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 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.