Notes to Kant's Views on Space and Time
1. See, inter alia, Buchdahl 1969, 587-9; Kemp Smith 1918, 140-2; Paton 1936, 1: 171-6; Broad 1978, 50-1; Heidegger 1962, 155; Martin 1955, 12-15; Wolff 1963, 4-8; Allison 1983, 12, 107-111; Guyer 1987, 350-6; and, van Cleve 1999, 114.
2. In §1 of the Jäsche Logic (Ak 9: 91), Kant writes: “All cognitions [Erkenntnisse], that is, all representations consciously referred to an object, are either intuitions or concepts. Intuition is a singular representation (repraesentatio singularis), the concept is a general (repraesentatio per notas communes) or reflected representation (repraesentatio discursiva).” For an illuminating discussion of these issues, see Thompson 1972, 323.
3. For several influential accounts that differ in the details, see Thompson 1972, Friedman 1992, Parsons 1992, and most recently, Posy 2000.
4. Hence some interpreters have understood intuition as providing us with singular direct reference—see especially Posy 2000 for an illuminating understanding of that, and several related, ideas.
5. It does so because in Kant's terminology, <desk> contains <furniture> which means, in turn, that <desk> is a species of the genus, <furniture>. It is also possible to read Kant as arguing that concepts represent objects mediately not because of the higher-level genus of which they are a species, but because of the lower-level species for which they serve as a genus. I do not have the space to explore the details of that reading here, but see A68-9/B93-4.
6. Commentators sometimes think that Kant's use of Begriff here presents a problem, since Kant himself tries to show that the representation of space is not begrifflich (conceptual) in character (see below). But Begriff also has the general meaning of a notion or a representation, which seems to be the usage here. The term also has a more technical meaning in the Kantian vocabulary—one noted above—but the two should not be conflated.
7. The full passage reads as follows (L 5: 47): “I will show here how men come to form the notion [la notion] of space. They consider that many things exist at once and they observe in them a certain order of co-existence, according to which the relation of one thing to another is more or less simple. It's their situation or distance. When it happens that one of those co-existent things changes its relation to a multitude of others, which do not change their relation among themselves; and that another new thing acquires the same relation to the others, as the former had, this change we call a motion in that body wherein is the immediate cause of the change. And though many, or even all, the co-existent things should change according to certain known rules of direction and swiftness, yet one may always determine the relation of situation, which every co-existent acquires with respect to every other co-existent; and even that relation which any other co-existent would have to this, or which this would have to any other, if it had not changed, or if it had changed any other way. And supposing, or feigning, that among those co-existents there is a sufficient number of them which have undergone no change, then we may say, that those which have such a relation to those fixed existents, as others had to them before, now have the same place which those others had. And that which comprehends all those places, is called space. Which shows, that in order to have the idea of place, and consequently of space, it suffices to consider these relations and the rules of their changes, without needing to form an absolute reality [réalité absolue] out of the things whose situation we consider.”
8. One of Leibniz's points seems to be that his relationalism is perfectly compatible with the contention that the representation of space is empirical (for the view that some of the arguments in the Metaphysical Exposition are intended to undermine Leibnizian relationalism, see Guyer 1987, 349; Wojtowicz 1997, 79, 84, 87; Brandt 1997, 96-7; Walker 1978, 42-4; Parsons 1992, 68). He apparently employs this tactic to show that perce