Definition.

Existence of certain things im

of others.

CHAPTER IV.

REASONING AND INFERENCE.

WHAT is meant by Reasoning is the deriving from judgments previously given, of other judgments founded upon them; or "that operation of the mind through which it forms one judgment from many others." The constitution of things is such that certain facts are so connected with certain other facts, or so involved in them, that the existence of the former implies that of the latter, and if we plied in that know the one we know the other also, though we may have no means of knowing the latter, except through the medium of our knowledge of the former. Thus, if I see a man on this side of a long river at ten o'clock in the morning, and see him on the other side at eleven o'clock, I know that he has crossed the river in the meantime, though I have not seen him do so, nor in any way perceived the act of crossing, nor have learned it through any testimony. I know it simply from the relations of the other known facts, which are such that if they are or were actual, this must also be actual. And I know this just as certainly as if I had myself perceived it. This I take to be substantially a type of most of our reasoning.

The determination of the relation of facts, whether perceptions, acts, deliverances of the Inner-Sense, or of the regulative faculty, is by a process of the mind which has

already been described, and which is designated as Judgment. The expression of this in language is called a Proposition. As previously shown, the essential element in reasoning, as in all preliminary thinking processes, is judgment. We reason from judgment to judgments; and the determining of the relations of judgments, and what is involved in them, and whether it be inferential or not, is of the nature of a judgment.

Reasoning is commonly divided into Deductive and Inductive — or reasoning from general classes to particular classes or to individuals, and reasoning from Deductive individuals or particular classes to general facts and inducand principles.

tive.

A difference is also to be observed between Reasoning and Inference. The difference is much the same as between

Analytic and Synthetic reasoning. In the former Reasoning

ence.

case the conclusion is stated first in the form and infer of a proposition to be proved; in the latter the grounds or facts from which we reason are stated first, and the conclusion inferred from them.

All oaks are vegetables, because all trees are vegetables, and all oaks are trees.

This is analytic reasoning; that is, a proposition is stated, and we look about for its proof. We separate into parts, and compare the several parts with Analytic another object in such a way that we find a reasoning. substantial reason for the truth of the proposition.

All trees are vegetables;

All oaks are trees;

All oaks are vegetables.

This is synthetic. Two propositions are found in such relations to each other that they necessarily imply a third, or by a combination-a synthesis of the eleSynthetic reasoning. ments of the two- we have a third which is an inference from them.

Inference

immediate.

Inference is further either Immediate or Mediate. mediate and It is immediate when one judgment is inferred from another without the intervention or mediation of a third judgment. There are several forms of Immediate Inference, the most common of which are by Opposition and by Conversion.

Opposition.

OPPOSITION.

Two judgments are said to be in opposition when they have the same subject and predicate, but differ in quantity or quality, or both. When they differ in quality only, it is called Contrary or Sub-contrary opposition.

When they differ in quantity only, it is called Subaltern opposition.

When they differ in both quality and quantity it is called Contradictory opposition.

The value of this method of reasoning is that we immediately infer from one proposition the truth or falsehood of the opposite.

All men are poets. A.

No men are poets. E.

These two propositions are in contrary opposition. From the truth of the former we infer the falsity of the latter;

Contrary opposition.

but not the truth of the latter from the falsity of the former; since both cannot be true, but both may be false, as in this particular case.

These are Sub-contraries. From the falsity of the one we infer the truth of the other; but from the Sub-contrary truth of the one we infer nothing concerning opposition. the other, since they may both be true, as in this instance they are.

In each case if the former is true, the latter must be true also; but from the truth of the latter nothing follows con

cerning the former. From the falsehood of Subaltern

the latter the falsehood of the former follows; opposition. though from the falsehood of the former nothing follows concerning the latter.

Contradic

Here it will be seen that in each case, if either of the two opposites be true, the other must be false; if either be false, the other must be true; and that one must be false and the other true. This is the strongest tory opposikind of opposition. This kind of inference is useful in cases where, though it would not be convenient, perhaps not possible, to prove the truth or falsehood of a

tion.

Value of inference by means of opposition.

particular proposition, we may nevertheless easily prove the truth or falsehood of its opposite; and if the opposition is of the kind that serves our purpose, we may draw an immediate inference from the proposition proved as to the truth or falsehood of its opposite. Thus in any argument we say sometimes, "It is impossible to prove a negative." This is not always true, but it is sometimes true. In such a case as this, if we can find means to prove the truth of the contradictory of the proposition we wish to negative, this is equivalent to disproving the proposition in question, since the truth of the contradictory implies the falsehood of its opposite.

Conversion

CONVERSION.

By this we mean the changing of places of the subject and predicate, in such a way that the Converse is an inference from the Convertend. This is the only defined. kind of illative conversion, or that in which an inference may be drawn from the original proposition to its converse. Thus,

Some men are wise beings;

Some wise beings are men,

is an illative conversion, since the latter proposition is a necessary and obvious inference from the former.

All dogs are animals;

All animals are dogs, —

this is conversion, but it is not illative; there is no inference of the latter from the former.