FOOTNOTES
[1] Locke's Essay, i, 1, §§ 2, 4.
[2] Caird, i, 10.
[3] B. 19, M. 12.
[4] Kant is careful to exclude from the class of a priori judgements proper what may be called relatively a priori judgements, viz. judgements which, though not independent of all experience, are independent of experience of the facts to which they relate. "Thus one would say of a man who undermined the foundations of his house that he might have known a priori that it would fall down, i. e. that he did not need to wait for the experience of its actual falling down. But still he could not know this wholly a priori, for he had first to learn through experience that bodies are heavy and consequently fall, if their supports are taken away." (B. 2, M. 2.)
[5] It may be noted that in this passage (Introduction, §§ 1 and 2) Kant is inconsistent in his use of the term 'pure'. Pure knowledge is introduced as a species of a priori knowledge: "A priori knowledge, if nothing empirical is mixed with it, is called pure". (B. 3, M. 2, 17.) And in accordance with this, the proposition 'every change has a cause' is said to be a priori but impure, because the conception of change can only be derived from experience. Yet immediately afterwards, pure, being opposed in general to empirical, can only mean a priori. Again, in the phrase 'pure a priori' (B. 4 fin., M. 3 med.), the context shows that 'pure' adds nothing to 'a priori', and the proposition 'every change must have a cause' is expressly given as an instance of pure a priori knowledge. The inconsistency of this treatment of the causal rule is explained by the fact that in the former passage he is thinking of the conception of change as empirical, while in the latter he is thinking of the judgement as not empirical. At bottom in this passage 'pure' simply means a priori.
[6] In reality, these tests come to the same thing, for necessity means the necessity of connexion between the subject and predicate of a judgement, and since empirical universality, to which strict universality is opposed, means numerical universality, as illustrated by the proposition 'All bodies are heavy', the only meaning left for strict universality is that of a universality reached not through an enumeration of instances, but through the apprehension of a necessity of connexion.
[7] B. 5, M. 4.
[8] Ibid.
[9] B. 10, M. 7.
[10] Straightness means identity of direction.
[11] Kant points out that this certainty has usually been attributed to the analytic character of mathematical judgements, and it is of course vital to his argument that he should be successful in showing that they are really synthetic.
[12] B. x-xii, M. xxvi.
[13] Cf. pp. 101-2.
[14] To object that the laws in question, being laws which we have thought, may not be the true laws, and that therefore there may still be other laws to which reality conforms, is of course to reintroduce relation to the thinking subject.
[15] Cf. Bosanquet, Logic, vol. ii, p. 2.
[16] In saying that a universal judgement is an immediate apprehension of fact, it is of course not meant that it can be actualized by itself or, so to say, in vacuo. Its actualization obviously presupposes the presentation of individuals in perception or imagination. Perception or imagination thus forms the necessary occasion of a universal judgement, and in that sense mediates it. Moreover, the universal judgement implies an act of abstraction by which we specially attend to those universal characters of the individuals perceived or imagined, which enter into the judgement. But, though our apprehension of a universal connexion thus implies a process, and is therefore mediated, yet the connexion, when we apprehend it, is immediately our object. There is nothing between it and us.
[17] For a fuller discussion of the subject see Chh. IV and VI.
[18] i. e. as not having a place in the reality which, as we think, exists independently of the mind.
[19] Cf. Ch. IV. This distinction should of course have been examined by one whose aim it was to determine how far our knowledge can reach.
[20] For the self-evidence of mathematics to Kant compare B. 120, M. 73 and B. 200, M. 121.
[21] This is stated B. 200, M. 121. It is also implied B. 122, M. 75, B. 263-4, M. 160, and by the argument of the Analytic generally.
[22] This appears to be the real cause of the difference of treatment, though it is not the reason assigned by Kant himself, cf. B. 120, M. 73-4.
[23] His remarks about pure natural science in B. 20, M. 13 and Prol. § 4 sub fin., do not represent the normal attitude of the Critique.