Even if the laws of logic are intrinsic principles of being, which Aristhomism asserts they are, logical concepts still require an intelligence adequate to them in order to exist as intelligible principles. Even if all existence were reduced to a plain white orb of iron, which we shall call Alf, and though Alf would obey such logical principles as identity (e.g., Alf is Alf), non-contradiction (e.g., Alf is not non-Alf), transitivity (e.g., if 'Alf' is Alf, then Alf is 'Alf'), etc., yet unless Alf itself could grasp the logic of its own ontic principles, the Alf-cosmos would lack logic as an intelligible order of being. There is no point in trying to account for being, since being by necessity exists. There is, however, a great need to account for how being can be grasped. Unless intelligence is as intrinsic to existence as intelligibility, then intelligibility is not actually intelligible.
By rough analogy, if there were never any objects capable of perception or sensation, it would be meaningless to say the world contained perceptible and sensible objects, since those latter objects are intrinsically perceptible-sensible only in the act of being perceived and sensed. Likewise, if there were never any intellect capable of intelligibly grasping logical concepts, it would be meaningless to speak of intelligible objects. Intelligible to whom? Intelligible in what terms? Intelligible where, on virtual leaf loose paper inscribed in quarks? Dreams without dreamers? Visions without seers? Alternatively we can imagine a world devoid of all concepts for measurement (e.g., inches, numbers, relative grades, spatial demarcations, etc.), and thus see the incoherence of positing measurable objects. Measurable objects presuppose adequate measuring devices; sensible objects presuppose sentient beings; intelligible order presupposes intelligence.
The modal suffixes (i.e., -ible and -able) point to the potentiality (potentia) of perceptibility, measurability, and intelligibility; it is only in connection with active (agens) perception, measurement, and intellection that such potencies become actual in existence. The more intrinsic such potencies are in the order of being, the more intrinsic their requisite acts-of-being are in being. Intelligibility is more intrinsic and universal in being than measurability, but measurability is more intrinsic and universal in being than sensibility. Therefore, the act of intelligence is most intrinsic and universal in being, measurement less so, and perception still less inclusive and less penetrative. This order of active ontic appropriation makes sense of the ability of theology and metaphysics to outstrip the reach of empirico-theoretical science, as well the ability of exact theoretical science to outstrip the reach of human sentience.
Logic is only logical when grasped by a mind capable of conformity with the principles of logic. I can show a pet rock sheet after sheet of Venn diagrams, but the rock, lacking intelligence, will of necessity never be suffused with logic qua conceptual truth. It will, like Alf, obey the laws of logic in itself, but it is only because we, in the course of imagining Alf and the pet rock, already grasp the intelligibility of logic that we can superimpose logical categories on the pet rock's (unwitting) ontological intelligibility. Logical truths, qua the principles of being, possess a dual modality: one mode of intelligible being is ontic (viz., identity, non-contradiction, transitivity, etc.), the other mode is conceptual. Only if logic is manifest both in the structure of being and to the intellect as it participates in being, can we say that logic is fully itself, in both modes of its ontic universality and conceptual comprehensibility.
If existence is intrinsically intelligible, it is intrinsically grasped by intellect. Moreover, if existence is eternally intelligible, then existence is eternally intellectual. If, however, nature's intelligibility is a mere fluke of later historical emergence, which we then impose upon nature without nature itself already possessing logical intelligibility, then rational discourse, science, philosophy, and language are sheer constructivist illusions. If the universe depends on our minds for its logical ordering, then its logical order is contingent, in which case logic itself is contingent on non-logical principles. If, however, existence has, at all times, been in accord with logical principles, then intellect has existed just as long to grasp those principles as logical. The intrinsic logic of being is coterminous with existence only insofar as existence is coterminous with intrinsic intelligence. Because we discover the logic of being, we of necessity admit its preexistence as actively intelligible. This is hardly pure idealism, since implicit in the recognition of intelligible order is the fact that logical order exists in actual being. Hence, intelligibility requires intellect without, however, sacrificing actual being to sheer virtuality. In God alone do the eternal principles of logic and the inexhaustible actuality of being coincide as one pure act of intelligible being. In knowing Himself in His Logos, God knows all things in His Logos; in the Λόγος του θεοῦ (Logos tou Theou), all things are intelligible as proper objects of intelligence. We participate in the intelligibility of logic in the same way we participate in the music of Mozart: we discover it and then properly defer to it as the expression of a greater mind suffused with that beauty. On that final Day, we will see God as He is in Himself, according, that is, to our mode of vision in the order of grace; and then will know all things, including ourselves, in His light, in «l'amor che move il sole e l'altre stelle» ("the Love … That moves the sun in heav'n and all the stars", Paradiso, Canto 33).