2. All particulars do not distribute the subject.
3. All negatives distribute the predicate.
4. All affirmatives do not distribute the predicate.
The above rules are based upon logical reasoning. The reason for the first two rules is quite obvious, for when the subject is universal, it follows that the whole subject is involved; when the subject is particular it follows that only a part of the subject is involved. In the case of the third rule, it will be seen that in every negative proposition the whole of the predicate must be denied the subject, as for instance, when we say: "Some animals are not horses," the whole class of horses is cut off from the subject, and is thus distributed. In the case of the fourth rule, we may readily see that in the affirmative proposition the whole of the predicate is not denied the subject, as for instance, when we say that: "Horses are animals," we do not mean that horses are all the animals, but that they are merely a part or portion of the class animal—therefore, the predicate, animals, is not distributed.
In addition to the forms of Propositions given there is another class of Propositions known as Definitive or Substitutive Propositions, in which the Subject and the Predicate are exactly alike in extent and rank. For instance, in the proposition, "A triangle is a polygon of three sides" the two terms are interchangeable; that is, may be substituted for each other. Hence the term "substitutive." The term "definitive" arises from the fact that the respective terms of this kind of a proposition necessarily define each other. All logical definitions are expressed in this last mentioned form of proposition, for in such cases the subject and the predicate are precisely equal to each other.
CHAPTER X.
IMMEDIATE REASONING
In the process of Judgment we must compare two concepts and ascertain their agreement of disagreement. In the process of Reasoning we follow a similar method and compare two judgments, the result of such comparison being the deduction of a third judgment.
The simplest form of reasoning is that known as Immediate Reasoning, by which is meant the deduction of one proposition from another which implies it. Some have defined it as: "reasoning without a middle term." In this form of reasoning only one proposition is required for the premise, and from that premise the conclusion is deduced directly and without the necessity of comparison with any other term of proposition.
The two principal methods employed in this form of Reasoning are; (1) Opposition; (2) Conversion.