This may be seen in one of the above examples.  It was argued that a certain metal must be copper, because every metal is copper that turns green when dipped in vinegar.  So far the proof appealed to a general proposition, and was deductive.  But when we ask how the general proposition is known to be true, experiments or facts must be alleged; and this is inductive evidence.  Deduction then depends on Induction.  But if we ask, again, how any number of past experiments can prove a general proposition, which must be good for the future as well as for the past, the uniformity of causation is invoked; that is, appeal is made to a principle, and that again is deductive proof.  Induction then depends upon Deduction.

We may put it in this way:  Deduction depends on Induction, if general propositions are only known to us through the facts:  Induction depends on Deduction, because one fact can never prove another, except so far as what is true of the one is true of the other and of any other of the same kind; and because, to exhibit this resemblance of the facts, it must be stated in a general proposition.

Sec. 4.  The use of Logic is often disputed:  those who have not studied it, often feel confident of their ability to do without it; those who have studied it, are sometimes disgusted with what they consider to be its superficial analysis of the grounds of evidence, or needless technicality in the discussion of details.  As to those who, not having studied Logic, yet despise it, there will be time enough to discuss its utility with them, when they know something about it; and as for those who, having studied it, turn away in disgust, whether they are justified every man must judge for himself, when he has attained to equal proficiency in the subject.  Meanwhile, the following considerations may be offered in its favour: 

Logic states, and partly explains and applies, certain abstract principles which all other sciences take for granted; namely, the axioms above mentioned—­the principles of Contradiction, of the Syllogism and of Causation.  By exercising the student in the apprehension of these truths, and in the application of them to particular propositions, it educates the power of abstract thought.  Every science is a model of method, a discipline in close and consecutive thinking; and this merit Logic ought to possess in a high degree.

For ages Logic has served as an introduction to Philosophy that is, to Metaphysics and speculative Ethics.  It is of old and honourable descent:  a man studies Logic in very good company.  It is the warp upon which nearly the whole web of ancient, mediaeval and modern Philosophy is woven.  The history of thought is hardly intelligible without it.

As the science of proof, Logic gives an account of the general nature of evidence deductive and inductive, as applied in the physical and social sciences and in the affairs of life.  The general nature of such evidence:  it would be absurd of the logician to pretend to instruct the chemist, economist and merchant, as to the special character of the evidence requisite in their several spheres of judgment.  Still, by investigating the general conditions of proof, he sets every man upon his guard against the insufficiency of evidence.