12.Ibid.p.29(bk.i,ch.iii,section 1).

13.Ibid.p.49(bk.i,ch.iii,section 15).

14.Ibid.p.35(bk.i,ch.iv,section 6).

15.Ibid.p.38(bk.i,ch.iv,section 7).

16.Logic,p.40(bk.i,ch.iv,section 8).

17.Ibid.p.41(bk.i,ch.iii,section 9).

18.Logic,p.43(bk.i,ch.iv,section 10).

19.Ibid.p.68(bk.i,ch.v,section 6).

20.Logic,p.61(bk.i,ch.v,section 3).

21.Ibid.p.63(bk.i,ch.v,section 4).

22.It would be interesting to compare this part of Mill with the corresponding part of Hume's Treatise.Hume,like Mill,begins by accepting causation as one of the relations involved,and then explains it as merely derivative.His treatment of relations generally,especially the division of relations into the two classes,which do or do not depend upon the 'ideas'themselves,has a bearing upon Mill's doctrine too intricate to be considered here.[Treatise of Human Nature,pt.vi.sec.1.]I do not think that Mill was very familiar with Hume's writings.A note to the concluding chapter of the Examination of Hamilton seems to imply that he was not acquainted with the Treatise;nor does he appear from his posthumous Essays to have studied Hume's writings upon theology.Whether T.H.Green was right in holding that Hume had a more distinct view than his successor of some metaphysical difficulties,I need not inquire.

23.Logic,p.70(bk.i,ch.v,section 7).

24.Ibid.p.434(bk.iv,ch.iii,section 2n.).

25.Logic,p.132(bk.ii.ch.v,section 4).

26.Especially the early review of Whately.

27.This suggests a parallel to the old English system of pleading --as a preparatory process for bringing out the issues really involved in a dispute --which is said to have been thoroughly logical,though it became excessively cumbrous and technical.

28.Logic,p.327(bk.v,ch.vi,section 3).So in Examination of Hamilton,ch.xxii.'The syllogism is not the form in which we necessarily reason,but a test of reasoning.'

29.James Mill's Analysis,ii.427.

30.Logic,p.131.(bk.ii,ch.iii,section 5).

31.Logic,p.72(bk.i,ch.vi,section 2).

32.Ibid.p.113(bk.ii,ch.ii,section 5).

33.Autobiography,p.181.The passage to which Mill refers is apparently that in Stewart's Works,iii,24-36and 113-52.

Stewart quotes a passage from Dr Beddoes'Observations on the Nature of Demonstrative Evidence (1793),which anticipates Mill's view that the 'mathematical sciences are sciences of experiment and observation,founded solely on the induction of particular facts.'Stewart professes to follow Locke (see Locke's Essay,bk.iv,ch.xii,section 15),and gives some references to other discussions on the questions.

34.Logic,p.94(bk.i,ch.viii,section 5).

35.Logic,p.125(bk.ii,ch.iii,section 3).

36.Logic,p.126(bk.ii,ch.iii,section 4).

37.Ibid.p.107(bk.ii,ch.i,section 3).

38.Whiston (Memoirs,i,35)reports that Newton saw by intuition,or previously to formal demonstration,the equality of all parallelograms described about the conjugate diameters of an ellipse.Most of us can only learn the fact by painful construction.

39.Hume's Works (Grose and Green),ii,432and iv,134.Hume's statement is criticised by G.H.Lewes in his Problems,etc.i,391,but,I think,on an erroneous interpretation.

40.Logic,p.149(bk.ii,ch.v.section 1).

41.Ibid.p.151(bk.ii.ch.v.section 4).

42.Ibid.p.147(bk.ii.ch.v.section 1).

43.Ibid.p.183(bk.ii.ch.vii section 5).In the Examination of Hamilton he is less confident.It is 'not only inconceivable to us,but inconceivable that it should be mad conceivable'that the same statement should be both true and false (ch.vi.p.67).

Afterwards (ch.xxi.p.418)he will only decide that such laws are now 'invincibly'laws of thought,though they may or may not be 'capable of alteration by experience.'

44.Logic,p.148(bk.ii.ch.v.section 1).

45.Ibid.p.168(bk.ii.ch.vi.section 2).

46.Ibid.p.400(bk.iii.ch.xxiv.section 5).

47.Ibid.p.401(bk.iii.ch.xxiv.section 5).

48.Ibid.p.170(bk.ii.ch.vi.section 3).

49.Ibid.p.167(bk.ii.ch.vi.section 2).

50.Logic,p.212(bk.iii.ch.v.section 1).

51.Logic,p.401(bk.iii.ch.xxiv.section 6).

52.Logic,fourth edition,i.356(bk.iii.ch.v.section 1).

This phase is omitted in the last edition (p.211),but the meaning is apparently not altered.

53.Ibid.p.399(bk.iii.ch.xxiv.section 5).

54.See Logic,p.177(bk.ii.ch.vii.section 3),and p.493(bk.v.ch.ii.section 3).

55.Ibid.p.370(bk.ii.ch.xxi.section 1).

56.Logic,p.206(bk.iii.ch.iii.section 3).

57.Ibid.p.213(bk.iii.ch.v.section 2).

58.Logic,bk.iii.ch.v.

59.Ibid.p.217(bk.iii.ch.v.section 3).

60.Logic,p.221(bk.iii.ch.v.section 5).

61.Ibid.p.227(bk.iii.ch.v.section 8).

62.Ibid.p.224(bk.iii.ch.v.section 7).

63.Logic,p.243(bk.iii.ch.vi.section 1).

64.Logic,p.245(bk.iii.ch.vi.section 2).

65.Grove's work was first published in 1846,i.e.after the first edition of the Logic.

66.Logic,fourth edition,p.477(bk.iii.ch.x.section 4).In the eighth edition this passage was suppressed,and Mill discusses the theory of 'conservation or persistence of force,"as he calls it,in an earlier section.--Logic,p.228(bk.iii.ch.v.section 10).

67.Logic,p.501(bk.v.ch.iii.section 8).

68.See,for example,his criticism of a 'luminiferous ether'in answer to Whewell,Logic,p.328(bk.iii.ch.xiv.section 6).

He agrees here with Comte (Phil.Positive,ii.639),whom he perhaps follows.

69.See especially the chapter on causation in the Examination of Hamilton.

70.Tyndall,e.g.in his Heat as a Mode of Motion,quotes Bacon's anticipation.It is summed up by Whewell (Phil.Ind.ii.Sciences,ii.239)in the statement that the 'form of heat is an expansive,restrained motion,modified in certain ways,and exerted in the smaller particles of the body.'

71.Logic,p.500(bk.v.ch.iii.section 7).

72.Logic,p.288(bk.iii.ch.x.section 3).