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

Mediate

Deductive

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 :

Reasoning is either Inductive or Deductive. The latter is again either (1) Immediate, or (2) Mediate, according as the conclusion follows from one premiss or from more than one. A Mediate Deductive Reasoning is called a Syllogism, when it conforms to the axiom called Dictum de omni et nullo,—“Whatever is affirmed or denied of a class distributively, may be affirmed or denied of any thing belonging to that class," or to some similar axiom or axioms. It may be called Mathematical, when it conforms to some one or other of the axioms in mathematics, such as (1) that things which are equal to the same thing are equal to one another, (2) that the sums of equals are equal, (3) the principle or axiom called Argumentum a fortiori, that 'a thing which is greater than a second, which is greater than a third, is greater than the third.' The subdivisions of the other main division cannot be discussed in this book.

A Reasoning, regarded objectively, is the inference of a relation from one or more given relations among things and attributes. When a general or universal relation is inferred from one, a few, or many particular relations, the reasoning or inference is Inductive. When the relation inferred is not more general than the given relation or relations, and is, in fact, contained in, or implied by, the latter, the reasoning or inference is called Deductive. It is Immediate when the inference is drawn from one given relation or premiss, and Mediate when drawn from more than one. word inference, it should be noted, has, at least, three meanings:(1) the process of reasoning, (2) the product of reasoning consisting of the premisses and the conclusion, and (3) the conclusion only. We have here used the word in the second sense, but it is frequently used in the first, and more frequently in the third.

The

A reasoning, expressed in language, is called an Argument. There are thus as many kinds or varieties of the latter as there are of the former. The simplest form of argument corresponding to the simplest form of reasoning, namely, Immediate, consists of two propositions,-the premiss and the conclusion. A Mediate deductive reasoning gives rise to an argument consisting of more than two propositions, namely, the premisses and the conclusion.

An Inductive reasoning gives rise to an argument consisting of many propositions, namely, the particular instances constituting the data, and the general conclusion justified by them. The word 'argument' also denotes a series of reasonings advanced to establish a certain conclusion.

It should be carefully noted that so far as Logic is concerned with reasoning, it treats of the principles of correct reasoning, and lays down the conditions to which reasoning must conform in order that it may be valid. It is no part of Logic to give an account of the various processes according to which men do or may reason, but of those according to which they ought to reason, and must reason if their reasonings are to be valid. The former is the business of the science of Psychology, the latter only is the business of Logic1.

Examples of Different Kinds of Reasoning or Inference.

1 No attempt is made here to give an exhaustive account of all the processes of reasoning either from the psychological or from the logical point of view. In this chapter, the subject is treated for the purposes of this work. There is great diversity of view among Logicians (1) as to the nature of reasoning or inference,―as to what is and what is not inference, and (2) as to its fundamental kinds and varieties. The theory of Reasoning and Inference, like the theory of Predication and of the Import of Propositions, is a most important subject in Logic and Psychology, and would demand a thorough treatment in a complete treatise on Logic.

Mathematical reasonings are usually regarded as valid, if they conform to the axioms of mathematics. By taking the axioms as major premisses, and the data of the reasonings as minor premisses, they may, however, be reduced to the syllogistic form. Examples 6 and 7 given above may be stated syllogistically as follows:

6. Things which are equal to the same thing are equal to one another; the two things A and C are equal to the same thing (B); therefore the two things A and C are equal to one another.

7. A thing which is greater than a second, which is greater than a third, is greater than the third; the thing A is greater than a second (B), which is greater than a third (C); therefore the thing A is greater than the third (C).