immediately enables us to decide that the former hypothesis is true and the latter false." In the above statements regarding the _verification_ of hypotheses we see references made to the testing of the latter upon the "facts" of the case. These _facts_ may be either the observed phenomena or facts apparent to the perception, or else _facts_ obtained by deductive reasoning. The latter may be said to be facts which are held to be true if the hypothesis be true. Thus if we erect the hypothesis that "All men are mortal," we may reason deductively that it will follow that each and every thing that is a _man_ must die sooner or later. Then we test our hypotheses upon _each and every man_ whom we may subject to observation and experiment. If we find a single man who does not die, then the test disproves our hypotheses; if on the contrary all men (the "facts" in the case) prove to be mortal, then is our hypotheses proven or established. The deductive reasoning in this case is as follows: "_If_ so-and-so is true regarding such-and-such a class; and if this particular thing belongs to that class; then it will follow that so-and-so is true regarding this particular thing." This argument is expressed in what is called a Hypothetical Proposition (see Chapter IX), the consideration of which forms a part of the general subject of Deductive Reasoning. Therefore as Jevons has said, "Deductive Reasoning is the Third Step in Inductive Reasoning, and precedes Verification", which we have already considered. Halleck says: "After Induction has classified certain phenomena and thus given us a major premise, we may proceed _deductively_ to apply the inference to any new specimen that can be shown to belong to that class. Induction hands over to deduction a ready-made major premise.... Deduction takes that as a fact, making no inquiry about its truth.... Only after general laws have been laid down, after objects have been classified, after major premises have been formed, can _deduction_ be employed." In view of the above facts, we shall now proceed to a consideration of that great class of Reasoning known under the term--Deductive Reasoning. CHAPTER XV. DEDUCTIVE REASONING We have seen that there are two great classes of reasoning, known respectively, as (1) Inductive Reasoning, or the discovery of general truth from particular truths; and (2) Deductive Reasoning, or the discovery of particular truths from general truths.