e subjects for logic,
as being, at all events, the sole methods of Proof, which (unless Dr.
Whewell be correct in his view that inductions are simply conceptions
consistent with the facts they colligate) is the principal topic of
logic.

FOOTNOTE:

[1] Chap. IX. consists of 'Miscellaneous Examples of the Four Methods,'
which cannot be well represented in an abridged form.

CHAPTER X.

PLURALITY OF CAUSES, AND INTERMIXTURE OF EFFECTS.

The difficulty in tracing the laws of nature arises chiefly from the
Intermixture of Effects, and from the Plurality of Causes. The
possibility of the latter in any given case--that is, the possibility
that the same effect may have been produced by different causes--makes
the Method of Agreement (when applied to positive instances)
inconclusive, if the instances are few; for that Method involves a tacit
supposition, that the same effect in different instances, which have
_one_ common antecedent, must follow in all from the same cause, viz.
from their common antecedent. When the instances are varied and very
many (how many, it is for the Theory of Probability to consider), the
supposition, that the presence in all of the common antecedent may be
simply a coincidence, is rebutted; and this is the sole reason why mere
_number_ of instances, differing only in immaterial points, is of any
value. As applied, indeed, to negative instances, i.e. to those
resembling each other in the absence of a certain circumstance, the
Method of Agreement is not vitiated by Plurality of Causes. But the
negative premiss cannot generally be worked unless an affirmative be
joined with it: and then the Method is the Joint Method of Agreement and
Difference. Thus, to find the cause of Transparency, we do not enquire
in what circumstance the numberless _non_-transparent objects agree; but
we enquire, first, in what the few transparent ones agree; and then,
whether all the opaque do not agree in the _absence_ of this
circumstance.

Not only may there be Plurality of Causes, the whole of the effect being
produced now by one, now by another antecedent; but there may also be
Intermixture of Effects, through the interference of different causes
with each other, so that part of the total effect is due to one, and
part to another cause. This latter contingency, which, more than all
else, complicates, the study of nature, does not affect the enquiry into
those (the exceptional) cases, where, as in chemistry, t