CHAPTER IX.

PROPOSITIONS

We have seen that the first step of Deductive Reasoning is that which we call Concepts. The second step is that which we call Propositions.

In Logic, a _Proposition_ is: "A sentence, or part of a sentence, affirming or denying a connection between the terms; limited to express assertions rather than extended to questions and commands." Hyslop defines a Proposition as: "any affirmation or denial of an agreement between two conceptions."

_Examples of Propositions_ are found in the following sentences: "The rose is a flower;" "a horse is an animal;" "Chicago is a city;" all of which are affirmations of agreement between the two terms involved; also in: "A horse is not a zebra;" "pinks are not roses;" "the whale is not a fish;" etc., which are denials of agreement between the terms.

The _Parts of a Proposition_ are: (1) the _Subject_, or that of which something is affirmed or denied; (2) the _Predicate_, or _the something_ which is affirmed or denied regarding the _Subject_; and (3) the _Copula_, or the verb serving as a link between the Subject and the Predicate.

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In the Proposition: "Man is an animal," the term _man_ is the Subject; the term _an animal_ is the Predicate; and the word _is_, is the Copula. The Copula is always some form of the verb _to be_, in the present tense indicative, in an affirmative Proposition; and the same with the negative particle affixed, in a negative Proposition. The Copula is not always directly expressed by the word _is_ or _is not_, etc., but is instead expressed in some phrase which implies them. For instance, we say "he runs," which implies "he is running." In the same way, it may appear at times as if the Predicate was missing, as in: "God is," by which is meant "God is existing." In some cases, the Proposition is inverted, the Predicate appearing first in order, and the Subject last, as in: "Blessed are the peacemakers;" or "Strong is Truth." In such cases judgment must be used in determining the matter, in accordance with the character and meaning of the terms.

An _Affirmative Proposition_ is one in which the Predicate is _affirmed_ to agree with the Subject. A _Negative Proposition_ is one in which the agreement of the Predicate and Subject is _denied_. Examples of both of these classes have been given in this chapter.

Another classification of Propositions divides them in three classes, as follows (1) Categorical; (2) Hypothetical; (3) Disjunctive.

A _Categorical Proposition_ is one in which the affirmation or denial is made without reservation or qualification, as for instance: "Man is an animal;" "the rose is a flower," etc. The fact asserted may not be _true_, but the statement is made positively as a statement of reality.

A _Hypothetical Proposition_ is one in which the affirmation or denial is made to depend upon certain conditions, circumstances or suppositions, as for instance: "If the water is boiling-hot, it will scald;" or "if the powder be damp, it will not explode," etc. Jevons says: "Hypothetical Propositions may generally be recognized by containing the little word 'if;' but it is doubtful whether they really differ much from the ordinary propositions.... We may easily say that 'boiling water will scald,' and 'damp gunpowder will not explode,' thus avoiding the use of the word 'if.'"

A _Disjunctive Proposition_ is one "implying or asserting an alternative," and usually containing the conjunction "or," sometimes together with "either," as for instance: "Lightning is sheet or forked;" "Arches are either round or pointed;" "Angles are either obtuse, right angled or acute."

Another classification of Propositions divides them in two classes as follows: (1) Universal; (2) Particular.

A _Universal Proposition_ is one in which the _whole quantity_ of the Subject is involved in the assertion or denial of the Predicate. For instance: "All men are liars," by which is affirmed that _all_ of the entire race of men are in the category of liars, not _some_ men but _all_ the men that are in existence. In the same way the Proposition: "No men are immortal" is Universal, for it is a _universal denial_.

A _Particular Proposition_ is one in which the affirmation or denial of the Predicate involves only a _part or portion_ of the whole of the Subject, as for instance: "_Some_ men are atheists," or "_Some_ women are not vain," in which cases the affirmation or denial does not involve _all_ or the _whole_ of the Subject. Other examples are: "A _few_ men," etc.; "_many_ people," etc.; "_certain_ books," etc.; "_most_ people," etc.

Hyslop says: "The signs of the Universal Proposition, when formally expressed, are _all_, _every_, _each_, _any_, _and whole_ or words with equivalent import." The signs of Particular Propositions are also certain adjectives of quantity, such as _some_, _certain_, _a few_, _many_, _most_ or such others as denote _at least a part_ of a class.

The subject of the Distribution of Terms in Propositions is considered very important by Logicians, and as Hyslop says: "has much importance in determining the legitimacy, or at least the intelligibility, of our reasoning and the assurance that it will be accepted by others." Some authorities favor the term, "Qualification of the Terms of Propositions," but the established usage favors the term "Distribution."

The definition of the Logical term, "Distribution," is: "The distinguishing of a universal whole into its several kinds of species; the employment of a term to its fullest extent; the application of a term to its fullest extent, so as to include all significations or applications." A Term of a Proposition is _distributed_ when it is employed in its fullest sense; that is to say, _when it is employed so as to apply to each and every object, person or thing included under it_. Thus in the proposition, "All horses are animals," the term _horses_ is distributed; and in the proposition, "Some horses are thoroughbreds," the term _horses_ is not distributed. Both of these examples relate to the distribution of the _subject_ of the proposition. But the predicate of a proposition also may or may not be distributed. For instance, in the proposition, "All horses are animals," the predicate, _animals_, is not distributed, that is, _not used in its fullest sense_, for all _animals_ are not _horses_--there are _some_ animals which are not horses and, therefore, the predicate, _animals_, not being used in its fullest sense is said to be "_not distributed_." The proposition really means: "All horses are _some_ animals."

There is however another point to be remembered in the consideration of Distribution of Terms of Propositions, which Brooks expresses as follows: "Distribution generally shows itself in the form of the expression, but sometimes it may be determined by the thought. Thus if we say, 'Men are mortal,' we mean _all men_, and the term men is distributed. But if we say 'Books are necessary to a library,' we mean, not 'all books' but 'some books.' The _test of distribution_ is whether the term applies to '_each and every_.' Thus when we say 'men are mortal,' it is true of each and every man that he is mortal."

The Rules of Distribution of the Terms of Proposition are as follows:

1. All _universals_ distribute the _subject_.

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.