[Footnote 11:  See especially his chapter ii. on the Sensations of Sight, pp. 222, 241—­247, in the second edition of this work.]

[Footnote 12:  Descartes says, in his ‘Principia Philosophiae,’ i 51—­’Et quidem substantia quae nulla plane re indigeat, unica tantum potest intelligi—­nempe Deus.  Alias vero omnes, non nisi ope concursus Dei existere posse perspicimus.  Atque ideo nomen substantiae non convenit Deo et illis univoce, ut dici solet in scholis, hoc est, nulla ejus nominis significatio potest distincte intelligi, quae Deo et creaturis sit communis.’]

[Footnote 13:  At the same time, we cannot go along with Mr Mill in the following affirmation (p. 201):—­

’This natural probability is converted into certainty when we take into consideration that universal law of our experience which is termed the Law of Causation, and which makes us unable to conceive the beginning of anything without an antecedent condition, or cause.’ Such ‘inability to conceive’ appears to us not in correspondence with facts.  First, it cannot be properly either affirmed or denied, until agreement is obtained what the word cause means.  If three persons, A, B, and C, agree in affirming it—­A adopting the meaning of Aristotle, B that of Sir William Hamilton, and C that of Mr Mill—­the agreement is purely verbal; or rather, all three concur in having a mental exigency pressing for satisfaction, but differ as to the hypothesis which satisfies it.

Next, if we reason upon Mr Mill’s theory as to Cause, certainly those who deny his theory can have no difficulty in conceiving events without any cause (in that sense):  nor have those who adopt this theory any greater difficulty.  These latter believe that there are, throughout, constant and uniform conditions on which the occurrence of every event depends; but they can perfectly conceive events as occurring without any such uniform sequence.  In truth, the belief in such causation, as pervading all nature, is an acquired result of scientific training.  The greater part of mankind believe that some events occur in regular, others in irregular succession.  Moreover, a full half of the metaphysical world espouse the doctrine of free-will, and consider that all volitions occur without any cause at all.]

[Footnote 14:  Among the various authorities (upon this question of quantifying the predicate) collected by Sir W. Hamilton in the valuable Appendix to his ‘Lectures on Logic,’ we find one (p. 311) which takes the same ground of objection as Mr Mill, in these words:—­’The cause why the quantitative note is not usually joined with the predicate, is, that there would thus be two quaesita at once; to wit, whether the predicate were affirmed of the subject, and whether it were denied of everything beside.  For when we say, all man is all rational, we judge that all man is rational, and judge likewise that rational is denied of everything but man.  But these are, in reality, two different quaesita; and therefore it has become usual to state them, not in one, but in two several propositions.  And this is self-evident, seeing that a quaesitum, in itself, asks only—­Does or does not this inhere in that? and not Does or does not this inhere in that, and at the same time inhere in nothing else?’