that every case of the latter is excluded from at least one case, and it may be from every case, of the former. On all the views, 'B' is always taken in its entire extent, 'A' always in a part, and sometimes also in the whole of its extent. This fact is, what is meant by saying that the predicate of an O proposition is distributed and the subject undistributed. § 5. Recapitulation.-Representing 'A' and 'B,' the subject and the predicate of a proposition, by two circles, and the copula, by the mutual position or relation of the two circles, A is represented by the two diagrams (1) and (2), I by the four diagrams (4), (5), (6), and (7), and O by the three diagrams (8), (9), and (10). On a comparison of these diagrams, it will be seen that (1) and (6), (2) and (7), (3) and (10), (4) and (8), (5) and (9) are identical, and that there are altogether five fundamental diagrams. To help the memory of the student, these five diagrams are given below in a definite order : These diagrams will be henceforth called the 1st, 2nd, 3rd, 4th, and 5th respectively, and the student is advised to remember their respective numbers. A is represented by the 1st and 2nd, E by the 4th, I by the 1st, 2nd, 3rd, and 5th, and O by the 3rd, 4th, and 5th. The subject of A is distributed, and the predicate undistributed. Both the subject and predicate of E are distributed. Both the subject and predicate of I are undistributed. The predicate of O is distributed, and the subject undistributed. That is, only universal propositions distribute their subjects, and only negative propositions distribute their predicates. § 6. Exercises on the meaning and representation of propositions by diagrams. I. Show how the four propositional forms-viz., A, E, I, and O -may be represented by diagrams. II. Draw the five fundamental diagrams representing all propositions in their proper order, and state which of them represent A, which E, which I, and which O respectively. III. Which of the four propositional forms-A, E, I, and O-may be represented by the 1st, which by the 2nd, which by the 3rd, which by the 4th, and which by the 5th diagram ? IV. Name the diagrams which represent A, E, I, and O respectively. V. Represent each of the following propositions by its appropriate diagrams, and state its meaning according to the various theories of predication and of the import of propositions: 13. Water boils at 100° C. under a pressure of 760 m.m. 14. Heat expands bodies. 15. Friction produces heat. PART III. REASONING OR INFERENCE. CHAPTER I. THE DIFFERENT KINDS OF REASONING OR INFERENCE. A Reasoning is the act of the mind by which we pass from one or more given judgments to another following from them. When we pass from one judgment to another different from it, but contained in, or directly implied by it, the reasoning is called Immediate. When we pass from two or more judgments to another different from any of them, but justified by all of them jointly, the reasoning is called Mediate. The new judgment, or the judgment obtained from the given judgment or judgments, is called the Conclusion, and the given judgment or judgments, the Premiss or Premisses. If the conclusion be not more general than either of the premisses in a mediate reasoning, the reasoning is called Deductive. If the conclusion be, on the other hand, more general than any of the premisses, the reasoning is called Inductive. In Deductive Reasoning the conclusion is a development of what is contained in, or implied by, the premisses. In Inductive Reasoning the conclusion contains or implies more than what is contained in or implied by any or all of the premisses. Thus we get the following kinds of reasoning : Immediate REASONING Deductive Mediate Inductive Are there also two kinds, Deductive and Inductive, under Immediate Inference? Immediate Reasoning, as it is usually treated of, is all Deductive, that is, in no case is the conclusion more general than the premiss. But if we define Immediate Reasoning as a reasoning in which a judgment is obtained from another judgment, it is evident, that the former may be more general as well as less general than the latter. If the conclusion be more general, the reasoning should certainly be called Inductive. If, for example, we could, in any case, draw the general conclusion from a single instance,—that is, from a single judgment or proposition-the reasoning, in that case, would be Immediate, as consisting of a single premiss only, and should be called Inductive, as leading to a conclusion more general than the premiss. In Deductive Logic, however, all immediate reasoning and all mediate reasoning are deductive, and the following classification is, therefore, preferable :— |