Logic | Page 7

unlike another in
certain attributes, as that iron is in many ways like tin or lead, and in
many ways unlike carbon or sulphur: (ii) that attributes co-exist or
coinhere (or do not) in the same subject, as metallic lustre, hardness, a
certain atomic weight and a certain specific gravity coinhere in iron:
and (iii) that one event follows another (or is the effect of it), as that the
placing of iron in water causes it to rust. The relations of likeness and
of coinherence are the ground of Classification; for it is by resemblance
of coinhering attributes that things form classes: coinherence is the
ground of judgments concerning Substance and Attribute, as that iron is
metallic; and the relation of succession, in the mode of Causation, is the
chief subject of the department of Induction. It is usual to group
together these relations of attributes and of order in time, and call them
qualitative, in order to contrast them with the quantitative relations
which belong to Mathematics. And it is assumed that qualitative
relations of things, when they cannot be directly perceived, may be
proved indirectly by assuming the axiom of the Syllogism (chap. ix.)
and the law of Causation (chap. xiv.).
So far, then, Logic and Mathematics appear to be co-ordinate and

distinct sciences. But we shall see hereafter that the satisfactory
treatment of that special order of events in time which constitutes
Causation, requires a combination of Logic with Mathematics; and so
does the treatment of Probability. And, again, Logic may be said to be,
in a certain sense, 'prior to' or 'above' Mathematics as usually treated.
For the Mathematics assume that one magnitude must be either equal
or unequal to another, and that it cannot be both equal and unequal to it,
and thus take for granted the principles of Contradiction and Excluded
Middle; but the statement and elucidation of these Principles are left to
Logic (chap. vi.). The Mathematics also classify and define magnitudes,
as (in Geometry) triangles, squares, cubes, spheres; but the principles of
classification and definition remain for Logic to discuss.
(b) As to the concrete Sciences, such as Astronomy, Chemistry,
Zoology, Sociology--Logic (as well as Mathematics) is implied in them
all; for all the propositions of which they consist involve causation,
co-existence, and class-likeness. Logic is therefore said to be prior to
them or above them: meaning by 'prior' not that it should be studied
earlier, for that is not a good plan; meaning by 'above' not in dignity,
for distinctions of dignity amongst liberal studies are absurd. But it is a
philosophical idiom to call the abstract 'prior to,' or 'higher than,' the
concrete (see Porphyry's Tree, chap. xxii. § 8); and Logic is more
abstract than Astronomy or Sociology. Philosophy may thank that
idiom for many a foolish notion.
(c) But, as we have seen, Logic does not investigate the truth,
trustworthiness, or validity of its own principles; nor does Mathematics:
this task belongs to Metaphysics, or Epistemology, the criticism of
knowledge and beliefs.
Logic assumes, for example, that things are what to a careful scrutiny
they seem to be; that animals, trees, mountains, planets, are bodies with
various attributes, existing in space and changing in time; and that
certain principles, such as Contradiction and Causation, are true of
things and events. But Metaphysicians have raised many plausible
objections to these assumptions. It has been urged that natural objects
do not really exist on their own account, but only in dependence on

some mind that contemplates them, and that even space and time are
only our way of perceiving things; or, again, that although things do
really exist on their own account, it is in an entirely different way from
that in which we know them. As to the principle of Contradiction--that
if an object has an attribute, it cannot at the same time and in the same
way be without it (e.g., if an animal is conscious, it is false that it is not
conscious)--it has been contended that the speciousness of this
principle is only due to the obtuseness of our minds, or even to the
poverty of language, which cannot make the fine distinctions that exist
in Nature. And as to Causation, it is sometimes doubted whether events
always have physical causes; and it is often suggested that, granting
they have physical causes, yet these are such as we can neither perceive
nor conceive; belonging not to the order of Nature as we know it, but to
the secret inwardness and reality of Nature, to the wells and reservoirs
of power, not to the spray of the fountain that glitters in our
eyes--'occult causes,' in short. Now these doubts and surmises are
metaphysical spectres which it remains for Metaphysics to lay. Logic
has no direct concern with them (although,