The Art of Logical Thinking; Or, The Laws of Reasoning

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."

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: