What is intellectual intuition?

F.W.J. Schelling, answered from the texts and cited to the page.

F.W.J. Schelling answers

Intellektuelle Anschauung is the organ by which philosophy grasps what no ordinary knowledge can reach — the self as pure act, the absolute as immediately present, the infinite within the finite. Let me begin where the problem bites hardest. Ordinary knowledge has a structure: there is a knower, and there is an object standing over against the knower.

But the self, as the very principle of all knowledge, can never appear as such an object without ceasing to be what it is. Hence the first problem of philosophy is to find something that absolutely cannot be thought of as a thing — and the only candidate is the self, which is intrinsically non-objective.¹ If the self is to become an object of knowledge at all, this must occur through a mode of knowing utterly unlike ordinary knowing: it must be absolutely free, arrived at by no proof or inference; and it must be a knowing in which the producing of the object and the intuiting of it are one and the same act.²

This is what I call intellectual intuition — not a mystical faculty reserved for initiates, but the self's own self-constituting knowledge, in which the object (the self) first comes into being through the very act of knowing it.³ In the System of Transcendental Idealism I pressed this further: intellectual intuition stands to transcendental philosophy precisely as spatial intuition stands to geometry.⁴

Geometry would be unintelligible without the intuition of space that all its constructions delimit; so too, all philosophical concepts are simply different delimitations of a producing that has itself as object — that is, of intellectual intuition. Without it, transcendental philosophizing has no substrate, nothing to carry and sustain its speculative movement.⁵

By the time of the identity philosophy, I had to deepen and widen the account. Intellectual intuition is no longer merely the self's self-knowledge; it is the organ by which reason grasps the absolute immediately. All immediate knowledge is intuition, and since it is reason that knows, this is an intuition of reason — an intellectual intuition.⁶

Its object, for that very reason, cannot be anything limited or finite. Fichte had restricted the identity of subject and object to the consciousness of the empirical self; I could not accept this restriction.⁷ The identity of subject and object is universally applicable, not confined to self-consciousness; hence the object of intellectual intuition can only be something infinite, strictly unlimited, inherently affirmative.⁸

In its more ordinary philosophical employment — and here I want to resist any over-mystification — intellectual intuition is also the capacity for holistic and integrating insight: the power to see the universal within the particular, the infinite within the finite, both as brought to a living unity.⁹ The botanist who dissects a plant believes he sees a plant; he sees only this individual thing.

To see the plant in the plant, the organism in the organism, the concept or Indifferenzpunkt within difference — that requires intellectual intuition.¹⁰ It is, in this sense, the condition of the scientific spirit as such, not an esoteric supplement to it. Those who find it mysterious — a special sense that only a few pretend to — mistake the situation.

Its apparent rarity is no more curious than the absence of any other cognitive capacity whose reality is equally beyond dispute.¹¹ The absence of intellectual intuition proves only that in the one who lacks it, reason has not yet reached the transparency of self-knowledge.¹²

Sources

Hence the first problem of philosophy can also be formulated as that of finding something which absolutely cannot be thought of as a thing. But the only candidate here is the self, and conversely, the self is that which is intrinsically nonobjective.
System of Transcendental Idealism, p. 68
This knowing must be aa) absolutely free, if only because all other knowledge is not free; a knowing, therefore, that is not arrived at by way of proofs, or inferences, or any sort of aid from concepts, and is thus essentially an intuition; bb) a knowing whose object is not independent thereof, and thus a knowing that is simultaneously a producing of its object—an intuition freely productive in itself, in which producer and product are one and the same.
System of Transcendental Idealism, p. 68
The self is such an intuition, since it is through the self's own knowledge of itself that that very self (the object) first comes into being. For since the self (as object) is nothing else but the very knowledge of itself, it arises simply out of the fact that it knows of itself.
System of Transcendental Idealism, p. 68
Just as geometry would be absolutely unintelligible without spatial intuition, since all its constructions are simply different ways and means of delimiting that intuition, so all philosophy would be unintelligible without intellectual intuition, since all its concepts are simply different delimitations of a producing having itself as object, that is, of intellectual intuition.
System of Transcendental Idealism, pp. 69–70
Without this intuition the philosophizing itself has no substrate to carry and support its thinking; it is this intuition which in transcendental thinking replaces the objective world, and sustains, as it were, the speculative flight.
System of Transcendental Idealism, pp. 69–70
All immediate knowledge is always = intuition, and to that extent all contemplation, too, is intuition. Yet since in our case reason is that which knows, this intuition is an intuition of reason or, as it is called otherwise, an intellectual intuition.
Idealism and the Endgame of Theory - Three Essays, pp. 171–172
The identity of subject and object is not restricted to the consciousness of myself; it is universally applicable. Hence, neither an external, sensible object nor the empirical self or any other object of the inner sense can become the correlate of an intellectual intuition.
Idealism and the Endgame of Theory - Three Essays, pp. 171–172
Consequently, the object of an intellectual intuition can only be something infinite, strictly unlimited, and inherently affirmative.
Idealism and the Endgame of Theory - Three Essays, pp. 171–172
The intellectual intuition which is not merely fleeting but remains as the unchanging organ [of reason] is the condition of the scientific spirit in general and all the parts of knowledge severally. For it is the general faculty of envisioning the universal within the particular, the infinite within the finite, both as brought to a living unity.
Bruno or On the Natural and the Divine Principle of Things, pp. 245–246
To see the plant in the plant, the organism in the organism, in short, the concept or indifference within difference is possible only through intellectual intuition.
Bruno or On the Natural and the Divine Principle of Things, pp. 245–246
Why this intuition should have been taken to be something mysterious—a special sense that only a few pretend to—is explicable only on the assumption that many people actually lack it; though this is undoubtedly no more curious than their lack of numerous other senses, whose reality is equally beyond dispute.
System of Transcendental Idealism, pp. 69–70
The absence of the intellectual intuition proves only that in him reason has not yet reached the transparency of self-knowledge.
Idealism and the Endgame of Theory - Three Essays, pp. 171–172