proceed by a regular method, to test every judgment by the principles of
Logic, and to distrust whatever cannot be made consistent with them.
Logic does not, in the first place, teach us to reason. We learn to
reason as we learn to walk and talk, by the natural growth of our powers
with some assistance from friends and neighbours. The way to develop
one's power of reasoning is, first, to set oneself problems and try to
solve them. Secondly, since the solving of a problem depends upon one's
ability to call to mind parallel cases, one must learn as many facts as
possible, and keep on learning all one's life; for nobody ever knew
enough. Thirdly one must check all results by the principles of Logic.
It is because of this checking, verifying, corrective function of Logic
that it is sometimes called a Regulative or Normative Science. It cannot
give any one originality or fertility of invention; but it enables us to
check our inferences, revise our conclusions, and chasten the vagaries
of ambitious speculation. It quickens our sense of bad reasoning both in
others and in ourselves. A man who reasons deliberately, manages it
better after studying Logic than he could before, if he is sincere about
it and has common sense.

Sec. 5. The relation of Logic to other sciences:

(a) Logic is regarded by Spencer as co-ordinate with Mathematics, both
being Abstract Sciences--that is, sciences of the _relations_ in which
things stand to one another, whatever the particular things may be that
are so related; and this view seems to be, on the whole, just--subject,
however, to qualifications that will appear presently.

Mathematics treats of the relations of all sorts of things considered as
quantities, namely, as equal to, or greater or less than, one another.
Things may be quantitatively equal or unequal in _degree_, as in
comparing the temperature of bodies; or in _duration_; or in _spatial
magnitude_, as with lines, superficies, solids; or in _number_. And it
is assumed that the equality or inequality of things that cannot be
directly compared, may be proved indirectly on the assumption that
'things equal to the same thing are equal,' etc.

Logic also treats of the relations of all sorts of things, but not as to
their quantity. It considers (i) that one thing may be like or 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