[Footnote 2:  We are happy to find such high authorities as Dr Whewell, Mr Samuel Bailey, and Sir John Herschel concurring in this estimation of the new logical point of view thus opened by Mr Mill.  We will not call it a discovery, since Sir John Herschel thinks the expression unsuitable.—­See the recent sixth edition of the ‘System of Logic,’ vol. i. p. 229.]

[Footnote 3:  See Sir William.  Hamilton’s ‘Lectures on Logic’ (Lect. xvii. p. 320, 321; also Appendix to those Lectures, p. 361).  He here distinguishes also formal induction from, material induction, which latter he brings under the grasp of syllogism, by an hypothesis in substance similar to that of Whately.  There is, however, in Lecture xix. (p. 380), a passage in a very different spirit, which one might almost imagine to have been written by Mr Mill:  ’In regard to simple syllogisms, it was an original dogma of the Platonic school, and an early dogma of the Peripatetic, that science, strictly so called, was only conversant with, and was exclusively contained in, universals; and the doctrine of Aristotle, which taught that all our general knowledge is only an induction from an observation of particulars, was too easily forgotten or perverted by his followers.  It thus obtained almost the force of an acknowledged principle that everything to be known must be known under some general form or notion.  Hence the exaggerated importance attributed to definition and deduction; it not being considered that we only take out of a general notion what we had previously placed therein, and that the amplification of our knowledge is not to be sought for from above but from below—­not from speculation about abstract generalities, but from the observation of concrete particulars.  Bat however erroneous and irrational, the persuasion had its day and influence, and it perhaps determined, as one of its effects, the total neglect of one half, and that not the least important half of the reasoning process.’

These very just observations are suggested to Sir William Hamilton by a train of thought which has little natural tendency to suggest them, viz., by the distinction upon which he so much insists, between the logic of comprehension and the logic of extension, and by his anxiety to explain why the former had been exclusively cultivated and the latter neglected.

That which Sir William Hamilton calls here truly the doctrine of Aristotle (enunciated especially at the close of the Analyt.  Post.), and which he states to have been forgotten by Aristotle’s followers, was not always remembered by Aristotle himself.]

[Footnote 4:  The distinction is given by Stier and other logicians. 1.  Infinitum simpliciter. 2.  Infinitum secundum quid, sive in certo genere.]

[Footnote 5:  This doctrine has been affirmed (so far as reason is concerned, apart from revelation) not merely by Mr Mansel, but also by Pascal, one of the most religious philosophers of the seventeenth century, in the ’Pensees’:—­