Induction, one of the great processes of scientific discovery and proof. It is the operation of discovering and proving general propositions; while deduction, on the other hand, is the method of applying general propositions once discovered to particular cases considered to be included within their scope. By induction we establish the law that heat expands bodies; by deduction we apply it to explain why a clock goes slower in summer than in winter, owing to the changes of the length of the pendulum. It should be mentioned that what has been called perfect induction—the observation of all the instances and a statement of the result in one general proposition—is not by Mill or the moderns recognised as proper induction at all.
Induction is the process of real inference—in other words, by it we proceed from the known to the unknown; or from a limited range of facts we affirm what will hold in an unlimited range. All things that we do not know by actual trial or ocular demonstration we know by an inductive operation. Deduction is not real inference in this sense, since the general proposition already covers the case that we apply it to; in a proper deduction the conclusion is more limited than the premises. By the inductive method we obtain a conclusion much larger than the premises; we adventure into the sphere of the unknown, and pronounce upon what we have not yet seen. Nothing is more common than the making of bad inductions, and accordingly it is now considered a part of logic to lay down the rules for the right performance of this great operation. For the principles and rules of induction, see Mill's Logic (book iii.), Fowler's Inductive Logic, and Venn's Principles of Empirical or Inductive Logic (1890); and see the article LOGIC.