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and mere analogy. Between these two there is a continuous series of weakening agreements, which we have divided into parts by the words, identity, sameness, resemblance, analogy. Identity is a secure basis of reasoning, but we cannot absolutely affirm it; sameness, a close agreement in qualities, admits considerable doubt; resemblance, a less close agreement, renders the argument insecure; while analogy, an agreement in relations, may only call out a presumption. (3) The two forms of reasoning differ, therefore, broadly in the force of the conclusion; in the one it is demonstrative, in the other it has every shade of certainty less than the highest. (4) They differ also in form. The syllogism belongs to deduction only; if applied to induction, it is either incomplete or assumes the thing to be proved. Life is thus permeated with both elements, with certainty and with doubt. Wisdom and strength are found in handling the two conjointly.

We have followed the ordinary division of reasoning, though we doubt its completeness. We prefer to regard reasoning of three orders, according as it deals with pure intuitive data, with empirical data, or with these data assumed as absolute. Mathematics is the chief example of the first order. Pure mental conceptions are unfolded through long trains of reasoning into appropriate formulae arid propositions. The connection under which this is done is that of equality or equivalence. The reasoning proceeds by affirming or denying an exact equality. The conclusion is identical with the premises as clearly understood. This reasoning may be termed production, the leading onward of data from one form of expression to another. In dealing with things, we are constantly embarrassed by the want of perfect insight. We hesitatingly reach a general conclusion by combining under it few or many examples. This is induction. Such a conclusion being reached, and expressed