The Art of Logical Thinking Part 3

CHAPTER VIII.

JUDGMENTS

The first step in the process of reasoning is that of Conception or the forming of Concepts. The second step is that of Judgment, or the process of perceiving the agreement or disagreement of two conceptions.

_Judgment_ in Logic is defined as: "The comparing together in the mind of two notions, concepts or ideas, which are the objects of apprehension, whether complex or incomplex, and p.r.o.nouncing that they agree or disagree with each other, or that one of them belongs or does not belong to the other. Judgment is therefore affirmative or negative."

When we have in our mind two concepts, we are likely to compare them one with the other, and to thus arrive at a conclusion regarding their agreement or disagreement. This process of comparison and decision is what, in Logic, is called _Judgment_.

In every act of Judgment there must be at least two concepts to be examined and compared. This comparison must lead to a Judgment regarding their agreement or disagreement. For instance, we have the two concepts, _horse_ and _animal_. We examine and compare the two concepts, and find that there is an agreement between them. We find that the concept _horse_ is included in the higher concept of _animal_ and therefore, we a.s.sert that: "_The horse is an animal._" This is a statement of _agreement_ and is, therefore, a _Positive Judgment_. We then compare the concepts _horse_ and _cow_ and find a disagreement between them, which we express in the statement of the Judgment that: "_The horse is not a cow._" This Judgment, stating a disagreement is what is called a _Negative Judgment_.

In the above ill.u.s.tration of the comparison between the concepts _horse_ and _animal_ we find that the second concept _animal_ is broader than the first, _horse_, so broad in fact that it includes the latter. The terms are not equal, for we cannot say, in truth, that "an animal is the horse." We may, however, include a _part_ of the broader conception with the narrower and say: "some animals are horses." Sometimes both concepts are of equal rank, as when we state that: "Man is a rational animal."

In the process of Judgment there is always the necessity of the choice between the Positive and the Negative. When we compare the concepts _horse_ and _animal_, we must of necessity decide either that the horse _is_ an animal, or else that it is _not_ an animal.

The importance of the process of Judgment is ably stated by Halleck, as follows: "Were isolated concepts possible, they would be of very little use. Isolated facts are of no more service than unspun wool. We might have a concept of a certain cla.s.s of three-leaved ivy, as we might also of poisons. Unless judgment linked these two concepts and decided that this species of ivy is poisonous, we might take hold of it and be poisoned. We might have a concept of bread and also one of meat, fruit and vegetables. If we also had a concept of food, unrelated to these, we should starve to death, for we should not think of them as foods. A vessel, supposing itself to be far out at sea, signaled another vessel that the crew were dying of thirst. That crew certainly had a concept of drinkable things and also of water. To the surprise of the first, the second vessel signaled back, 'Draw from the sea and drink. You are at the mouth of the Amazon.' The thirsty crew had not joined the concept _drinkable_ to the concept of water over the ship's side. A man having taken an overdose of laudanum, his wife lost much valuable time in sending out for antidotes, because certain of her concepts had not been connected by judgment. She had good concepts of coffee and of mustard; she also knew that an antidote to opium was needed; but she had never linked these concepts and judged that coffee and mustard were antidotes to opium. The moment she formed that judgment she was a wiser woman for her knowledge was related and usable.... Judgment is the power revolutionizing the world. The revolution is slow because nature's forces are so complex, so hard to be reduced to their simplest forms and so disguised and neutralized by the presence of other forces....

Fortunately judgment is ever silently working and comparing things that, to past ages, have seemed dissimilar; and it is continually abstracting and leaving out of the field of view those qualities which have simply served to obscure the point at issue."

Judgment may be both a.n.a.lytic or synthetic in its processes; and it may be neither. When we compare a narrow concept with a broader one, as a part with a whole, the process is synthetic or an act of combination.

When we compare a part of a concept with another concept, the process is a.n.a.lytic. When we compare concepts equal in rank or extent, the process is neither synthetic nor a.n.a.lytic. Thus in the statement that: "A horse is an animal," the judgment is synthetic; in the statement that: "some animals are horses," the judgement is a.n.a.lytic; in the statement that: "a man is a rational animal," the judgment is neither a.n.a.lytic nor synthetic.

Brooks says: "In one sense all judgments are synthetic. A judgment consists of the union of two ideas and this uniting is a process of synthesis. This, however, is a superficial view of the process. Such a synthesis is a mere mechanical synthesis; below this is a thought-process which is sometimes a.n.a.lytic, sometimes synthetic and sometimes neither a.n.a.lytic nor synthetic."

The same authority states: "The act of mind described is what is known as _logical judgment_. Strictly speaking, however, every intelligent act of the mind is accompanied with a _judgment_. To know is to discriminate and, therefore, to judge. Every sensation or cognition involves a knowledge and so a judgment that it exists. The mind cannot think at all without judging; to think is to judge. _Even in forming the notions which judgment compares, the mind judges._ Every notion or concept implies a previous act of judgment to form it: in forming a concept, we compare the common attributes before we unite them; and comparison is judgment. It is thus true that 'Every concept is a contracted judgment; every judgment an expanded concept.' This kind of judgment, by which we affirm the existence of states of consciousness, discriminate qualities, distinguish percepts and form concepts, is called _primitive or psychological judgment_."

In Logical Judgment there are two aspects; _i.e._, Judgment by Extension and Judgment by Intension. When we compare the two concepts _horse_ and _animal_ we find that the concept _horse_ is contained in the concept _animal_ and the judgment that "_a horse is an animal_" may be considered as a Judgment by Extension. In the same comparison we see that the concept _horse_ contains the _quality of animality_, and in attributing this quality to the _horse_, we may also say "_the horse is an animal_," which judgment may be considered as a Judgment by Intension. Brooks says: "Both views of Judgment are correct; the mind may reach its judgment either by extension or by intension. The method by extension is usually the more natural."

When a Judgment is expressed in words it is called a Proposition. There is some confusion regarding the two terms, some holding that a Judgment and a proposition are identical, and that the term "proposition" may be properly used to indicate the judgment itself. But the authorities who seek for clearness of expression and thought now generally hold that: "_A Proposition is a Judgment expressed in words._" In the next chapter, in which we consider Propositions, we shall enter into a more extended consideration of the subject of Judgments as expressed in Propositions, which consideration we omit at this point in order to avoid repet.i.tion.

Just as the respective subjects of Concepts and Terms necessarily blend into each other, so do the respective subjects of Judgments and Propositions. In each case, too, there is the element of the mental process on the one hand and the verbal expression of it on the other hand. It will be well to keep this fact in mind.

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 a.s.sertions 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.

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: "G.o.d is," by which is meant "G.o.d 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 cla.s.ses have been given in this chapter.

Another cla.s.sification of Propositions divides them in three cla.s.ses, 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 a.s.serted 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, circ.u.mstances 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 a.s.serting 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 cla.s.sification of Propositions divides them in two cla.s.ses as follows: (1) Universal; (2) Particular.

A _Universal Proposition_ is one in which the _whole quant.i.ty_ of the Subject is involved in the a.s.sertion 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 quant.i.ty, such as _some_, _certain_, _a few_, _many_, _most_ or such others as denote _at least a part_ of a cla.s.s.

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 a.s.surance 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 cla.s.s 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 cla.s.s animal--therefore, the predicate, _animals_, is not distributed.

In addition to the forms of Propositions given there is another cla.s.s of Propositions known as _Definitive or Subst.i.tutive 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 subst.i.tuted for each other. Hence the term "subst.i.tutive." 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.