space is a magnitude, because “quantity” for Kant is a determination that belongs to the understanding—it is a category—and Kant wants to insist that space is something given and that this condition of givenness is of the very essence of space.
This, then, is how we should understand the meaning of Größe or magnitude: as quantity. Now, what does it mean when Kant says that space (as well as time) is an infinite magnitude? “Infinite” is a determination of quantity; that is, according to its idea, it has to do with the question of how-much. Regardless of whether we can determine the how-much makes no difference to the meaning of “infinite”—it still refers to a certain quantity: an endless quantity—or as one says, a quantity that I can go on determining ad infinitum without ever reaching a limit. But the ability to be endlessly determined (in the sense of “never reaching an end”) is not and cannot be the meaning of “infinite” in this context, at least so long as “magnitude” means the same as “quantity.” “Quantity”—the essence of every determined quantum—can never have this or that size. And that means: by its very essence, it can never be subjected to endless determination. [302] Rather, magnitude in the sense of quantity—as an endlessly ongoing determining—is the finitely infinite condition of possibility of being-quantitative, which is what underlies everything that has this-or-that quantum.
But then what is meant by an “infinite” magnitude? From what I said about “endlessness,” it is clear that “infinite” does not refer to something in the field of continuity but rather something that underlies continuity itself and that Kant expresses in this way: Space and time are infinite magnitudes. This means that insofar as space and time get determined, they are always in relation to what is determined as the whole is in relation to the part. The character of wholeness is essentially different from the character of the part, or more exactly, the character of part-ness. If I begin with something that is, by essence, a part and that is unable to exist except as a part (as is the case with any specific space as contrasted with space as such)—if I begin with what is essentially a part, I will never get to the whole. Every part—in this case, every specific space, even if we can think of it as determinable ad infinitum—and therefore even an infinite space, a space that can be determined ad infinitum—always presupposes space as a whole. Therefore, this infinity in the sense of the unlimitedness of proceeding, is possible only on the basis of the infinity that Kant now understands as “the whole.” Kant never investigates and determines the concepts of “infinite” and “finite” in a univocal sense (the terms have various meanings in Kant). Nonetheless it is clear that in the present context he is using the words “infinite” and “infinity” in Descartes’s sense of infinitudo. Descartes himself, however, did not determine infinitudo in a positive sense. Speaking of it in his Meditations,