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of those separate instances which are only to be gathered and interpreted by patient, careful, and often doubtful induction. Each party thus neglects a valuable field which the other exclusively cultivates. All that Mill regards as reasoning, Hamilton scornfully rejects from the province of logic as invalid, as not presenting with certainty the conclusions in the premises from which they are taken. Mill, on the other hand, can only look on the complicated syllogisms of Hamilton as a cumbersome restatement of work already done, of knowledge already gained.

Much is undoubtedly included by Hamilton, in the formal expansion of his terminology, as reasoning, which would generally be regarded as simple statement, as the fruit of single judgments, as the results of perception. This desk contains this drawer: This drawer contains this paper: Therefore this desk contains this paper. These propositions form a syllogism under one of the forms into which he divides deductive reasoning. Most would regard them as in no proper sense reasoning, but rather as a formal, unserviceable statement of a fact, learned by observation. So also his inductive reasoning is made up of cumbersome formulae of classification. "Gold is a metal, yellow, ductile, fusible, and so on: These qualities constitute this body (are all of its parts): Therefore this body is gold." Here is no argument properly so called, but the rendering of the results of the experimental test of a bit of metal, with the accompanying act of classification. There would seem to be room in a logic, covering all the forms of reasoning, and those of reasoning only, both for deduction and induction, using the words in their more general and generally accepted meanings. An important branch of logic finds representation in Hamilton and Mill respectively.

What is reasoning? It is the reaching of a new conclusion, certain or probable, by means of two or more interlocked