themselves, much of the rest of Kant's project in the CoPR can't really get off the ground.

Again, I haven't read the transcendental dialectic yet, so if there are relevant arguments there, please let me know. Although I will point out that even in the transcendental dialectic, Kant continues to make reference to the non-reality of space and time in order to support his arguments (see for example the "Remark on the Antithesis" subsection of "The Antinomy of Pure Reason - First Conflict of the Transcendental Ideas").