Imagine an equation, such as a2+b2=c2. Now, draw a right triangle with sides 3,4,5. Presuming all sensations and thoughts are associated with brain states, we can't say a percept is more "outside" of your brain than a thought is. So, the equation is "inside" your brain just as the percept is. Is whatever is generating the equation the same as, or the same kind as, whatever is generating the perceptual triangle? Mathematics is said to be the language of nature--could both it and perceptual nature be coming from the same source? What do they have in common?
Their common quality is that they are both involved in mankind's search for Truth. Empiricism and mathematics are both key to discovering scientific principles. The Universe is so set up as for it to obey man when he discovers and employs said principle. This nature is built into the human mind, so that the human mind contains all Truth in an obscured fashion. Full comprehension of that Truth is possible only in principle, not in practice—in practice man can only grasp the Truth fractionally in terms of universal principles or shards of the Truth.
When we interact with the Universe, then, what we find are either “shards of Truth” (principles), or conscious beings (humans, dogs, possibly insects), or else “shadows” of the interplay of the Truth on what our minds identify as our nervous systems. Principles, individuals, and the amorphous totality of Truth. What is the ontological status of the Universe?
I propose the Universe is the thought of God, in the sense that the Universe is creative astrophysically, microphysically, and bio-evolutionarily, but does not have consciousness of any kind in of itself, any more than the Platonic archetypes have consciousness. It is all in the mind of God. What we experience day-to-day through our perception and thoughts is how our minds approach the thoughts of God, and the overall impression of space, solidity, colour, vividness, immediacy, logicality, and so on is a convenience for us but only represents a shadow, “through a glass darkly” (1 Cor. 13:12).