One application of the science of proof deserves special mention:  namely, to that department of Rhetoric which has been the most developed, relating to persuasion by means of oratory, leader-writing, or pamphleteering.  It is usually said that Logic is useful to convince the judgment, not to persuade the will:  but one way of persuading the will is to convince the judgment that a certain course is advantageous; and although this is not always the readiest way, it is the most honourable, and leads to the most enduring results.  Logic is the backbone of Rhetoric.

It has been disputed whether Logic is a science or an art; and, in fact, it may be considered in both ways.  As a statement of general truths, of their relations to one another, and especially to the first principles, it is a science; but it is an art when, regarding truth as an end desired, it points out some of the means of attaining it—­namely, to 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.