I'm coming into this a bit late, but the OP reminded me of something I thought I'd share about the topic referenced in the quote by Schopenhauer. Here is Schopenhauer scholar Robert Wicks, who summarizes:
Schopenhauer is not mentioned in Douglas R. Hofstadter's Pulitzer Prize winning book, Goedel, Escher, Bach: An Eternal Golden Braid (1979), but as we have seen in our presentation of The World as Will and Representation, §7, §27, and §39, Schopenhauer should be recognized as among those philosophers who utilize the 'strange loop' structure at the very basis of their thought. In Schopenhauer, to recall, this involves the peculiarity of saying that although my mind is in my head, my head is in my mind, and although my head is in my mind, my mind is in my head. This mind-bending thought gives one extended pause.
He then expands (in a different book):
An even better model that displays a sharper reversal of 'inside' and 'outside,' while also preserving a transition between the two, is characteristic of the type of image represented by M.C. Escher's Drawing Hands (1948), where one hand draws another hand, which in turn draws the hand that drew it. Each hand is sequentially 'outside' of the other, while each hand depends upon and issues from the other. Such comparisons suggest that we have here, in Schopenhauer, a 'strange loop' phenomenon that has been described well, and at great length, by Douglas R. Hofstadter, who writes: 'the 'Strange Loop' phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started.'
If we accept the comparison between Schopenhauer's remarks on the reciprocal containment of realism and idealism, and the 'strange loop' images such as Escher's Drawing Hands, we can make more sense out of Schopenhauer's remarks concerning the relationship between intellect and brain. When referring to how brains are the result of the principle of sufficient reason's constructive activity, he speaks from an idealistic view and explains the spatio-temporal world as an illusion created by our mental activity. Then, immersing himself within the contents of that mental construction, he then identifies his own body, and then, his brain as a part of that body. Upon noting how this experiential perspective issues from his body within that construction, he then locates his perception within his brain. Once again reflecting that his brain is a product of the principle of sufficient reason, and with this, shifting from an external to an internal standpoint upon his body, he finds himself once again at the beginning of the strange loop.
An upshot of this unusual looping structure is that Schopenhauer can refer either to the brain as a function of the intellect, or to the intellect as a function of the brain, depending upon his assumed philosophical location within the loop. Appreciating this more complicated structure of Schopenhauer's philosophy - what Hofstadter would refer to as a 'tangled hierarchy' - helps resolve what seemed earlier to be a devastating criticism. Standing outside of the strange loop, as did Escher when he drew Drawing Hands, would be Schopenhauer himself; i.e. the philosopher in general, reflecting upon human experience in an effort to understand it.
This reference to strange loops and reciprocal containment may explain why Schopenhauer believed that his chapter on 'Physical Astronomy' was among the most important in his philosophical writings. Although the chapter does not contain the key arguments that we find in WWR, it does describe the movement through the hierarchy of nature, from inorganic, to organic, to human levels, and then, at the human level, describe how this hierarchy itself depends upon the human being's own intellectual construction.
Wicks is surely wrong to say anyone can stand outside of the strange loop just described (except maybe in aesthetic experience or in the denial of the will), but I think he explains the idea quite well all the same. I might also add that this problem, or paradox, is resolved by the will. The materialist collapses the mind into brain or subject into object, while the idealist collapses the brain into mind or object into subject. Schopenhauer says that each of these views is true, but deficient, since they mutually presuppose one another. Whatever the true nature of reality, it is neither material nor mental. So Schopenhauer advocates for neutral monism, which then becomes voluntarism when he identifies the nature of reality as will, which is neither a material object nor a subjective idea.
