The Art of Logical Thinking Part 2

Another general cla.s.sification of Terms divides them into the following two respective cla.s.ses; (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, n.o.ble, 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; n.o.bility; 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 cla.s.sify them as _Mixed Terms_, as for instance the terms: "government; religion; philosophy;" etc.

Another general cla.s.sification of Terms divides them into two respective cla.s.ses 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 _a.s.serting_ 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 cla.s.sification, 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 cla.s.ses however are regarded by some as the result of "carrying too far" the tendency toward cla.s.sification, and the two general cla.s.ses, Positive and Negative, are thought sufficient for the purpose of the general student.

The same objection applies to a cla.s.sification 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 cla.s.s, and all else into a separate one. Examples of this cla.s.s 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 cla.s.sification of Terms divides them into two respective cla.s.ses, 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 cla.s.sification: "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 cla.s.sify terms as _higher and lower_; also as _broad and narrow_. This cla.s.sification is meant to indicate the content and extent of the term. For instance, when we cla.s.sify, we begin with the individuals which we then group into a small cla.s.s. These cla.s.ses we then group into a larger cla.s.s, according to their resemblances. These larger cla.s.ses then go to form a part of still larger cla.s.ses, and so on. As these cla.s.ses advance they form _broader_ terms; and as we retreat from the general cla.s.s 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 const.i.tute what is called its _content_; the individuals it embraces const.i.tute 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 cla.s.s _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, cla.s.sifying 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 pa.s.s 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 cla.s.sifications 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 a.s.sociations 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 cla.s.sification of the degrees of _extension_ of a general term is expressed by the two terms, _Genus_ and _Species_, respectively. The cla.s.sification 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 cla.s.s of objects containing several species; a cla.s.s more extensive than a species; a universal which is predicable of several things of different species."

_Species_ is a term denoting: "a smaller cla.s.s 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 cla.s.s is contained in another, and accordingly we call the cla.s.s 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 cla.s.s is a "genus" to the cla.s.s below it in extension; and each cla.s.s is a "species" to the cla.s.s 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 cla.s.s 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."

Pa.s.sing on to the cla.s.sification 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 distinguis.h.i.+ng mark of a cla.s.s. 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 circ.u.mstance which may or may not belong to a cla.s.s, accidentally as it were; or, whatever does not really const.i.tute 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 cla.s.sification 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 a.n.a.lysis 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 s.h.i.+p." 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 ill.u.s.tration; 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 a.n.a.lysis and Synthesis.

_a.n.a.lysis_ is a term denoting: "The separation of anything into its const.i.tuent 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 a.n.a.lyze 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 a.n.a.lysis." In stating a definition we must necessarily join together the various essential qualities, properties and attributes, which we have discovered by the process of a.n.a.lysis; and the synthesized combination, considered as a whole, is the definition of the object expressed by the term.