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, of course, metaphysical
discussion is expected to be logical), but keeps the plain path of plain
beliefs, level with the comprehension of plain men. Metaphysics, as