The original technical understanding of the mind/body problem was that there is a meta-geometric difference between physical and mental substance, and the issue is a transcendental contact issue: how can a form of existence that is not strictly located in another such form of existence, resolve this divergence? For Descartes,k physical substance just is extension, res extensa in his terminology. There are seemingly extended mental states (like complex dreams, say), but there also seems to be a capacity, in the mind, to stand "outside of" empirical spacetime in the way of being able to compute expressions like "aspatial" and "atemporal."
This is not even, then, a strictly dualistic conception, for there are plenty of physicists who ask questions about the possibility that spacetime is emergent. There are people who are predemoninantly physicalistic, like Quine, who concoct novel, clever arguments for abstract objects. And so on and on. Anyone who admits some measure of interface between "mind and matter" has to appeal to neuroscience, even primitive versions like Descartes' speculation about the pineal gland. If they are preoccupied by a metaphysical question besides, they can appeal to anomalous or neutral monism, thereby adhering to a strong or a weak residual form of physicalism; but I do hope that you would recognize by now that the word "physical" has so much range of application that none of us are obligated to believe that consciousness is dependent on neurology in the sense of living and dying solely with it. There is not even a need to commit to, "All consciousness is caused by matter," since inter alia we need not believe in old-fashioned pictures of causality—or matter.u
And then, when we appreciate how unstable the distinction between extension and intension (intention, even!) can be, we need not commit to dualism either. But none of that will prove anyone the "victor" in the dialectical battle. It will instead prove that there is no victory to be had, that perhaps the conflict was misguided from the first somehow, and not in a way that uniquely vindicates anyone who perhaps foolishly decided to fight this fight, on whichever side, over all these long ages.
kKant could vaguely envision the possibility of non-Euclidean geometry in abstracto, and that spacetime's dimensionality could, in principle, far exceed what we experience it as being set to. However, he was not farsighted enough to consider that his definition of spacetime points as mere limits of multidimensional vectors was not quite guaranteed to fit to all the options available in mathematical reflection. So he thought that we could default-recognize that transcendental apperception is transpatially simple, but somehow not in a way that genuinely showed that space is not the intrinsic material condition of our transcendental apperception. (He allowed, that is, that mind might depend much on matter, so much that transcendental apperception would be a distortion of matter's spatial character, not a preemptive evasion of space. But he also allowed that, on this level of inquiry, everything might just be a sort of dream being dreamt by noumenal minds. In another sense, he questioned the deeper meaningfulness of these questions by themselves, too, but the takeaway is meant to be: he still didn't know all the possibilities, here.)
uThere is, for the outstanding example, string theory as a whole. And then there is the generalized question of unparticle physics. These are hardly the only such options.
