Kitabı oku: «The Art of Logical Thinking; Or, The Laws of Reasoning», sayfa 3

The last named authority also says: "Sometimes the same word may seem to have two or even more distinct negatives. There is much difference between undressed and not-dressed, that is 'not in evening dress.' Both seem to be negatives of 'dressed,' but this is because the word has two distinct meanings."

Some authorities insist upon closer and further classification, as for instance, in the case of what they call a Privative Term, denoting the absence of qualities once possessed by the object, person or thing, as: "deaf, dead, blind, dark," etc. Hyslop says that these terms "are Positive in form and Negative in matter or meaning." Also in the case of what they call a Nego-positive Term, denoting "the presence of a positive quality expressed in a negative manner," as: disagreeable, inhuman, invaluable, etc. These last mentioned classes however are regarded by some as the result of "carrying too far" the tendency toward classification, and the two general classes, Positive and Negative, are thought sufficient for the purpose of the general student. The same objection applies to a classification occasionally made i. e., that which is called an Infinitated Term, denoting a term the intent of which is to place in a distinct category every object, person or thing other than that expressed in the corresponding Positive Term. The intent of the term is to place the positive idea in one class, and all else into a separate one. Examples of this class of terms are found in: "not-I, not-animal, not-tree, unmoral," etc. Hyslop says of these terms: "They are not always, if ever, recognized as rhetorically elegant, but are valuable often to make clear the really negative, or infinitatively negative nature of the idea in mind."

Another general classification of Terms divides them into two respective classes, as follows: (1) Absolute Terms; and (2) Relative Terms.

An Absolute Term is a term denoting the presence of qualities intrinsic to the object, and not depending upon any relation to any other object, as for instance: "man; book; horse; gun;" etc. These terms may be related to many other terms, but are not necessarily related to any other.

A Relative Term is a term denoting certain necessary relations to other terms, as for instance: "father; son; mother; daughter; teacher; pupil; master; servant;" etc. Thus it is impossible to think of "child" except in relation to "parent," or vice versa. The one term implies the existence of its related term.

Hyslop says of the above classification: "Relative Terms suggest the thought of other individuals with the relation involved as a part of the term's meaning, while Absolute Terms suggest only the qualities in the subject without a relation to others being necessarily involved."

Some authorities also classify terms as higher and lower; also as broad and narrow. This classification is meant to indicate the content and extent of the term. For instance, when we classify, we begin with the individuals which we then group into a small class. These classes we then group into a larger class, according to their resemblances. These larger classes then go to form a part of still larger classes, and so on. As these classes advance they form broader terms; and as we retreat from the general class into the less general and more particular, the term becomes narrower. By some, the broader term which includes the narrower is called the higher term, and the narrower are called the lower terms. Thus animal would be a higher and broader term than dog, cat or tiger because it includes the latter. Brooks says: "Since a concept is formed by the union of the common attributes of individuals, it thus embraces both attributes and individuals. The attributes of a concept constitute what is called its content; the individuals it embraces constitute its extent."

Accordingly, the feature of including objects in a concept or term is called its extension; while the feature of including attributes or qualities is called its intension. It follows as a natural consequence that the greater the extension of a term, the less its intension; the greater its intension, the less its extension. We will understand this more clearly when we consider that the more individuals contained in a term, the fewer common properties or qualities it can contain; and the more common properties, the fewer individuals. As Brooks says: "The concept man has more extension than poet, orator or statesman, since it embraces more individuals; and less intension, since we must lay aside the distinctive attributes of poet, orator and statesman in order to unite them in a common class man." In the same way the general term animal is quite extended for it includes a large number of individual varieties of very different and varied characteristics and qualities; as for instance, the lion, camel, dog, oyster, elephant, snail, worm, snake, etc. Accordingly its intension must be small for it can include only the qualities common to all animals, which are very few indeed. The definition of the term shows how small is its intension, as: "Animal. An organic being, rising above a vegetable in various respects, especially in possessing sensibility, will and the power of voluntary motion." Another narrows the intension still further when he defines animal as: "a creature which possesses, or has possessed, life." Halleck says: "Animal is very narrow in intension, very broad in extension. There are few qualities common to all animals, but there is a vast number of animals. To give the full meaning of the term in extension, we should have to name every animal, from the microscopic infusoria to the tiger, from the angleworm to the whale. When we decrease the extension to one species of animal, horse, the individuals are fewer, the qualities more numerous."

The importance of forming clear and distinct concepts and of grouping, classifying and generalizing these into larger and broader concepts and terms is recognized by all authorities and is generally regarded as forming the real basis of all constructive thought. As Brooks says: "Generalization lies at the basis of language: only as man can form general conceptions is it possible for him to form a language… Nearly all the ordinary words in our language are general rather than particular… This power of generalization lies also at the basis of science. Had we no power of forming general ideas, each particular object would be a study by itself, and we should thus never pass beyond the very alphabet of knowledge. Judgments, except in the simplest form, would be impossible; and it is difficult to see how even the simplest form of the syllogism could be constructed. No general conclusion could be drawn from particulars, nor particular conclusions from generals; and thus neither inductive nor deductive reasoning would be possible. The classifications of science could not be made; and knowledge would end at the very threshold of science."

CHAPTER VII.
THE MEANING OF TERMS

Every term has its meaning, or content, as some authorities prefer to call it. The word or words of which the term is composed are merely vocal sounds, serving as a symbol for the real meaning of the term, which meaning exists only in the mind of the person understanding it. To one not understanding the meaning of the term, the latter is but as a meaningless sound, but to one understanding it the sound awakens mental associations and representation and thus serves its purpose as a symbol of thought.

Each concrete general term has two meanings, (1) the actual concrete thing, person or object to which the term is applied; and (2) the qualities, attributes or properties of those objects, persons or things in consequence of which the term is applied. For instance, in the case of the concrete term book, the first meaning consists of the general idea of the thing which we think of as a book, and the second meaning consists of the various qualities which go to make that thing a book, as the printed pages, the binding, the form, the cover, etc. Not only is that particular thing a book, but every other thing having the same or similar properties also must be a book. And so, whenever I call a thing a book it must possess the said qualities. And, whenever I combine the ideas of these qualities in thought, I must think of a book. As Jevons says: "In reality, every ordinary general term has a double meaning: it means the things to which it is applied, … it also means, in a totally different way, the qualities and peculiarities implied as being in the things. Logicians say that the number of things to which a term applies is the extension of the term; while the number of qualities or peculiarities implied is the intension."

The extension and intension of terms has been referred to in the previous chapter. The general classification of the degrees of extension of a general term is expressed by the two terms, Genus and Species, respectively. The classification of the character of the intension of a term is expressed by the term, Difference, Property and Accident, respectively.

Genus is a term indicating: "a class of objects containing several species; a class more extensive than a species; a universal which is predicable of several things of different species."

Species is a term denoting: "a smaller class of objects than a genus, and of two or more of which a genus is composed; a predicable that expresses the whole essence of its subject in so far as any common term can express it."

An authority says: "The names species and genus are merely relative and the same common term may, in one case, be the species which is predicated of an individual, and in another case the individual of which a species is predicated. Thus the individual, George, belongs to the logical species Man, while Man is an individual of the logical species Animal." Jevons says: "It is desirable to have names by which to show that one class is contained in another, and accordingly we call the class which is divided into two or more smaller ones, the genus, and the smaller ones into which it is divided, the species." Animal is a genus of which man is a species; while man, in turn, is a genus of which Caucasian is a species; and Caucasian, in turn, becomes a genus of which Socrates becomes a species. The student must avoid confusing the logical meaning of the terms genus and species with the use of the same terms in Natural History. Each class is a "genus" to the class below it in extension; and each class is a "species" to the class above it in extension. At the lowest extreme of the scale we reach what is called the infima species, which cannot be further subdivided, as for instance "Socrates" – this lowest species must always be an individual object, person or thing. At the highest extreme of the scale we reach what is summum genus, or highest genus, which is never a species of anything, for there is no class higher than it, as for instance, "being, existence, reality, truth, the absolute, the infinite, the ultimate," etc. Hyslop says: "In reality there is but one summum genus, while there may be an indefinite number of infimae species. All intermediate terms between these extremes are sometimes called subalterns, as being either genera or species, according to the relation in which they are viewed."

Passing on to the classification of the character of the intension of terms, we find:

Difference, a term denoting: "The mark or marks by which the species is distinguished from the rest of the genus; the specific characteristic." Thus the color of the skin is a difference between the Negro and the Caucasian; the number of feet the difference between the biped and the quadruped; the form and shape of leaves the difference between the oak and the elm trees, etc. Hyslop says: "Whatever distinguishes one object from another can be called the differentia. It is some characteristic in addition to the common qualities and determines the species or individual under the genus."

Property, a term denoting: "A peculiar quality of anything; that which is inherent in or naturally essential to anything." Thus a property is a distinguishing mark of a class. Thus black skin is a property of the Negro race; four feet a property of quadrupeds; a certain form of leaf a property of the oak tree. Thus a difference between two species may be a property of one of the species.

Accident, a term denoting: "Any quality or circumstance which may or may not belong to a class, accidentally as it were; or, whatever does not really constitute an essential part of an object, person or thing." As, for instance, the redness of a rose, for a rose might part with its redness and still be a rose – the color is the accident of the rose. Or, a brick may be white and still be a brick, although the majority of bricks are red – the redness or whiteness of the brick are its accidents and not its essential properties. Whately says: "Accidents in Logic are of two kinds – separable and inseparable. If walking be the accident of a particular man, it is a separable one, for he would not cease to be that man though he stood still; while, on the contrary, if Spaniard is the accident connected with him, it is an inseparable one, since he never can cease to be, ethnologically considered, what he was born."

Arising from the classification of the meaning or content of terms, we find the process termed "Definition."

Definition is a term denoting: "An explanation of a word or term." In Logic the term is used to denote the process of analysis in which the properties and differences of a term are clearly stated. There are of course several kinds of definitions. For instance, there is what is called a Real Definition, which Whately defines as: "A definition which explains the nature of the thing by a particular name." There is also what is called a Physical Definition, which is: "A definition made by enumerating such parts as are actually separable, such as the hull, masts, etc., of a ship." Also a Logical Definition, which is: "A definition consisting of the genus and the difference. Thus if a planet be defined as 'a wandering star,' star is the genus, and wandering points out the difference between a planet and an ordinary star." An Accidental Definition is: "A definition of the accidental qualities of a thing." An Essential Definition is: "a definition of the essential properties and differences of an object, person or thing."

Crabbe discriminates between a Definition and an Explanation, as follows: "A definition is correct or precise; an explanation is general or ample. The definition of a word defines or limits the extent of its signification; it is the rule for the scholar in the use of any word; the explanation of a word may include both definition and illustration; the former admits of no more words than will include the leading features in the meaning of any term; the latter admits of an unlimited scope for diffuseness on the part of the explainer."

Hyslop gives the following excellent explanation of the Logical Definition, which as he states is the proper meaning of the term in Logic. He states:

"The rules which regulate Logical Definition are as follows:

1. A definition should state the essential attributes of the species defined.

2. A definition must not contain the name of word defined. Otherwise the definition is called a circulus in definiendo.

3. The definition must be exactly equivalent to the species defined.

4. A definition should not be expressed in obscure, figurative, or ambiguous language.

5. A definition must not be negative when it can be affirmative."

A correct definition necessarily requires the manifestation of the two respective processes of Analysis and Synthesis.

Analysis is a term denoting: "The separation of anything into its constituent elements, qualities, properties and attributes." It is seen at once that in order to correctly define an object, person or thing, it is first necessary to analyze the latter in order to perceive its essential and accidental properties or differences. Unless the qualities, properties and attributes are clearly and fully perceived, we cannot properly define the object itself.

Synthesis is a term denoting: "The act of joining or putting two or more things together; in Logic: the method by composition, in opposition to the method of resolution or analysis." In stating a definition we must necessarily join together the various essential qualities, properties and attributes, which we have discovered by the process of analysis; and the synthesized combination, considered as a whole, is the definition of the object expressed by the term.

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 pronouncing 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 assert 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 illustration 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 class 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 analytic 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 analytic. When we compare concepts equal in rank or extent, the process is neither synthetic nor analytic. 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 analytic; in the statement that: "a man is a rational animal," the judgment is neither analytic 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 analytic, sometimes synthetic and sometimes neither analytic 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 repetition. 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.