Rules for Real or Essential Definitions. NOTE V. The following Rules should be observed in the formation of definitions not only, but in the examination of statements purporting to be definitions. Especially should this be done with the "Definitions" given in Text Books for Schools. If the definition be a good one, this examination gives the student a just idea of its meaning and fitness, and thus enables him the more easily to learn it; while, if the definition be erroneous, the student will, by this means, be enabled to discover and to correct the error. 28. RULE I. The words of the Definition must be more familiar to the student, than the term which is defined. NOTE VI. The teacher must be the judge as to the student's familiarity with the words of the definition. It is a great error to suppose that the meanings of short words are familiar to the learners, and that the meanings of long words are unfamiliar to them. All words, whether short or long, are alike familiar and easy to those who are familiar with the ideas named by these words. EXAMPLES. 1. Addition is the aggregation of entities composing an entirety. 2. Addition is finding a number equal to two or more addends. 3. Addition is finding a number equal in value to two or more given numbers. 4. Addition is putting several smaller numbers into one larger number. 29. RULE II. A Definition must be a true statement. That is; first, it must not omit a part of that which is named by the term ; second, it must not include that which is not named by the term; third, it must not include a statement which does not assist in defining the term. EXAMPLES. 1. Addition is the process of finding a number equivalent to two or more addends. If the words of this definition be more familiar to the learner than the term, Addition, then it is a good definition as far as Rule I. is concerned. If it be a true statement, then it is a good definition as far as Rule II. is concerned. 2. Addition is finding a whole number equivalent to two or more whole numbers. Ex., 2, is faulty, as a definition. It omits something which the term, Addition, includes. Addition is finding a number equivalent to two or more given numbers, whether these numbers be whole, fractional, or mixed. 3. A Non-decimal or Common fractional number is one whose denominator is not one of the ordinals, tenth, hundredth, thousandth, etc. 4. "A Common fraction is one whose unit is divided into any number of equal parts." Ex., 4, as a definition, is faulty, because it includes too much. According to it, every fractional is a common or non-decimal and, of course, no fractional number is left to be defined as a decimal. 5. A Decimal fractional is one whose denominator is one of the ordinals, tenth, hundredth, thousandth, etc. 6. "A Decimal fraction is one whose denominator is tenth, hundredth, thousandth, etc., and is not expressed." Ex., 6, is false, as a definition, because no fractional number can be expressed by using a single number only. See Arith., Fractional Numbers. 7. "A Decimal fraction is one whose denominator is ten, one hundred, one thousand, etc." Ex., 7, as a definition, is absurd, because no cardinal number can be used as the denominator of a fractional. All denominators must be ordinal numbers. 8. "The subject of the sentence is the agent, actor, doer." This is faulty, as a definition, because the name of the receiver may be used as the Subject. Thus, wood is cut by John, in which the name of the receiver is used as the Subject of the sentence. Ex., 8, is false, as a definition, because it is not the idea of the agent, actor or doer that is used as the Subject, but the name of that idea. 9. "A Noun is a name." This is faulty, because it includes too much. Every word is the name of some idea, and hence, according to this definition, every word must be a noun, which is absurd. NOTE VII. The great number of faulty and false statements, given as definitions, which are, of course, worse than useless, has led many to neglect the study of the names or terms of certain of the sciences; as, in Arithmetic; while the definitions are carefully memorized in other studies; as, in Grammar, Geography, etc. The study of no part of a science contributes more to mental discipline than the careful study of its names or terms. 30. RULE III. The definition of a class or kind should contain the name of the basis, according to which the classification was made. (See Chap. VI., Classification.) EXAMPLES. 1. A Simple thought is one whose immediate elements are ideas or groups of ideas. 2. A Compound thought is one whose immediate elements are thoughts. The basis, according to which thoughts are divided into Simple, and Compound, is their immediate elements. 3. A Proper fractional is one whose value is less than a unit. 4. An Improper fractional is one whose value equals or exceeds a unit. Value is the basis according to which fractionals are divided into Proper, and Improper. NOTE VIII. At the option of the teacher, the Literal may be given before the Real definition; or, the Real before the Literal. 5. Literal Definition. The word, euphony, means sounding pleasantly. Real Definition. The term, Euphony, is the name of the science and art of making sounds easy for the organs of speech, and to the ear. 6. Real Definition. The term, Euphony, is the name, etc. Literal Definition. The word, euphony, means, etc. In examples, 5, 6, the definitions are Subjective or Analytic in the statement. In example, 7, the definitions are stated Objectively or Synthetically. 7. Real Definition. The science and art of making sounds easy for the organs of speech is called Euphony. Because ;Literal Definition. The word, euphony, means, etc. Nomenclature or Terminology. LIT. DEF. The word, nomenclature,1 means the office of that which opens or unlocks a name. 1 NOMENCLATURE. ure, office of; t, that which; cla, opens, unlocks, splits; nomen, words, names, terms. LIT. DEF. The word, terminology,' means the science of limits or bounds 31. NOMENCLATURE or TERMINOLOGY is applied to that part of a science which includes its names or terms and their definitions. 32. According to the relation existing between its literal and real definitions, a Name or Term is said to be Scientific, Semi-scientific, and Unscientific or Barbarous. LIT. DEF. The word, scientific, means made from that which was known or learned. 2 33. A SCIENTIFIC Name or Term is one whose literal definition suggests its real. Thus, the literal definition of the word, photography, which is drawing with the light, readily suggests its real definition, a drawing made by the light; hence, Photography is a scientific term. LIT. DEF. The word, semi-scientific, means half or partially scientific. 34. A SEMI-SCIENTIFIC Name or Term is one whose literal but partially suggests its real meaning. Thus, the word, multiplication, literally, means the science and art of that which is folded many times; or, has many folds. Originally, it was applied to the process of finding a number equivalent to two or more times a certain number. Now, the term is applied to finding the result of a number taken one time, a fractional part of a time, and no time. (See Arith., Multiplication.) LIT. DEF. The word, unscientific, means not scientific. 3 LIT. DEF. The word, barbarous, means something rough or bearded. 35. An UNSCIENTIFIC OR BARBAROUS Name or Term is one whose literal does not suggest its real or essential meaning. Thus, the word, isthmus, which, literal, means fixed, set, established, is applied by Geographers to a narrow neck of land connecting two larger portions. This name was first applied to the neck of land now known as the "Isthmus of Corinth; " because, certain games were celebrated there at certain fixed, set or established times. In like manner, the word, barbarous, which, literally, means having a beard, is now applied to denote a certain degree in the scale of civiliza 1 TERMINOLOGY. ye, being, having; olog, sciences; termin, bounds, limits, terms, fences, 2 SCIENTIFIC. (ific, made; (e)nt, from that which; sci, is known, or has been learned. That is, Science is made by arranging or classifying our knowledge of a subject. 7 BARBAROUS. ous, —; ar, office of, state of; barb, point, beard, roughness. tion. Among the Roman, the expression, barba horrida [rough bearded], was used to distinguish a rustic, who neglected the hair and beard, from a citizen, by whom the hair and beard were carefully trimmed and anointed. LIT. DEF. The word, use,' means habit, way, method. LIT. DEF. The word, office,' means employment, method. 36. The USE or OFFICE of a word is the part which it takes in the construction of a phrase, or of a sentence. PHRASES. 37. The science of Phrases includes; first, the Definitions; second, the Formation; and third, the Classifications of Phrases. 38. First, the DEFINITIONS. The word, phrase,3 means something said or uttered. A PHRASE is the expres sion or name of a group of ideas. (See Chap. I., Group of Ideas.) EXAMPLES. 1. A friend of the race. The friend of Ellen. Ellen's friend. General Analysis. Logically, a friend of the race is a group of ideas, of which, friend is the principal idea; a, race, subordinates to friend; the, subordinate to race; and of, an idea of the relation of race to friend. Rhetorically, a friend of the race is a phrase; because, it expresses or names a group of ideas. 39. Second, the FORMATION OF PHRASES. The Immediate Elements, used in the formation of Phrases, are the Words, and the Phrases, naming the immediate elements of the group which the Phrase expresses. 2. A fine house. Those large trees. Many learned men. General Analysis. Logically, a fine house is a group of ideas, whose immediate elements are ideas. Rhetorically, a fine house is a phrase; 1 USE e, belonging to; s=t, that which; u, does, keeps. 2 OFFICE. e,; fic, made, done; ofob, through, on account of. |