Assume that human cognition has its scope and limits, and that it comes with a borderline outside of which things are, in one way or another, unknowable.
Question: Does a known borderline have the same status as an unknown one?
On the one hand, the answer is evident from the terms: K ~ (~K) on the other hand, a known borderline hems in exactly the same things as an unknown one.
All this leans hard on a metaphor of cognitive space – thought can go this far and no further. We set up borders for any number of reasons, like:
1.) As defensive structures: “Reason can go this far, and after that, revelation!” Or “We can understand reality this far, and after that, depression and endless controversy!”
2.) As foundational structures “The cogito is absolutely certain, everything else is doubtful – so we should build upon the former and not the latter” or “Truths of sense are opinion, truths of reason are unchangeable”
3.) As attempts to articulate an anthropology “the proper object of the intellect is sensibly concretized being/ simple impressions/ God’s ideas and not an impossible “material” world, etc. Outside of this we have nothing at all/ things known by analogy/ the adequate object of the intellect, etc.
There are no doubt all sorts of human modalities of consciousness and linguistic structures that can make no sense of this “cognitive space” metaphor, but this does not need mean that it is not a real insight. In fact, we have a good reason to take it as a very good insight: the metaphor is richer than it looks and can even account for those modalities of consciousness that could never speak of cognitive space.
Space is both isomorphic and indefinite, or with a single intelligible form and with no intelligible form. It is both nothing before we draw on it (or at least articulate it as a surface for drawing) and yet also what has to be already given in order for there to be anything to draw. Without a definite shape, there can be absolutely nothing at all for geometry to study; and yet geometry itself is also nothing but a manifestation of the possibilities in of this “absolute nothing”. This is clear when we compare the different geometries: on the one hand there is nothing in Euclid except a series of claims about points, lines, circles, etc.; on the other hand it is nothing but the making explicit of the peculiar symmetries and isomorphic character of Euclidean space.
This dual character of space shines a light both on the Heideggerian
sein and Davidson’s claim that conceptual schemes are incoherent and on the familiar critical tradition in philosophy that defines human cognition within scope and limits.