Note 1513 — Chapter II · THE ANTINOMY OF PURE REASON[1495]

Kant regarded the point as a limit, i.e. as a boundary (Dissertation, § 14, 4; § 15, C: “The simple in space is not a part but a limit”; A 169-70 = B 211); whereas certain modern mathematicians take the point as one of the undefined elements. When the point is regarded in this latter manner, space may perhaps be satisfactorily defined as a set of points. In arguing for the antithesis, and in the passages just cited, Kant also assumes that, in the case of space, the properties of the class are determined by the properties of its elements. This questionable assumption is involved in his assertion that space can consist only of spaces.