Kitabı oku: «The Art of Logical Thinking; Or, The Laws of Reasoning», sayfa 2

CHAPTER IV.
THE USE OF CONCEPTS

Having observed the several steps or stages of a concept, let us now consider the use and misuse of the latter. At first glance it would appear difficult to misuse a concept, but a little consideration will show that people very commonly fall into error regarding their concepts.

For instance, a child perceives a horse, a cow or a sheep and hears its elders apply the term "animal" to it. This term is perfectly correct, although symbolizing only a very general classification or generalization. But, the child knowing nothing of the more limited and detailed classification begins to generalize regarding the animal. To it, accordingly, an "animal" is identical with the dog or the cow, the sheep or the horse, as the case may be, and when the term is used the child thinks that all animals are similar to the particular animal seen. Later on, when it hears the term "animal" applied to a totally different looking creature, it thinks that a mistake has been made and a state of confusion occurs. Or, even when a term is applied within narrower limits, the same trouble occurs. The child may hear the term "dog" applied to a mastiff, and it accordingly forms a concept of dog identical with the qualities and attributes of the mastiff. Later, hearing the same term applied to a toy-terrier, it becomes indignant and cries out that the latter is no "dog" but is something entirely different. It is not until the child becomes acquainted with the fact that there are many kinds of creatures in the general category of "dog" that the latter term becomes fully understood and its appropriate concept is intelligently formed. Thus we see the importance of the step of Presentation.

In the same way the child might imagine that because some particular "man" had red hair and long whiskers, all men were red-haired and long-whiskered. Such a child would always form the concept of "man" as a creature possessed of the personal qualities just mentioned. As a writer once said, readers of current French literature might imagine that all Englishmen were short, dumpy, red-cheeked and irascible, and that all Englishwomen had great teeth and enormous feet; also that readers of English literature might imagine that all Frenchmen were like monkeys, and all Frenchwomen were sad coquettes. In the same way many American young people believe that all Englishmen say "Don't you know" and all Englishwomen constantly ejaculate: "Fancy!" Also that every Englishman wears a monocle. In the same way, the young English person, from reading the cheap novels of his own country, might well form the concept of all Americans as long-legged, chin-whiskered and big-nosed, saying "Waal, I want to know;" "I reckon;" and "Du tell;" while they tilted themselves back in a chair with their feet on the mantelpiece. The concept of a Western man, entertained by the average Eastern person who has never traveled further West than Buffalo, is equally amusing. In the same way, we have known Western people who formed a concept of Boston people as partaking of a steady and continuous diet of baked beans and studiously reading Browning and Emerson between these meals.

Halleck says: "A certain Norwegian child ten years old had the quality white firmly imbedded in his concept man. Happening one day to see a negro for the first time, the child refused to call him a man until the negro's other qualities compelled the child to revise his concept and to eliminate whiteness. If that child should ever see an Indian or a Chinaman, the concept would undergo still further revision. A girl of six, reared with an intemperate father and brothers, had the quality of drunkenness firmly fixed in her concept of man. A certain boy kept, until the age of eleven, trustworthiness in his concept of man. Another boy, until late in his teens thought that man was a creature who did wrong not from determination but from ignorance, that any man would change his course to the right path if he could but understand that he was going wrong. Happening one day to hear of a wealthy man who was neglecting to provide comforts for his aged mother in her last sickness, the boy concluded that the man did not know his mother's condition. When he informed the man, the boy was told to mind his own business. The same day he heard of some politicians who had intentionally cheated the city in letting a contract and he immediately revised his concept. It must be borne in mind that most of our concepts are subject to change during our entire life; that at first they are made only in a tentative way; that experience may show us, at any time, that they have been erroneously formed, that we have, abstracted too little or too much, made this class too wide or too narrow, or that here a quality must be added or there one taken away."

Let us now consider the mental processes involved in the formation and use of a concept. We have first, as we have seen, the presentation of the crude material from which the concept must be formed. Our attention being attracted to or directed toward an object, we notice its qualities and properties. Then we begin a process of comparison of the object perceived or of our perception of it. We compare the object with other objects or ideas in our mind, noting similarities and differences and thereby leading towards classification with similar objects and opposed dissimilar ones. The greater the range of other objects previously perceived, the greater will be the number of relations established between the new object or idea and others. As we advance in experience and knowledge, the web of related objects and ideas becomes more intricate and complex. The relations attaching to the child's concept of horse is very much simpler than the concept of the experienced adult. Then we pass on to the step of analysis, in which we separate the qualities of the object and consider them in detail. The act of abstraction is an analytical process. Then we pass on to the step of synthesis, in which we unite the materials gathered by comparison and analysis, and thus form a general idea or concept regarding the object. In this process we combine the various qualities discerned by comparison and analysis, and grouping them together as in a bundle, we tie them together with the string of synthesis and thus have a true general conception. Thus from the first general conception of horse as a simple thing, we notice first that the animal has certain qualities lacking in other things and certain others similar to other things; then we analyze the various qualities of the horse, recognized through comparison, until we have a clear and distinct idea of the various parts, qualities and properties of the horse; then we synthesize, and joining together these various conceptions of the said qualities, we at last form a clear general concept of the horse as he is, with all his qualities. Of course, if we later discover other qualities attached to the horse, we add these to our general synthesized concept – our concept of horse is enlarged.

Of course these various steps in the formation and use of a concept are not realized as distinct acts in the consciousness, for the processes are largely instinctive and subconscious, particularly in the case of the experienced individual. The subconscious, or habit mind, usually attends to these details for us, except in instances in which we deliberately apply the will to the task, as in cases of close study, in which we take the process from the region of the involuntary and place it in the voluntary category. So closely related and blended are these various steps of the process, that some authorities have disputed vigorously upon the question as to which of the two steps, comparison or analysis, precedes the other. Some have claimed that analysis must precede comparison, else how could one compare without having first analyzed the things to be compared. Others hold that comparison must precede analysis, else how could one note a quality unless he had his attention drawn to it by its resemblance to or difference from qualities in other objects. The truth seems to lie between the two ideas, for in some cases there seems to be a perception of some similarity or difference before any analysis or abstraction takes place; while in others there seems to be an analysis or abstraction before comparison is possible. In this book we have followed the arrangement favored by the latest authorities, but the question is still an open one to many minds.

As we have seen, the general concept once having been formed, the mind proceeds to classify the concept with others having general qualities in common. And, likewise, it proceeds to generalize from the classification, assuming certain qualities in certain classes. Then we proceed to make still further generalizations and classifications on an ascending and widening scale, including seeming resemblances less marked, until finally we embrace the object with other objects in as large a class as possible as well as in as close and limited a sub-class as possible. As Brooks says: "Generalization is an ascending process. The broader concept is regarded as higher than the narrower concept; a concept is considered higher than a percept; a general idea stands above a particular idea. We thus go up from particulars to generals; from percepts to concepts; from lower concepts to higher concepts. Beginning down with particular objects, we rise from them to the general idea of their class. Having formed a number of lower classes, we compare them as we did individuals and generalize them into higher classes. We perform the same process with these higher classes, and thus proceed until we are at last arrested in the highest class, Being. Having reached the pinnacle of generalization, we may descend the ladder by reversing the process through which we ascend."

From this process of generalization, or synthesis, we create from our simple concepts our general concepts. Some of the older authorities distinguished between these two classes by terming the former "conceptions," and reserving the term "concepts" for the general concepts. Brooks says of this: "The products of generalization are general ideas called concepts. We have already discussed the method of forming conceptions and now consider the nature of the concept itself… A concept is a general idea. It is a general notion which has in it all that is common to its own class. It is a general scheme which embraces all the individuals of the class while it resembles in all respects none of its class. Thus my conception of a quadruped has in it all four-footed animals, but it does not correspond in all respects to any particular animals; my conception of a triangle embraces all triangles, but does not agree in details with any particular triangle. The general conception cannot be made to fit exactly any particular object, but it teems with many particulars. These points may be illustrated with the concepts horse, bird, color, animal, etc."

So we may begin to perceive the distinction and difference between a concept and a mental image. This distinction, and the fact that a concept cannot be imaged, is generally difficult for the beginner. It is important that one should have a clear and distinct understanding regarding this point, and so we shall consider it further in the following chapter.

CHAPTER V.
CONCEPTS AND IMAGES

As we have said, a concept cannot be imaged – cannot be used as the subject of a mental image. This statement is perplexing to the student who has been accustomed to the idea that every conception of the mind is capable of being reproduced in the form of a mental image. But the apparently paradoxical statement is seen as quite simple when a little consideration is given to it.

For instance, you have a distinct general concept of animal. You know what you mean when you say or think, animal. You recognize an animal when you see one and you understand what is meant when another uses the word in conversation. But you cannot form a mental image of the concept, animal. Why? Because any mental image you might form would be either a picture of some particular animal or else a composite of the qualities of several animals. Your concept is too broad and general to allow of a composite picture of all animals. And, in truth, your concept is not a picture of anything that actually exists in one particular, but an abstract idea embracing the qualities of all animals. It is like the algebraic x– a symbol for something that exists, but not the thing itself.

As Brooks says: "A concept cannot be represented by a concrete image. This is evident from its being general rather than particular. If its color, size or shape is fixed by an image, it is no longer general but particular." And Halleck says: "It is impossible to image anything without giving that image individual marks. The best mental images are so definite that a picture could be painted from them. A being might come under the class man and have a snub nose, blonde hair, scanty eyebrows, and no scar on his face. The presence of one of these individual peculiarities in the concept man would destroy it. If we form an image of an apple, it must be either of a yellow, red, green, or russet apple, either as large as a pippin or as small as a crab-apple. A boy was asked what he thought of when 'apple' was mentioned. He replied that he thought of 'a big, dark-red, apple with a bad spot on one side, near the top.' That boy could image distinctly, but his power of forming concepts was still in its infancy."

So we see that while a mental image must picture the particular and individual qualities, properties and appearances of some particular unit of a class, a concept can and must contain only the class qualities– that is, the qualities belonging to the entire class. The general concept is as has been said "a general idea … a general notion which has in it all that is common to its own class." And it follows that a "general idea" of this kind cannot be pictured. A picture must be of some particular thing, while a concept is something above and higher than particular things. We may picture a man, but we cannot picture Man the concept of the race. A concept is not a reproduction of the image of a thing, but on the contrary is an idea of a class of things. We trust that the student will consider this point until he arrives at a clear understanding of the distinction, and the reason thereof.

But, while a concept is incapable of being pictured mentally as an image, it is true that some particular representative of a class may be held in the mind or imagination as an idealized object, as a general representative of the class, when we speak or think of the general term or concept, providing that its real relation to the concept is recognized. These idealized objects, however, are not concepts – they are percepts reproduced by the memory. It is important, however, to all who wish to convey their thought plainly, that they be able to convert their concepts into idealized representative objects. Otherwise, they tend to become too idealistic and abstract for common comprehension. As Halleck well says: "We should in all cases be ready to translate our concepts, when occasion requires, into the images of those individuals which the concept represents. A concept means nothing except in reference to certain individuals. Without them it could never have had existence and they are entitled to representation. A man who cannot translate his concepts into definite images of the proper objects, is fitted neither to teach, preach, nor practice any profession… There was, not long ago, a man very fond of talking about fruit in the abstract; but he failed to recognize an individual cranberry when it was placed before him. A humorist remarked that a certain metaphysician had such a love for abstractions, and such an intense dislike for concrete things, as to refuse to eat a concrete peach when placed before him."

In the beginning many students are perplexed regarding the difference between a percept and a concept. The distinction is simple when properly considered. A percept is: "the object of an act of perception; that which is perceived." A concept is: "a mental representation." Brooks makes the following distinction: "A percept is the mental product of a real thing; a concept is a mere idea or notion of the common attributes of things. A percept represents some particular object; a concept is not particular, but general. A percept can be described by particulars; a concept can be described only by generals. The former can usually be represented by an image, the latter cannot be imagined, it can only be thought." Thus one is able to image the percept of a particular horse which has been perceived; but he is unable to image correctly the concept of horse as a class or generic term.

In connection with this distinction between perception and conception, we may as well consider the subject of apperception, a term favored by many modern psychologists, although others steadfastly decline to recognize its necessity or meaning and refuse to employ it. Apperception may be defined as: "perception accompanied by comprehension; perception accompanied by recognition." The thing perceived is held to be comprehended or recognized – that is, perceived in a new sense, by reason of certain previously acquired ideas in the mind. Halleck explains it as: "the perception of things in relation to the ideas which we already possess." It follows that all individuals possessed of equally active organs of perception, and equally active attention, will perceive the same thing in the same way and in the same degree. But the apperception of each individual will differ and vary according to his previous experience and training, temperament and taste, habit and custom. For instance, the familiar story of the boy who climbed a tree and watched the passers-by, noting their comments. The first passer-by noticing the tree, says aloud: "That would make a good stick of timber." "Good morning, Mr. Carpenter," said the boy. The next man said: "That tree has fine bark." "Good morning, Mr. Tanner," said the boy. Another said, "I bet there's a squirrel's nest up in that tree." "Good morning, Mr. Hunter," said the boy.

The woman sees in a bird something pretty and "cunning." The hunter sees in it something to kill. The ornithologist sees it as something of a certain genus and species, and perhaps also as something appropriate for his collection. The farmer perceives it to be something destructive of either insects or crops. A thief sees a jail as something to be dreaded; an ordinary citizen, something useful for confining objectionable people; a policeman, something in the line of his business. And so on, the apperception differing upon the previous experience of the individual. In the same way the scientist sees in an animal or rock many qualities of which the ordinary person is ignorant. Our training, experience, prejudices, etc., affect our apperception.

And so, we see that in a measure our concepts are determined not only by our simple perceptions, but also materially by our apperceptions. We conceive things not only as they are apparent to our senses, but also as colored and influenced by our previous impressions and ideas. For this reason we find widely varying concepts of the same things among different individuals. Only an absolute mind could form an absolute concept.

CHAPTER VI.
TERMS

In logic the words concept and term are practically identical, but in the popular usage of the terms there is a distinct difference. This difference is warranted, if we depart from the theoretical phase of logic, for the word concept really denotes an idea in the mind, while the word term really denotes a word or name of an idea or concept – the symbol of the latter. In a previous chapter we have seen that Denomination, or "the act of naming or designating by a name" is the final step or stage in forming a concept. And it is a fact that the majority of the words in the languages of civilized people denote general ideas or concepts. As Brooks says: "To give each individual or particular idea a name peculiar to itself would be impracticable and indeed impossible; the mind would soon become overwhelmed with its burden of names. Nearly all the ordinary words of our language are general rather than particular. The individuals distinguished by particular names, excepting persons and places, are comparatively few. Most objects are named only by common nouns; nearly all of our verbs express general actions; our adjectives denote common qualities, and our adverbs designate classes of actions and qualities. There are very few words in the language, besides the names of persons and places, that do not express general ideas."

In logic the word term is employed to denote any word or words which constitute a concept. The word concept is employed strictly in the sense of a subject of thought, without reference to the words symbolizing it. The concept, or subject of thought, is the important element or fact and the term denoting it is merely a convenient symbol of expression. It must be remembered that a term does not necessarily consists of but a single word, for often many words are employed to denote the concept, sometimes even an entire clause or phrase being found necessary for the current term. For the purpose of the consideration of the subjects to be treated upon in this book, we may agree that: A term is the outward symbol of a concept; and that: The concept is the idea expressed by the term.

There are three general parts or phases of Deductive Logic, namely: Terms, Propositions and Syllogisms. Therefore, in considering Terms we are entering into a consideration of the first phase of Deductive Logic. Unless we have a correct understanding of Terms, we cannot expect to understand the succeeding stages of Deductive Reasoning. As Jevons says: "When we join terms together we make a Proposition; when we join Propositions together, we make an argument or piece of reasoning… We should generally get nothing but nonsense if we were to put together any terms and any propositions and to suppose that we were reasoning. To produce a good argument we must be careful to obey certain rules, which it is the purpose of Logic to make known. But, in order to understand the matter perfectly, we ought first to learn exactly what a term is, and how many kinds of terms there may be; we have next to learn the nature of a proposition and the different kinds of propositions. Afterwards we shall learn how one proposition may by reasoning be drawn from other propositions in the kind of argument called the syllogism."

Now, having seen that terms are the outward symbols or expression of concepts, and are the names of things which we join together in a proposition, let us proceed to consider the different kinds of terms, following the classifications adopted by the authorities.

A term may contain any number of nouns, substantive or adjective or it may contain but a single noun. Thus in, "Tigers are ferocious," the first term is the single substantive "tigers;" the second term is the single adjective "ferocious." And in the proposition, "The King of England is the Emperor of India," there are two terms, each composed of two nouns, "King of England" being the first term and "Emperor of India" being the second term. The proposition, "The library of the British Museum is the greatest collection of books in the world," contains fifteen words but only two terms; the first term being "The library of the British Museum," in which are two substantives, one adjective, two definite articles and one preposition; the second term being, "the greatest collection of books in the world," which contains three substantives, one adjective, two articles, and two prepositions. The above illustration is supplied by Jevons, who adds: "A logical term, then, may consist of any number of nouns, substantive or adjective, with the articles, prepositions and conjunctions required to join them together; still it is only one term if it points out, or makes us think of a single object, or collection, or class of objects." (A substantive, is: "the part of speech which expresses something that exists, either material or immaterial.")

The first classification of terms divides them into two general classes, viz., (1) Singular Terms; and (2) General Terms.

A Singular Term is a term denoting a single object, person or thing. Although denoting only a single object, person or thing, it may be composed of several words; or it may be composed of but one word as in the case of a proper name, etc. The following are Singular Terms, because they are terms denoting but a single object, person or thing: "Europe; Minnesota; Socrates; Shakespeare; the first man; the highest good; the first cause; the King of England; the British Museum; the Commissioner of Public Works; the main street of the City of New York." It will be noted that in all of the examples given, the Singular Term denotes a particular something, a specific thing, a something of which there is but one, and that one possesses particularity and individuality. As Hyslop says: "Oneness of kind is not the only or distinctive feature of Singular Terms, but individuality, or singularity, as representing a concrete individual whole."

A General Term is a term which applies, in the same sense, to each and every individual object, person or thing in a number of objects, persons or things of the same kind, or to the entire class composed of such objects persons or things of the same kind. For instance, "horse; man; biped; mammal; trees; figures; grain of sand; matter," etc. Hyslop says, regarding General Terms: "In these instances the terms denote more than one object, and apply to all of the same kind. Their meaning is important in the interpretation of what are called universal propositions."

Another general classification of Terms divides them into two respective classes, as follows: (1) Collective Terms; and (2) Distributive Terms. Hyslop says of this classification: "This division is based upon the distinction between aggregate wholes of the same kind and class terms. It partly coincides with the division into Singular and General Terms, the latter always being distributive."

A Collective Term is one which denotes an aggregate or collected whole of objects, persons or things of the same or similar kind, which collective whole is considered as an individual, although composed of a totality of separate individual objects, persons or things. Thus the following terms: "regiment; congregation; army; family; crowd; nation; company; battalion; class; congress; parliament; convention;" etc. are Collective Terms, because they denote collective, aggregate or composite wholes, considered as an individual.

A Distributive Term is a term which denotes each and every individual object, person or thing in a given class. For example, are the terms: "man; quadruped; biped; mammal; book; diamond; tree." As Hyslop says: "General terms are always distributive." Also: "It is important also to keep clear the distinction between class wholes and collective wholes… They are often confused so as to call a term denoting a class a Collective Term."

Another general classification of Terms divides them into the following two respective classes; (1) Concrete Terms; and (2) Abstract Terms.

A Concrete Term is a term denoting either a definite object, person or thing which is subject to perception and experience, and may be considered as actually existent concretely, as for instance: horse; man; mountain; dollar; knife; table; etc., or else an attribute thought of and used solely as an attribute, as for instance: "beautiful, wise, noble, virtuous, good," etc.

An Abstract Term is a term denoting the attribute, quality or property considered as apart from the object, person or thing and as having an abstract existence, as for instance: "beauty; wisdom; nobility; goodness; virtue," etc. As we have seen elsewhere, these qualities have no real existence in themselves, but are known and thought of only in connection with concrete objects, persons and things. Thus we cannot know "Beauty," but may know beautiful things; we cannot know "Virtue," but we may know virtuous people, etc.

An attribute or quality is concrete when expressed as an adjective; and abstract when expressed as a noun; as for instance, "beautiful" and "beauty," respectively, or "virtuous" and "virtue," respectively. The distinction may be summed up as follows: A Concrete Term is the name of a thing or of a quality of a thing expressed as an adjective and as merely a quality; while an Abstract Term is the name of a quality of a thing, expressed as a noun and as a "thing" in itself.

Certain terms may be used as either Concrete Terms or as Abstract Terms, and certain authorities have seen fit to classify them as Mixed Terms, as for instance the terms: "government; religion; philosophy;" etc.

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

A Positive Term is a term which denotes its own qualities, as for instance: "good, human, large, square, black, strong," etc. These terms indicate the presence of the quality denoted by the term itself.

A Negative Term is a term denoting the absence of a quality, as for instance: "inhuman, inorganic, unwell, unpleasant, non-conducive," etc. These terms deny the presence of certain qualities, rather than asserting the presence of an opposite quality. They are essentially negative in nature and in form. Jevons says: "We may usually know a Negative Term by its beginning with one of the little syllables un-, in-, a-, an-, non-, or by its ending with – less." Hyslop says: "The usual symbols of Negative Terms are in, un, less, dis, a, or an, anti, mis, and sometimes de, and non and not." Jevons adds: "If the English language were a perfect one, every term ought to have a Negative Term exactly corresponding to it, so that all adjectives and nouns would be in pairs. Just as convenient has its negative inconvenient; metallic, non-metallic; logical, illogical; and so on; so blue should have its negative, non-blue; literary, non-literary; paper, non-paper. But many of these Negative Terms would be seldom or never used, and if we happen to want them, we can make them for the occasion by putting not-, or non-, before the Positive Term. Accordingly, we find in the dictionary only those Negative Terms which are much employed."