Kant's second argument is stated as follows: "Space is represented as an infinite _given_ magnitude. Now every conception must indeed be considered as a representation which is contained in an infinite number of different possible representations (as their common mark), and which therefore contains these _under itself_, but no conception can, as such, be thought of as though it contained _in itself_ an infinite number of representations. Nevertheless, space is so conceived, for all parts of space _ad infinitum_ exist simultaneously. Consequently the original representation of space is an _a priori perception_ and not a _conception_." In other words, while a conception implies an infinity of individuals which come under it, the elements which constitute the conception itself (e. g. that of triangularity or redness) are not infinite; but the elements which go to constitute space are infinite, and therefore space is not a conception but a perception. Though, however, space in the sense of the infinity of spaces may be said to contain an infinite number of spaces if it be meant that it _is_ these infinite spaces, it does not follow, nor is it true, that space in this sense is object of perception. The aim of the arguments just considered, and stated in § 2 of the _Aesthetic_, is to establish the two characteristics of our apprehension of space,[26] from which it is to follow that space is a property of things only as they appear to us and not as they are in themselves. This conclusion is drawn in § 4. §§ 2 and 4 therefore complete the argument. § 3, a passage added in the second edition of the _Critique_, interrupts the thought, for ignoring § 2, it once more establishes the _a priori_ and perceptive character of our apprehension of space, and independently draws the conclusion drawn in § 4. Since, however, Kant draws the final conclusion in the same way in § 3 and in § 4, and since a passage in the _Prolegomena_,[27] of which § 3 is only a summary, gives a more detailed account of Kant's thought, attention should be concentrated on § 3, together with the passage in the _Prolegomena_. [26] viz. that it is _a priori_ and a pure perception. [27] §§ 6-11. It might seem at the outset that since the arguments upon which Kant bases the premises for his final argument have turned out invalid, the final argument itself need not be considered. The argument, however, of § 3 ignores the preceding arguments for the _a priori_ and perceptive character of our apprehension of space. It returns to the _a priori_ synthetic character of geometrical judgements, upon which stress is laid in the Introduction, and appeals to this as the justification of the _a priori_ and perceptive character of our apprehension of space.