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judgments. We would lay stress on the word new, and on the words certain or probable. Our necessary ideas and our theories suffer expansion by a purely deductive process. Geometry is a deductive science, derived from intuitions, definitions, and axioms. Astronomy and mechanics are full of pure deductions, resting on conceptions of force confirmed by experience. How much is involved in certain, simple statements, we often only learn by a series of related judgments. This is one of the earliest forms of scientific reasoning, and presents in mathematics, pure and mixed, its most extended and serviceable results. The certainty, and, when fitting data are found, the celerity of its conclusions, abundantly explain its fascination, and the position it has held in investigation. The introduction of a mathematical unit, and application of number to a subject, have usually been the signal for a rapid advance.

This deductive reasoning rests on intuitive steps, and will readily fall into a syllogistic form. The syllogism is perfect; for the premises as premises, in their very statement are seen to contain the conclusion. No outside circumstances affect their relation.

Inductive reasoning, on the other hand, deals only with probabilities, because it pertains to things imperfectly known and to facts whose conditions are ever changing. It rests at bottom on the intuition of causation, the simplest statement of which is, Every event must have a cause. Its corollaries are, that every effect measures its cause, that the two are exactly commensurate, and, that sameness in one is proof of sameness in the other. These spring from the original, independent conception of causation. Proof under this notion, would be as certain as under the ideas of space and time, were we always dealing with perfectly fixed and perfectly known premises. We do not by observation so penetrate the nature of objects, and the character of complex