Commenting on our last consideration of the problem of the definition of space (after taking the time to apply some warranted scrutiny), Amos of KTL found that same consideration to be missing something essential: the proper requisites of the very definition itself seem to have been lost on that previous consideration:
How is the coinciding permeation of space by time a definition, rather than a fact about space? Could not one ask, if space were its own being permeated by time as something other, what would it be prior to this permeation such that it could be permeated?
It is only from within the confines of the problematic of space as it was first introduced (over at A City in Speech) that a proper response can now be ventured to these important observations offered by Amos, if only because one must never fail to exercise a certain respect for the place where he already is, and this a fortiori in the case of a consideration of the a priori nature of space. What we have tried to show in our previous consideration was that the subterranean understanding which governed the initial introduction of this problematic is one that can and must be brought to light and drawn out in meticulous fashion along lines that are unmistakably Kantian. If we keep this hermeneutic situation firmly in view, then a certain light falls upon the otherwise tangled thicket of possible responses to Amos' question regarding the temporal permeation of space.
What does it mean to think space as a pure form of finite intuition? More specifically, when we ask the question "What is space?", how is our search for this 'what' impacted by the peculiarity that space is not intuited like something spatial, but is rather intuited a priori along with and in advance of anything (in space)? The question of what something is either has an object or it does not. If it does, then this is a possible object of experience about which an empirical question may be raised; if it does not, then this is a condition for the possibility of such experience about which a transcendental question may be raised. In the case of the former, namely, the empirical question, what is aimed at is constituted at the most fundamental level by two elements: 1.) the receptivity of intuition and 2.) the spontaneity of the understanding; any possible object of experience, any "what" about which we make inquiry, depends upon 'what' is intuited (the sense manifold) and 'what' is understood (i.e. the categorical organization of the sense manifold). Kant sometimes calls this dual dependency which combines intuition and understanding the "unity of representation". Strictly speaking, only if space, considered in exclusion from anything else, required the unity of representation could it possibly be an object of experience to which an empirical question may be plied. Only if this is the case can we extend our knowledge about space and discover, as Amos would have it, "a fact about space". And, indeed, Kant does more than concede that such discoveries are, in point of fact, possible; his entire first Kritik relies upon and, in another way, founds such discoveries. They are none other than what Kant calls formal intuitions, and in the case of space, they are to be found in that familiar body of apodictic knowledge known as geometry. But a formal intuition of space can in no wise be confused with the form of intuition of space:
Space, represented as object (as we are required to do in geometry), contains more than the mere form of intuition; it also contains combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only the manifold, the formal intuition gives unity of representation.(CPR B161)
Space, insofar as it is formally intuited, is given as a unity of representation in reference to which facts can be established. Thus we may ask and give definitive answer to the question "what is a line?" But the question "what is space?" asks for what any such formal intuition, in its unity of representation, depends upon, namely the transcendental form of intuition of space. To this latter transcendental question and its answer the synthetic a priori judgment capable of establishing facts about space is necessarily indebted. Therefore the question "what is space?" can neither offer a definition produced by the understanding nor ipso facto can it look for that unity given in and by the "unity of representation". The definition of space as a pure intuition must be given in its unity by pure intuition. The oneness or unity of pure space can only be discovered only when its borders or confines are seen, and yet because this unity is not the unity of representation, these borders cannot be de-fined by the understanding, but rather must be intuited. It is as if we must in some way see rather than apprehend the definition of space. But how is such seeing to take place if what is to be seen is neither something we can experience nor even conceivable? It must take place by way of an intuition that is non-empirical, i.e. pure. And for this reason we cannot expect it to be positively demonstrated (and therefore understood in its necessity); it must instead be given, i.e. intuited.
Now, if there were nothing to be purely intuited other than space, then the form of the intuition of space would have to be able to give itself, in its unity, and therefore constitute itself as self-defining. But because something else is given as a form in pure intuition, namely time, this is not necessary. The question remains: is it possible? The only answer to this question must be found by way of recourse to pure intuition. Kant himself indicates the answer by the following observation:
Whatever the origin of our representations,...whether they arise a priori, or being appearances [i.e. possible objects of experience] have an empirical origin, they must all, as modifications of the mind, belong to inner sense. All our knowledge [i.e. any intuition, concept, or unity of representation] is thus finally subject to time, the formal condition of inner sense. In it they must all be ordered, connected and brought into relation.(CPR, A 98)
Kant's observation can be supplied with the testimony of a quick reference to our awareness of anything in space: this awareness itself is not spatial, it is not something that we might bump into like a tree in the forest. It is not defined by space. On the other hand, what about space? If it can be said to be anything, and it is already lost to any attempt to conceive of it, than it must be received as an intuition, i.e. as a form given in the intuition of a sense manifold. But, as Kant just observed, not just the understanding, but intuition too, and any sort of representation, takes place in time. So much is this the case that when Amos proposes the possibility of the alternative, namely,"Could not one ask, if space were its own being permeated by time as something other, what would it be prior to this permeation such that it could be permeated?" he has already presupposed time insofar as he speaks of "space prior to this permeation" ---in other words, the priority is nothing if it is not a temporal one.
When this problematic of the temporal definition of space as Kant has framed it is reflected upon, a paradoxical formulation which it seems we must be content with asserts itself regarding the definition of space: the essence of space is, in the immediate pure intuition of space, lost in that intuition. Space, because it is definable by the pure intuition of time and this alone, must first be lost, since the essence of space is not only, according to the order of intuition, found later, but above all because it is found precisely as what is found later. The de-finition of space is found as what has been lost in space. And it is in this sense that I would like, at least initially, to read the last and most astute comment Amos has left in connection with our recent post on Ereignis:
Also, is space as it transpires in the shifting encounter an example of what "always comes too late?"