It's kind of strange to me that with the decline of Logical Positivism, that there has been so little rethinking of the problems and prospects for transcendental idealism.
Every variety of transcendental idealism fails because it ends up violating its own strictures about what can and can't be said. Kant- causality only applies to things in the phenomenal realm (due to the mind's constitutive powers), yet objects in the noumenal realm also cause the mind's experience of them. Heidegger- beings only exist in a substantial way as present-at-hand abstractions from Dasein's world of projects, yet without Dasein there would still be (be!) beings, just not being. Logical Positivism- Only those assertions which are empirically verifiable are true or false. The previous assertion is true. Putnam's Internal Realism- an independent world does not constrain our theories about it, and causal connections with the independent world prohibits us from being brains in the vat (I need to do more work to show that Putnam's incoherence is a species of the broader incoherence; really it's probably best presented as a bad reaction to that broader incoherence). Dummettian anti-realism- Fitch's paradox (this is probably a problem for all the views under consideration; the claim that it's an instance of the broader problem here is something I'm arguing in a paper right now).
The dominant reaction to all of this has been to lapse back into a pretty unreflective realism, with almost constitutional irritation at those still moved by the Kantian problems with unreflective realism (leads to implausible skepticism and unworkable antinomies).
As far as I know only John McDowell, Graham Priest, and the new Heideggerian Realists (Alva Noe and Graham Harman in different ways) have work that is relevant to taking very seriously the initial Kantian impetus while being congnizant of the problem.
Here's some ignorant speculation (I don't understand the following thinkers well enough for it to be anything but). Among the informed responses to this situation include: (1) newly enforced quietism, (2) dialectics, and (3) animism/pan-theism.
(1) Quietism tries to avoid the contradictions in transcendental idealism by further limiting what can be said. (2) Dialectics either (2a) tries to make sense of a contextually situated interplay between the noumenal and phenomenal to license talking about the noumenal, or (2b) involves indexing phenomenal speech such that there is no contradiction and no collapse back into simple idealism (which happens with Fitch's paradox, which must be understood in this broader context). (3) The animism/pan-theism response is to characterize reality as being in some sense already intentional and normative in such a way that you don't fall into simple idealism but also avoid the problems that Kant attributes to realism (and here the Kripke-Wittgenstein paradox has to be seen in the broader light of the initial drive towards transcendental idealism).
Some of Schopenhauer can be presented as (1). Russell's type theory, Dummett's open-textured notion of proof, temporal indexing responses to Fitch like paradoxes, and possibly meta-linguistic resolutions of truth paradoxes can be presented as (2b), and possibly Heidegger's interplay between earth and world in the art lecture is an instance of (2a). McDowell can be presented as a combination of (1) and (3), while Hegel can be presented as a combination of (2) and (3). I don't know to what extent the pantheistic and animistic ideas of Strawson and Chalmers (3) can be presented in this light; and the characterization of Harman probably only works in terms of (3) if you already (not always, but rather prior to reading Heidegger) thought the modes and structures of Dasein where particularly mental/intentional.
What are the other options? Should Priest's Beyond the Limits of Thought dialetheism count as an option alongside these other ones? Maybe it's the null hypothesis for how one could remain a realist? Then his critique of Kant, Heidegger, Wittgenstein etc. all work to argue against transcendental idealist approaches. I need to re-read his great book. I read it right when it came out and I didn't know that much at the time.
I realize this is just casually throwing a lot of things together. Part of what really interests me in both Schopenhauer and Heidegger is that while both were transcendental idealists, both undermined canonical forms of transcendental idealism of their age, and also both did the most to provide resources for plausible forms of realism. Some day I'd like to be able to think that through in a more systematic way, but as my favorite philosophers Bon Scott and the brother's Young once argued:
I know Monty Python has this whole thing where all Australian philosophers are named Bruce and drink with one another. I have this goofy idea that they all completely rock out to AC/DC together. Can it possibly be an accident that the country that produced the greatest rock band of all time also produces a disproportionate amount of excellent philosophy? I don't think so. I think their philosophy is in fact high voltage philosophy, the analog to the following (again, also produced in Australia, for all we know, across the street from Smart and Armstrong's apartment house):