In his essay, “On the Fundamental View of Idealism,” (Chapter 1; The World as Will and Representation, Volume II), he writes: “Matter is the representation of the intellect; the intellect is that in the representation of which alone matter exists. Both together constitute the world as representation, which is precisely Kant's phenomenon, and consequently something secondary. What is primary is that which appears, namely the thing-in-itself, which we… recognize as the will. In itself this is neither the representer nor the represented, but is quite different from its mode of appearance.”
To explain his conception of intellect and matter, and to bring to light the fundamental mistake in most other systems, Schopenhauer offers a dialogue in which The Subject and The Matter argue with each other about what came first in the world. Here’s the complete dialogue:
The Subject I am, and besides me there is nothing. For the world is my representation.
Presumptuous folly! I am, and besides me there is nothing: For the world is my fleeting form. You are a mere result of a part of this form, and quite accidental.
The Subject What silly conceit! Neither you nor your form would exist without me; you are conditioned through me. Whoever thinks me away, and then believes he can still think of you, is involved in a gross delusion; for your existence outside my representation is a direct contradiction, a wooden-iron. You are, simply means you are represented by me. My representation is the locality of your existence; I am therefore its first condition.
Fortunately the boldness of your assertion will soon be refuted in a real way, and not by mere words. A few more moments, and you—actually are no more; with all your boasting and bragging, you have sunk into nothing, floated past like a shadow, and suffered the fate of every one of my fleeting forms. But I, I remain intact and undiminished from millennium to millennium, throughout endless time, and behold unmoved the play of my changing forms.
This endless time, to live through which is your boast, is, like the endless space you fill, present merely in my representation; in fact, it is the mere form of my representation which I carry already prepared within me, and in which you manifest yourself. It receives you, and in this way do you first of all exist. But the annihilation with which you threaten me does not touch me, otherwise you also would be annihilated. On the contrary, it concerns merely the individual which for a short time is my bearer, and which, like everything else, is my representation.
Even if I grant you this, and go so far as to regard your existence, which is inseparably linked to that of these fleeting individuals, as something existing by itself, it nevertheless remains dependent on mine. For you are subject only in so far as you have an object; and that object is I. I am its kernel and content, that which is permanent in it, that which holds it together, without which it would be as incoherent and as wavering and unsubstantial as the dreams and fancies of your individuals, that have borrowed even their fictitious content from me.
You do well to refrain from disputing my existence on account of its being linked to individuals; for just as inseparably as I am tied to these, so are you tied to form, your sister, and you have never yet appeared without her. No eye has yet seen either you or me naked and isolated; for we are both only abstractions. At bottom it is one entity that perceives itself and is perceived by itself, but its being-in-itself cannot consist either in perceiving or in being perceived, as these are divided between us.
So we are inseparably connected as necessary parts of one whole, which includes us both and exists through us both. Only a misunderstanding can set up the two of us as enemies in opposition to each other, and lead to the false conclusion that the one contests the existence of the other, with which its own existence stands and falls.
This whole, including both, is the world as representation, or the phenomenon. After this is taken away, there remains only the purely metaphysical, the thing-in-itself, which in the second book we shall recognize as the will.