Just as the itch requires more than its sensation for the determination of its cause, so too must an object’s relation to you, that it is left or right, that it is above or below, that it is this or that, require more than its mere perception. — Mww
It comes down to the meaning of perception.
From the Wikipedia article on
Perception
Perception is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. Perception is not only the passive receipt for of these signals, but it is also shaped by the recipient's learning, memory, expectation, and attention.
Many philosophers, such as Jerry Fodor, write that the purpose of perception is knowledge. However, evolutionary psychologists hold that the primary purpose of perception is to guide action. They give the example of depth perception, which seems to have evolved not to aid in knowing the distances to other objects but rather to aid movement. Evolutionary psychologists argue that animals ranging from fiddler crabs to humans use eyesight for collision avoidance, suggesting that vision is basically for directing action, not providing knowledge.
Perception is more than sensation. Perception is what interprets sensations. Perception is what gives us the spatial relationship between objects, whether to the left or to the right, whether above or below.
Perhaps this is why one reads in the SEP article on
Kant's Views on Space and Time that
But leaving that complication aside, it is surely very surprising to hear that intuition, which in some regards is akin to perception (Parsons 1992, 65–66; Allais 2015, 147ff), can also be empirical or a priori in character.
According to Locke’s view, a version of which was also defended by Hume (Treatise, 1.2.3), we obtain a representation of space—not of places, but of the one all-encompassing space, which may be akin to geometric space—from the perception of spatial relations.
It is our perception of the world that allows us to distinguish left from right, above from below.
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Understanding. Plain and simple. It’s all in the text. Not in wiki. Space and time are irrefutably merely representations, all representations are products of either sensibility as phenomena, or thought as conceptions. Both sensibility and cognition insofar as they are active processes of the human intellect, are not themselves innate, thus it follows that neither are their respective products. That humans can sense and can think may indeed be innate, but the process by which these are done, which implies a system, is not that by which they are possible, which is given from a certain kind of existence alone. — Mww
From SEP -
Kant's Views on Space and Time
Space is not an empirical concept which has been derived from outer experiences. A23/B38
Finally, transcendental idealism, in so far as it concerns space and time, has the following essential component: we have a non-empirical, singular, immediate representation of space. Part of Kant’s innovation is to introduce into the philosophical lexicon the very idea that we can have non-empirical intuition.
As you say, the ability to think is probably innate. The question is, is what we think, our understanding, limited or not by our "natural instincts".
For Kant, our non-empirical intuition of time and space doesn't come from observation, doesn't come from any perception of the world, but comes from pure cognition in our minds.
The question is, what is the link between the innate ability to think and what is thought. Even if we accept Innatism, that the mind is born with already-formed ideas, knowledge, and beliefs, is it possible for our thoughts to be independent of such ideas, knowledge and beliefs. Does our innate ability to think determine what we think, or can what we think be independent of such innate ability of thought.
Any thoughts we have must be expressed in the physical state of the brain. There must be some correspondence at any moment in time between what we are thinking and the physical state of the brain. Any new thought must require an altered state of the physical brain. But any physical change requires a physical cause, in that a physical state cannot spontaneously change without a preceding physical cause. An effect needs a cause.
Summing up, any new thought requires a change in the state of the physical brain, but any change in the state of the physical brain requires a preceding physical cause. But in its turn, any preceding physical cause must require its own preceding physical cause, and so on, leaving no possibility that our thoughts have not been determined by a pre-existing physical state of the brain.
IE, understanding cannot be free of the physical state of the brain. Cognition is a function of the state of the physical brain, not something that can be achieved free of the state of the physical brain.
So in answer to my question, regarding Kant's non-empirical intuition, if such intuition is non-empirical, then where is the source of such intuition. The source can only be the momentary physical state of the brain, which has been determined by the preceding physical state of the brain, and so on, eventually leading back, to the innate ability of humans to think. In other words, Innatism.