Class 
 
 Book.. 
 
 COPYRIGHT DEPOSE 
 
Essentials of Logic 
 
I^[l!ll 
 
Essentials of Logic 
 
 By 
 
 William Dinwiddie, LL.D, 
 
 Chancellor, and Professor of Philosophy, 
 Southwestern Presbyterian University 
 
 New York 
 
 The Neale Publishing Company 
 
 1914 
 

 Copyright, 1914, by 
 The Neale Publishing Company 
 
 MAY -5 1914 
 
 CI.A369956 
 
CONTENTS 
 
 PART I 
 
 GENERAL 
 CHAPTER PAGE 
 
 I What Logic Is n 
 
 II Notions 15 
 
 III The Primary Laws of Thought . . 46 
 
 IV Propositions 52 
 
 PART II 
 
 DEDUCTIVE INFERENCE 
 
 V Immediate Deduction 75 
 
 VI Mediate Deduction 86 
 
 VII Deductive Fallacies 122 
 
 PART III 
 
 INDUCTIVE INFERENCE 
 
 VIII The Nature and Laws of Induction . 139 
 IX The Causal Basis for Induction . . 146 
 
 X Results of Induction 169 
 
 Index 175 
 
PREFACE 
 
 This is intended to be a working handbook of 
 logic, and not a history of the subject. No nov- 
 elty is claimed, except the novelty of simplicity, and 
 freedom from needless technicalities, hereditary 
 nomenclature, and other barnacles ; as, for example, 
 in the treatment of the syllogism and of fallacies. 
 With teachableness and early practical application 
 in view, traditional accretions and controversies 
 have been omitted; and yet, it is believed, without 
 sacrifice of essentials. There is constant endeavor 
 to make evident the relation between different parts 
 of the subject. 
 
 Quotation marks have been used freely where 
 they seemed advantageous, but not according to any 
 hard and fast rule. 
 
 The book contains a large collection of examples 
 for practice, selected also for their intrinsic value, 
 and illustrating the forms of thought that occur in 
 actual literature, and not merely in logical exer- 
 cises. Adequate use of these will double the work- 
 ing length of the book. 
 
 W. D. 
 
 Clarksville, Tennessee, 
 October, 1913. 
 
PART I — GENERAL 
 
ESSENTIALS OF LOGIC 
 
 CHAPTER I 
 
 WHAT LOGIC IS 
 
 i. Logic Defined. — Correctness of thought is 
 vital to success in everyday affairs, to progress in 
 knowledge, to science, to literature, to philosophy, 
 to theology, to logic itself. Hence it is of great 
 importance to know the laws of correct thinking, 
 and this knowledge is acquired by the study of 
 logic, which may be defined as the science of the 
 forms and laws of correct thought. 
 
 2. Logic not Art but Science. — Science dif- 
 fers from other knowledge in being systematically 
 arranged. Science is knowledge classified or sys- 
 tematized. Such knowledge often forms the basis 
 for the highest skill, or art; but art is concerned 
 with doing, science with knowing. The closeness 
 of this relation of science and art is the reason why 
 the two are often confused or identified. A man, 
 however, may know the science of architecture in 
 minute detail, and yet not have the art to build; a 
 doctor may know the position and use of every tis- 
 sue in the body, and yet have no skill as a surgeon. 
 
 ii 
 
12 ESSENTIALS OF LOGIC 
 
 Logic is a science, not an art. Logic does not 
 give us the power to think correctly, but it acquaints 
 us with the laws of correct thought; it gives us the 
 knowledge of what correct thinking must be. The 
 ability to think correctly may be possessed without 
 the study of formal logic, for it is an ability natural 
 to man, but fuller knowledge of What is correct in 
 thought results naturally and increasingly in the 
 use of what is correct. 
 
 3. Logic a Distinct Science. — Scientific 
 knowledge is divided into* branches, each called a 
 science, and each distinguished from others by the 
 distinct nature of the facts it investigates and sys- 
 tematizes. Systematized facts as to the human body 
 form the sciences of anatomy and physiology; the 
 plants give us botany; the stars, astronomy; the 
 weather, meteorology; the mind, psychology; 
 thought gives logic. The distinctness of logic from 
 other sciences is due to the distinctness of the facts 
 of thought from the facts treated of in other sci- 
 ences. 
 
 We need to distinguish carefully from each other 
 sciences whose facts are closely related, as physiol- 
 ogy and anatomy, physics and chemistry, geology 
 and mineralogy, psychology and logic, or grammar 
 and logic. Grammar, psychology, and logic all have 
 to do with thought. Grammar, however, is con- 
 cerned not with the correctness of the thought, but 
 merely with the expression of the thought; that is, 
 
WHAT LOGIC IS 13 
 
 with the language. Psychology treats of thought 
 solely as an activity of mind, while logic deals with 
 the thought itself; psychology looks at the mind as 
 it thinks, logic at the thought ; psychology considers 
 the mind as it produces thoughts, logic considers the 
 product. Psychology asks: What does the mind 
 do when it thinks? Logic asks: What is the 
 thought ? 
 
 As to the nature of thought it is enough to say 
 here, somewhat loosely, that the affirmation or the 
 denial that one of two things, groups of things, 
 qualities, or ideas is related to the other of the two, 
 is a product of thought, or, in brief, a thought. 
 For such affirmation or denial to be warranted, it 
 is evident that its two terms, the subject and the 
 predicate, must first have been compared in mind 
 with each other or with some third term. Thought 
 affirms or denies that one thing is contained in or 
 comprised under another. 
 
 4. Logic Related to All Science. — Since sci- 
 ence is knowledge classified or systematized, and 
 since it is thought that classifies or systematizes, and 
 logic that treats of thought, it follows that logic is 
 vitally related to every science. The things we 
 think about are many; the correct ways we think 
 about them are few; and as everything we think 
 about must be thought about in some definite way, 
 or form, according to some definite law, if we think 
 correctly ; then it follows that the science of any set 
 
14 ESSENTIALS OF LOGIC 
 
 of things or facts depends on the forms or laws 
 correct thought must use, in other words, on the 
 facts of logic. Since all science involves thought, 
 every science depends on logic, the science of 
 thought. Logic itself can be a science only by con- 
 forming to the laws of thought of which logic 
 treats. 
 
 Logic, then, is a science of forms in which a 
 countless variety of thoughts about many things 
 may be cast. Logic treats, not of the things we 
 think about, but of the ways in which we think 
 about things, in trivial everyday affairs or in high- 
 est regions of scientific deliberation. Its realm is 
 the universe of thought. One of the forms of 
 thought is the term, or notion. Examples of the 
 notion are: apple, red, sphere, thought, man, each 
 of which, as will appear later, stands for the result 
 of prior comparisons. Other thought-forms are 
 judgments, by means of which we affirm or deny 
 that two notions are related to each other, as : the 
 earth is a sphere, snow is white, justice is not 
 mercy; also, subject and predicate, genera and spe- 
 cies, inferences, syllogisms, and many others. The 
 form can be made clear only by filling it with mat- 
 ter, which is a step beyond pure logic, but used 
 freely in pure logic for illustration. 
 
CHAPTER II 
 
 NOTIONS 
 
 5. What Notions Are. — Grammatically, a no- 
 tion is a noun or an adjective, as for example, " ap- 
 ple," " red " ; logically, a notion is either a " mark," 
 or quality of a thing, as red is a quality of apple; 
 or the notion stands for a group of qualities, and is 
 called a concept, as apple stands for round, juicy, 
 edible, etc. ; or it stands for a group of things, as 
 apple stands for every member of the group called 
 by that name; psychologically, the notion is the re- 
 sult of abstraction, conception, and generalization. 
 For example, looking at a certain object, we " ab- 
 stract," or take away in our minds, and consider 
 apart from other qualities, that which we see, and 
 say, the object is red ; handling it, we abstract shape 
 and weight from other qualities and say, it is round, 
 it is heavy; smelling it, we say it is fragrant, and 
 so for each quality perceived by the senses. It is 
 evident that abstraction is purely a mental process 
 in no way affecting the object or its qualities. Each 
 of the abstractions above is expressed in the form of 
 a " judgment," which is thus used in forming no- 
 
 iS 
 
16 ESSENTIALS OF LOGIC 
 
 tions, as well as the notion in forming other judg- 
 ments. The judgment is discussed in Chapter IV. 
 
 The second mental step in forming a notion gath- 
 ers into one the various marks noted by abstraction, 
 and for convenience gives this bundle of marks a 
 name. This bundle of marks is called " concept," 
 or " gathered together." Thus the red, round, 
 heavy, juicy, edible object of the above illustration 
 of abstraction is called " apple " ; and apple is the 
 concept which includes, or " connotes " the marks 
 red, round, etc. 
 
 The third mental step in forming a notion is gen- 
 eralization. The marks red, etc., and the concept 
 apple refer only to the one particular object we have 
 been examining; but we receive similar impressions 
 from other objects, and we say they are red, round, 
 juicy, etc. ; that is, all these objects have these 
 marks, all are apples. Thus we " generalize " the 
 concept apple, we say it includes every object of a 
 certain group, or class, or " genus." In this way 
 we classify our knowledge, we get the genera of 
 science. 
 
 The order in which conception and generaliza- 
 tion are mentioned above is arbitrary. We may 
 either bundle the marks of one object into a con- 
 cept and then generalize, or we may observe a num- 
 ber of objects having similar marks, and generalize 
 each of these marks before forming them into a 
 concept. 
 
NOTIONS 17 
 
 Marks and concepts are notions. Each form can 
 be changed into the other. The difference is solely 
 in the way the form is used, and may be disregarded 
 in the development of the science of logic. 
 
 It is evident that a concept may be viewed as a 
 group of marks or a group of things. " Apple" is 
 said to " connote " the marks juicy, subacid, etc., 
 and to " denote " all apples. To give the marks 
 which a notion includes is to " define " it; to give 
 the classes of things contained under a notion is to 
 " divide " it. Logical definition and division are 
 discussed in sections 7 b and 7 c below. 
 
 Many concepts include a practically unlimited 
 number of marks : hence in defining the concept by 
 giving its marks, we select only those essential to 
 the nature of the object or the class, those without 
 which the object would not be what it is. The con- 
 cept man includes the marks, two-legged, having 
 hair on the head, erect, and many others, the absence 
 of which would still allow the objects denoted by 
 the concept to be men; but the marks animal and 
 rational must be present, else the objects denoted 
 will not be men. 
 
 According to what is known as " the law of in- 
 verse ratio," the fewer marks a concept contains, 
 the greater the number of things it includes, and 
 the reverse. If to the marks of apple we add 
 " red," the objects included under " red apple " are 
 evidently fewer than those under " apple " ; if from 
 
18 ESSENTIALS OF LOGIC 
 
 the marks of " rocking-chair " we take the mark 
 " rocking," we have " chair," a class containing 
 more objects than " rocking-chair." All the marks 
 contained in a concept are called the " intension " of 
 the concept; the things contained under a concept 
 are called the " extension " of the concept; and the 
 above law of inverse ratio may be stated thus : The 
 greater the intension, the less the extension, and the 
 reverse. 
 
 A notion is also called a " term " (Latin, 
 terminus, end), because in its use as subject or predi- 
 cate it is the end of the sentence. A notion often 
 consists of a group of words, as, for example: 
 North American Indians, rivers which flow into the 
 Atlantic Ocean. 
 
 PRACTICE ON SECTION 5 
 
 1. What marks do you find in your notion of gov- 
 
 ernment, campus, home, railroad, beauty, food, 
 athletics, miser, education, money? 
 
 2. What classes or kinds do you think of as included 
 
 under each of the above notions? 
 
 3. Name some marks common to two or more of 
 these notions. 
 
 4. Name two or more concepts having one of the 
 
 following marks in common: free, heavy, four- 
 legged, juicy, upright, smooth, false, yellow. 
 
 5. Does every mark you think of as belonging to 
 one of these concepts, belong to every one of 
 the classes under the concept? 
 
NOTIONS 19 
 
 6. Can you name a mark that belongs to some of the 
 classes under a concept, and not to others? 
 
 7. Add some mark to one of the above concepts, 
 and show that the resulting concept denotes fewer 
 things; then add other marks successively, not- 
 ing the effect on the number of things. 
 
 8. Illustrate any of the above exercises by using 
 five other concepts. 
 
 9. Add two classes of things, such as acute and right 
 
 triangle, say what mark has been lost, then add 
 another class to the result, and so on. 
 
 10. Give other illustrations of the above exercise. 
 
 11. Illustrate abstraction, conception, and generaliza- 
 tion by any of the above notions. 
 
 12. State the intension and the extension of any of 
 the above notions. 
 
 13. Change any of them from marks to concepts, and 
 the reverse. 
 
 14. Name some of the marks connoted and some of 
 the kinds denoted by each of the two meanings 
 of the following terms: school, band, mark, no- 
 tion, bed, log, yard, party. 
 
 15. Would a perfect language have words of two 
 meanings ? 
 
 6. Kinds of Notions. — The following are the 
 most important of the many ways in which notions 
 may be grouped in classes: 
 
 6 a. Notions are " concrete " or " abstract." 
 A concrete notion is the name of a thing or of a 
 quality thought as being in a thing: for example, 
 
20 ESSENTIALS OF LOGIC 
 
 " green " is a concrete notion, because it can in this 
 form be thought only as belonging to grass or other 
 green things. It is of course the adjective and not 
 the noun " green," of which this is true. An ab- 
 stract notion is a quality of a thing thought as being 
 itself a separate thing; for example, greenness, 
 truth, morality, hardness. These are not things, 
 though named as if they were; they are qualities 
 only; respectively, say, of grass, assertions, conduct, 
 iron. All adjectives are concrete. Many nouns 
 originally abstract have by change in usage become 
 concrete; as, "relation" for "relative," "action" 
 for " act." 
 
 6 b. Notions are " particular " or " general." 
 A particular, or " singular," or " individual " no- 
 tion denotes one object; as John, Mr. Brown, this 
 hat, my house. The objects we see, hear, or know 
 through any sense, are particular objects. Abstrac- 
 tion and conception, the first two steps in the forma- 
 tion of notions, described in Section 5, have to do 
 with particular notions; the third step, generaliza- 
 tion, with the general notion, or the notion which 
 denotes a " genus," or " kind," or " class " ; as 
 martyr, bean, horse, and all common nouns. The 
 general does not exist except in thought ; real things 
 are individual, singular, particular, and not general. 
 The general notion, however, is often made to de- 
 note a particular object by the use of some limiting 
 word or group of words, as " this," " that," " his," 
 
NOTIONS 21 
 
 " the," a relative clause, etc. Sometimes there is 
 ambiguity, and care must be taken, as always, to get 
 at the actual meaning of the words. For example, 
 in the sentence: a man is a complex creature, "a 
 man " is general, and the meaning is the same as : 
 man is a complex creature; but in the sentence: a 
 man is running down the street, " a man " is partic- 
 ular, denoting only one man. Again, in: the ox is 
 patient, and, the ox is dead, we have the double use 
 of " the " ; the first either general or particular, the 
 second particular. The limiting words, phrases, or 
 clauses, which thus reduce the general notion to 
 the particular, are called " particular marks." 
 
 It is therefore obvious that all strictly proper 
 names are particular. The difference between the 
 proper name and the common name in its particular 
 use, as above, is that the latter implies marks, the 
 former not. For example, " George " has no mean- 
 ing whatever, is a mere sign arbitrarily associated 
 with an individual person ; but to designate the same 
 person George as " that boy," attributes to him all 
 the marks of the concept " boy." So-called proper 
 names, however, often show sex, or other marks, 
 and are to that extent not strictly proper: John is 
 of the male sex; the latter part of " Clarksville " 
 means city; so "port," "burg," "ton," and other 
 parts of names. 
 
 A proper noun may be used as a general name, 
 some prominent mark possessed by the owner of 
 
22 ESSENTIALS OF LOGIC 
 
 a well-known proper name being thus attributed to 
 others; as, a Daniel come to judgment; or, he is a 
 Nero, a Herod. 
 
 6 c. Notions are " obscure " or " clear." 
 Obscure notions are those not well enough known 
 to be separated in thought from others nearly alike ; 
 as, perhaps, caribou, moose; adhesion, cohesion, at- 
 traction; college, university; thought, feeling, con- 
 sciousness, desire; memory, imagination. On the 
 other hand, we have a clear knowledge of dog, 
 house, ocean, school, etc. 
 
 Clear notions may be " indistinct " or " distinct." 
 We have a clear notion of " grass " for example, 
 but our knowledge is not distinct unless we know 
 the marks and the kinds of grass. " Table," " car- 
 pet," " bread," " book " are examples of notions 
 distinctly known, for we know their marks and 
 their kinds, the two phases or parts of distinct 
 knowledge. 
 
 It appears that clearness is attained by denials, 
 which say what a thing is not; distinctness by af- 
 firmations, which say what a thing is : as, he is no 
 fool, he is a man of great ability; a mandolin is 
 not a violin, it is not played with a bow, it has a 
 larger air-chamber, it is played with a plectrum. 
 
 Distinct notions may be " inadequate " or " ade- 
 quate." Inadequate notions are those that do not 
 imply enough marks for them to represent accurately 
 and fully the things in question; while adequate 
 
NOTIONS 23 
 
 notions are those which imply enough marks for the 
 particular purpose in view. 
 
 Distinct notions are also " intuitive " or " sym- 
 bolic." Intuitive notions are those used in thought 
 by means of a mental image of one of the things 
 included under the notion; as, for example, bed, 
 house, dog, if accompanied by a visual image of a 
 bed, a house, a dog ; or intuitive notions may be ac- 
 companied by the actual perception of one object 
 of the class, as when we are looking at a bed, etc., 
 or at a picture of the object. If not so accom- 
 panied, the words, bed, house, dog, etc., are mere 
 symbols, and we do not look the thing in the face, 
 as " intuition " means. Many notions, therefore, 
 may be used either intuitively or symbolically ; many 
 others are too complex to be imaged by the mind, 
 and can be used only symbolically; as, education, 
 prosperity, peace, the velocity of light, the govern- 
 ment of the United States. 
 
 Perfect knowledge is clear, distinct, adequate, 
 intuitive. Most of our knowledge is imperfect ; but 
 the possibility of progress toward perfection is ever- 
 present, and the effort to make the progress is a 
 duty. 
 
 Language is the vehicle and the storehouse of 
 thought, and the notion is the fundamental word. 
 The child can make its wants known surprisingly 
 well without other words than the noun. A verb 
 can be resolved always into the verb " be " and a 
 
24 ESSENTIALS OF LOGIC 
 
 notion. The explanation of the notion is the ex- 
 planation of language. Without language, the 
 progress of thought would be very narrowly re- 
 stricted. By imperfect language, the accuracy and 
 the communication of thought are jeopardized. 
 The abstract should be frequently tested by the con- 
 crete, the general by the particular, the symbolic by 
 the intuitive. 
 
 6 d. The following classifications of marks 
 are important: 
 
 ist. Marks are " positive," or " negative " : 
 " wet " is a positive, " dry " a negative mark, mean- 
 ing merely the absence of moisture. Marks are 
 positive or negative in themselves, without regard 
 to any particular concept to which they may be- 
 long. 
 
 2nd. Marks are " essential " or " accidental " ; 
 as, " for heating " is an essential, " self-feeding " 
 an accidental mark of stove. Marks are not essen- 
 tial or accidental in themselves, but with regard to 
 the concepts to which they belong. 
 
 3rd. Marks are " common " or " peculiar," ac- 
 cording as they belong to a concept in common with 
 other concepts, or belong to that concept only : " liv- 
 ing " is common to man and horse, " laughing " is 
 peculiar to man, " neighing " is peculiar to horse. 
 
NOTIONS 25 
 
 PRACTICE ON SECTION 6 
 
 1. Name ten concrete, and ten abstract notions. 
 
 2. Name five concrete, and the five corresponding 
 
 abstract terms. 
 
 3. Change the following notions from general to 
 particular, or the reverse: bread, a storm, the 
 horse, truth, pleasure, fire, charity, king, that 
 tree. 
 
 4. Which, if any, of the following are proper names : 
 
 Caesar, Czar, Kaiser, Pharaoh, President, Mr. 
 President, Bible, Episcopal Prayer-Book, High 
 School, University of Berlin, Mathematics? 
 What marks are connoted by any which are not 
 proper names? 
 
 5. Write a list of ten general terms. Of ten par- 
 ticular terms. 
 
 6. Mention several notions not clear to you, naming 
 those not separated clearly from them in your 
 thought. 
 
 7. What are some notions you know clearly, but not 
 
 distinctly ? 
 
 8. Can you think of a notion you know clearly and 
 
 distinctly, but not adequately? 
 
 9. Give examples of the intuitive and the symbolic 
 representation of several concepts. 
 
 10. Mention something your knowledge of which you 
 
 deem perfect. 
 
 11. Are the following marks positive or negative; 
 that is, do they indicate the presence of a quality, 
 or mere absence: original, negative, essential, 
 
26 ESSENTIALS OF LOGIC 
 
 complex, sober, protestant, pure, reckless, rest- 
 ful, clean, insane, impartial, silent, dark, weak, 
 hard, soft, paralyzed, oblique? 
 
 12. Give the opposite negative or positive mark cor- 
 
 responding to each of the above. 
 
 13. Which of the marks in list a are essential to any 
 of the concepts in list b? a. round, juicy, living, 
 dead, harmful, peaceable, long-winded, intelligent. 
 b. horse, poison, pencil, orange, bore, corpse, 
 earth, circle. 
 
 14. Can you name essential marks of house, kitchen, 
 
 stove, study, book, star, plow, spoon, chair, ball, 
 bird, dog, logic, college? 
 
 15. Name, if you can, notions of which one of the 
 following is an essential mark : square, blue, loud, 
 sour, smooth, fragrant, animal, logical, mental, 
 conscious, extended, rational, military, strong, 
 scientific, stingy. 
 
 16. Use 14 and 15 above, substituting accidental for 
 
 essential. 
 
 17. What marks can you think of that are peculiar 
 
 to any of the notions in 14? What that are 
 common to any two or more of these notions? 
 
 7. Relations of Notions. — It was seen in Sec- 
 tion 5 that a notion may be viewed either as a group 
 of marks or as a class of things, the marks being 
 the " intension," the things the " extension " of the 
 notion. Intensively, notions may agree, and there- 
 fore unite in thought; as, good and great, tall and 
 manly, hardness and weight; or they may disagree 
 
NOTIONS 27 
 
 in the sense that they do not actually co-exist in 
 one object, which is however a question of matter, 
 not of form, and therefore not in the realm of pure 
 logic; for example, a blue toothache, a happy tree; 
 or again, the two notions may contradict each other, 
 and therefore can not be combined either in thought 
 or in fact, which is the only true logical disagree- 
 ment; as, theistic and atheistic, wet and dry, 
 learned and ignorant. 
 
 Extensively, two notions may represent classes of 
 things in any of five relations: 
 
 1st. The two classes may exclude each other 
 and not be immediately contained under some wider 
 class : as desk and walk, spoon and wheelbarrow. 
 This relation may be called " exclusion," and is 
 shown by the fact that no member of either class is 
 a member of the other. 
 
 2nd. The two notions may exclude each other, 
 and yet be immediately contained under some wider 
 class; as, Catholic and Protestant under Christian, 
 Greek and Roman under Catholic, right angle and 
 oblique angle under angle. This is the relation of 
 " co-ordination," each notion being of the same rank 
 (Latin, ordo) with respect to the wider class imme- 
 diately containing it. 
 
 3rd. The relation of the notion contained under 
 another to this other is " subordination." 
 
 4th. Again, each of two notions may have a 
 part in common with the other, and a part not in 
 
28 ESSENTIALS OF LOGIC 
 
 common ; as, Europeans and Turks, wholesome food 
 and flesh, men and students. This relation is " in- 
 tersection." 
 
 5th. Lastly, two notions may be equivalent; as 
 negro and darkey, sun and fixed star, leaves and 
 foliage. Such notions are said to be in the relation 
 of " co-extension." The test is that every member 
 of either class is also a member of the other. 
 
 Each notion may be represented by a circle, two 
 circles outside of each other illustrating co-ordina- 
 tion, if they are contained in a third circle, or ex- 
 clusion if there be no third circle; one circle within 
 another illustrates subordination; and two inter- 
 secting circles, intersection. 
 
 7. a. Classification. — It is evident that a no- 
 tion which is subordinate to another may have other 
 notions subordinate to it; and that the notion to 
 which others are subordinate may itself be sub- 
 ordinate to some wider notion, so that a system of 
 notions, or classes may be formed. This is classifi- 
 cation. 
 
 If, as in co-ordination, two classes exclude each 
 other, one of the classes must have at least one mark 
 that the other does not have ; or, to state the matter 
 differently, one class has a positive mark not be- 
 longing to the other, while the other has the cor- 
 responding negative mark; without this difference 
 in marks, the two classes would of course coincide, 
 and the relation would be co-extension instead of co- 
 
NOTIONS 29 
 
 ordination. For example, Protestant includes the 
 mark, denying authority of the Pope, while Catholic 
 does not ; right angle has the mark, having a definite 
 magnitude, while oblique angle has not. In fact, 
 each of two co-ordinate classes contains every mark 
 of the wider class to which they are subordinate, 
 and each contains in addition one other mark; as, 
 Catholic and Protestant contain all the marks of 
 Christian, and in addition, respectively, the marks, 
 accepting the authority of the Pope, and, not accept- 
 ing the authority of the Pope; or, the classes red 
 raspberries and raspberries of other colors have each 
 all the marks of the class raspberry, and in addi- 
 tion, respectively, the marks red and not-red. 
 
 It is evident that we are here considering the 
 three processes in the formation of concepts, de- 
 scribed in Section 5, from a somewhat different 
 point of view ; for it is by abstraction that we learn 
 the marks, by conception that we form the notion, 
 and when we generalize, we form a class. It is 
 further evident that the law of inverse ratio, of Sec- 
 tion 5, applies here, so that each of two co-ordinate 
 classes, as man and brute, having each one mark, 
 as rational and non-rational, respectively, more than 
 the wider class, animal, to which they belong, con- 
 tains fewer things. To add marks is to diminish 
 the number of things included under the concept, to 
 divide the things under the former concept into two 
 classes, one having the mark in question, the other 
 
So ESSENTIALS OF LOGIC 
 
 not; it is to classify, to make classes, or species. 
 On the other hand, to take away marks is to add 
 things, to generalize, to make genera (plural of 
 genus). So genus and species are relative terms; 
 any genus may be divided into species, and these 
 species may in turn be genera of lower species; so 
 any genus except the highest may be in turn a spe- 
 cies under a higher genus. 
 
 What are the limits to the process? How far 
 can we continue to add marks, to cut off things? 
 Theoretically, until all common marks are included, 
 that is, until we reach a class such that not even 
 any two of its members have a common mark which 
 is not also a mark of all the other members of the 
 class. In such a case there can be no further di- 
 vision into classes, for unless at least two things 
 have such a common mark, division will result not 
 in classes or species, but in separate individuals; 
 and if all the other members of the class have the 
 only marks that are common to any members, any 
 attempt at division would include the whole class, 
 and be no division. For example, a group of men 
 contains one lawyer, one doctor, one merchant, one 
 statesman, and one railroad president, and can be 
 divided on the basis of profession only into indi- 
 viduals. This illustrates the lowest logical species, 
 the species that can not be a genus and be divided 
 into lower species, but only into individuals. 
 
 On the other hand, how far can we continue to 
 
NOTIONS 31 
 
 generalize, to subtract marks, to add things ? Theo- 
 retically, until all things are included. Disregard- 
 ing the metaphysical distinction of matter and form, 
 the widest class, the " summum genus," therefore, 
 is " thing," which has only the one mark, " exist- 
 ing," and denotes everything. For practical sci- 
 entific ends, classifications do not have to begin with 
 this highest class, but with the class most suitable in 
 the different sciences. Astronomy, for example, 
 starts with heavenly body ; botany, with plant ; and so 
 on. When we do not know the proper class for an 
 object, or do not care to be scientific, we refer it to 
 the " summum genus," and call it a " thing." 
 
 The two relations of notions, co-ordination and 
 intersection, are of such importance that they are 
 treated more in detail in Sections 7 b and 7 c imme- 
 diately below. 
 
 PRACTICE ON SECTIONS 7 and 7 a 
 
 1. Pick from the following such pairs of notions as 
 
 (1) may unite in thought, or (2) do not actually 
 unite in an object, or (3) can not unite in thought 
 or in fact: wide, clear, poor, savage, blue, sweet, 
 arm, pain, wealthy, mean, man, music, sorrow, 
 gentle, short. 
 
 2. Illustrate the five extensive relations by various 
 pairs of notions. 
 
 3. Draw a pair of circles representing each of these 
 
 relations. 
 
 4. Show that the following notions are subordi- 
 
32 ESSENTIALS OF LOGIC 
 
 nate to other notions, and also have other notions 
 subordinate to them: lock, brick, grass, dog, con- 
 cept, college, lake, bird, stone, monarchy. 
 
 5. What mark has one member of each of the fol- 
 
 lowing pairs of co-ordinate notions, that the other 
 has not? man and brute, straight chair and 
 rocker, right triangle and oblique, plant and ani- 
 mal, steamer and sailboat (or other kind) ? 
 
 6. What wider class, in each case, includes the pairs 
 
 above, and what mark, positive or negative, has 
 each member of the pair, that the wider class 
 has not? 
 
 7. Select five other pairs of co-ordinate species, and 
 their proximate genera, stating in each case the 
 distinctive mark of each species. 
 
 8. See how far you can continue the division into 
 species, begun above. 
 
 9. How far can you carry the process in the other 
 
 direction, toward the widest genus? 
 10. Can you supply the other species for each upward 
 
 step in 9? 
 n. Can you reach a class in 8 or 9 above, beyond 
 
 which the process can not possibly be carried? 
 
 If so, can you say why? 
 
 7. b. Co-ordination and Logical Division. — 
 
 Physical division separates from each other in 
 space, actual things or parts of things, as when an 
 apple is plucked from the tree, or is cut in two. 
 Logical division separates in thought one logical 
 class from another. Physical division is " quanti- 
 
NOTIONS 33 
 
 tative," one amount, part, or quantity being thereby 
 separated from another; logical division is "quali- 
 tative," for thereby one class having a certain qual- 
 ity is thought as separated by the possession of that 
 quality from another not having the quality. Phys- 
 ically, " a tree " may be divided into any number 
 of actual parts, trunk, branches, twigs, leaves, bark, 
 roots, etc. ; logically, " tree " may be divided into 
 the classes fruit-tree, and other kinds, separated in 
 thought from each other by the presence and the 
 absence of the mark, fruit-bearing; and in an in- 
 definite number of ways by selecting other marks. 
 Physically, we divide with a knife; logically, with 
 a mark. 
 
 With physical division logic has nothing to do, 
 except as a test to distinguish the individual from the 
 class; for the individual is pictured in imagination 
 as physically divided into parts, and never logically 
 into classes, while the general notion or class-name 
 is logically divided into classes, and not into parts. 
 We may think a notion, however, either " math- 
 ematically," that is, as a quantity or an individual, 
 separable into parts ; or we may think it " logically," 
 as a class, separable into kinds. With reference to 
 this mathematical or logical division, notions are 
 called " wholes." " A tree " is a mathematical 
 whole, for it can not be thought as divided into 
 classes ; while " tree " is a logical whole, for it can 
 not be divided into parts, but into kinds, as oak-tree, 
 
34 ESSENTIALS OF LOGIC 
 
 pine-tree, etc. The test for the kind of " whole," 
 therefore, is that wholes separable into kinds like 
 the whole, are logical ; those separable only into parts 
 of the whole, unlike it, are mathematical. 
 
 The division illustrated in Section 7 a, resulting 
 in only two co-ordinate classes, differing only in that 
 one class has a certain mark, and the other has it 
 not, is called "dichotomy" (cut in two). This 
 is the only strict logical division, giving contradic- 
 tories, as " stone " and " non-stone," " man " and 
 " non-man," or under the class, animal, " man and 
 brute." "Trichotomy" (cut in three), and " po- 
 lytomy " (cut in many) are used for divisions 
 other than strictly logical ; as if " tree " be divided 
 into oaks, pines, birches, etc. Dichotomy would 
 divide tree into oaks and non-oaks, etc. A trichot- 
 omy, or a polytomy may be a convenient summary 
 of successive dichotomies ; as living things are plants, 
 men, and brutes. Apparent continuity in the thing 
 divided, or lack of sharp definition of terms often 
 makes it difficult to dichotomize, and not leave a 
 middle, neutral term ; as in hot and cold, with warm 
 between; poor and rich, light and dark. 
 
 Successive logical division, resulting in a logical 
 system of classes, must conform to certain rules: 
 
 1st. The same ground of division must be used 
 throughout. If not, the resulting classes will over- 
 lap, and cause confusion; as if books be divided 
 into octavo, duodecimo, works of reference, text- 
 
NOTIONS 35 
 
 books, Greek, and Latin books. This is called 
 " cross division," and the relation between the over- 
 lapping classes is not that of co-ordination, but of 
 intersection. In the above example, the ground of 
 division is first size, then purpose, then language. 
 
 2nd. The one ground of division should be 
 an essential (Section 6 d) mark, or a mark 
 important for the purpose of the division. The 
 ground of division may thus vary according to the 
 end in view, but it must not be changed in any one 
 system. We might, for instance, divide books ac- 
 cording to size to fit our shelves, or according to 
 use for convenience of reference, or according to 
 language for a similar reason. The scientist for 
 varying reasons divides man into classes according 
 to race, color, language, religion, government, etc. 
 
 3rd. The genus must be divided into species im- 
 mediately subordinate to it. Intermediate classes 
 must not be omitted. When geometry is called the 
 science of space, science is thought as divided into 
 the science of space and other sciences, and an in- 
 tervening class, mathematics, is omitted. Science 
 should be divided into mathematics and other sci- 
 ences, and mathematics into geometry and other 
 branches. Such strictness is necessary for scientific 
 accuracy, but not for much of the ordinary inter- 
 change of thought. We speak of a dog as an af- 
 fectionate animal, rather than an affectionate brute, 
 thus passing over some of the intervening classes; 
 
36 ESSENTIALS OF LOGIC 
 
 and of clover as a valuable plant, omitting several 
 intervening botanical classes. 
 
 4th. The two classes, or species, resulting from 
 division, must constitute the whole of the genus di- 
 vided. There must be no part not included, for 
 this part would form a third class, and the division 
 would not be a dichotomy. If fence be divided 
 into rail fence and wire fence, this rule is violated, 
 for plank fence, stone fence, etc., are not included. 
 
 PRACTICE ON SECTION 7 b 
 
 1. Indicate the physical, the logical, and the mathe- 
 matical division of the following: sword, house, 
 dog, grain, school, landscape. 
 
 2. As given, are the above logical or mathematical 
 
 wholes? Transfer each to the other kind of 
 whole. 
 
 3. Illustrate the above exercises by five other ex- 
 amples. 
 
 4. Divide the following, each in several ways by (1) 
 
 dichotomy; (2) trichotomy; (3) polytomy: 
 school, hair, shoe, farm, prison. 
 
 5. Give other examples of these three kinds of divi- 
 sion. 
 
 6. State what mark is the basis of the division in 
 each example in 4 and 5. 
 
 7. Divide and subdivide any class notion four or 
 five times in accordance with Rule I. 
 
 8. Illustrate cross division. 
 
 q. In how many ways can you divide building, for 
 
NOTIONS 37 
 
 example, and for what important purpose in each 
 case? 
 10. Test the following for violation of the principles 
 of logical division: 
 
 (i) Science: of form and of matter; or, sys- 
 tematized and unsystematized. 
 
 (2) Government: monarchy, aristocracy, and 
 democracy. 
 
 (3) Flower: annual and perennial; or, shrubs 
 and vines. 
 
 (4) Church : Catholic and Protestant ; or, true 
 and false. 
 
 (5) Men: moral and immoral; civilized and 
 pagan; black and white; laborer and 
 capitalist; rich and poor; handsome and 
 ugly; native and foreign. 
 
 (6) Thing: animate, inanimate, plant, animal, 
 brute, man. 
 
 (7) Student: studious and idle; athletic and 
 weak. 
 
 (8) Figure : plane and solid ; rectilinear and 
 curvilinear. 
 
 (9) Metal : heavy and light ; precious and 
 plentiful ; white and yellow. 
 
 (10) Year: spring, autumn, summer, winter; 
 B. C. and A. D. 
 
 (11) The ten virgins : five wise and five foolish. 
 
 (12) Heavenly bodies: planets, meteors, com- 
 ets, stars, and suns. 
 
 (13) Brute: animal and other; living and 
 dead; biped and quadruped. 
 
3$ ESSENTIALS OF LOGIC 
 
 (14) Literature: prose, poetry, fiction, drama, 
 history. 
 
 (15) Racehorses and carriage horses; automo- 
 biles and street-cars. 
 
 (16) His conduct is either foolish or crazy. 
 
 11. Divide and subdivide man so as to include white, 
 black, yellow, red; and citizens, to include na- 
 tives, Europeans, Germans, Tennesseeans. 
 
 12. Criticise the table of contents of this text on 
 logic. 
 
 13. Give examples of violations of Rule 3. 
 
 7. c. Intersection and Logical Definition. — 
 
 Taking the genus man, and selecting the mark, be- 
 lieving in a God, we divide man into two species, 
 theist, having the chosen mark, and atheist, not hav- 
 ing it, thus determining by strict dichotomy two 
 classes, theist and atheist, co-ordinate with each 
 other and subordinate to the genus, man. We are 
 here dealing with the things denoted by the notion 
 man, that is, with its extension (Section 5, end), 
 and we are looking down the logical scale from 
 greater extension to less. 
 
 Again, taking the species, theist, and looking up 
 the logical scale, we say, a theist is a man believing 
 in a God, or similarly, an atheist is a man not be- 
 lieving in a God. This, the reverse of logical di- 
 vision, is logical definition, involving a species, its 
 proximate genus, and the distinctive mark separat- 
 ing the species from its co-ordinate species. This 
 
NOTIONS 39 
 
 mark is called the " specific difference," that is, the 
 mark in which the two species differ. 
 
 The logical relation of intersection (Section 7, 
 4th) is here shown; theist, for example, being the 
 part common to the two intersecting classes, man, 
 and believer in God, each of these two classes hav- 
 ing also a part not common to the other. In a 
 definition, therefore, the genus and the specific dif- 
 ference may be viewed as intersecting notions, the 
 notion defined being the common part. 
 
 Here, as always, extensive and intensive forms 
 are interchangeable. We may define a theist as a 
 human believer in God, thus exchanging genus and 
 specific difference; or we may use marks only and 
 say, a theist is human and believing in God. This 
 purely intensive form is the primary form of the 
 definition, which renders a notion distinct by analyz- 
 ing it into its component marks, while division ren- 
 ders it clear by separating it into classes. 
 
 Logical definition, therefore, requires two essen- 
 tial marks (Section 6 a) ; or a genus higher than 
 the notion defined and a specific difference; or two 
 intersecting classes with a part common and a part 
 not common; all these, as we have seen, being es- 
 sentially the same. A notion, therefore, having 
 only one mark, as, thing, can not be defined. Other 
 examples are space, time, infinity, choice. 
 
 An individual can be identified, but not defined, 
 for we can not sum up in one all the marks of an 
 
4 o ESSENTIALS OF LOGIC 
 
 individual save one distinctive mark. There are 
 no two intersecting classes whose sole common part 
 is an individual. Only general notions may be de- 
 fined; individuals may be pointed out, described, 
 located in space and time, but not in a logical sys- 
 tem. 
 
 A logical definition must be: 
 
 ist. Not too wide. The genus and species, as 
 in division, must be proximate, no intervening class 
 being omitted. If geometry be defined as the sci- 
 ence of space, instead of the mathematics of space, 
 this fault is committed. 
 
 2nd. Not too narrow. The specific difference, 
 as in division, must be a mark belonging to every 
 member of the species, and not only to some, as 
 when a dog is defined as an animal that barks, which 
 is not true of Eskimo dogs. 
 
 3rd. Not tautological. Neither the name of the 
 thing defined nor a synonym or a word of the same 
 derivation may be used in the definition, as w T hen 
 logic is defined as the science of logical forms, or 
 life as the sum of the vital functions. Some of 
 the definitions in dictionaries are logical definitions, 
 many are mere verbal explanations, by means of 
 synonymous terms, and often tautological. This, 
 however, may accomplish the purpose of the dic- 
 tionary. 
 
 4th. Not superfluous. If a hexagon be defined 
 as a polygon with six sides and six angles, this 
 
NOTIONS 41 
 
 principle is violated; or if an oak be defined as a 
 kind of tree, for the name of a logical form, as 
 " kind," can not be part of a real definition of a 
 thing. 
 
 5th. Not figurative. Figures indicate not what 
 a thing really is, which is the aim of definition, but 
 what it is like; as, gratitude is the memory of the 
 heart. 
 
 6th. Essential. (Section 6 d, 2nd.) The spe- 
 cific difference must be an essential mark of the 
 notion defined, as: plants and animals are living 
 things ; and not an accidental mark, as : plants and 
 animals are useful things. 
 
 7th. Clear. If not, the purpose of the definition 
 will be defeated, as when a net is defined as a reticu- 
 lated texture with large interstices. 
 
 8th. Short. That is, no longer than necessary. 
 Too great brevity is also a defect, for it may destroy 
 clearness. If all that is superfluous be omitted, and 
 equally clear brief expressions be substituted for 
 lengthy phrases, this end will be attained. A phrase 
 or a clause may often be condensed. 
 
 9th. Positive, if the notion defined be positive; 
 negative, if that be negative. A negative definition 
 of a positive notion, or the reverse, shows only what 
 the notion is not, and not what it is, and is there- 
 fore not a real definition. If a point be defined as 
 position without magnitude, the specific difference 
 is negative. But the negative notion, silence, is 
 
42 ESSENTIALS OF LOGIC 
 
 properly defined as the absence (a negative term) 
 of sound. 
 
 PRACTICE ON SECTION 7 c 
 
 1. Illustrate definition by any of the examples of 
 correct division under the last head, pointing out 
 in each case the genus and the specific difference. 
 
 2. Show how each is a case of intersection, and that 
 the part common to the two intersecting notions 
 is the thing defined. 
 
 3. Show that either of the two intersecting notions 
 may be used as the genus in definition, and the 
 other as the specific difference. 
 
 4. Show that, therefore, there is a double subordi- 
 nation in every case of correct definition. 
 
 5. State each of the above definitions intensively. 
 
 6. Select ten dictionary definitions for criticism. 
 
 7. Test the following by the principles for correct 
 definition. 
 
 ( 1 ) True knowledge is knowing how little we 
 really do know. 
 
 (2) A wise man is a fool who has found 
 himself out. 
 
 (3) An equilateral triangle is one whose sides 
 and whose angles are equal. 
 
 (4) An acute-angled triangle is one which has 
 an acute angle. 
 
 (5) Lead is a metal heavier than iron. 
 
 (6) Cheese is a caseous preparation from 
 milk. 
 
 (7) A fallacy is an incorrect mode of rea- 
 soning. 
 
NOTIONS 43 
 
 (8) Conversion is changing the terms of a 
 proposition. 
 
 (9) A pump is a machine for raising water. 
 
 (10) Man is a featherless biped. 
 
 (11) An elephant is an animal that drinks 
 through its nostrils. 
 
 (12) Silence is the entire absence of sound. 
 
 (13) Truth is that part of human thought 
 which has proven correct. 
 
 (14) Logic is the art of thinking. 
 
 (15) A triangle is half a parallelogram. 
 
 (16) Logic is the science of thought. 
 
 (17) Mind is unextended substance. 
 
 (18) A cur is a kind of dog. 
 
 (19) Geometry is the science of extension. 
 
 (20) Psychology is the science of mental life. 
 
 (21) Psychology is the science of mind. 
 
 (22) Psychology is the science of the phe- 
 nomena of mind. 
 
 (23) Psychology is the science of conscious- 
 ness. 
 
 (24) Thinking may be defined in one of its as- 
 pects at least as the process of inter- 
 preting the special by the general, or the 
 new experience by the old. (Hibben.) 
 
 (25) A moral being is one who has a con- 
 science. 
 
 (26) Evolution is a continuous change from 
 indefinite incoherent homogeneity to defi- 
 nite coherent heterogeneity of structure 
 and function, through successive dil- 
 
44 ESSENTIALS OF LOGIC 
 
 ferentiations and integrations. (Spen- 
 cer.) 
 
 (27) Capital is income-producing investment. 
 
 (28) Wages is the price of labor. 
 
 (29) Green is a color composed of blue and 
 yellow. 
 
 (30) A synopsis is an outline of a topic. 
 
 (31) Motion is change of place. 
 
 (32) Space is indefinite extension. 
 
 (33) Dirt is matter in the wrong place. 
 
 (34) Health is freedom from disease. 
 
 (35) Wealth is accumulated property. 
 
 (36) A sphere is a geometrical solid bounded 
 by a surface every point of which is 
 equally distant from a point within, called 
 the center. 
 
 (37) An angle is the space between two lines. 
 
 (38) Conscience is that faculty of the soul 
 which discerns right and wrong in con- 
 duct. 
 
 (39) A rocker is a chair with rockers. 
 
 (40) A straight chair is a chair without rock- 
 ers. 
 
 (41) A plow is an instrument for cultivating 
 the soil. 
 
 (42) A house is a building to live in. 
 
 (43) An animal is a brute or a human being. 
 
 (44) An ostrich is a large swift bird that hides 
 its head in the sand. 
 
 (45) A story is an interesting account of an 
 incident. 
 
NOTIONS 45 
 
 (46) A peacock is a bird with brilliant plum- 
 age. 
 8. Correct any of the above that are defective. 
 
CHAPTER III 
 
 THE PRIMARY LAWS OF THOUGHT 
 
 8. Introductory. — If we think, we must use 
 the notion and the judgment (Sections 3 and 5) ; 
 that is, we must affirm or deny that two notions are 
 in some one of the logical relations of Section 7. 
 The necessity implied in the word, " must," is the 
 essence of law, and the expression of what is neces- 
 sary for correct thought constitutes the laws of 
 thought. 
 
 The two species, as " plant " and " animal," re- 
 sulting from the dichotomy of a genus, as " living 
 thing," are logical "contradictories," and can not 
 co-exist in a thought about the same object. This 
 opposition persists, of course, between any respective 
 subordinate members of the original co-ordinate 
 species, as " plant " and " dog," " potato " and " ani- 
 mal," " potato " and " dog " ; but all these are ex- 
 amples of opposition only within the limits of the 
 class divided, and in the case of the last three pairs 
 above, the opposition is still further limited. These 
 last three and similar cases are not called contra- 
 dictories, but contraries. 
 
 Absolute contradictories are those that result from 
 46 
 
PRIMARY LAWS OF THOUGHT 47 
 
 logical division of the universe of things, as man 
 and non-man, brute and non-brute, and the test is 
 that every notion whatever belongs only to one 
 class or to the other. Limited contradictories are 
 those that result from the division of some genus 
 lower than the highest, as man and brute ; these are 
 contradictory only within the sphere of the divided 
 genus, that is, every member of that genus belongs 
 only to one or the other ; every animal is either man 
 or brute. Contraries are pairs resulting from 
 trichotomy or polytomy or from combinations like 
 those in the above paragraph; no notion within the 
 sphere of the class divided can belong to both of the 
 contrary classes, but there are notions that belong 
 to neither. 
 
 It must be kept in mind that in logic we are deal- 
 ing with the form of the thought, and not with the 
 matter or with the language; and examples used to 
 illustrate forms of thought must, therefore, be so 
 worded as to show the form fully and clearly, and 
 the logician has the right to make any change in the 
 wording that will accomplish this end. 
 
 9. The Law of Affirmation. — Any notion not 
 contradictory to another notion may be affirmed of 
 it. This law covers (1) the relation of co-exten- 
 sion, or entire identity, as, all gems are jewels, or 
 all jewels are gems; (2) the relation of subordina- 
 tion, both from the point of view of the species, as, 
 all base-balls are globes ; or from the point of view 
 
48 ESSENTIALS OF LOGIC 
 
 of the genus, as, some globes are base-balls ; and this 
 applies not only to species proximate to the genus, 
 but to those further down the logical series, as in 
 the above examples; (3) the relation of intersec- 
 tion, which is merely a double subordination, as, 
 man is an animal, and man is a rational being ; also, 
 some animals are men, some rational beings are 
 men. But the law does not forbid the affirmation 
 of one of two notions, which are not contradictory 
 (nor contrary), of the other, though the affirmation 
 may not be true ; as, the earth is a cube, every man 
 is a liar, no plant is good for food. The law, there- 
 fore, does not establish truth, but merely forbids a 
 specific error. 
 
 10. The Law of Denial. — Any notion contra- 
 dictory to another notion, must be denied of it. This 
 law deals with the relation of co-ordination, includ- 
 ing the limited contradictories and contraries, each 
 within its proper sphere (Section 8) ; examples are: 
 no' man is a brute ; no man is a horse ; no white man 
 is a brute, or a horse ; no circle is square ; no lumin- 
 ous body is non-luminous, etc. 
 
 Apparent contradiction is often used to give point 
 to real truth; as, make haste slowly; when I am 
 weak, then am I strong. 
 
 11. The Law of Exclusion. — Of two contra- 
 dictory notions, one must be affirmed of any third 
 notion. Or, any notion must be either affirmed or 
 denied of any other notion. A is either B or non-B ; 
 
PRIMARY LAWS OF THOUGHT 49 
 
 volcanoes are either in eruption or not in eruption; 
 houses are either brick or not brick. If the contra- 
 diction be not absolute (Section 8), then the "third 
 notion " of the above law is limited to this lower 
 genus, and the law is true only within the scope of 
 that genus ; as, every animal is either man or brute. 
 " Exclusion " means, therefore, that a third possi- 
 bility is excluded. 
 
 The laws of denial and exclusion may be com- 
 bined and variously stated; as, of two contradic- 
 tory notions, one must be affirmed, the other denied 
 of any third notion ; or, any notion must be affirmed 
 of one of two contradictory notions, and denied of 
 the other. 
 
 12. The Scope of the Laws. — Such are the 
 primary laws of thought. From them are derived 
 the many secondary laws and rules of logic. These 
 laws do not establish truth. Their observance 
 merely eliminates error in the form of the thought. 
 We may reason correctly about false statements or 
 non-existent things. What these laws and those 
 derived from them forbid must be rejected; what 
 they do not forbid may or may not be true; it is 
 beyond the province of pure logic to decide. Logic, 
 therefore, gives only negative and partial tests of 
 error, and no positive criterion of truth. Truth de- 
 pends on the matter of the thought. 
 
50 ESSENTIALS OF LOGIC 
 
 PRACTICE ON SECTIONS 8 to 12 
 
 1. Select from the following list pairs of (1) con- 
 tradictories; (2) contraries: sharp, white, clear, 
 alive, cowardly, obscure, dull, hard, dead, black, 
 brave, soft. 
 
 2. Name five other pairs of (1) absolute contra- 
 dictories; (2) limited contradictories; (3) con- 
 traries resulting from trichotomy or polytomy. 
 
 3. Which of the following notions does the law of 
 
 affirmation allow to be affirmed of the notion 
 " cube " : round, square, pink, fragrant, spheri- 
 cal, soft, conical, alive, costly, true? 
 
 4. Which of the above list does the law of contra- 
 
 diction require to be denied of the notion cube? 
 
 5. Give five examples of apparent contradiction with 
 real meaning. 
 
 6. Complete the following according to the law of 
 exclusion: food is wholesome or . . . ; govern- 
 ments are monarchical or . . . ; everything is 
 useful or . . . ; religions are true or . . . ; ani- 
 mals are rational or . . . 
 
 7. Which of the three kinds of pairs in 2 above il- 
 lustrate exclusion? 
 
 8. What point under this general head is illustrated 
 
 by the following examples: 
 
 (1) He was the lion of the party. 
 
 (2) After he changed the figure, it was a 
 circle with the corners square. 
 
 (3) True knowledge is knowing how little 
 we really do know. 
 
PRIMARY LAWS OF THOUGHT 51 
 
 (4) His conduct is either foolish or crazy. 
 
 (5) A wise man is a fool who has found him- 
 self out. 
 
 (6) He is beside himself. 
 
 (7) His alter ego was responsible for that 
 deed. 
 
 (8) That was the wettest rain I ever was in. 
 
 (9) He was so thin he could not tell whether 
 he had the backache or the other kind. 
 
 (10) I saw right through him. 
 
 (11) He had reached a great height of hu- 
 mility. 
 
 (12) He was either at home or in his bedroom. 
 
 (13) A liar told the truth. 
 
 (14) There is one thief who never steals. 
 
 (15) Here lies a man named "Miles," from 
 Cincinnati, aged 59. 
 
 (16) Iron is a very soft metal. Iron is hard. 
 What is hard is soft. 
 
 (17) It is decreed that you the enemy will 
 slay. 
 
 (18) He is a wise fool. 
 
 (19) The friendship of the world is enmity 
 with God. Friendship is enmity. 
 
 (20) He that findeth his life shall lose it; and 
 he that loseth his life for my sake shall 
 find it. 
 
 (21) But many that are first shall be last; and 
 the last shall be first. 
 
CHAPTER IV 
 
 PROPOSITIONS 
 
 13. What Propositions are. — A judgment is 
 an affirmation or a denial that one notion is con- 
 tained in another, that the two are identical in whole 
 or in part. Either marks are thought as contained 
 in a concept or not; as plants are non-sentient, liv- 
 ing, existing; or things are thought as contained in 
 a class or not; as, plants are non-sentient living 
 things. It is evident that the judgment deals with 
 notions and their relations, and affirms or denies ac- 
 cording to the primary laws of thought, the law of 
 exclusion forbidding any third possibility. Also, 
 when we remember that by abstraction we find that 
 plants are non-sentient and living and existing, thus 
 forming the concept, plant, we see that a judgment 
 is primarily an explicit statement of what the con- 
 cept already contains. We are, therefore, merely 
 looking at things already familiar, but from a 
 slightly different point of view. Concepts are judg- 
 ments in a nutshell; judgments are the kernels of 
 concepts. 
 
 A proposition is a judgment expressed in language, 
 and must therefore consist of the names of the two 
 
 52 
 
PROPOSITIONS 53 
 
 notions compared, and the verb affirming or denying 
 their relation. The notion of which another is af- 
 firmed or denied, is as in grammar called the sub- 
 ject ; the other, the predicate. In strict logical form, 
 affirmation is always made by the verb " is " or the 
 plural, "are"; for the relation of the two notions 
 is not dependent on time, but on their real nature, 
 and general truth is expressed by the present tense. 
 Denials are made only by " is not," and " are not." 
 The " is " or " are " is called the copula, and " not " 
 is said to qualify it ; every other word in the sentence 
 belongs either to the subject or the predicate. Strict 
 logical treatment requires every proposition to be 
 put in the form, " subject is predicate," and any 
 change in order or in expression which is necessary 
 for arrangement in this form, must be allowed, the 
 thought itself of course not being affected. As has 
 been said, the subject and the predicate are also 
 called the " terms " (Latin, terminus, end) of the 
 proposition; and notions also are therefore called 
 terms. 
 
 Examples of propositions in strict form are : God 
 is (i. e., is existing) ; water is necessary to life; the 
 sum of the angles of a triangle is two right angles; 
 the doctrine that the earth is the center of the uni- 
 verse is not now held by astronomers. The sub- 
 ject or the predicate may be a word, a phrase, a 
 clause, or even a whole sentence; the subject, how- 
 ever, is substantive, the predicate substantive or 
 
54 ESSENTIALS OF LOGIC 
 
 adjective, according as the thought is extensive or 
 intensive (Section 5, end). 
 
 14. Kinds of Propositions. — Conditional 
 propositions are those which (1) affirm the de- 
 pendence of one of two propositions on the other, 
 as, if land be rich and well- watered, it is fertile; or 
 (2) affirm that one of two contradictories is true of 
 some third notion, as, Cook either reached the North 
 Pole or not; or (3) combine these two, as, if her 
 husband dies, she will either marry again, or remain 
 a widow. These forms are discussed in Section 23. 
 
 Categorical propositions are those which affirm 
 or deny without condition or alternative, as, rich 
 and well- watered land is fertile; Cook reached the 
 North Pole; Cook did not reach the North Pole. 
 
 Simple categorical propositions are those which 
 have only one independent subject and predicate ex- 
 pressed or implied, as the examples in the last para- 
 graph of Section 13; while compound propositions 
 have more than one independent judgment expressed 
 or implied ; as, gold is heavy and yellow, cotton and 
 corn are raised in the South, he is their only friend, 
 none but the brave deserve the fair, all but two were 
 killed. For strict logical treatment, compound are 
 resolved into simple propositions. The above ex- 
 amples would yield the simple propositions: gold is 
 heavy, gold is yellow, cotton is raised in the South, 
 corn is raised in the South, he is their friend, no 
 other than he is their friend, the brave deserve the 
 
PROPOSITIONS 55 
 
 fair, no coward deserves the fair, nearly all were 
 killed, two were not killed. 
 
 A proposition simple in form, may be attended in 
 mind by its opposite, and should in that case be 
 treated as compound, and both components ex- 
 pressed. If I say, some people are not selfish, with 
 the emphasis on " some," I mean also, some are 
 selfish, and the full expression of the thought re- 
 quires both propositions. In speech, the mere tone 
 or emphasis may be the only difference between com- 
 pound and simple forms. 
 
 The grammatically complex proposition, having 
 subordinate clauses, is logically simple ; as, men who 
 are eager to be rich are likely to be unscrupulous; 
 this may be reduced to the simple form : men eager 
 to be rich are likely to* be unscrupulous. 
 
 15. Quality, Quantity, and Symbols of Prop- 
 ositions. — Propositions affirm or deny, and are 
 said to have affirmative or negative " quality." 
 Care must be exercised to ascertain whether the 
 negative belongs to the proposition, that is, to the 
 copula, and not merely to the subject or the predi- 
 cate ; especially as the transfer of the negative from 
 copula to predicate or the reverse, is often easy. In 
 " the universal cry was, no quarter," the negative 
 belongs to the predicate, and the proposition is af- 
 firmative; in " all is not gold that glitters," the nega- 
 tive belongs with the " all," and the meaning is : 
 " not all is gold that glitters," which, however, in 
 
56 ESSENTIALS OF LOGIC 
 
 strict form becomes : " some things that glitter are 
 not gold," and the proposition is negative; in " no 
 news is good news," the negative belongs to the sub- 
 ject, which is equivalent to " the lack of news," and 
 the proposition is affirmative ; in " he is no gentle- 
 man," the negative belongs grammatically to the 
 predicate, " gentleman," though the proposition is 
 obviously a logical denial. The positive and the 
 negative aspects of a thought lie close together in 
 the mind, yet the expression of the two is usually 
 quite distinct, and we cannot say that the mere ex- 
 pression of the one aspect implies the other, though 
 we may have both in mind when we express only 
 one. 
 
 According to their " quantity," judgments are 
 divided into "total" and "partial." Total judg- 
 ments are those which affirm or deny the predicate 
 of the whole subject; partial judgments, of only part 
 of the subject; whether very little or nearly all, or 
 however much, makes no difference in logic. The 
 only distinction is that between the total, involving 
 all, and the partial, involving only some of the sub- 
 ject; with the relative magnitude of part and whole, 
 logic has nothing to do. In strict form, every prop- 
 osition begins either with " all," or an equivalent, 
 (negative, " no," " none") ; or with " some " (neg- 
 ative, " some . . . not "). 
 
 Every thought must and does deal with either some 
 or all of the subject, and if fully expressed, the 
 
PROPOSITIONS 57 
 
 quantity would appear; but because of the customary 
 omissions of speech, or through carelessness, it is 
 not always possible to decide even from the context 
 whether the subject be total or partial. It is not 
 a question of what we would mean, but what the 
 quantity was in the mind of the thinker. Of such 
 cases we must judge according to our opinion of the 
 probabilities, in fairness admitting the possibility of 
 doubt. If in irritation some one says : men are 
 fools, I judge him to mean some men, possibly only 
 one; if some one says: boys will be boys, I judge 
 the meaning to be all boys. 
 
 Some of the w T ords indicating quantity are as 
 follows : 
 
 Total: a, an, all, always, any, both, each, every, 
 individual name, name of substance, my, your, etc., 
 the, this, that, etc., whoever, etc. ; with the nega- 
 tives : neither, never, no, none, not any, nowhere. 
 
 Partial: a, an, a few, a little, almost all, certain, 
 many, most, nearly all, one, two, etc., some, some- 
 times, somewhere, the, the majority, there are; with 
 the negatives : all . . . not, few, hardly any, little, 
 not all, not always, not every, rare, rarely, scarcely 
 any, seldom, slight, small. 
 
 It will be noticed that "a," " the," "all," 
 " few," " little," appear in both lists. Examples 
 of the double use are as follows: Total: a or the 
 mule is a hybrid, all fixed stars are suns; partial 
 affirmative: a few were saved, a little learning is a 
 
58 ESSENTIALS OF LOGIC 
 
 dangerous thing, a or the mule is a tricky animal; 
 partial negative: all trees are not pines, few were 
 saved, little learning is thorough. 
 
 Propositions whose subjects are individual or 
 mathematical wholes (Section 7 b), are called in- 
 dividual propositions, and are total; other total 
 propositions whose subjects are classes, are called 
 universal propositions. 
 
 The division of propositions into affirmative and 
 negative, and again into total and partial, gives 
 four kinds, the total affirmative, the total negative, 
 the partial affirmative, and the partial negative. 
 Taking the first two vowels of " affirmo " (Latin, 
 I affirm), the total affirmative is symbolized by A, 
 the partial affirmative by I; while the vowels of 
 nego (I deny) give E for the total negative, O 
 for the partial negative. Examples are: 
 
 A, All men are rational beings; E, No men are 
 brutes ; I, Some men are blacksmiths ; O, Some men 
 are not blacksmiths. 
 
 Propositions whose predicates as well as their 
 subjects are mathematical wholes, or quantities, are 
 mathematical or quantitative propositions. As 
 their subjects are always total, never partial, they 
 are always symbolized by A or E, never I or O; 
 as, the sun is the center of the solar system; x is 
 equal to y; the sum of any two angles of a tri- 
 angle is greater than the third angle. There is a 
 class of propositions which may be viewed either 
 
PROPOSITIONS 59 
 
 as mathematical or as compound: as, all present 
 are all the members of this class, evidently mathe- 
 matical as just defined, and yet resolvable into: all 
 present are members, and, all members are pres- 
 ent. 
 
 PRACTICE ON SECTIONS 13 to 15 
 
 The following list is purposely long, that different 
 examples may be selected at different times, or for 
 different classes. 1st. Put each proposition in strict 
 logical form; 2nd, if compound, put each component 
 in logical form; 3rd, affix to each the proper symbol, 
 showing whether it be affirmative or negative, total 
 or partial ; 4th, point out any that are individual, and 
 any that are mathematical. 
 
 1. Every mistake is not a proof of ignorance. 
 
 2. All but one have disappeared. 
 
 3. There's not a joy the world can give like that 
 
 it takes away. 
 
 4. Metals are all good conductors of heat. 
 
 5. Nothing is beautiful except truth. 
 
 6. Not many of the metals are brittle. 
 
 7. There is no place like home. 
 
 8. Not many, if any, metals are without luster. 
 
 9. All gold mines cannot be wrought with profit. 
 
 10. Heaven is all mercy. 
 
 11. Romulus and Remus were twins. 
 
 12. One kind of metal at least is liquid. 
 
 13. Charity affords relief as far as possible. 
 
 14. Few are acquainted with themselves. 
 
 15. Some of our muscles act without volition. 
 
60 ESSENTIALS OF LOGIC 
 
 16. God's word, exclusively, is to be received without 
 
 question. 
 
 17. Only citizens can hold property. 
 
 18. Nearly all the troops have left the town. 
 
 19. Only ignorant persons hold such opinions. 
 
 20. Few persons are proof against temptation. 
 
 21. Over the mountains poured the barbarian horde. 
 
 22. Logic is only common sense formulated. 
 
 23. Some students do not fail in anything, while all 
 
 do not succeed. 
 
 24. No illogical author is truly scientific. 
 
 25. Not every man could stand such hardships. 
 
 26. Work that cannot be paid for is alone worth 
 
 doing. 
 
 27. Necessity knows no law. 
 
 28. All men are at times actuated by unselfish mo- 
 
 tives. 
 
 29. No one who is not a taxpayer can vote in this 
 
 election. 
 
 30. What can't be cured must be endured. 
 
 31. Four years of study is required for a degree. 
 
 32. Unasked advice is seldom acceptable. 
 
 33. I shall not all die. 
 
 34. There is none righteous, no, not one. 
 
 35. They also serve who only stand and wait. 
 
 36. He was too impulsive not to have committed 
 
 many errors. 
 
 37. Mankind are all men and women. 
 
 38. A lie faces God, and shrinks from man. Bacon. 
 
 39. There is no man doth a wrong for the wrong's 
 
 sake. Bacon. 
 
PROPOSITIONS 61 
 
 40. Prosperity is not without many fears and dis- 
 
 tastes. Bacon. 
 
 41. A man that is busy and inquisitive is commonly 
 
 envious. Bacon. 
 
 42. It is a miserable state of mind to have few things 
 
 to desire and many things to fear. Bacon. 
 
 43. To spend too much time in studies is sloth, to 
 
 use them too much for ornament is affecta- 
 tion, to make judgment wholly by their rules 
 is the humor of a scholar. Bacon. 
 
 44. Measure not dispatch by the times of sitting, 
 
 but by the advancement of the business. 
 Bacon. 
 
 45. To choose time is to save time. Bacon. 
 
 46. It never troubles the wolf how many the sheep 
 
 be. Bacon. 
 
 47. No people overcharged with tribute is fit for em- 
 
 pire. Bacon. 
 
 48. There is nothing makes a man suspect much 
 
 more than to know little. Bacon. 
 
 49. Certainly, the best mean(s), to clear the way 
 
 in this same wood of suspicions, is frankly 
 to communicate them with the party that 
 he suspects. Bacon. 
 
 50. The principal thing that hath been the destruc- 
 
 tion of most plantations, has been the base 
 and hasty drawing of profit in the first years. 
 Bacon. 
 
 51. As the baggage to an army, so is riches to vir- 
 
 tue. Bacon. 
 
 52. Of great riches there is no real use, except it 
 
62 ESSENTIALS OF LOGIC 
 
 be in the distribution; the rest is but con- 
 ceit. Bacon. 
 
 53. Men mark when they hit, and never mark when 
 
 they miss. Bacon. 
 
 54. Nature is often hidden, sometimes overcome, 
 
 seldom extinguished. Bacon. 
 
 55. There be monks in Russia for penance, that will 
 
 sit a whole night in a vessel of water, till 
 they be engaged with hard ice. Bacon. 
 
 56. Commonwealths and good governments do nour- 
 
 ish virtue grown, but do not much mend the 
 seeds. Bacon. 
 
 57. No man prospers so suddenly as by others' er- 
 
 rors. Bacon. 
 
 58. There are a number of little and scarce dis- 
 
 cerned virtues, or rather faculties and cus- 
 toms, that make men fortunate. Bacon. 
 
 59. Those who ascribe openly too much to their own 
 
 wisdom and policy, end unfortunate. Bacon. 
 
 60. Certainly there be, whose fortunes are like 
 
 Homer's verses, that have a slide and easi- 
 ness more than the verses of other poets. 
 Bacon. 
 
 61. They say that it is a pity the devil should have 
 
 God's part, which is the tithe. Bacon. 
 
 62. Some books are to be read only in parts; others 
 
 to be read but not curiously (i. e., atten- 
 tively) ; and some few to be read wholly, 
 and with diligence and attention. Bacon. 
 
 63. Histories make men wise; poets, witty; the 
 
 mathematics, subtle; natural philosophy, 
 
PROPOSITIONS 63 
 
 deep; moral, grave; logic and rhetoric, able 
 to contend. Bacon. 
 
 64. Some men's behavior is like a verse, wherein 
 
 every syllable is measured. Bacon. 
 
 65. To praise a man's self cannot be decent, except 
 
 it be in rare cases. Bacon. 
 
 66. Bismarck was a great statesman. 
 
 6y. Bismarck was the greatest statesman of his time. 
 
 68. The fear of the Lord is to hate evil. Bible. 
 
 69. There is that speaketh like the piercings of a 
 
 sword. Bible. 
 
 70. The eyes of the Lord are in every place, be- 
 
 holding the evil and the good. Bible. 
 
 71. He that loveth pleasure shall be a poor man. 
 
 Bible. 
 J2. He that hath no rule over his own spirit is like 
 a city that is broken down and without walls. 
 Bible. 
 
 73. A whip for the horse, a bridle for the ass, and 
 
 a rod for the fool's back. Bible. 
 
 74. As a mad man who casteth firebrands, arrows, 
 
 and death, so is the man that deceiveth his 
 neighbor, and saith, Am I not in sport? 
 Bible. 
 
 75. Where no wood is, there the fire goeth out: so 
 
 where there is no talebearer, the strife ceas- 
 eth. Bible. 
 
 76. He that by usury and unjust gain increaseth his 
 
 substance, he shall gather it for him that 
 will pity the poor. Bible, 
 yy. Though he heap up silver as the dust, and pre* 
 
64 ESSENTIALS OF LOGIC 
 
 pare raiment as the clay; he may prepare 
 it, but the just shall put it on, and the inno- 
 cent shall divide the silver. (Said of the 
 "wicked man.") Bible. 
 
 78. The wealth of the sinner is laid up for the just. 
 
 Bible. 
 
 79. For God giveth to a man that is good in his 
 
 sight wisdom, and knowledge, and joy: but 
 to the sinner he giveth travail, to gather 
 and to heap up, that he may give to him that 
 is good before God. Bible. 
 
 80. The words of wise men are heard in quiet more 
 
 than the cry of him that ruleth among fools. 
 Bible. 
 
 81. Not every one that saith unto me, Lord, Lord, 
 
 shall enter into the kingdom of heaven; but 
 he that doeth the will of my Father which 
 is in heaven. Bible. 
 
 82. Nature, like liberty, is but restrained 
 
 By the same laws which first herself ordained. 
 Pope. 
 
 83. Nor is it Homer nods, but we that dream. Pope. 
 
 84. Of all the causes which conspire to blind 
 Man's erring judgment, and misguide the mind, 
 What the weak head with strongest bias rules, 
 Is pride, the never-failing voice of fools. Pope. 
 
 85. {Some to church repair, 
 
 Not for the doctrine, but the music there. Pope. 
 
 86. Some ne'er advance a judgment of their own, 
 But catch the spreading notion of the town: 
 They reason and conclude by precedent. 
 
PROPOSITIONS 65 
 
 And own stale nonsense which they ne'er invent. 
 Some judge of authors' names, not works, and 
 
 then 
 Nor praise nor blame the writings, but the men. 
 
 Pope. 
 
 87. Some praise at morning what they blame at 
 
 night ; 
 But always think the last opinion right. Pope. 
 
 88. Fondly we think we honor merit then, 
 
 When we but praise ourselves in other men. 
 Pope. 
 
 89. All seems infected that th' infected spy, 
 
 As all looks yellow to the jaundiced eye. Pope. 
 
 90. In human works, though labored on with pain, 
 A thousand movements scarce one purpose gain ; 
 In God's, one single can its end produce ; 
 
 Yet serves to second too some other use. Pope. 
 
 91. Tis but a part we see, and not a whole. Pope. 
 
 92. And who but wishes to invert the laws 
 
 Of Order, sins against the Eternal Cause. Pope. 
 
 93. And if each system in gradation roll 
 Alike essential to the amazing whole, 
 The least confusion but in one, not all 
 
 That system only, but the whole must fall. 
 Pope. 
 
 94. All nature is but art, unknown to thee; 
 
 All chance, direction, which thou canst not see; 
 
 All discord, harmony not understood; 
 
 All partial evil, universal good; 
 
 And spite of pride, in erring reason's spite, 
 
 One truth is clear, Whatever is, is right. Pope, 
 
66 ESSENTIALS OF LOGIC 
 
 95. Love, hope, and joy, fair pleasure's smiling 
 
 train, 
 Hate, fear, and grief, the family of pain, 
 These mixed with art, and to due bounds con- 
 fined, 
 Make and maintain the balance of the mind. 
 Pope. 
 
 96. The merchant's toil, the sage's indolence, 
 The monk's humility, the hero's pride, 
 
 All, all alike, find reason on their side. Pope. 
 
 97. Fixed to no spot is happiness sincere, 
 
 'Tis nowhere to be found, or everywhere : Pope. 
 
 98. Who thus define it, say they more or less 
 Than this, that happiness is happiness? Pope. 
 
 99. To whom can riches give repute, or trust, 
 Content, or pleasure, but the good and just? 
 
 Pope. 
 
 100. Who wickedly is wise, or madly brave, 
 
 Is but the more a fool, the more a knave. Pope. 
 
 1 01. He has no hope who never had a fear. Cowper. 
 
 102. Seldom, alas ! the power of logic reigns 
 
 With much sufficiency in royal brains; Cowper. 
 
 103. The diadem, with mighty projects lined, 
 To catch renown by ruining mankind, 
 
 Is worth, with all its gold and glittering store, 
 Just what the toy will sell for, and no more. 
 Cowper. 
 
 104. There is no one who feels anger where the object 
 
 seems impracticable to his revenge. Aristotle. 
 
 105. To overcome is pleasant, not to the ambitious 
 
 only, but even to all. Aristotle. 
 
PROPOSITIONS 67 
 
 106. Neither splendor of vestments, nor preeminence 
 
 of beauty, nor the amount of gold, con- 
 tributes so much to the commendation of a 
 woman as good management in domestic af- 
 fairs, and a noble and comely manner of life. 
 Aristotle. 
 
 107. He is free who lives as he likes ; who is not sub- 
 
 ject to compulsion, to restraint, or to vio- 
 lence. Epictetus. 
 
 108. The cause of all human evils is the not being able 
 
 to apply general principles to special cases. 
 Epictetus. 
 
 109. No living being is held by anything so strongly 
 
 as by its own needs. Epictetus. 
 
 no. Eloquence is a gift not of mind only, but of lungs 
 and strength. Cicero. 
 
 in. Except among the virtuous friendship cannot ex- 
 ist. Cicero. 
 
 112. Friendship is nothing else than a complete union 
 
 of feeling on all subjects, divine and human. 
 Cicero. 
 
 113. To whom can life be worth living, who does not 
 
 repose on the mutual kind feeling of some 
 friend? Cicero. 
 
 114. We do not use fire and water on more occasions 
 
 than we do friendship. Cicero. 
 
 115. Just as a man has most confidence in himself, 
 
 and as he is most completely fortified by 
 worth and wisdom, so that he needs no one's 
 assistance, and feels that all his resources 
 reside in himself, in the same proportion he 
 
68 ESSENTIALS OF LOGIC 
 
 is most highly distinguished for seeking out 
 and forming friendships. Cicero. 
 
 116. There is no greater enemy to friendship than 
 covetousness of money. Cicero. 
 
 ii J. Not only is fortune blind herself, but she com- 
 monly renders blind those whom she em- 
 braces. Cicero. 
 
 1 1 8. No one person ever was so dear to another as 
 
 you are to the people of Rome. Seneca (to 
 Nero). 
 
 119. Trifling evils may cheat us and elude our ob- 
 
 servation, but we gird up our loins to attack 
 great ones. Seneca. 
 
 120. It often happens, that even when they (orators 
 
 who are bad men) speak the truth, belief is 
 not accorded them. Quintilian. 
 
 121. The idle man excuseth him in winter because of 
 
 the great cold, and in summer then by reason 
 of the heat. Chaucer. 
 
 122. Honor is nothing else but to do reverence to 
 
 another person for the good and virtuous dis- 
 position that is in him. Caxton. 
 
 123. Ofttime battle is advanced more for getting of 
 
 silver than by the force and strength of men. 
 Caxton. 
 
 124. There is no man so assured of his honor, of his 
 
 riches, health, or life but that he may be de- 
 prived of either, or all, the very next day 
 or hour to come. Raleigh. 
 
 125. There are no fewer forms of minds than of bod- 
 
 ies amongst us. Jonson. 
 
PROPOSITIONS 69 
 
 126. Some are fit to make divines, some poets, some 
 
 lawyers, some physicians, some to be sent to 
 the plow, and trades. Jonson. 
 
 127. There be some that are forward and bold; and 
 
 these will do every little thing easily. These 
 never perform much, but quickly. They are 
 what they are on the sudden; they show 
 presently like grain that, scattered on the top 
 of the ground, shoots up, but takes no root; 
 has a yellow blade, but the ear empty. Jon- 
 son. 
 
 128. There want not men of equal authority and 
 
 credit, that prefer action to be the more ex- 
 cellent (of the two, action and contempla- 
 tion). Walton. 
 
 129. There is nothing strictly immortal but immor- 
 
 tality. Browne. 
 
 130. Revolutions of ages do not oft recover the loss 
 
 of a rejected truth. Milton. 
 
 131. But when God hath decreed servitude on a sin- 
 
 ful nation, fitted by their own vices for no 
 condition but servile, all estates of a govern- 
 ment are alike unable to avoid it. Milton. 
 
 132. That infection which is from books of contro- 
 
 versy in religion is more doubtful and dan- 
 gerous to the learned than to the ignor- 
 ant. Milton. 
 
 133. Many boys are muddy-headed till they be clari- 
 
 fied with age, and such afterward prove the 
 best. Fuller. 
 
 134. All the whetting in the world can never set a 
 
70 ESSENTIALS OF LOGIC 
 
 razor's edge on that which hath no steel in 
 it. Fuller. 
 
 135. No man is more miserable than he that hath no 
 
 adversity. Taylor. 
 
 136. Of all mankind there are none so shocking as 
 
 these injudicious civil people. Steele. 
 
 137. Any affectation whatsoever in dress implies in 
 
 my mind a flaw in the understanding. Ches- 
 terfield. 
 
 138. Good manners are to particular societies what 
 
 good morals are to society in general. Ches- 
 terfield. 
 
 139. Men who converse only with women are friv- 
 
 olous, effeminate puppies, and those who 
 never converse with them are bears. Chester- 
 field. 
 
 140. No man is ridiculous for being what he really is, 
 
 but for affecting to be what he is not. 
 Chesterfield. 
 
 141. Nothing appears more surprising to those who 
 
 consider human affairs with a philosophical 
 eye than the easiness with which the many 
 are governed by the few. Hume. 
 
 142. When men act in a faction, they are apt, without 
 
 shame or remorse, to neglect all the ties of 
 honor and morality, in order to serve their 
 party. Hume. 
 
 143. This fierce spirit of liberty is stronger in the 
 
 English colonies probably than in any other 
 people of the earth. Burke. 
 
 144. How seldom, friend, a good great man inherits 
 
Propositions ft 
 
 Honor or wealth with all his worth and pains! 
 Coleridge. 
 
 145. It seems little to be perceived, how much the great 
 
 Scriptural idea of the worldly and the un- 
 worldly is found to emerge in literature as 
 well as in life. De Quincey. 
 
 146. There is always hope in a man that actually and 
 
 earnestly works; in Idleness alone is there 
 perpetual despair. Carlyle. 
 
 147. Judgment for an evil thing is many times de- 
 
 layed some day or two, some century or two, 
 but it is sure as life, it is sure as death. 
 Carlyle. 
 
 148. Among mental as among bodily acquisitions, the 
 
 ornamental comes before the useful. Spen- 
 cer. 
 
 149. Whatsoever every man chiefly loves above all 
 
 other things, that he persuades himself is 
 best for him. Boethius. 
 
 150. There is no one that has not need of some addi- 
 
 tion, except God alone. Boethius. 
 
 151. How can that be evil which the mind of every 
 
 man considers to be good, and strives after, 
 and desires to obtain? Boethius. 
 
 152. Many people show gratitude for trifling, but there 
 
 is hardly one who does not show ingratitude 
 for great favors. Rochefoucauld. 
 
 153. A man thinking or working is always alone, let 
 
 him be where he will. Thoreau. 
 
 154. No ceremony that to great ones 'longs, 
 
 Not the king's crown nor the deputed sword, 
 
72 ESSENTIALS OF LOGIC 
 
 The marshal's truncheon nor the judge's robe, 
 Become them with one-half so good a grace 
 As mercy does. Shakespeare. 
 
 155. In law, what plea so tainted and corrupt 
 But, being seasoned with a gracious voice, 
 Obscures the show of evil? Shakespeare. 
 
 156. There is no vice so simple but assumes 
 
 Some mark of virtue on his outward parts. 
 Shakespeare. 
 
 157. Our remedies oft in ourselves do lie, 
 Which we ascribe to heaven. Shakespeare. 
 
PART II 
 DEDUCTIVE INFERENCE 
 
CHAPTER V 
 
 IMMEDIATE DEDUCTION 
 
 1 6. Nature and Kinds of Inference. — As to 
 
 their origin, judgments are of two kinds, psycho- 
 logical, called intuitions; logical, called inferences. 
 Intuitions are not derived from other judgments, 
 but are primary facts of consciousness, known 
 through the senses or by the intellect; as the pri- 
 mary laws of thought, the judgment that I exist, 
 that I see color, hear sound, etc. Inferences are 
 judgments derived from one or more other judg- 
 ments; as when from, all men are animals, we in- 
 fer, some animals are men ; or from, no Greeks are 
 barbarians, and Socrates is a Greek, we infer, Soc- 
 rates is not a barbarian. Intuitions may be and 
 often are the judgments from which inference is 
 made; but the intuition is not a thought, only the 
 inference is a thought. 
 
 There are two kinds of inference, that from a 
 judgment concerning some of a notion to a judg- 
 ment concerning all of the notion, as when from 
 the judgment based on experience, that some gold 
 melts at 1200 degrees, we infer that all gold melts 
 at 1200 degrees. This inference from some to all 
 
 75 
 
^6 ESSENTIALS OF LOGIC 
 
 is inductive inference, and is discussed in Part III 
 below. 
 
 The other kind of inference, called deduction, 
 infers from all to all, all to some, or some to some 
 of the notion; and it is evident that induction and 
 deduction include all possible inferences. Ex- 
 amples of deduction are the inference from, no iron 
 is soft, to, no soft thing is iron; from, all iron is 
 hard, to, some hard things are iron ; and from some 
 iron is brittle, to, some brittle things are iron. 
 
 These examples are all cases of immediate de- 
 duction, that is, deduction without a medium, or 
 third notion; only the same two notions being used 
 in the original judgment and in the inference de- 
 rived from it. Mediate deduction is considered in 
 the next chapter. 
 
 Sometimes a judgment is implied with or in an- 
 other, and might seem to be an inference, when it 
 is really not a new judgment, but already thought 
 more or less obscurely with the other. Logicians 
 differ here, but we are at liberty to decide what we 
 shall exclude from the class we have called in- 
 ferences, so long as no principle is violated. All 
 such cases might be included among inferences, but 
 it is simpler to limit inference as much as we may 
 without manifest error. It is hardly to be said 
 that from, John strikes Henry, we infer, Henry is 
 struck by John; or, if I say, O yes, some men are 
 honest, implying by emphasis on " some " that some 
 
IMMEDIATE DEDUCTION yy 
 
 are not honest, the latter is not inferred from the 
 former, but thought along with it; it is not infer- 
 ence to say that because man is mortal then man is 
 a mortal being, or the reverse; nor that because 
 James is the son of Joe, therefore Joe is the father 
 of James. There is in such cases no real progress 
 of thought, and we shall therefore not count as in- 
 ferences (i) the change from active to equivalent 
 passive, and the reverse; (2) the judgment thought 
 together with another, even if not fully expressed 
 or indicated; (3) the change from intensive to ex- 
 tensive thought, or the reverse; (4) the transfer of 
 the thought from one of two correlatives to the 
 other. 
 
 Finally, as has been said, deductive inference can 
 not pass from some to all, but only from all to all, 
 all to some, and some to some of a notion. In 
 other words, in deduction the quantity of a term 
 can not be increased. 
 
 17. Methods of Immediate Inference. The 
 question now arises, by what legitimate methods 
 may we pass immediately from one judgment to 
 another. There are four general ways : 
 
 1st. Method. By Combination. The two terms 
 of the given judgment may be combined each with 
 the same mark or concept, or with strictly equiva- 
 lent marks or notions, thus forming a new judg- 
 ment. If a house be a building then, a brick house 
 is a brick building; if law be just, then legal ac- 
 
78 ESSENTIALS OF LOGIC 
 
 tion is just action; if a college be an institution for 
 higher education, and if definite entrance require- 
 ments are beneficial to the schools, then, a college 
 with definite entrance requirements is an institu- 
 tion for higher education with something beneficial 
 to the schools. So, too, may judgments be sep- 
 arated into equivalent components, but only when 
 the same mark is taken from both terms; for the 
 equivalence of other elements than marks is not 
 known from the judgment itself. In either case, 
 absolute equivalence must be the rule. For ex- 
 ample, a mouse is an animal, but a large mouse is 
 not a large animal; a carpenter is a citizen, but 
 a bad carpenter is not therefore a bad citizen. This 
 is usually called " determination." 
 
 2nd. Method. By Contradiction. By the pri- 
 mary laws of thought (Section 8), if a notion be 
 affirmed of another, its contradictory must be de- 
 nied of that other, and the reverse. For example, 
 if animals are mortal, it follows that animals are 
 not immortal ; if some men are easy to please, then 
 some men are not hard to please; if no member of 
 this class is late, then every member of this class is 
 on time; if some people are not honest, then some 
 are dishonest* Thus each of the four propositions 
 A, I, E, O, as illustrated above, will by this process 
 yield a new form, equivalent to the old in essen- 
 tial meaning, yet a different form of thought, an 
 inference. For when, for example, we say, ani- 
 
IMMEDIATE DEDUCTION 79 
 
 mals are mortal, we affirm animals to be contained 
 is the class, mortal beings; but when we say, ani- 
 mals are not immortal, we do not affirm this, but 
 deny that they are in the opposite class, immortal 
 beings. The two thoughts may be together in 
 mind, but they are not identical, either being an in- 
 ference from the other. 
 
 This kind of immediate inference is sometimes 
 called inrmitation, sometimes obversion. 
 
 3rd. Method. By Conversion. If one notion, 
 the subject, be related to another, the predicate; 
 then the predicate must be in some relation to the 
 subject, and that relation may be affirmed by re- 
 versing the proposition, that is, by exchanging its 
 subject and predicate. But, as the predicate of an 
 affirmative is not totally involved, it can not be- 
 come the subject of a total proposition; while the 
 predicate of a negative being totally involved may 
 be the subject of a total proposition. The process, 
 which is called " conversion," has three varieties, 
 as follows : 
 
 First, Simple Conversion. If no misers are happy 
 men, then no happy men are misers; if some trees 
 are living things, then some living things are 
 trees. This simple exchange of subject and predi- 
 cate is applicable to E, for both subject and predi- 
 cate of E are total ; it is applicable to I, for both sub- 
 ject and predicate of I are partial ; it is not applicable 
 to A, for the subject of A is total and the predicate 
 
8o ESSENTIALS OF LOGIC 
 
 partial ; nor to O, for the subject of O is partial and 
 the predicate total. 
 
 Second, Conversion by Limitation. The proposi- 
 tion, all crows are birds, affirms the identity of the 
 subject, crows, with only part of the predicate, 
 birds; that is, we can not say from this statement 
 whether or not all birds are meant, and must there- 
 fore " limit " the inference as to birds to, some 
 birds are crows, and the judgment originally total 
 becomes " by limitation " partial. This is also 
 named conversion " per accidens." It may be ap- 
 plied to E, giving O, but as E will give E by sim- 
 ple conversion, it would be absurd to apply this 
 method, when more general truth can be attained 
 by the other. It is therefore especially applicable 
 to A. 
 
 Third, the Conversion of O. The truth is, O 
 can not be converted, for it would give O, a nega- 
 tive with a total predicate, and the subject of the 
 original proposition is partial and can not there- 
 fore be predicate of O. A similar difficulty in the 
 case of A was overcome just above by reducing 
 the quantity of the subject from total to partial, 
 but the trouble here is with the quantity of the 
 predicate, and as the predicate of a negative is al- 
 ways totally denied, there is no way of reducing 
 that, except by changing the proposition to an 
 affirmative. This is done by the method of using 
 the contradictory (2nd. Method above), which 
 
IMMEDIATE DEDUCTION 81 
 
 gives I, and this can then be converted simply. For 
 example, if some engines are not locomotives, we 
 can not say, therefore some locomotives are not 
 engines; because excluding only some engines from 
 the class, locomotives, does not prevent locomotives 
 from being included in some other part of the class, 
 engines. So we adopt the method described above, 
 the use of the contradictory predicate giving, some 
 engines are non-locomotives, and simple conversion 
 of this giving, some non-locomotives are engines. 
 
 This is sometimes called conversion by contra- 
 position, but it is evidently not a new method, as 
 shown above. It may be applied to A, as well as to 
 O. 
 
 As a predicate must be either a mark or a class, 
 a proposition with an individual subject, such as, 
 Brutus was an assassin, or the earth is a sphere, can 
 not be converted, for the subject of the individual 
 proposition is neither a mark nor a class, and can 
 not become a predicate. The words may be turned 
 around, but the thought is not reversed. 
 
 4th. Method. By the Relation of Propositions. 
 Any two of a set of the four kinds of propositions, 
 A, E, I, O, with the same subject and predicate, 
 bear certain fixed relations to each other, such that 
 the truth or the falsity of one involves the truth or 
 the falsity of others. For example, if all grass be 
 green, then it is true that some grass is green, but 
 false that no grass is green, and that some grass is not 
 
82 ESSENTIALS OF LOGIC 
 
 green; that is, if A be true, I is true, but E and O 
 are false. Again, if no man be perfect, it is true 
 that some men are not perfect, but false that all 
 men are perfect, and that some men are perfect; 
 that is, if E be true, O is true, but A and I are 
 false. Still again, if some fruits be food, it is false 
 that no fruits are food, and undetermined as to, 
 all fruits are food, and, some fruits are not food; 
 that is, if I be true, E is false, but A and O are 
 undetermined. Lastly, if some animals be not 
 bipeds, it is false that all animals are bipeds, and 
 undetermined as to, no animals are bipeds, and, 
 some animals are bipeds; that is, if O be true, A is 
 false, and O and I are undetermined. 
 
 Similarly it will be found that if A be false, O is 
 true, E and I undetermined; if E be false, I is true, 
 A and O undetermined; if I be false, E and O are 
 true, A false; and if O be false, A and I are true, 
 E false. 
 
 It appears from the above examination that (i) 
 of the two pairs, A and O, E and I, one proposition 
 in either pair is always true, the other false; ac- 
 cording to the primary laws (Sections 10, n), 
 these are " contradictories ; " (2) of the pair, A 
 and E, both can not be true, but both may be false, 
 and they are called "contraries;" for they are in 
 the same relation as any pair of the members of a 
 trichotomy or polytomy (Section 7 b), which ex- 
 clude each other but leave a third class, or more ; as 
 
IMMEDIATE DEDUCTION 83 
 
 a tree can not be both oak and pine, but may be 
 neither; (3) of the pair I and O, both may be true, 
 but both can not be false, and they are called " sub- 
 contraries ; " (4) of the pairs A and I, E and O, 
 if the universal be true, the particular is true; if the 
 particular be false, the universal is false; I and O 
 are " subalternate " respectively to A and E. 
 
 Successive application of the above principles to 
 a proposition would produce many derived forms. 
 The following are some of these: 
 
 First : " Controversion," sometimes called 
 "contraposition," is obversion (Section 17, 2nd. 
 Method) followed by conversion, of A, E, or O. 
 
 Second : " Contraposition " is obversion, con- 
 version, then obversion again, of A, E, O; or it is 
 contraversion followed by obversion. 
 
 Third : " Inversion " is contraposition followed 
 by conversion, then obversion, of A, or E. The 
 resulting proposition has for subject the contra- 
 dictory of the original subject, and for predicate the 
 contradictory of the original predicate. The vari- 
 ous steps indicated are necessary to prove the cor- 
 rectness of the process, but once proven, we may 
 pass to the inverse form directly. A gives I; E 
 gives O. 
 
 17 a. Immediate Inference of Mathematical 
 Propositions. — The mathematical proposition 
 has both subject and predicate always total, never 
 partial. It follows that the principle of combina- 
 
84 ESSENTIALS OF LOGIC 
 
 tion of Section 17 reduces to the familiar axioms: 
 if equals or unequals be added to equals (or sub- 
 tracted from them, etc.) the results are equals or 
 unequals, respectively. 
 
 The principle of using the contradictory applies 
 only in that if two quantities be equal, they are not 
 unequal, and the reverse. 
 
 Finally, subject and predicate both being always 
 total, the mathematical proposition may always be 
 converted simply. The sun is the center of the 
 solar system, therefore the center of the solar sys- 
 tem is the sun ; x is equal to y, therefore y is equal to 
 x; the sum of any two angles of a triangle is greater 
 than the third angle, therefore any angle of a tri- 
 angle is less than the sum of the other two angles. 
 
 PRACTICE ON SECTIONS 16 and 17 
 
 Using any of the examples for practice in the pre- 
 ceding section, first reduced to simple propositions in 
 strict logical form, copious practice should be had 
 under the following heads: 
 
 1. Select some suitable mark, and form a new judg- 
 
 ment by combining it with the two terms of any 
 proposition. 
 
 2. Combine assigned pairs of suitable propositions, 
 
 such as Nos. 5 and 16, 17 and 41, 2.2, and 24, 40 
 and 41, 71 and y2. 
 
 3. Deny the contradictory of any simple proposi- 
 
 tion (i. e. " infmitate " it, or give its " obverse "). 
 
IMMEDIATE DEDUCTION 85 
 
 4. Convert simply any that admit of simple conver- 
 
 sion. 
 
 5. Convert by limitation any convertible only in that 
 
 way. 
 
 6. Convert any partial negative (O) by infinitating 
 
 and then converting simply (i. e. by " contra- 
 position "). 
 
 7. Convert by any of the above methods, and as 
 
 many as are applicable, any examples assigned. 
 
 8. Select any proposition. If it be true, are the other 
 
 three (of A, E, I, O) with the same subject 
 and predicate, true or false? 
 
 9. Suppose each one selected to be false. Are the 
 
 other three true or false, as above? 
 
 10. Contravert any assigned. 
 
 11. Invert any assigned, in some showing each step, 
 
 in others directly. 
 
CHAPTER VI 
 
 MEDIATE DEDUCTION 
 
 1 8. Nature of Mediate Inference. — Mediate 
 inference is inference through a medium, or " mid- 
 dle 'term." Three notions are used, and not only- 
 two, as in immediate inference. The two notions 
 which are being investigated, are each compared 
 with the third notion, and as a result of the compari- 
 son, their relation to each other is determined. 
 For example, all true statesmen are servants of the 
 state rather than of self, most politicians are not 
 servants of the state rather than of self, therefore, 
 most politicians are not true statesmen. Not being 
 able, perhaps, to judge immediately of the relation 
 of the two notions, true statesmen, and most poli- 
 ticians, each is compared with the third notion, serv- 
 ants of the state rather than of self, and one be- 
 ing found to agree with this, the other not, the two 
 are therefore judged not to agree with each other. 
 
 19. The Syllogism and its Parts. — The full 
 expression of a mediate inference is called a " syl- 
 logism," and evidently requires three propositions. 
 The two in which the middle term occurs are called 
 the " premises " ; the third, in which the two no- 
 
 86 
 
MEDIATE DEDUCTION 87 
 
 tions under investigation are compared, is the " con- 
 clusion " (Latin, shut up together). The subject 
 of the conclusion is called the " minor " term, be- 
 cause it is affirmed or denied to be contained in the 
 predicate, which is therefore the " major " term. 
 The premise in which the major term is compared 
 with the middle term, is called the major premise; 
 that in which the minor and the middle are com- 
 pared, the minor premise. 
 
 The order of the propositions is unimportant, but 
 for convenience in logical study, the order, major, 
 minor, conclusion, is adopted. 
 
 20. Rules of the Syllogism. — Some of the 
 following rules are based on what has just been 
 said, the others have additional reasons given. 
 
 First. Every syllogism has three terms and no 
 more. It we should compare the major and the 
 minor terms with two other different terms, no 
 conclusion could be drawn. Even the same word 
 or group of words with different meanings, would 
 count as two terms, and make the total four, just 
 as if two different words were used; for the term 
 is not the mere words, but the real meaning. An 
 example is: school children are pupils, pupils are 
 part of the eye, therefore school children are part 
 of the eye. 
 
 Second. Every syllogism has three propositions, 
 and no more. This is evident from the nature of 
 the syllogism. 
 
88 ESSENTIALS OF LOGIC 
 
 Third. The middle term must be total (or, " dis- 
 tributed ") in at least one of the premises. For 
 if we compare the major term with only part of 
 the middle, and the minor term with only part, the 
 two parts might be entirely distinct, and no con- 
 clusion would follow. This would be equivalent 
 to having four terms. If chairs be seats, and 
 benches be seats, we can not conclude that chairs 
 are benches, for we have used in each premise only 
 part of the class, seats, and the parts may be, and 
 in this case are distinct; nor, for the same reason, 
 if spheres be round things, and balls be round 
 things, can we conclude that balls are spheres, 
 though we know it be true. 
 
 Violation of this principle is called " undistributed 
 middle." 
 
 Fourth. No term may be total in the conclusion, 
 unless total in a premise. For that would be to 
 conclude about all of a term from a judgment 
 about only some of it. It is important to remem- 
 ber here that the subjects of A and E, and the predi- 
 cates of E and O, are always total, or " distributed/' 
 while terms in other positions are partial, or " un- 
 distributed." 
 
 Violation of this principle is called the " illicit 
 process," or proceeding illegally from some to all in 
 thought. If from, all statesmen are patriots, and 
 no self-seekers are statesmen, we conclude, no self- 
 seekers are patriots, the major term, patriot, is par- 
 
MEDIATE DEDUCTION 89 
 
 tial in the premise and total in the conclusion, and 
 the reasoning is fallacious, though the conclusion 
 is true. This is " illicit major," and can evidently 
 occur only when the conclusion is negative. If 
 from, no self-seekers are statesmen, and some self- 
 seekers are politicians, we conclude, no politicians 
 are statesmen, the fault is " illicit minor," and evi- 
 dently can occur only when the conclusion is total. 
 
 Fifth. If both premises be negative, no conclu- 
 sion follows. For if neither the major nor the 
 minor term agrees with the middle, we can not 
 judge their relation to each other. 
 
 Sixth. If one premise be negative, the conclusion 
 is negative. For then either the major or the minor 
 agrees with the middle term, and the other dis- 
 agrees, so that they must disagree with each other, 
 which means the conclusion is negative. 
 
 To sum up briefly: 
 
 Rule 1. A syllogism has three terms, three 
 propositions, and at least one affirmative premise. 
 
 Rule 2. If one premise be negative, the conclu- 
 sion is negative. 
 
 Rule 3. The middle term must be total at least 
 once. 
 
 Rule 4. A term total in the conclusion, must be 
 total in the premise. 
 
 The above four rules constitute the sufficient test 
 of syllogistic reasoning. The general principle jus- 
 tifying the syllogism may be derived as follows: 
 
90 ESSENTIALS OF LOGIC 
 
 By the law of affirmation (Section 9) a notion 
 not contradictory to another may be affirmed of it; 
 by the law of denial a notion contradictory to an- 
 other must be denied of it. From these laws it fol- 
 lows that if two notions agree with a third, so that 
 all of the third is involved once (Rule 3 above) 
 they agree with each other; also that if one of the 
 two agrees with the third, and the other not (Rule 
 2 above), so that the whole of the third is involved 
 once, then they disagree with each other ; and lastly, 
 if neither agrees with the other (Rule 1 above), 
 nothing can be concluded as to their agreement with 
 each other. 
 
 These principles are evidently equivalent to the 
 four rules of the above summary. It is of course 
 evident, also, that any notion may be substituted for 
 an equivalent notion. 
 
 21. Syllogisms Incompletely Expressed. — 
 Complete expression of syllogistic reasoning is rare 
 in the actual conveyance of thought, obvious parts 
 being left to the mind of the reader or hearer to 
 supply; yet for the purpose of critical examination 
 of the thought, the full form is often necessary. 
 Incomplete syllogisms are called " enthymemes " 
 (Greek, in the mind). The logician has of course 
 the right to full expression. 
 
 The kind of enthymeme most common in or- 
 dinary interchange of thought, and far more com- 
 mon than the fully expressed syllogism, omits one 
 
MEDIATE DEDUCTION 91 
 
 of the three propositions of the syllogism, the omit- 
 ted member being readily supplied from general 
 knowledge or from specific circumstances. If we 
 say, all braggarts are cowards, Falstaff is a brag- 
 gart, therefore Falstaff is a coward, the syllogism 
 is complete; but if we say only, Falstaff is a cow- 
 ard, for he is a braggart, we have an enthymeme, 
 for the major premise is " in the mind " ; or if we 
 say, Falstaff is a coward, because all braggarts are 
 cowards, the minor premise is " in the mind " ; or, 
 finally, if we say, all braggarts are cowards, and 
 Falstaff is a braggart, the conclusion is " in the 
 mind." 
 
 Less common, but still often used, is the en- 
 thymeme with two propositions omitted, the major 
 premise being the one expressed, in nearly, if not 
 quite every instance, and the minor being usually, if 
 not always, suggested by the actual circumstances. 
 A proverb or other popular saying, any general 
 statement by way of insinuation, epitaphs, etc., may 
 be the major premise o<f the enthymeme of only one 
 expressed proposition. Hearing of an attempt on 
 the life of a ruler, we say, " uneasy lies the head 
 that wears a crown " ; the minor premise, the head 
 of this ruler wears a crown, being suggested at 
 once. Seeing a clumsy effort to do something more 
 easily done otherwise, we say, " lazy people take 
 the most trouble " ; the other propositions being ob- 
 vious. 
 
92 ESSENTIALS OF LOGIC 
 
 22. Series of Syllogisms. — Reasoning is sel- 
 dom limited to one mediate inference, but is con- 
 tinued through a series of connected syllogisms, the 
 conclusion of one becoming a premise of the next, 
 as any conclusion may. The syllogism of which 
 the repeated proposition is the conclusion, is the 
 " prosyllogism," the syllogism of which it is a prem- 
 ise, is the " episyllogism." Usually only one prem- 
 ise of the prosyllogism is expressed, and it is 
 therefore an enthymeme. For example: vice is 
 odious, and avarice is vice, for it makes men slaves ; 
 therefore avarice is odious. Here the minor prem- 
 ise is the conclusion of a prosyllogism whose 
 minor premise, avarice makes men slaves, is ex- 
 pressed, but whose major premise, whatever makes 
 men slaves is a vice, is " in the mind." Both prem- 
 ises of the episyllogism may be supported in this 
 way, and the full expression of the reasoning in 
 that case would require three syllogisms; as if above 
 we had said : vice is odious, for whatever exalts the 
 animal above the moral is odious. The name " epi- 
 chirema" has been given to the reasoning when 
 limited to one pair of pro- and episyllogism ; " dou- 
 ble epichirema " to the case where each of the two 
 premises of the same episyllogism is supported by a 
 prosyllogism. 
 
 If this relation of prosyllogism and episyllogism 
 be continued through several syllogisms, the result- 
 ing chain is called a "sorites" (Greek, heap). 
 
MEDIATE DEDUCTION 93 
 
 Thus, the prudent are temperate, the temperate are 
 constant, the constant are unperturbed, the unper- 
 turbed are happy, therefore the prudent are happy. 
 While this reasoning may be fully expressed in a 
 series of pro- and episyllogisms, the mind does not 
 in the actual process stop to form the various in- 
 termediary conclusions, but runs through the suc- 
 cessive middle terms easily and naturally, sees that 
 each wholly contains the next, and concludes finally 
 that the first term agrees or not with the last. The 
 separate syllogisms would be as follows: first, the 
 prudent are temperate, the temperate are constant, 
 therefore the prudent are constant; second, the pru- 
 dent are constant, the constant are unperturbed, 
 therefore the prudent are unperturbed; and so on 
 to the end. The arrangement of premises may be 
 reversed: the unperturbed are happy, the constant 
 are unperturbed, the temperate are constant, the 
 prudent are temperate, therefore the prudent are 
 happy. 
 
 In the first form, the last premise may be nega- 
 tive; in the second form, of course, the first prem- 
 ise; if any other be negative, illicit process would re- 
 sult. In the first form, the first premise may be 
 partial; in the second form, the last premise; if any 
 other be partial, undistributed middle would re- 
 sult. 
 
94 ESSENTIALS OF LOGIC 
 
 PRACTICE ON SECTIONS 19 to 22 
 
 The following examples should be supplemented 
 by others, selected from various sources, by the in- 
 structor, and especially by the class from their own 
 studies, and used for further practice as follows: 
 1st. Put each in strict logical form with three terms 
 and three propositions, any missing propositions being 
 supplied. 2nd. Point out the minor, the major, the 
 middle term in that order. 3rd. Indicate the major 
 premise, the minor premise, the conclusion. 4th. 
 Are both premises negative? If so, what follows? 
 5th. Is the middle term total at least once? 6th. Is 
 any term total in the conclusion? If so, is it also 
 total in its premise? If not, what follows? 
 
 As a further exercise, the class should be required 
 to find or invent cases of undistributed middle, illicit 
 major, and illicit minor and to bring examples of the 
 three kinds of enthymemes. 
 
 In case any example contains parts of two or more 
 syllogisms, each one should be fully expressed, and 
 tested as above. See especially Section 22. 
 
 1. Some wars being justifiable, while all are inex- 
 pedient, it is easy to see that not all inexpedient 
 acts are unjustifiable. 
 
 2. Since caterpillars have two legs, while worms do 
 not, they cannot be worms. 
 
 3. This man, unlike a thief, shares his money with 
 the poor. 
 
 4. All men are sinners and yet some of them are not 
 
 cruel 
 
MEDIATE DEDUCTION 95 
 
 5. He must be an atheist, for he holds these opinions 
 
 that are held by all atheists. 
 
 6. All who were pledged voted for him, but as Jones 
 
 was not pledged, it follows that he did not. 
 
 7. No science is perfect, but every science ought to 
 be cultivated, and so the things we ought to cul- 
 tivate are imperfect. 
 
 8. No one is rich who is not content, so of course 
 no miser is rich, for he could not possibly be con- 
 tent. 
 
 9. All horned animals are ruminants, and so is the 
 
 elk, which is therefore horned. 
 
 10. Every good citizen is ready to defend his coun- 
 
 try, and of course is patriotic, and therefore 
 every patriotic man is ready to defend his country. 
 
 11. Few of the passengers could swim, and yet not 
 
 many perished, so that some who were saved 
 could not swim. 
 
 12. No plants have the power of locomotion, but the 
 lower forms of animal life are of course not 
 plants. 
 
 13. There was heavy dew this morning, so it could 
 
 not have been a cloudy night. 
 
 14. Wisdom is the principal thing; therefore get wis- 
 
 dom. Bible. 
 
 15. Keep thy heart with all diligence; for out of it 
 
 are the issues of life. Bible. 
 
 16. How many syllogisms can be made from these ex- 
 
 amples from the Bible? The fear of the Lord is 
 the beginning of knowledge. The fear of the 
 Lord is to hate evil. The fear of the Lord pro- 
 
96 ESSENTIALS OF LOGIC 
 
 longeth days. The fear of the Lord is a fountain 
 of life. The fear of the Lord, that is wisdom, 
 and to depart from evil is understanding. 
 
 17. And Joshua said unto the people: Ye cannot 
 
 serve the Lord: for he is an holy God; he is a 
 jealous God; he will not forgive your trans- 
 gressions nor your sins. Bible. 
 
 18. And he said to David, Thou art more righteous 
 than I : for thou hast rewarded me good, whereas 
 I have rewarded thee evil. Bible. 
 
 19. Doth Job fear God for nought? Hast thou not 
 made an hedge about him? Bible. 
 
 20. The Lord is my shepherd; I shall not want. 
 Bible. 
 
 21. For thy name's sake, O Lord, pardon mine in- 
 iquity ; for it is great. Bible. 
 
 22. Fear God, and keep his commandments: for this 
 is the whole duty of man. Bible. 
 
 23. Repent ye : for the kingdom of heaven is at hand. 
 Bible. 
 
 24. Blessed are the poor in spirit: for theirs is the 
 kingdom of heaven. Bible. 
 
 25. John came neither eating nor drinking, and they 
 
 say, He hath a devil. The Son of man came 
 eating and drinking, and they say, Behold a man 
 gluttonous, and a winebibber, a friend of pub- 
 licans and sinners. Bible. 
 
 26. He that is of God heareth God's words : ye there- 
 fore hear them not, because ye are not of God. 
 Bible. 
 
 27. By the deeds of the law there shall no flesh be 
 
MEDIATE DEDUCTION 97 
 
 justified in his sight ; for by the law is the knowl- 
 edge of sin. Bible. 
 
 28. Being justified by faith, we have peace with God. 
 Bible. 
 
 29. Hope that is seen is not hope; for what a man 
 
 seeth, why doth he yet hope for? Bible. 
 
 30. Whom he did foreknow, he also did predestinate 
 to be conformed to the image of his Son, that he 
 might be the firstborn among many brethren. 
 Moreover, whom he did predestinate, them he 
 also called; and whom he called, them he also 
 justified; and whom he justified, them he also 
 glorified. Bible. 
 
 31. For whosoever shall call upon the name of the 
 Lord shall be saved. How then shall they call 
 on him in whom they have not believed? and 
 how shall they believe in him of whom they have 
 not heard? and how shall they hear without a 
 preacher? And how shall they preach, except 
 they be sent? Bible. 
 
 32. Let every soul be subject unto the higher powers. 
 For there is no power but of God. Whosoever 
 therefore resisteth the power, resisteth the ordi- 
 nance of God. Bible. 
 
 33. He that will not apply new remedies must expect 
 new evils; for time is the greatest innovator. 
 Bacon. 
 
 34. Riches are for spending, and spending for honor 
 
 and good actions; therefore extraordinary ex- 
 pense must be limited by the worth of the oc- 
 casion. Bacon. 
 
98 ESSENTIALS OF LOGIC 
 
 35. He must needs be a wise man, he speaks so much 
 of himself. Bacon. 
 
 36. Of ambitions, it is less harmful the ambition to 
 prevail in great things, than that other to appear 
 in everything; for that breeds confusion, and 
 mars business. Bacon. 
 
 37. Let not a man trust his victory over his nature too 
 
 far; for nature will be buried a great time, and 
 yet revive upon the occasion, or temptation. 
 Bacon. 
 
 38. Since there must be borrowing and lending, and 
 men are so hard of heart as they will not lend 
 freely, usury must be permitted. Bacon. 
 
 39. The discommodities of usury are, first, that it 
 makes fewer merchants; for were it not for this 
 lazy trade of usury, money would not lie still, 
 but would in great part be employed upon mer- 
 chandising. Bacon. 
 
 40. It (usury) bringeth the treasure of a realm or state 
 
 into a few hands ; for the usurer being at cer- 
 tainties, and others at uncertainties, at the end 
 of the game most of the money will be in the 
 box. Bacon. 
 
 41. It (usury) beats down the price of land; for the 
 
 employment of money is chiefly either merchan- 
 dising, or purchasing, and usury waylays both. 
 Bacon. 
 
 42. On the other side, in some other respect usury 
 advanceth merchandising; for it is certain that 
 the greatest part of trade is driven by young 
 merchants upon borrowing at interest. Bacon. 
 
MEDIATE DEDUCTION 99 
 
 43. Men had need beware how they be too perfect 
 in compliments ; for be they never so sufficient 
 otherwise, their enviers will be sure to give them 
 that attribute, to the disadvantage of their greater 
 virtues. Bacon. 
 
 44. I grant that men, continuing what they are, 
 Fierce, avaricious, proud, there must be war. 
 
 Cow per. 
 
 45. Why has not man a microscopic eye? 
 
 For the plain reason, man is not a fly. Pope. 
 
 46. Wisdom is a most beautiful thing, and Love is 
 of the beautiful ; and therefore Love is also a 
 philosopher or lover of wisdom, and being a lover 
 of wisdom is in a mean between the wise and 
 the ignorant. Plato. 
 
 47. To overcome is pleasant, not to the ambitious 
 
 only, but even to all ; for there arises an imagina- 
 tion of superiority, for which all, either in a 
 faint or more violent degree, have an appetite. 
 But since to overcome is pleasant, it must follow, 
 of course, that amusements where there is field 
 for rivalry, as those of music and disputations, 
 are pleasant ; for it frequently occurs, in the 
 course of these, that we overcome. Aristotle. 
 
 48. Happiness does not consist in amusement; for it 
 is absurd that the end should be amusement. 
 Aristotle. 
 
 49. To amuse ourselves in order that we may be seri- 
 
 ous seems to be right; for amusement resembles 
 relaxation. Aristotle. 
 
 50. He is free who lives as he likes ; who is not sub- 3 
 
ioo ESSENTIALS OF LOGIC 
 
 ject to compulsion, to restraint, or to violence; 
 whose pursuits are unhindered, his desires suc- 
 cessful, his aversions unincurred. Who, then, 
 would wish to lead a wrong course of life? No 
 one. No wicked man, then, lives as he likes; 
 therefore no such man is free. Epictetus. 
 
 51. Since, then, neither they who are called kings nor 
 the friends of kings live as they like, who, then, 
 after all, is free? Epictetus. 
 
 52. To whatever objects a person devotes his atten- 
 
 tion, these objects he probably loves. Do men 
 ever devote their attention then to (what they 
 think) evils? By no means. Or even to things 
 indifferent ? No, nor this. It remains, then, that 
 good must be the sole object of their attention; 
 and if of their attention, of their love too. Who- 
 ever, therefore, understands good, is capable like- 
 wise of love ; and he who cannot distinguish good 
 from evil, and things indifferent from both, how 
 is it possible that he can love? The wise per- 
 son alone, then, is capable of loving. Epictetus. 
 
 53. You will act in the wisest way, if you deem his 
 
 piety, virtue, and industry to be your own, to be 
 with you, wherever you are ; for those things 
 which we hold in mind are no less ours than those 
 we behold with our eyes. Cicero. 
 
 54. We ought to watch and avoid the love of money; 
 
 for nothing so truly characterizes a narrow, 
 groveling disposition as to love riches. Cicero. 
 
 55. An inordinate passion for glory is likewise to be 
 guarded against; for it deprives us of liberty, 
 
MEDIATE DEDUCTION ioi 
 
 the only prize for which men of elevated senti- 
 ments ought to contend. Cicero. 
 
 56. But, since most persons are of opinion that the 
 achievements of war are more glorious than civil 
 affairs, this judgment needs to be restricted; for 
 many, as generally is the case with high minds 
 and enterprising spirits, especially if they are 
 adapted to military life and are fond of warlike 
 achievements, have often sought opportunities of 
 war from their fondness for glory; but if we 
 are willing to judge truly, many are the civil 
 employments of greater importance, and of more 
 renown, than the military. Cicero. 
 
 57. In this respect friendship is superior to relation- 
 
 ship, because from relationship benevolence can 
 be withdrawn and from friendship it cannot ; for 
 with the withdrawal of benevolence the very name 
 of friendship is done away, while that of rela- 
 tionship remains. Cicero. 
 
 58. Because nature can never change, therefore true 
 
 friendships are eternal. Cicero. 
 
 59. He (Scipio) indeed used to say that nothing was 
 more difficult than that friendship should con- 
 tinue to the end of life; for it often happened 
 either that the same course was not expedient 
 to both parties or that they held different views 
 of politics. Cicero. 
 
 60. When going into exile, he (Tarquin) found out 
 
 whom he had as faithful friends, and whom un- 
 faithful ones, since then he could no longer show 
 gratitude to either party. Cicero. 
 
io2 ESSENTIALS OF LOGIC 
 
 61. The reason why cruelty is the most hateful of all 
 vices is that it goes first beyond ordinary limits, 
 and then beyond those of humanity; that it de- 
 vises new kinds of punishments, calls ingenuity 
 to aid it in inventing devices for varying and 
 lengthening men's torture, and takes delight in 
 their sufferings. Seneca. 
 
 62. An anonymous information was laid before me, 
 
 containing a charge against several persons, who 
 upon examination denied they were Christians, or 
 had ever been so. They repeated after me an 
 invocation to the gods, and offered religious rites 
 with wine and incense before your statue (which 
 for that purpose I had ordered to be brought, 
 together with those of the gods), and even re- 
 viled the name of Christ: whereas there is no 
 forcing, it is said, those who are really Christians 
 into any of these compliances : I thought it 
 proper, therefore, to discharge them. Pliny. 
 
 63. Anonymous informations ought not to be re- 
 
 ceived in any sort of prosecution. It is intro- 
 ducing a very dangerous precedent, and is quite 
 foreign to the spirit of our age. Trajan's reply 
 to Pliny. 
 
 64. There needed no licensing of books among them 
 
 (the Spartans), for they disliked all but their 
 own laconic apothegms, and took a slight occasion 
 to chase Archilochus out of the city, perhaps for 
 composing in a higher strain than their own sol- 
 dierly ballads and roundels could reach to. Mil- 
 ton. 
 
MEDIATE DEDUCTION 103 
 
 65. Where there is much desire to learn, there of 
 
 necessity will be much arguing, much writing, 
 many opinions: for opinion in good men is but 
 knowledge in the making. Milton. 
 
 66. There is scarce any profession in the common- 
 wealth more necessary, which is so slightly per- 
 formed. The reasons whereof I conceive to be 
 these: First, young scholars make this calling 
 their refuge; yea, perchance, before they have 
 taken any degree in the university, commence 
 schoolmasters in the country, as if nothing else 
 were required to set up this profession but only 
 a rod and a ferula. Secondly, others who are 
 able, use it only as a passage to better prefer- 
 ment to patch the rents in their present fortune, 
 till they can provide a new one, and betake them- 
 selves to some more gainful calling. Thirdly, 
 they are disheartened from doing their best with 
 the miserable reward which in some places they 
 receive, being masters to their children and slaves 
 to their parents. Fourthly, being grown rich, 
 they grow negligent, and scorn to touch the 
 school but by the proxy of the usher. Fuller. 
 
 6y. Hard, rugged, and dull natures of youth acquit 
 themselves afterwards the jewels of the country, 
 and therefore their dullness at first is to be borne 
 with, if they be diligent. Fuller. 
 
 68. The reason that there is such a general outcry 
 
 among us against flatterers is that there are so 
 very few good ones. Steele. 
 
 69. The man of business despises the man of pleasure 
 
104 ESSENTIALS OF LOGIC 
 
 for squandering his time away ; the man of pleas- 
 ure pities or laughs at the man of business for 
 the same thing ; and yet both concur superciliously 
 and absurdly to find fault with the Supreme 
 Being for having given them so little time. 
 Bolingbroke. 
 
 jo. There never can be wanting some who distinguish 
 desert, who will consider that no dictionary of 
 a living tongue can ever be perfect, since, while 
 it is hastening to publication, some words are 
 budding and some falling away. Johnson. 
 
 71. Foolish men imagine that because judgment for 
 an evil thing is delayed, there is no justice, but 
 an accidental one, here below. Carlyle. 
 
 J2. What, then, is the use of history, and what are 
 its lessons? If it can tell us little of the past, 
 and nothing of the future, why waste our time 
 over so barren a study? 
 
 First, it is a voice ever sounding across the cen- 
 turies the laws of right and wrong. Opinions 
 alter, manners change, creeds rise and fall, but 
 the moral law is written on the tablets of eter- 
 nity. For every false word or unrighteous deed, 
 for cruelty and oppression, for lust or vanity, the 
 price has to be paid at last, not always by the 
 chief offenders, but paid by some one. Justice 
 and truth alone endure and live. Injustice and 
 falsehood may be long-lived, but doomsday comes 
 at last to them, in French revolutions and other 
 terrible ways. 
 
 That is one lesson of history. Another is, that we 
 
MEDIATE DEDUCTION 105 
 
 should draw no horoscope; that we should ex- 
 pect little, for what we expect will not come to 
 pass. Revolutions, reformations, — those vast 
 movements into which heroes and saints have flung 
 themselves, in the belief that they were the dawn 
 of the millennium, — have not borne the fruit 
 which they looked for. Froude. 
 
 73. Few things are needed to make a wise man happy ; 
 nothing can make a fool content; that is why 
 most men are miserable. Rochefoucauld. 
 
 74. Thou art not thyself: 
 
 For thou exist'st on many a thousand grains 
 That issue out of dust. Shakespeare. 
 
 23. Conditional Propositions. — Conditional 
 propositions are of two kinds, hypothetical and dis- 
 junctive. They assert, not absolutely, as do cate- 
 gorical propositions (Section 14), but dependently 
 on some supposition or alternative. Let us analyze 
 some examples. 
 
 First, the hypothetical proposition : 
 
 a. With the same subject in the two clauses: 
 if iron be impure, it is brittle; or if iron be a metal, 
 it has luster. The first example is equivalent to 
 the simple proposition, impure iron is brittle; the 
 second is an enthymeme with the major premise " in 
 the mind," and the minor stated, not as a fact, but 
 as a supposition, thus: (metals have luster), if iron 
 be a metal, then iron has luster. 
 
 b. With the subject of the first clause as predi- 
 
lo6 ESSENTIALS OF LOGIC 
 
 cate of the second: if metals have luster, carbon is 
 not a metal. This is an enthymeme with the minor 
 premise " in the mind," and the major stated as a 
 supposition, thus: if metals have luster (carbon 
 has not luster), therefore carbon is not a metal. 
 In this form the second clause must be negative, 
 else undistributed middle; as if it were said: if met- 
 als have luster, iron is a metal (iron having lus- 
 ter). 
 
 c. With the predicate of the first clause as sub- 
 ject of the second: if iron be a metal, some metals 
 are hard; the full syllogism being: (iron is hard), 
 and if iron be a metal, some metal is hard. In this 
 form the second clause must be partial, else illicit 
 minor. 
 
 d. With the same predicate in the two clauses : 
 if metals have luster, iron has luster; an enthymeme 
 yielding: if metals have luster, (iron is a metal), 
 therefore iron has luster. 
 
 e. With different terms for subjects and predi- 
 cates of both clauses : if the temperate are constant, 
 the prudent are unperturbed, yields the sorites : 
 (the prudent are temperate), and if the temperate 
 are constant, and (the constant are unperturbed) 
 therefore the prudent are unperturbed. 
 
 f. With only two terms as subject and predicate 
 of both clauses. Such propositions express all the 
 forms of immediate inference allowed by Section 
 17, as: 
 
MEDIATE DEDUCTION 107 
 
 (1) Combination: if a house be a building, a 
 brick house is a brick building. 
 
 (2) Contradiction: if animals are mortal, ani- 
 mals are not immortal. 
 
 (3) Conversion in all legitimate forms, as: if 
 no misers are happy men, no happy men are misers, 
 etc. 
 
 (4) Relation of propositions: if all grass be 
 green, some grass is green, etc. 
 
 It appears, therefore, that the hypothetical propo- 
 sition is equivalent to a simple proposition, or is an 
 immediate inference, or is an enthymeme subject to 
 the rules of the syllogism. 
 
 Second, the disjunctive proposition: as, for ex- 
 ample : actions are either right or wrong, evidently 
 a direct application of the primary laws of Sections 
 9, 10, and 11 : of two contradictories, one must be 
 true, the other false. If the division be not dichot- 
 omous, the disjunction is still correct, provided the 
 resulting parts exhaust the notion divided, and do 
 not overlap, as : angles are right, acute, or obtuse. 
 Strict logical form would require contradictories : 
 angles are either right or oblique. We speak 
 loosely, however, in ordinary interchange of 
 thought, or we limit possible affirmation to two op- 
 posites not strict contradictories by assuming or 
 asking that it be granted that any third possibility 
 be not allowed; as: that tree is a birch or a beech, 
 when it might be neither; or a suicide is either de- 
 
io8 ESSENTIALS OF LOGIC 
 
 merited or cowardly, when he might be both, or, per- 
 haps, neither. 
 
 Every disjunctive is equivalent to four hypotheti- 
 cals ; actions are either right or wrong, yields the fol- 
 lowing: if they are right, they are not wrong; if 
 they are not right, they are wrong; if they are 
 wrong, the are not right; and if they are not wrong, 
 they are right. 
 
 Third, the hypothetical and the disjunctive com- 
 bined : 
 
 a. With the same condition, and different con- 
 clusions : if A is B, C is D ; or if A is B, E is F. 
 
 b. With different conditions, and the same con- 
 clusion: if A is B, C is D ; or if E is F, C is D. 
 
 c. With different conditions, and different con- 
 clusions : if A is B, C is D ; or if E is F, G is H. 
 
 Subjects or predicates might be repeated as in 
 the simple hypothetical above. Being formed of 
 the hypothetical and the disjunctive, no new princi- 
 ples are needed to explain the combination. A di- 
 vision into more than two classes, co-exclusive, and 
 exhaustive would be of the form : either A is B, or 
 C is D, or E is F ; this would yield a. combined form : 
 if A is not B, C is D ; or if A is not B, E is F; and 
 other similar forms. It appears, then, that these 
 compound forms originate in non-dichotomous di- 
 visions. 
 
MEDIATE DEDUCTION 109 
 
 PRACTICE ON SECTION 23 
 
 For each conditional proposition in the following: 
 1st. Is it hypothetical or disjunctive? 2nd. If hypo- 
 thetical, is it an immediate inference, and of what 
 kind? 3rd. Or is it an enthymeme? If so, complete 
 the syllogisms, and test by the rules of Section 20. 
 In case undistributed middle or illicit process be 
 found, exchanging the subject and predicate of a 
 proposition supplied to complete the syllogism, will 
 probably correct the error. 4th. If disjunctive, test 
 the disjunction, and give at least some of the re- 
 sulting conjunctives. 5th. If a simple proposition, 
 state it. 
 
 1. Men leave their riches either to their kindred or 
 to the public ; and moderate portions prosper best 
 in both. Bacon. 
 
 2. If a man write little, he had need have a great 
 memory; if he confer little, he had need have a 
 present wit; and if he read little, he need have 
 much cunning, to seem to know that he doth not. 
 Bacon. 
 
 3. Wherever he goes, there is trouble. 
 
 4. If you love me, tell me so. 
 
 5. If wishes were horses, beggars would ride. 
 
 6. He has gone to his cottage or bungalow. 
 
 7. Neither money nor threats could make him change 
 his mind. 
 
 8. Everything pleasant consists either in the percep- 
 tion of pleasant objects, or in the remembrance 
 of those which have already been, or in the hope 
 
no ESSENTIALS OF LOGIC 
 
 of such as are yet to be; for men exercise per- 
 ception on present, memory on past, and hope on 
 future objects. Aristotle. 
 9, Unless parents afford their children a fit pattern 
 of life, they will leave them an obvious excuse 
 to quote against themselves. Aristotle. 
 
 10. If I am wrong in this, that I believe the souls of 
 men to be immortal, I willingly delude myself. 
 Cicero. 
 
 11. Nothing is more noble and more exalted than to 
 
 despise riches if you have them not, and if you 
 have them, to employ them in beneficence and 
 liberality. Cicero. 
 
 12. If it were expediency that cemented friendships, 
 the same when changed would dissolve them. 
 Cicero. 
 
 13. There is no reason why power should do any 
 
 harm, if only it be wielded in accordance with 
 the laws of nature. Seneca. 
 
 14. No man, unless he be good, can ever be an orator. 
 
 Quintilian. 
 
 15. The mind cannot be in a condition for pursuing 
 
 the most noble of studies, unless it be entirely 
 free from vice. Quintilian. 
 
 16. Virtue is teachable, if it is knowledge; for surely 
 knowledge is teachable. 
 
 17. Sorrowful and mishappy is the condition of a 
 poor beggar, for if he asks not his meat he dieth 
 of hunger, and if he ask he dieth for shame; and 
 dire necessity constraineth him to ask. Chau- 
 cer, quoting Innocent. 
 
MEDIATE DEDUCTION in 
 
 18. If we never flattered ourselves the flattery of 
 others would not hurt us. Rochefoucauld. 
 
 19. Those many had not dared to do that evil 
 If the first man that did the edict infringe 
 Had answered for his deed. Shakespeare. 
 
 20. If ye then, being evil, know how to give good 
 gifts unto your children, how much more shall 
 your Father which is in heaven give good things 
 to them that ask Him? Bible. 
 
 21. Had ye believed Moses, ye would have believed 
 
 me; for he wrote of me. But if ye believe not 
 his writings, how shall ye believe my words? 
 Bible. 
 
 22. If ye believe not that I am he, ye shall die in your 
 sins. Bible. 
 
 23. If God were your Father, ye would love me; for 
 
 I proceedeth forth and came from God ; neither 
 came I of myself, but he sent me. Bible. 
 
 24. If a man keep my saying, he shall never see death. 
 Bible. 
 
 25. Neither hath this man sinned, nor his parents. 
 Bible. 
 
 26. If this counsel or this work be of men, it will 
 come to nought; but if it be of God, ye cannot 
 overthrow it ; lest haply ye be found even to fight 
 against God. Bible. 
 
 27. If God be for us, who can be against us? Bible. 
 
 28. If ye were Abraham's seed, ye would do the 
 works of Abraham. Bible. 
 
 29. I will not letthee go, unless thou bless me. Bible. 
 
 30. If this which I have mentioned be the meaning of 
 
ii2 ESSENTIALS OF LOGIC 
 
 the word liberty, in the ordinary use of language : 
 as I trust that none that has ever learned to talk, 
 and is unprejudiced, will deny: then it will follow 
 that in propriety of speech neither liberty, nor its 
 contrary, can properly be ascribed to any being or 
 thing but that which has such a faculty, power 
 or property as is called will. Edwards. 
 
 31. The taxes are indeed very heavy, and, if those 
 laid on by the government were the only ones we 
 had to pay, we might more easily discharge them ; 
 but we have many others, and much more griev- 
 ous to some of us. Franklin. 
 
 32. If time be of all things the most precious, wasting 
 
 time must be the greatest prodigality. Franklin. 
 
 33. If you would have a faithful servant, and one that 
 you like, serve yourself. Franklin. 
 
 34. If you would know the value of money, go and 
 
 try to borrow some. Franklin. 
 
 35. If a man have no heroism in his soul — no ani- 
 mating purpose beyond living easily and faring 
 sumptuously — I can imagine no greater mistake 
 on his part than that of resorting to authorship as 
 a vocation. Greeley. 
 
 36. If the bell rings, why should we run? Thoreau. 
 
 See 9, page 128. 
 
 37. It is worth the expense of youthful days and costly 
 hours, if you learn only some words of an an- 
 cient language, which are raised out of the 
 trivialness of the street, to be perpetual sugges- 
 tions and provocation. Thoreau. 
 
 38. When works of importance are pressing, generals 
 
MEDIATE DEDUCTION 113 
 
 themselves may take up the pickax and the spade. 
 Bolingbroke. 
 
 39. No man would have any reason to fear the fury 
 of a tyrant, if he had no authority over any but 
 from fear ; since, as a single man, his bodily force 
 can reach but a small way, and all the further 
 power he possesses must be founded either on 
 our own opinion, or on the presumed opinion of 
 others. Hume. 
 
 40. If we suffer ourselves to imagine that their senses 
 present to different men different images of 
 things, this skeptical proceeding will make every 
 sort of reasoning on every subject vain and friv- 
 olous. Burke. 
 
 41. But should any man be found who declares that 
 to him tobacco has a taste like sugar, and that 
 he cannot distinguish between milk and vinegar; 
 or that tobacco and vinegar are sweet, milk bit- 
 ter, and sugar sour; we immediately conclude 
 that the organs of this man are out of order, 
 and that his palate is utterly vitiated. Burke. 
 
 42. Indeed, my lord, I greatly deceive myself, if in 
 this hard season (after the loss of his son), I 
 would give a peck of refuse wheat for all that 
 is called fame and honor in the world. Burke. 
 
 43. If it be admitted that a man possessing absolute 
 
 power may misuse that power by wronging his 
 adversaries, why should a majority not be liable 
 to the same reproach? De Tocqueville. 
 
 44. When a community actually has a mixed govern- 
 
 ment — that is to say, when it is equally divided 
 
ii4 ESSENTIALS OF LOGIC 
 
 between two adverse principles — it must either 
 pass through a revolution or fall into complete 
 dissolution. De Tocqueville. 
 
 45. When an individual or party is wronged in the 
 
 United States, to whom can he apply for redress ? 
 If to public opinion, public opinion constitutes 
 the majority; if to the legislature, it represents 
 the majority, and implicitly obeys its instructions; 
 if to the executive power, it is appointed by the 
 majority, and is a passive tool in its hands. The 
 public troops consist of the majority under arms; 
 the jury is the majority invested with the right 
 of hearing judicial cases; and in certain cases, 
 even the judges are elected by the majority. 
 However iniquitous or absurd the evil of which 
 you complain may be, you must submit to it as 
 well as you can. 
 If, on the other hand, a legislative power could be so 
 constituted as to represent the majority without 
 necessarily being the slave of its passions, an 
 executive so as to retain a certain degree of un- 
 controlled authority, and a judiciary so as to re- 
 main independent of the other two powers, a 
 government would be formed which would still 
 be democratic, without incurring any risk of 
 tyranny. De Tocqueville. 
 
 46. On a hot sunshiny afternoon came on a sudden 
 
 storm and spoiled the farmer's hay; and this is 
 called ill luck. We will suppose the same event 
 to take place when meteorology shall have been 
 perfected into a science, provided with unerring 
 
MEDIATE DEDUCTION 115 
 
 instruments; but which the farmer had neglected 
 to examine. This is no longer ill luck, but im- 
 prudence. Coleridge. 
 
 47. Take away Stonehenge from Salisbury Plain, and 
 
 it is nothing more than Hounslow Heath, or 
 any other uninclosed down. Byron. 
 
 48. It cannot be true: if Alexander were dead, the 
 whole habitable world would have smelt of his 
 carcass. Demades, quoted by Grote. 
 
 24. So-Called Conditional " Syllogisms." — 
 
 Examples are as follows: 
 
 First, based on hypothetical propositions : if A 
 is B, C is D; but A is B, therefore C is D: or, but 
 C is not D, therefore A is not B. 
 
 Second, based on disjunctive propositions: A is 
 either B or non-B ; but A is B, therefore A is not 
 non-B, etc. 
 
 Third, based on the combined form: Either if 
 A is B, C is D ; or if E is F, G is H ; but either A 
 is B, or E is F ; therefore C is D, or G is H : or, but 
 either C is not D, or G is not H ; therefore A is not 
 B, or E is not F. 
 
 We have seen in Section 23 that the hypothetical 
 proposition is itself an incomplete syllogism; fur- 
 thermore, the above forms have more than three 
 terms, have not major and minor premises as de- 
 fined for the syllogism in Section 19, in which a 
 major and a minor term are compared respectively 
 with a middle term. These forms are therefore not 
 
n6 ESSENTIALS OF LOGIC 
 
 syllogisms, and the question arises what is their true 
 nature and their place in logic. Examination of 
 them will show that each constitutes a passage from 
 a supposition or an alternation, that is from a state- 
 ment of mere dependence, or connection, to an inde- 
 pendent statement of exactly the same subject-mat- 
 ter. In the original proposition, if hypothetical, it is 
 affirmed merely that the conclusion follows from the 
 condition, and the question of the truth of the con- 
 dition or conclusion is not involved; in the second 
 proposition either the truth of the condition or the 
 falsity of the conclusion is affirmed, and conclusion 
 is reached as to the truth of the other clause. Again, 
 if the original proposition be disjunctive, it is af- 
 firmed merely that one or the other of two contra- 
 dictories is true, the other false; but not which is 
 true, and which false; in the second proposition 
 the truth or the falsity of one alternative is af- 
 firmed, and the falsity of the truth of the other 
 concluded. This is evidently not an instance of 
 syllogistic reasoning. 
 
 Since logic deals with sequence, not with truth, 
 these forms of expression, convenient and frequent 
 as they are, are outside of its proper territory, and 
 are evidently not forms of reasoning, all the reason- 
 ing in them being confined to the original proposi- 
 tion, in itself a syllogism. For dealing with these 
 forms, however, it is convenient to express the fact 
 that in a correct syllogism true premises yield a 
 
MEDIATE DEDUCTION 117 
 
 true conclusion, and a false conclusion means a 
 false premise, in the following rules: 
 
 (1) Affirming the antecedent affirms the con- 
 sequent. 
 
 (2) Denying the consequent denies the ante- 
 cedent. 
 
 It will be seen that these rules cover the so- 
 called hypothetical syllogism, while for disjunctive 
 forms the laws of contradiction and exclusion apply 
 directly. 
 
 25. Mathematical Syllogisms. — Mathemati- 
 cal syllogisms are those whose premises are mathe- 
 matical propositions (Section 15, end). Just as 
 the methods and rules for immediate inference were 
 seen in Section 17 a to be simplified when applied 
 to the mathematical proposition, so it is with the 
 mathematical syllogism. All terms being total, and 
 equivalent in their quantity, there is no distinction 
 between major and minor term, or therefore be- 
 tween major and minor premise; no possibility of 
 " undistributed middle," or of " illicit process," be- 
 cause these errors depend upon the partial use of 
 a term. Figure and mood (see Appendix, page 
 118) have no significance. 
 
 The rules of the mathematical syllogism reduce 
 to the simple forms : two quantities equal to a third, 
 are equal to each other; and a quantity greater (or 
 less) than another which is greater (or less) 
 than a third, is still greater (or less) than the 
 
n8 ESSENTIALS OF LOGIC 
 
 third quantity. The mathematical forms of the 
 copula are: " is equal to," " is unequal to," the lat- 
 ter resolving into the two forms : " is greater than," 
 and " is less than." Many expressions such as : 
 " is part of," ■ - is included in," " contains," " is one 
 of," " is above," " is below," or any comparative 
 degree, are combinations of the mathematical copula 
 with other elements, and may easily be put in strict 
 form: John is taller than James, George is taller 
 than John, therefore George is taller than James, 
 would become: the height of John is greater than 
 that of James, etc. 
 
 APPENDIX TO CHAPTER VI 
 Figure and Mood. — As the middle term of a 
 syllogism may be either the subject or the predicate 
 of the major and of the minor premise, it is evident 
 that there are four possible combinations of the po- 
 sition of the middle term in the two premises, de- 
 termining what are called the " figures " of the syllo- 
 gism. In the first figure, the middle term is sub- 
 ject of the major premise and predicate of the 
 minor; in the second figure, it is predicate of both 
 premises; in the third, subject of both; and in the 
 fourth, predicate of the major and subject of the 
 minor premise. 
 
 Granted the rules of the syllogism in Section 20, 
 it follows that in figure 1 the major premise must 
 be total and the minor affirmative; in figure 2, the 
 
MEDIATE DEDUCTION 119 
 
 major must be total and one premise negative; in 
 figure 3, the minor premise must be affirmative and 
 the conclusion partial. The proof of these special 
 rules affords a valuable exercise for the student. It 
 is important to note in this connection that the only 
 positions in which a term is thought of totally are 
 the subject of A or E, and the predicate of E or O. 
 The fourth figure is open to criticism, and need not 
 be discussed here. 
 
 It is further evident that the major and minor 
 premises in any figure may be various combinations 
 of A, E, I, and O, the conclusion being of course 
 determined by the premises. Sixteen such combina- 
 tions, called " moods " of the syllogism, are possi- 
 ble: AA, AE, AI, AO, EA, EE, EI, EO, IA, IE, 
 II, IO, OA, OE, 01, 00. It can be shown that 
 EE, EO, IE, II, 10, OE, 01, 00, as premises, 
 would violate the rules in Section 20, the proof of 
 which can be used as an exercise. The only valid 
 combinations, then, are AA, AE, AI, AO, EA, EI, 
 IA, OA. 
 
 As a further exercise it can be proved from the 
 rules in Section 20 or from the special rules above, 
 that some of these eight moods are not valid in 
 some of the four figures, leaving only the following: 
 AA in figures 1, 3, and (4) ; AE in 2, (4) ; AI in 
 1, 3; AO in 2; EA in 1, 2, 3, (4) ; EI in 1, 2, 3, 
 (4) ; IA in 3, (4) ; OA in 3. These nineteen possi- 
 ble moods have been named, the vowels in the name 
 
120 ESSENTIALS OF LOGIC 
 
 of each being the symbols of its three propositions, 
 and the names of the moods in each figure are 
 grouped together in the following mnemonic hexa- 
 meters : 
 
 BARBARA, CELARENT, DARK, FERIOque 
 prioris : 
 
 CESARE, CAMESTRES, FESTINO, FA- 
 KOFO, secundae; 
 
 Tertia, DARAPTI, DISAMIS, DATISI, FE- 
 LAPTON, 
 
 DOKAMOK,* FERISON habet. Quarta in- 
 super addit 
 
 BRAMANTIP, CAMENES, DIMARIS, FE- 
 SAPO, FRESISON. 
 
 In these names the initial consonant is the same 
 as that of the mood (Barbara, Celarent, Darii, or 
 Ferio) in Figure i, to which the moods in the other 
 figures may be changed by following the directions 
 indicated by these other consonants in their names 
 (for processes, see Section 17) : 
 
 " s " means, convert simply the proposition 
 whose symbol precedes the " s " ; " p," convert by 
 limitation the preceding proposition ; " f," infer by 
 contradiction; "k," apply " f," and then " s " to 
 the preceding proposition ; " m," exchange the prem- 
 ises. 
 
 The other consonants in the names have no mean- 
 ing. For practice, any syllogism not in the first 
 *0r Fokmafokf. 
 
MEDIATE DEDUCTION 121 
 
 figure may be used, e. g., Some wars are justifiable, 
 all wars are inexpedient, and so some inexpedient 
 acts are justifiable, is Disamis, which becomes Darii, 
 as follows: All wars are inexpedient, some justi- 
 fiable acts are wars, and so some justifiable acts are 
 inexpedient. 
 
CHAPTER VII 
 
 DEDUCTIVE FALLACIES 
 
 26. The Nature of Fallacy. — Any violation 
 of the laws, principles, or rules of logic is a fallacy. 
 The only reason for separate consideration of the 
 subject here is that these errors may be brought to- 
 gether and classified, and their causes, some of which 
 lie outside of logical forms, examined. It must be 
 remembered that there are many false statements 
 which are not fallacies, that fallacy is not all, but 
 only part of error. 
 
 A fallacy, therefore, is a violation of one of the 
 following : 
 
 (1) The rules of division in Section yb; (2) 
 the rules of definition in Section yc; (3) the laws 
 of affirmation, denial, or exclusion in Sections 9, 
 10, 11 ; (4) the limits of immediate inference in Sec- 
 tion 17; (5) the rules of the syllogism in Section 
 20; (6) the right to clear expression of the thought. 
 
 If therefore we apply correctly these rules, we 
 can detect fallacy. There are, however, some more 
 or less obscure causes of such violation of logical 
 law, that it is helpful to examine closely. The chief 
 
 122 
 
DEDUCTIVE FALLACIES 123 
 
 of these are found in the Sections 2.7 and 28 follow- 
 ing. 
 
 27. Ambiguity. — The fallacy consists in 
 taking the wrong meaning, or in case of a syllogism, 
 in using first one, then the other meaning, which 
 gives four terms. There are two general cases. 
 
 First, an ambiguous term. 
 
 (1) The term has two meanings, as in: clubs 
 are organized groups of persons, some weapons are 
 clubs, therefore some weapons are organized groups 
 of persons ; or, all criminal actions ought to be pun- 
 ished, prosecution for theft is a criminal action, and 
 ought to be punished ; or again, a fox is a quadruped, 
 Herod is a fox, therefore a quadruped. 
 
 To the countless ambiguities of language are due 
 the frequent instances of this fallacy. Here, too, 
 belongs the duplicity of the pun. 
 
 (2) The term is used once collectively, once dis- 
 tributively, as : two and three are even and odd, two 
 and three are five, therefore five is even and odd. 
 
 (3) The wrong accent or tone causes ambigu- 
 ity: A asked the officer to arrest B, and the offi- 
 cer arrested him, or him. 
 
 (4) The term is once limited in some way, once 
 not, as : relieving pain is right, killing a sufferer re- 
 lieves his pain, therefore killing a sufferer is right. 
 
 Second, an ambiguous sentence, the fallacy being 
 to take the wrong sense. 
 
 ( 1 ) The sentence has an ambiguous grammati- 
 
i2 4 ESSENTIALS OF LOGIC 
 
 cal structure, as: I predict the enemy our troops 
 will defeat; Moses was the daughter of Pharaoh's 
 son; in athletics only he excelled; I will go and re- 
 turn next week; lost, an umbrella by a gentleman 
 with a carved head. 
 
 (2) The wrong accent may change the meaning 
 of the sentence, as above of a term; thus, the sen- 
 tence: no man is very fond of receiving useless 
 gifts, might be given five different meanings by em- 
 phasizing in turn each of the underscored words. 
 
 (3) Incorrect punctuation may cause this fal- 
 lacy, as : there were very few occupants who were 
 not injured; and, there were very few occupants, 
 who were not injured. 
 
 28. Misproof. — Correct proof proceeds from 
 premise to conclusion, according to the laws of logic. 
 If a premise be questioned, or questionable, it must 
 be shown to follow as a conclusion from unques- 
 tioned prior premises and these from others, and 
 so on, which means that the ultimate ground of 
 proof is found in the facts of consciousness given 
 to intellect or to sense. These, being self-evident 
 or established by scientific induction, are the sure 
 foundation for all deduced conclusions. Inductive 
 proof is considered in Part III. 
 
 But suppose we desire to prove a proposition false, 
 as in debate. Reference to the relation of proposi- 
 tions in Section 17 will show that A is overthrown 
 by its contradictory, O, and E by I. It is easier to 
 
DEDUCTIVE FALLACIES 125 
 
 overthrow a total proposition, and to prove a par- 
 tial proposition. 
 
 (1) Misproof occurs when some other than the 
 proposition stated is proved. This may occur from 
 confusion, or may be intentional, as in attacking the 
 character of an opponent (argumentum ad ho- 
 minem) ; appealing to the prejudice (ad populum) ; 
 or to authority without evidence of validity (ad 
 verecundiam). 
 
 (2) When we attempt to overthrow a proposi- 
 tion by any other than its contradictory. The fal- 
 lacy may be disguised by lengthy development of 
 the proof, or by some of the many forms of am- 
 biguity. 
 
 (3) Here may be mentioned the fallacy of in- 
 ferring the falsity of the conclusion from the falsity 
 of a premise, or the truth of a premise from the 
 truth of the conclusion ; especially in the form of the 
 so-called conditional syllogisms when the rules of 
 Section 24 are reversed and it is inferred that de- 
 nying the antecedent denies the consequent or 
 affirming the consequent affirms the antecedent. 
 
 (4) " Begging the question " has many varie- 
 ties, all of which include, however, the assumption 
 of some essential part of what is sought to be 
 proved. In other words, no premise may be used 
 without its truth being conceded or proven. 
 
 a. The assumption of the desired conclusion, or 
 of a premise which is afterward proved by the very 
 
126 ESSENTIALS OF LOGIC 
 
 conclusion it is supposed to establish. The final 
 conclusion is used as a premise in the course of the 
 argument, and the longer and more involved the 
 reasoning, the more difficult is it to detect the fal- 
 lacy. Plato in one of his writings seeks to prove 
 the immortality of the soul from its simplicity; in 
 another, its simplicity from its immortality. If we 
 say, glass is easily broken, because it is brittle, we 
 commit the fallacy. 
 
 b. The assumption of a universal premise in or- 
 der to prove a particular conclusion, as : this man is 
 a sinner, because all who suffer are sinners and he 
 is suffering. 
 
 c. To assume the particular and from it to argue 
 the universal, is both begging the question and il- 
 licit process ; if all the parts are assumed one by one, 
 it is begging the question only. 
 
 d. The assumption that implication, as in Sec- 
 tion 1 6, is proof. 
 
 e. The demand of a yes or no answer to a com- 
 pound question ; as : are you good and stupid ? is he 
 wicked and foolish? have I the wrong pig by the 
 ear? 
 
 /. The assumption of unproven facts in a ques- 
 tion ; as : have you ceased to steal chickens ? why is 
 a politician always a hypocrite? An imperfect dis- 
 junction is of this nature, as: either you have 
 ceased to steal chickens, or you are still stealing 
 them. If, however, the third possibility, the ex- 
 
DEDUCTIVE FALLACIES 127 
 
 istence of which renders the disjunction imperfect, 
 be shown or be granted false, no fallacy is involved. 
 In this case the third possibility is : you have not 
 been a chicken thief. And a politician may not 
 always be a hypocrite. 
 
 PRACTICE ON SECTIONS 26 to 28 
 The more obvious fallacies have already been exem- 
 plified under the various heads of definition, division, 
 inference, etc. Examine the following examples, and 
 point out what fallacy, if any, is present; classify 
 each fallacy according to the subdivisions of Sections 
 26, 2J, and 28; and, if possible, show how it may be 
 avoided. 
 
 1. Since God is Infinite, it follows that the Infinite 
 is God. 
 
 2. If John is the uncle of James, and Mary is John's 
 sister, then it follows that James is Mary's 
 nephew. 
 
 3. Penny wise, pound foolish. 
 
 4. As all animal life comes from eggs, it follows that 
 
 all eggs are the product of some animal. 
 
 5. The duke yet lives that Henry shall depose, 
 And him outlive, and die a violent death. Shake- 
 speare. 
 
 6. Scott's works were read not only by his country- 
 men, but by all educated people in Europe. 
 
 7. "Where's your father, boy?" "He's down at 
 the other end of the field with the hogs. You 
 can tell him by his hat." 
 
 8. " Young ladies, here is your new teacher, Mr. 
 
128 ESSENTIALS OF LOGIC 
 
 Chase. Tell him what your other teacher did 
 first, so he can go on in the same way." " She 
 kissed us." 
 9. " Ring the door-bell, Mister, I can't reach it." 
 " Thank you, sir. Now run." 
 
 10. If I can have the luxuries of life, I can do with- 
 
 out the necessities. 
 
 11. If you never succeed in anything you undertake, 
 you can never undertake anything in which you 
 will succeed. 
 
 12. Some possible cases are improbable, therefore 
 some probable cases are impossible. 
 
 13. He has little natural ability and still less educa- 
 tion. 
 
 14. He is the very man, of all others, whom I despise 
 most. 
 
 15. The secretary and treasurer of the company was 
 
 both the secretary and the treasurer. 
 
 16. Saddle me the ass; and they saddled him. 
 
 17. " You called me a sneak." "Yes, it is true, and 
 
 I am sorry." 
 
 18. Examine carefully the two next examples, or the 
 
 next two examples. 
 
 19. "Do you know the men on the jury?" "Yes, 
 more than half of them." " Are you willing to 
 swear to that ? " " Yes, I know more than all 
 of them." 
 
 20. If Croesus should wage war against the Persians, 
 
 he would destroy a mighty empire. 
 
 21. What is seen is visible, what is heard is audible, 
 
 therefore what is desired is desirable. 
 
 22. All the angles, A, B, and C, of a triangle, are 
 
DEDUCTIVE FALLACIES 129 
 
 less than two right angles; therefore A is less 
 than two right angles. 
 
 23. All the angles of a triangle are equal to two right 
 
 angles; therefore A is equal to two right angles. 
 
 24. Heat expands bodies, therefore cold contracts 
 them. 
 
 25. Beefsteak is wholesome food, and therefore good 
 
 for fever patients. 
 
 26. Gambling is wrong because it is opposed to sound 
 ethical principles. 
 
 27. The length of the day for labor ought not to be 
 fixed by law, for all legislation that interferes 
 with right of free contract is bad. 
 
 28. Why does not the King of England wish to be 
 buried in a Catholic graveyard? 
 
 29. Men of severe climates are hardy, therefore such 
 a climate is desirable. 
 
 30. If he did not steal the stuff, why did he hide it so 
 
 carefully ? 
 
 31. I will not have a doctor; all who have died of this 
 
 disease have had doctors. 
 
 32. Advice is useless for you must advise a man what 
 he will do or what he will not do. 
 
 33. Great minds run in the same channel. 
 
 34. Great men have been derided, just as I am now 
 being derided. 
 
 35. Iron is becoming rarer, for it is a useful metal, 
 and they are becoming rarer. 
 
 36. Epimenides the Cretan says that all the Cretans 
 
 are liars, and being a Cretan, he is a liar; but 
 being a liar, the Cretans are not liars, because this 
 liar says they are liars; therefore, being a Crs- 
 
130 ESSENTIALS OF LOGIC 
 
 tan, he is not a liar, and so on, as the surveyors 
 say, to the beginning. 
 
 37. In the meanwhile, the method I have observed 
 toward those who have been brought before me 
 as Christians is this : I asked them whether they 
 were Christians; if they admitted it, I repeated 
 the question twice, and threatened them with pun- 
 ishment ; if they persisted, I ordered them at 
 once to be punished; for I was persuaded what- 
 ever the nature of their opinions might be, a 
 contumacious and inflexible obstinacy certainly 
 deserved correction. Pliny. 
 
 38. We have computed the inhabitants and contem- 
 
 plated the public works of the Roman Empire. 
 The observation of the number and greatness of 
 its cities will serve to confirm the former and 
 multiply the latter. Gibbon. 
 
 39. For sale, an assorted lot of red men's socks. 
 
 40. The place contains some two or three hundred 
 
 houses and twenty-five hundred inhabitants, all 
 standing with their gable ends to the street. 
 
 41. If a wife be beautiful, she excites jealousy; if 
 
 she be ugly, she excites disgust; therefore it is 
 best not to marry. 
 
 42. Governments ought to be resisted, for they repress 
 
 the liberties of mankind. 
 
 43. All persons are hereby forbidden to ride or drive 
 
 cattle through this park. 
 
 44. L T pon which the Moor, seizing a bolster full of 
 
 rage and jealousy, smothered the unhappy Des- 
 demona. 
 
DEDUCTIVE FALLACIES 131 
 
 45. Erected to the memory of John Phillips, acci- 
 
 dentally shot as a mark of affection by his 
 brother. 
 
 46. If some people are wise, then, of course, some 
 are foolish. 
 
 47. An agnostic believes that nothing can be certainly 
 known. 
 
 48. Protagoras taught Euathlus law. Euathlus 
 agreed to pay his tuition when he won his first 
 case. He had no case, and Protagoras sued him, 
 saying, If the judgment of the court be against 
 you, it will give me the fee ; if in your favor, you 
 will owe me the fee, for you will have won your 
 first case. 
 
 Euathlus replied : "If the decree be in my favor, 
 I need not pay; if adverse, I shall have lost my 
 first case, and shall owe you nothing." 
 
 49. Let us compel every able-bodied male member of 
 
 the community, who is nineteen years of age, 
 and not absolutely indispensable at home, to vol- 
 unteer as a member of this military company. 
 
 50. What should be done with a man who marries 
 
 his deceased widow's sister? 
 
 51. Human thought is bounded only by the infinite. 
 
 52. Does one grain of corn make a heap? No? Do 
 two? Three? Etc. 
 
 53. If you pull one hair from a man's head, will it 
 make him bald? Will two? Three? Etc. 
 
 54. Every object that does not decompose white light, 
 
 is seen by white light, and therefore white; a 
 black object does not, and is white. 
 
132 ESSENTIALS OF LOGIC 
 
 55. Conscience is something within that tells me when 
 I have done wrong ; I had it once, and they had to 
 send for the doctor. 
 
 56. Nuisances are punishable by law; a noisy dog is 
 a nuisance. 
 
 57. Time is either past or future; the past is gone, 
 the future has not come; there is no time. 
 
 58. Whoever necessarily goes or stays is not a free 
 
 agent; but every one necessarily goes or stays, 
 and so no one is free. 
 
 59. I love to steal — I love to steal — I love to steal 
 a while away. 
 
 60. To pray for rain is to ask for a miracle; but 
 miracles have ceased. But, prayer for rain has 
 often been followed by rain; and men have suc- 
 ceeded in causing rain, and it is therefore impious 
 to suppose God cannot. 
 
 61. Prayer is useful if it informs God of what He 
 does not know, or if it effects a change in his 
 purposes ; but prayer can do neither, and is there- 
 fore useless. 
 
 62. Winning a large prize in a lottery is not an un- 
 
 common occurrence, and may therefore reason- 
 ably be expected. 
 
 63. He that is of God heareth the words of God; 
 for this cause ye hear them not, because ye are 
 not of God. Bible. 
 
 64. Everything of which there is an innate appetite 
 
 is pleasant; for appetite is a desire of what is 
 pleasant. 
 
 65. No man should choose young people to be cap- 
 
DEDUCTIVE FALLACIES 133 
 
 tains and governors, forasmuch as there is no 
 certainty in their wisdom. Alexander of Mace- 
 don vanquished and conquered Egypt, Judea, 
 Chaldee, Africa, and Assyria unto the marches 
 of Bargmans more by the counsel of old men 
 than by the strength of the young men. Caxton. 
 
 66. The heavier the fall of snow, the better, for it 
 provides the poor with more work in cleaning 
 it off. 
 
 67. " Step over and see how old Mrs. Jernigan is 
 this morning." Later. " She says she was 
 forty-nine her last birthday, and please, ma'am, 
 why did you want to know ? " 
 
 68. Instead of purity resulting from that arrange- 
 ment to India, England herself would soon be 
 tainted. Macaulay. 
 
 69. In one evening I counted twenty-seven meteors 
 sitting on my back porch. 
 
 70. " Fred got shot to-day." " Where? How? Was 
 he hurt much ? " He got shot in a hardware store. 
 
 71. "He's in the quicksand, you say? How far?" 
 
 " Up to his ankles." " Then, there's plenty of 
 time." " But he went in head first." 
 
 72. In order to show the relation of the religion of 
 
 Israel to that of heathen nations, Kuenen as- 
 sumes : " The Israelitish religion is one of those 
 religions; nothing less, but also nothing more." 
 J2>- At the outset of his book on " Prophets and 
 Prophecy," Kuenen says : " Prophecy is accord- 
 ing to this new view, a phenomenon, yet one of 
 the most important and remarkable phenomena, 
 
i 3 4 ESSENTIALS OF LOGIC 
 
 in the history of religion, but just on that ac- 
 count a human phenomenon, proceeding from 
 Israel, directed to Israel." 
 
 74. So soon as we derive a separate part of Israel's 
 religious life directly from God, and allow the 
 supernatural or immediate revelation to intervene 
 in even one single point, so long also our view 
 of the whole continues to be incorrect. Kuenen. 
 
 75. The patriarchs cannot be taken as individuals. 
 If individuals Reuben, Gad, and Judah never ex- 
 isted, it is plain that individuals Jacob, Esau, and 
 Abraham cannot have any more substantial real- 
 ity. We have to do here with figures of the 
 poetic or legend-building imagination. H. P. 
 Smith. 
 
 j6. God, in creating, theomorphises man; man, there- 
 fore, necessarily anthropomorphises God. Jacobi. 
 
 yy. Bethel, Hebron, Beersheba, and Shechem were re- 
 garded with peculiar veneration by the Israelites. 
 Because there were graves at some of these 
 places, Stade thinks their sacredness due to an- 
 cestor-worship. 
 
 78. A body moves either where it is or where it is 
 
 not, but it cannot move where it is for lack of 
 room; nor can it move where it is not, for it is 
 not there to move ; therefore a body cannot move. 
 
 79. Since we are forbidden to kill, capital punishment 
 is wrong. 
 
 80. A mouse is an animal, and it follows that a large 
 
 mouse is a large animal. 
 
 81. He who is hungriest eats most, and one who eats 
 
DEDUCTIVE FALLACIES 135 
 
 least is hungriest; therefore he who eats least, 
 
 eats most. 
 &2. What I see as the train recedes grows smaller and 
 
 smaller, but as the train does not grow smaller, 
 
 what I see is not the train. 
 83. No soldiers but those well qualified should be 
 
 brought on the field; therefore none but veterans 
 
 should be brought on. 
 
PART III 
 INDUCTIVE INFERENCE 
 
CHAPTER VIII 
 
 THE NATURE AND LAWS OF INDUCTION 
 
 29. Induction and Deduction. — We have seen 
 in Part II that by inference immediate or medi- 
 ate one proposition may be concluded from one or 
 two others as premises; also that these premises 
 may themselves be the conclusions of prior infer- 
 ence. The question is thus suggested, where is the 
 end of this process of referring one proposition to 
 another as its higher ground, and that to still an- 
 other, and so on; where, in short, is the beginning 
 of the chain, where is the original fountain of 
 knowledge? 
 
 The sources of knowledge are two, the intellect 
 and the senses. Through intellectual discernment 
 we know, for example, space, time, causation, moral 
 quality, and such truths as : things equal to the same 
 thing are equal to each other; two straight lines can- 
 not enclose an area ; one of two contradictories can- 
 not be affirmed of the other; all personal ac- 
 tions are right or wrong; every change has a cause. 
 These intellectual truths and the conclusions de- 
 rived from them by correct deduction constitute a 
 body of certain knowledge. Of this nature are the 
 
 139 
 
140 ESSENTIALS OF LOGIC 
 
 sciences of mathematics, logic, and ethics, and the 
 fundamental principles of all science. 
 
 From the other source of knowledge, the senses, 
 comes the knowledge, not of universal, necessary 
 truths like those above cited, but only of individual 
 facts perceived. From these facts, stated in the form 
 of particular propositions, we infer immediately 
 universal propositions, thus reasoning from " some," 
 often only one, to " all " cases of the kind. This is 
 " induction, " already mentioned in Section 16. If, 
 for example, we observe that several persons in a 
 place we are visiting speak with a peculiar accent, 
 we infer that others, perhaps all, speak so; if one 
 hot iron burns one finger, we infer that any iron, 
 equally hot, will burn any part of the body. 
 
 It is evident that this inference from " some " to 
 " all," which as deduction would be the " illicit 
 process " of Section 20, must therefore be justified 
 by other principles than those justifying deduction. 
 These are treated in Sections 31 and 32. 
 
 It is further evident that these inductive universal 
 propositions may be used as premises for deduc- 
 tions, thus constituting a body of knowledge whose 
 truth depends upon the truth of the original induc- 
 tive premises. 
 
 30. Scientific Induction. — As was indicated 
 above, induction is an immediate inference from a 
 particular premise to a universal conclusion ; that is, 
 from I to A, or from O to E. The two proposi- 
 
INDUCTION 141 
 
 tions are either both affirmative or both negative, 
 their subjects and their predicates are the same, the 
 only change being that the " some " of the premise 
 becomes the " all " of the conclusion. The mere in- 
 ductive step is seen to be very simple, but its sweep 
 takes in the universe, and must be carefully 
 guarded. For an inductive conclusion to be true, it 
 is necessary that (1) the premise be established by 
 correct observation; (2) the conclusion includes 
 cases beyond actual observation, else there is no in- 
 duction; (3) the step be justified by some authori- 
 tative principle. This justification is found in the 
 fact and the laws of causation, and we may define 
 scientific induction as an immediate inference that 
 a particular observed causal connection is uni- 
 versal. 
 
 Fuller discussion of causation will be found in 
 the next section. The " observation " mentioned 
 above means attention to what we see, hear, taste, 
 or perceive through any of our senses, including the 
 internal sense by means of which the mind per- 
 ceives its own states while they are actually pres- 
 ent. These " percepts " of the senses are what is 
 meant by " experience; " they are often called 
 " phenomena." The artificial arrangement of cir- 
 cumstances for purposes of observation, is called 
 experimenting. This greatly enlarges the scope of 
 observation, and furthers causal investigations. 
 
 The essential properties of things that we observe 
 
142 ESSENTIALS OF LOGIC 
 
 in co-existence, those qualities without which things 
 would not be what they are, but something else, 
 these are permanent unchanging relations, and form 
 the basis for the classifications described in Part I. 
 Other co-existing phenomena, and especially succes- 
 sive phenomena, we observe also, and it is these 
 " accidental " properties, or " changes," that form 
 the basis of inductive thought. 
 
 Knowledge of essential, permanent qualities, 
 therefore, is the basis of the classification of things 
 into systems of genera and species; knowledge of 
 their non-essential, changing qualities, is the basis 
 of assigning things to their causes. When every 
 body occupying space is properly classified in a sys- 
 tem of genera and species, and every change occu- 
 pying time is explained by reference to its cause, 
 natural science will be complete. 
 
 31. Causation. — We know that changes are 
 of constant occurrence. What we see, hear, touch, 
 etc., is continually changing. We know that these 
 changes are not brought about by our effort, we 
 know by intellectual discernment that they must 
 have a cause, and therefore we know that the law 
 that every change has a cause, is not a mere law 
 of mind, but is a real fact in the world of things 
 external to mind. 
 
 " Every change has a cause." What, then, is a 
 cause? Not a mere condition. A body can not 
 move except in space and time, both conditions, 
 
INDUCTION 143 
 
 neither a cause of motion. So the ear is a condi- 
 tion of normal hearing, the eye of sight, yet neither 
 one is the cause. Without the condition, the thing 
 it conditions can not be; given the condition, it still 
 may not be. Given the cause, the change must be. 
 A condition is negative, in that its absence prevents ; 
 a cause is positive, in that its presence compels. 
 
 The cause is that which actually produces the 
 change, or event. The cause includes all and only 
 those forms and amounts of energy necessary to 
 the change; the effect all and only those resulting 
 from the change. We look at circumstances, ma- 
 terial objects, forces, etc., without analysis, and we 
 may select one which interests us, which is added 
 last to those already present, or which attracts at- 
 tention for any reason, and we call that one the 
 cause. But a cause is usually not single or simple; 
 many circumstances, antecedents, forces, or what- 
 ever name be given them, may contribute to the ef- 
 fect, which is likewise complex. We say, a bullet 
 killed him, but another by his side may have been 
 struck by a bullet, and live. The velocity, the spot 
 hit, the condition of health, the strength of the con- 
 stitution, the skill of the physician, are all circum- 
 stances that may and do enter into the total which 
 we may correctly call the cause. Likewise the ef- 
 fect summed up as death, may also, when analyzed, 
 be seen to include the laceration of certain tissues, 
 the rupture of certain blood-vessels, the injury of a 
 
144 ESSENTIALS OF LOGIC 
 
 nerve, the fracture of a bone; whence is seen the 
 complexity of the effect also. 
 
 It is evidently a practical impossibility to state 
 all the elements of a cause or an effect ; but we can 
 approximate closely enough for reasonable cer- 
 tainty. 
 
 32. Uniformity. — Not only has every change 
 a cause, but we intuitively know that every like 
 change has a like cause, and every like cause has a 
 like effect. In other words, causes differing only 
 in time and place have effects differing only in time 
 and place, and effects differing only so have causes 
 differing only so. This principle of " uniformity " 
 needs no proof, can have none, is self-evident, and 
 universally admitted to be true. 
 
 Because of imperfect observation or other rea- 
 sons, we can not always distinguish causes that are 
 actually unlike, or effects that are. It often seems 
 that the same cause has different effects ; for exam- 
 ple, heat melts ice, bakes clay, contracts water, ex- 
 pands it, and so on. But the fact that we may not 
 see any difference in the causes does not shake our 
 belief that they are different; we are certain that 
 they are. We speak, however, of such cases as if 
 the same cause had unlike effects. We do this also 
 in cases where we do distinguish differences in the 
 cause. We say, for example, that a rose is beauti- 
 ful, is red, is fragrant, thus affirming that the one 
 cause, the rose, produces several distinct effects upon 
 
INDUCTION 145 
 
 me; but we know that what we call " the rose" is 
 a number of causes, that its form, its reflection of 
 light, its emission of particles which go into the 
 nasal passages, etc., all are different causes having 
 different effects. 
 
 The same is true of effects that we can not dis- 
 tinguish as unlike, and therefore speak of as if 
 really like and yet due to unlike causes; and here 
 again we so speak even of effects that we may be 
 able to distinguish by analysis. For example, we 
 say indigestion is due to kind of food, eyestrain, 
 nerve fatigue, grief, etc. ; so also of headache, death, 
 motion. Closer analysis would show that when in- 
 digestion, for instance, occurs following different 
 irritants, other effects due to their difference, are 
 also present, while the cause of the indigestion alone, 
 if ascertained, will be found to be the same. So 
 in every case where apparently like effects follow 
 unlike causes. 
 
 There is then no defect in the laws of uniformity, 
 no exception to them, apparent exceptions being due 
 to our imperfect observation. 
 
CHAPTER IX 
 
 THE CAUSAL BASIS FOR INDUCTION 
 
 33. Induction Based on Assumed Causal Con- 
 nection. — It is evident that induction itself is 
 extremely simple, and needs few rules, and no 
 elaborate explanation. It is an immediate infer- 
 ence fully warranted by the laws of causation and 
 uniformity. But, to have scientific value, to at- 
 tain real truth, it must be an inference from " an 
 observed causal connection," as stated at the close 
 of the first paragraph of Section 30. The estab- 
 lishment of causal connection, the basis for scien- 
 tific induction, is therefore of great importance, 
 for it is only because of this causal fact that we are 
 authorized to make the inductive " leap " from 
 some to all. Deferring consideration of the ways 
 of proving causal connection to the next section, let 
 us here examine two familiar uses of induction, 
 which do not rest on this scientific basis. 
 
 33 a. Enumeration of Cases. — It is a familiar 
 and accepted fact of mind that when experiences 
 have occurred together, and one recurs, the others 
 tend to recur with it ; and because this suggestion 
 of mental states by others originally associated 
 
 146 
 
CAUSAL BASIS FOR INDUCTION 147 
 
 with them, is so common and familiar, not only do 
 we usually expect this connection in memory, but 
 in the external world. When outside facts, things, 
 forces, impress themselves strongly and frequently 
 upon our minds, and when later one of these as- 
 sociated impressions recurs, we expect the others 
 to recur with it, not merely in memory, but as 
 actual new impressions due to renewed action of the 
 external cause upon us. 
 
 The more frequently, therefore, we receive im- 
 pressions 1 together, the more confidently will we 
 expect the recurrence of one to be attended by the 
 others. The basis of this expectation is, however, 
 as indicated above, not a scientifically established 
 causal connection, but merely psychological, a 
 transfer of the psychological law of suggestion 
 from the inner mental sphere, where it does 
 operate, to the outer material sphere, where it holds 
 no sway. The fact, however, that cause and effect 
 are always found together, justifies at least a sup- 
 position that two concurrent impressions may rep- 
 resent a causal connection, though not the belief 
 that they certainly do. This method of multiply- 
 ing cases of concurrent phenomena, therefore, is 
 valuable in suggesting causal connections among 
 circumstances constantly present, and in furnishing 
 occasions for testing such connections by the 
 methods of Section 34. It is valuable, also, for 
 the many cases in everyday life, where scientific 
 
148 ESSENTIALS OF LOGIC 
 
 analysis is impracticable, or not warranted because 
 of the trivial nature of the circumstances to be 
 explained. 
 
 Very many of our proverbial sayings, supersti- 
 tions, and popular rules are inductions based on 
 mere count of cases. They are often incorrect, the 
 cases being too few in number to indicate even 
 plausible connection, or the exceptions when only 
 one of the supposedly connected circumstances oc- 
 curs, being passed over without notice; e. g., all 
 crows are black, all malaria yields to quinine, all 
 men have their price. 
 
 33 b. Analogy. — The enumeration may be of 
 concurrent qualities in two cases, instead of pairs 
 of qualities, or marks, in many cases. The two 
 methods are often equally available. From simi- 
 larity of elevation, latitude, proximity to the sea 
 and to the mountains, we might infer by the method 
 of analogy that one place would have a season like 
 the other. From likeness in appearance, odor, 
 juiciness, consistency of two fruits, we might by 
 analogy infer likeness in another quality, taste. 
 Yet the two might be plum and persimmon. Mere 
 analogy is never proof. It often suggests lines of 
 investigation leading to proof. 
 
 Enumeration and analogy may be described re- 
 spectively as follows : if many cases have two com- 
 mon characteristics, then other cases having one of 
 these two, will probably have the other also; and, 
 
CAUSAL BASIS FOR INDUCTION 149 
 
 secondly, if two cases have many common charac- 
 teristics then other characteristics in the one will 
 probably be found in the other. As the " other " 
 characteristics in the inference may be any other, it 
 is equivalent to all others. This, taken strictly, 
 would mean absolute identity, so the expression can 
 not be strictly construed, but is to be considered as 
 merely suggestive. 
 
 It is evident that these two modes of induction 
 have no warrant except in the assumption that there 
 is causal connection between the concurring cir- 
 cumstances or characteristics. This connection be- 
 ing assumed, and not proven, the induction is there- 
 fore very hazardous, and should be so held, until 
 by some scientific method the assumed causal con- 
 nection is shown to be real. 
 
 33 c. Probability. — Such inductions as result 
 from enumeration or analogy are, then, not certain, 
 but only more or less probable. This probability 
 reaches a high degree in cases of phenomena con- 
 curring frequently and without exception through 
 a long period. That day and night will continue 
 to follow each other is highly probable, though not 
 certain; so also are changes in the tides, prevailing 
 winds, average weather for different seasons, ra- 
 cial characteristics, revolutions under oppression. 
 
 The mathematical doctrine of probability is of 
 service here. By it the " chance," or probability of 
 concurrence of phenomena, without causal connec- 
 
150 ESSENTIALS OF LOGIC 
 
 tion, may be estimated; then, if two phenomena oc- 
 cur together either more or less often than chance 
 would explain, they are probably causally connected. 
 If, for example, one bag contains five balls, three 
 of them white, the probability of drawing a white 
 ball is 3-5 ; if another bag contains seven balls, four 
 of them white, the probability of drawing a white 
 ball from it is 4-7. The probability of drawing two 
 white balls in succession, one from each bag, is 
 
 3-5 x 4-7, or I2 "35- 
 
 If, again, in a certain place, the average fre- 
 quency of rainy days for many years has been one 
 in three, while the average frequency of east winds 
 has been one in four, then the probability of rain 
 and east wind coming on the same day, without 
 causal connection, is 1-3 x 1-4, or 1-12. If, then, 
 rain and east wind concur on the average more than 
 one day in twelve, the probability is they are 
 causally connected; if less than one day in twelve, 
 that there is counteraction; if just about one in 
 twelve, that there is no causal bond. 
 
 In this way we can set aside phenomena probably 
 not causally affecting our investigation, thus nar- 
 rowing the field of observation of possible causes 
 and effects. 
 
 When a real exception occurs, the claim of reality 
 having been very carefully scrutinized, then we 
 must give up our universal, and be content with 
 " many " or " most " or " nearly all." 
 
CAUSAL BASIS FOR INDUCTION 151 
 
 Statistics covering a great number and variety of 
 cases, as the census, mortality tables, etc., are valu- 
 able instances of enumerative probability, form- 
 ing bases for induction as to the future of popula- 
 tion, crops, term of life, etc., thus giving us rules 
 from which we deduce conclusions as to particular 
 periods, or individuals, or groups. 
 
 34. Methods of Proving and Estimating 
 Causal Connection. — The words, " change," 
 " event," " circumstance," " phenomenon " are 
 used as practical equivalents. A " case," or " in- 
 stance " is a group of circumstances, including the 
 phenomenon under investigation, or associated with 
 it in some way. 
 
 Cause and effect always being found together, 
 the presence of either necessitating the presence of 
 the other, it follows: 
 
 (1) If two instances agree in every circumstance 
 but two, these two are cause and effect. 
 
 (2) If instances agree in only two circumstances, 
 these two are cause and effect. 
 
 (3) If two circumstances always vary together, 
 they are either cause and effect, or effects of a com- 
 mon cause. 
 
 (4) If some instances agree only in the presence 
 of two circumstances, while others agree only in 
 their absence, these two are cause and effect. 
 
 These methods are discussed in the following 
 sections. Their purpose is to solve the problem: 
 
152 ESSENTIALS OF LOGIC 
 
 given a cause, to find its effect; or, given an effect, 
 to find its cause. 
 
 34 a. The Method of Difference.—" If two 
 instances agree in every circumstance but two, 
 these two are cause and effect." The use of this 
 principle to prove causal connection is called the 
 " method of difference," because the two instances 
 differ only in the presence of the cause and the 
 effect, being alike in every other particular except, 
 of course, time and place. If, then, the phe- 
 nomenon under investigation, frost, let us say, be 
 present with a number of other circumstances such 
 as clear sky, still air, temperature freezing, dew- 
 point below freezing; while on another occasion, 
 all the circumstances being the same as above, ex- 
 cept that the temperature, for example, is above 
 freezing everywhere, and there is no frost; then we 
 conclude that frost and temperature are causally 
 connected. So we might reach a similar conclu- 
 sion if the second instance differed from the first 
 only in the absence of frost and the presence of 
 high wind, or in cloudy sky and no frost. 
 
 Or, if a cause be given to find its effect, as for 
 example the effect of benzoate of soda, as a food 
 preservative, upon health, two men as much alike 
 as possible in every way likely to influence the re- 
 sult, might be kept under the same conditions of 
 diet, exercise, and general hygiene, one being given 
 food with the benzoate, the other the same food 
 
CAUSAL BASIS FOR INDUCTION 153 
 
 without the benzoate. Should the former show 
 signs of injury to health, and the other not, the 
 conclusion would be that benzoate of soda is the 
 cause. 
 
 A room in a locality where there was much 
 yellow fever was divided by a partition of fine 
 wire screen. On one side the bedding and clothes 
 of yellow fever patients who had died, soiled with 
 the foul evidences of the dread disease, were used. 
 On the other side of the screen partition everything 
 was fresh and clean, but some mosquitoes which 
 had bitten yellow fever patients, were introduced. 
 Cases of fever developed on the clean side, where 
 the mosquitoes were; none on the foul side where 
 no mosquitoes were. The presence on one side 
 of the mosquitoes and the fever, and the absence 
 on the other side of only these two circumstances, 
 give an almost ideal instance of the method. The 
 addition of the foul bedding on the side where no 
 fever developed, could not prevent the fever, so 
 that the cogency of the method is not affected; and 
 as no fever followed the use of the contaminated 
 bedding, the presumption is that it is not a cause 
 of the fever. 
 
 When Stanley observed in Africa that those of 
 his party who slept under netting to avoid the an- 
 noyance of the mosquitoes, did not have malaria, 
 while others not so protected did, he concluded 
 rightly by the method of difference that the netting 
 
154 ESSENTIALS OF LOGIC 
 
 had something to do with the freedom from ma- 
 laria. He supposed, however, that the netting 
 strained the " miasma " out of the air; we now 
 know it kept the malaria-charged mosquitoes from 
 introducing the germs of the disease by their bite. 
 
 34 b. The Method of Agreement. — " If in- 
 stances agree in only two' circumstances, these two 
 are cause and effect." This principle gives us the 
 " method of agreement." If the phenomenon un- 
 der investigation, as, for example, indigestion, oc- 
 curs after dinner for a number of days, some warm, 
 some mild, some cool, the dinner being varied more 
 or less every day, and it is found that the only arti- 
 cle of food eaten every day was cabbage, that 
 would be indicated as the cause of the indigestion. 
 It would then be in order to apply the method of 
 difference, not eat the cabbage, and the indigestion 
 not recurring, we should have proof. 
 
 But why should we not be content with the evi- 
 dence of the method of agreement alone? Not be- 
 cause of any defect in theory, but because in prac- 
 tice we can not be sure of having observed all the 
 circumstances that are present and may cause the 
 phenomenon. In the example above, there might 
 be appendicitis, only now become acute, or nerv- 
 ous disorder, or some other circumstance not easily 
 observable; and if the indigestion persists after the 
 cabbage is eliminated, the case must be examined 
 more closely for other circumstances. 
 
CAUSAL BASIS FOR INDUCTION 155 
 
 The method, therefore, while valuable for its sug- 
 gestiveness, and often affording practical certainty, 
 yet because we can not always eliminate all but two 
 circumstances in a series of cases, or because we 
 can not always distinguish effects that are actually 
 unlike and therefore due to unlike causes, because, 
 in short, our powers of arrangement, observation, 
 and analysis are not always adequate, is often un- 
 certain in its results. 
 
 The greater the number of instances of agree- 
 ment, the greater is the probability of causal con- 
 nection, for in a series of many cases the likeli- 
 hood that an exception will occur is greater, if the 
 two circumstances which have many times con- 
 curred are not really cause and effect. If all but 
 a few circumstances have been eliminated in the 
 series of instances examined, experimenting with 
 these in turn may show which is the cause of the 
 effect investigated. 
 
 The method goes further than simple enumera- 
 tion, for it calls for the ultimate exclusion of all 
 but two circumstances, the cause and effect, in the 
 course of the series of cases observed; while 
 enumeration takes note merely of the fact that two 
 circumstances occur together, disregarding the 
 equally significant fact of the presence of others 
 which might be connected with these two by a 
 causal bond. 
 
 The method is useful in the many cases where 
 
156 ESSENTIALS OF LOGIC 
 
 it is not possible to eliminate the two circumstances, 
 as required by the method of difference, and as has 
 been shown above may finally suggest a way of us- 
 ing that more conclusive method, which is always 
 to be desired. 
 
 34 c. The Method of Variations. — This is not 
 a different method of establishing causality, but an 
 application of either of the preceding methods to 
 the change in quantity, degree, or intensity of cir- 
 cumstances, instead of the change in presence or 
 absence of the circumstance as a whole. 
 
 "If two circumstances always vary together, 
 they are either cause and effect, or effects of a com- 
 mon cause." It often happens that we can in a 
 series of cases eliminate neither the two circum- 
 stances which are causally connected, so> as to ap- 
 ply the method of difference, nor yet all other cir- 
 cumstances but these two so as to use the method of 
 agreement. In many such cases it happens that the 
 circumstances vary in intensity, or degree; and so, 
 substituting for the circumstance as a whole, its 
 quantity, or degree, substituting for its presence, 
 the amount of its energy, we take this amount for 
 a new circumstance, and proceed by the methods of 
 agreement or difference. 
 
 If two circumstances appear in one instance, and 
 in a second also these two appear, each with a dif- 
 ferent intensity from that of the first instance, no 
 others being changed, then the method of differ- 
 
CAUSAL BASIS FOR INDUCTION 157 
 
 ence warrants the conclusion of causal connection 
 between the two. 
 
 Or if, while several quantities vary in some of a 
 number of instances, yet only two vary in all of 
 these instances, the method of agreement points to 
 causal connection between these two varying quan- 
 tities. 
 
 The method is usually and more conveniently 
 treated as a distinct method, and is called " the 
 method of variations." 
 
 When two bodies are rubbed together, and the 
 force exerted is exactly measured, it is found that 
 the heat generated by the friction is exactly in pro- 
 portion to the force used in rubbing, whence 
 causal connection is inferred. 
 
 The tides vary as the position of the moon rela- 
 tive to the earth changes ; the mercury rises or falls 
 in the thermometer as the heat of the atmosphere 
 increases or diminishes; if crime be shown to in- 
 crease or diminish with poverty, causality may be 
 argued; so if earning power increases with school 
 period. 
 
 The method of variations is also of great value 
 in determining quantitative relations, the mathe- 
 matical laws of causes already discovered by other 
 methods. In this way the ratio of causal energy 
 to the energy of the effect is estimated. Care must 
 be taken that there is not some new cause operating 
 beyond the limits observed. It takes a certain 
 
158 ESSENTIALS OF LOGIC 
 
 amount of fuel to increase the speed of a steamer 
 one mile per hour, but the additional amount dif- 
 fers according to the amount already attained. It 
 takes more to fatten pork from 200 to 300 pounds, 
 than from 100 to 200. Water contracts with loss 
 of heat as a rule, but expands from 39 to 32 de- 
 grees. 
 
 34 d. The Joint Method of Agreement and 
 Difference. — " If some instances agree only in the 
 presence of two circumstances, while others agree 
 only in their absence, these two are cause and effect." 
 The first clause of this canon is evidently the method 
 of agreement exactly, and causal connection is 
 thereby indicated. For the " others " to add force 
 to the series of instances of this first clause, the 
 circumstances in these " others " should be as much 
 like those in the former series as possible. Were 
 the circumstances in any one instance of the latter 
 series exactly like those in any one of the former 
 series, except for the absence of two that were in 
 the former case, the conditions of the method of 
 difference would be fulfilled, and further instances 
 would be unnecessary. Hence the name of the 
 method above. 
 
 But the supposition is that the requirements of 
 the method of difference are not fulfilled, that there 
 are only many points of similarity between the sec- 
 ond series of instances and the first, and that while 
 any two or more of these latter cases may agree in 
 
CAUSAL BASIS FOR INDUCTION 159 
 
 several ways, yet there is nothing common to all of 
 them save the absence of the two circumstances con- 
 curring throughout the former series; that is, the 
 second set agree in the absence of the two. The 
 method is therefore called by some, the method of 
 double agreement. 
 
 The places in which the famous Albemarle pip- 
 pin reaches its highest excellence of beauty, fla- 
 vor, and soundness, agree in elevation, soil, and 
 climate. The same apple has been grown in many 
 other places like the former in many ways, yet not 
 all agreeing in any one particular except in differ- 
 ing considerably from the former places in eleva- 
 tion, soil, or climate ; in these latter places the super- 
 ior excellence of the fruit is notably absent. 
 
 In case of merely frequent, not invariable, pres- 
 ence or absence together of two circumstances, 
 there may be causal connection, some unobserved 
 third circumstance being part of the cause or the 
 effect, or operating to counteract the cause; be- 
 cause of its omission, if part of the whole cause, 
 the effect will not appear, even though the other 
 causal circumstance be present ; because of its pres- 
 ence, if counteractive, the cause will not produce 
 the effect. Sir John Herschel, for example, is said 
 to have thought that the full moon tends to clear 
 the sky of clouds, because of the warmth radiated 
 from its surface. If this be true, the reason some 
 nights of full moon are not clear would be found 
 
160 ESSENTIALS OF LOGIC 
 
 in the presence of some counteracting cause, or 
 in the absence of some circumstance equally neces- 
 sary to the production of the effect. 
 
 35. Combination of Causes. — It often hap- 
 pens that after certain parts of a complex effect 
 have been assigned to their causes, a yet unexplained 
 part remains. It is evident that this must be due 
 to some other cause than those already ascertained 
 and a more careful investigation may discover the 
 hitherto unobserved element. This is commonly 
 called the " method of residues," and proceeds ac- 
 cording to the following obvious rule: Setting 
 aside the known causes and their effects, any re- 
 maining circumstances of a complex case must in- 
 clude all other causes and effects in the case. This 
 is so evident that the principle hardly deserves the 
 name of a method; yet its frequent and great use- 
 fulness show its importance. 
 
 A stock example is the discovery of Neptune, 
 whose position at a stated time was calculated as the 
 explanation of a certain unexplained perturbation 
 in the movements of Uranus. 
 
 The passage of an electric discharge through the 
 air was observed to be attended by a peculiar odor, 
 further investigation of which led to the discovery 
 of ozone, a form of oxygen. 
 
 In the second place, in case of causes producing 
 effects of the same kind, such as the velocity of the 
 same body acted upon by several forces, the effect 
 
CAUSAL BASIS FOR INDUCTION 161 
 
 may often be calculated before it is observed. To 
 state it succinctly: From the laws of several 
 causes acting together, their joint effect, if of the 
 same kind, may be calculated. Given the velocity 
 of a stream and of a boat in still water, the speed 
 up and down stream is easily estimated; a very 
 simple example. Because, however, of balancing 
 forces, the practical use of the principle is often 
 much more difficult than might be expected from its 
 simplicity. The process has been called " the de- 
 ductive method," the term including the induction 
 leading to the laws of the causes, the deduction from 
 these to the joint effect, and the testing, or verifica- 
 tion of this deduction by actual observation. 
 
 36. Hypothesis. — When a phenomenon in- 
 terests us for the first time, or in a new way, and 
 we do not know its kind or its cause, we guess. 
 An unusual sound in the house at night, a strange 
 light in the sky, a curious pain, an unexpected cool- 
 ness on the part of a friend, any circumstance not un- 
 derstood, and sufficient to arouse interest, is fol- 
 lowed by an immediate effort of the imagination to 
 explain it by assigning it to its class or its cause. 
 The sound in the house is only a rat, the light must 
 have been a meteor, the pain was a twinge of neu- 
 ralgia, the coolness of the friend must have been 
 because of a false report. 
 
 This tendency is natural, universal, and in 
 trivial affairs, spontaneous. But it may also be de- 
 
i62 ESSENTIALS OF LOGIC 
 
 liberate, guided by intelligent volition, and of great 
 scientific value. In things we deem unimportant, 
 we are satisfied with a guess. In less trivial cases, 
 we investigate, test, and seek to prove. The scien- 
 tific use of the imagination in this connection, is to 
 make suppositions regarding causation. A cause 
 or its law may be assumed, or both ; or an effect or 
 its law; but the supposition that a certain cause 
 will be followed by such and such an effect has no 
 scientific significance, for the mere use of a cause 
 to learn what effect it would produce, gives us the 
 knowledge without the need of previous supposi- 
 tion. If, however, we are investigating a certain 
 effect, we must suppose some definite cause or other 
 may produce it, or we can not make any progress 
 toward learning the cause, unless it happen to fall 
 under our observation. The use of a cause to see 
 whether it will produce a certain effect implies that 
 we have made the supposition that it may; for if 
 we are sure it will not, we will not try it. A scien- 
 tific hypothesis, therefore, assumes a cause for a 
 given effect, or a law for a given cause, or a law for 
 a given effect. 
 
 Lying in the mind close to the bed-rock princi- 
 ple that every event has a cause, is the tendency to 
 ask and seek answer to the question, what is the 
 cause of this event which interests me? In observ- 
 ing a mere series of cases as in enumeration in 
 Section 33 a, we reject some circumstances, on the 
 
CAUSAL BASIS FOR INDUCTION 163 
 
 hypothesis that they are no part of the cause of the 
 event we seek to explain; and we select others on 
 the hypothesis that they are the cause. In analogy, 
 as described in Section 33 b, we suppose some cause 
 explains the similarity of qualities in the two cases. 
 Especially when we experiment, as for example, in 
 the method of difference, do we make hypothesis 
 that the omission of a certain circumstance will 
 be attended by the disappearance of the phe- 
 nomenon ; and we omit this circumstance. In fact, 
 we can make no progress without the aid of this 
 faculty, imagination, in framing hypotheses. 
 
 Despite the legal maxim that the accused is sup- 
 posed to be innocent until proven guilty, no trial 
 can proceed in seriousness unless the guilt of the 
 accused be supposed at least possible ; this much it is 
 the function of the grand jury to decide, and this 
 is the logical significance of the indictment, that 
 the hypothesis of guilt is possible. 
 
 Many hypotheses were made and cast aside be- 
 fore astronomy became heliocentric. Many and 
 varied speculations as to the structure of matter 
 preceded the atomic hypothesis, so long and so 
 usefully held, but even now apparently yielding to 
 the pressure of advancing knowledge. If we count 
 dead hypotheses, the science of medicine has buried 
 more than double as many as even a comic paper 
 would insinuate. 
 
 The multitude of these discarded relics of prog- 
 
1 64 ESSENTIALS OF LOGIC 
 
 ress suggests the question, asked sometimes in 
 scorn, yet a rightful question: of what value are 
 hypotheses, if so many have proven untrue? The 
 answer has already been suggested above. Hy- 
 potheses are the stepping-stones of science, and 
 if now and then one is overturned, or proves too 
 slippery for foothold, or is merely left behind for 
 another in advance, surely here is found argument 
 against neither stepping-stone nor hypothesis. 
 How, then, may true hypotheses be known from 
 false? The answer to this question will be found 
 in the next two sections. 
 
 37. Verification. — The test known as " veri- 
 fication " is so often thought to establish the truth 
 of an hypothesis, that it should be said at the out- 
 set that verification is never proof of the truth 
 of a general hypothesis, but is often proof of its 
 falsity; or it merely leaves the possibility of truth 
 untouched or even strengthened by the fact that a 
 test which might have proven falsity, did not. The 
 value of the process is therefore purely negative, 
 as will appear in the following discussion. 
 
 When, as in Section 35, from the known inductive 
 laws of certain causes, we deduce their joint effect, 
 and then by observation with or without experiment 
 we test our deductive conclusion by comparison with 
 the actual case, the process, often called "the de- 
 ductive method, " either " verifies " the conclusion 
 or proves it false. The important point is that 
 
CAUSAL BASIS FOR INDUCTION 165 
 
 it is the deductive conclusion, the particular fact, 
 that is verified or not, and not the inductive prem- 
 ise, the general proposition. We know from the 
 laws of the syllogism that if the conclusion be false, 
 a premise is false; while if the conclusion be true, 
 nothing follows as to the truth of the premises. 
 
 So in the use of hypotheses, when we seek to 
 find, not as above, the effect, but the cause of a 
 phenomenon, the steps in the procedure are the 
 same, the nature of the " verification " the same, 
 and the bearing upon truth or falsity the same. 
 The difference is that instead of having for prem- 
 ise the known inductive laws of causes, we make 
 hypothesis of a cause or its law, deduce from that 
 our conclusion, and test it by observation with or 
 without experiment as in the other case. 
 
 The significance of the result is the same. If 
 the observed facts agree with the deductive con- 
 clusion, that conclusion is " verified," but we know 
 that the truth of the premise, our hypothesis, does 
 not follow. So the verification is of the single 
 fact, not of the hypothesis. However, repeated 
 deductions from an hypothesis, verified without ex- 
 ception by observation, have a strong tendency to 
 foster belief in its truth ; and we must guard against 
 the acceptance of this negative confirmation as 
 proof; it is merely lack of evidence of falsity; it 
 affords presumption of truth, not proof. 
 
 On the other hand, if a conclusion correctly de- 
 
1 66 ESSENTIALS OF LOGIC 
 
 duced from an hypothesis, is by observation found 
 contrary to the fact, the hypothesis must be given 
 up; for the falsity of a conclusion does involve the 
 falsity of the premise. 
 
 The Ptolemaic hypothesis that the earth is the 
 center around which sun, moon, and planets revolve, 
 was discarded because the consequences deduced 
 from it were not in accord with the facts. 
 
 The deduction that, on the hypothesis of the 
 identity of lightning and terrestrial electricity, a 
 spark could be gotten from a kite-string, was veri- 
 fied by Franklin's experiment. 
 
 The hypothesis that sound is conveyed by vibra- 
 tory motion of the air has led to many deductions 
 verified by observation, one of the most striking 
 being the photographic shadow caused by the con- 
 densation of air particles in front of the advancing 
 sound wave. 
 
 The old hypothesis that nature abhors a vacuum, 
 offered to explain the rise of water in a pump, was 
 overthrown by the fact that the water would not 
 rise beyond a definite height. 
 
 Verifications, then, may overthrow an hypothesis, 
 or they may either establish or overthrow a deduc- 
 tion from an hypothesis. They are not proof, yet 
 many accept them as proof. What, then, is proof? 
 
 38. Proof. — As intimated in Section 34 b, 
 strict proof of causal relation is found only by the 
 
CAUSAL BASIS FOR INDUCTION 167 
 
 method of difference. However strong may be the 
 presumption of truth, however great our confidence 
 that we have found the truth, yet there is no strict 
 logical proof of causal relation short of exact ful- 
 fillment of the rigid requirements of the method of 
 difference. So must it be in the case of an hy- 
 pothesis, just as in any other case of causation. 
 First, the hypothesis must be shown to explain all 
 the facts ; that is, the cause we assume must be found 
 producing all the effects of the kind, deduced from 
 the hypothesis and tested by verification ; which cor- 
 responds to the first set of circumstances of the 
 method of difference. Secondly, it must be shown 
 that no other hypothesis can explain the facts; that 
 when the assumed cause is absent, the effects will 
 not be found; or that other hypotheses lead to con- 
 clusions contrary to facts. 
 
 In the example of Section 34 a, for instance, the 
 hypothesis was made that a mosquito which had 
 bitten a yellow fever patient might convey the dis- 
 ease. The experiment showed the hypothesis ex- 
 plained the fact, and the freedom from fever on 
 the other side of the screen, where a rival hypothe- 
 sis, the contagion of foul bedding, was tried, proved 
 that no other plausible hypothesis would explain 
 the conveyance of the fever. This was proof, and 
 therefore the surgeon-general of the United States 
 Army gave orders that the only special precaution 
 
1 68 ESSENTIALS OF LOGIC 
 
 to be taken in cases of yellow fever thereafter 
 should be the screening of patients so that mos- 
 quitoes could not bite them. 
 
 When the circumstances of a crime are such that 
 they can be explained only by the guilt of a certain 
 person, he is properly convicted on " circumstantial " 
 evidence. The prosecution will try to prove that 
 no other hypothesis will explain the crime; the de- 
 fense that some other will. If the defense fail to 
 establish some other tenable hypothesis, or of course, 
 some irreconcilable fact such as an alibi, the hy- 
 pothesis of guilt prevails, and rightly. 
 
 The radical change in the lives of many after 
 profession of Christian faith can be explained only 
 on the hypothesis of a radical change in their na- 
 ture, and such cases afford logical proof of the 
 vital power of Christianity. 
 
CHAPTER X 
 
 RESULTS OF INDUCTION 
 
 39. Discovery. — Any true induction may lead 
 to the discovery of new facts; for the sweep of the 
 inductive universal includes unobserved cases of the 
 operation of the cause in question; and we may use 
 the induction as a major premise from which to 
 draw a deductive conclusion of some less general 
 truth or some particular fact. Thus we are able to 
 predict that observation will confirm our conclusion ; 
 that a fact hitherto unknown will be found true. 
 This is evidently like the process described in Sec- 
 tion 35 under the head of " combination of causes," 
 and also that used in verifying hypotheses in Sec- 
 tion 37. All these are only instances of deduction 
 from general premises. 
 
 In this way the astronomer predicts eclipses, the 
 return of a comet, the position of a new planet ; the 
 chemist from his inductive law of progressive qual- 
 ities predicts new elements; the economist from in- 
 ductions regarding demand and supply predicts 
 changes in the market, panics, prosperity ; the geolo- 
 gist foretells future conditions of river-beds, moun- 
 tains, plains, valleys, and coasts. 
 
 169 
 
170 ESSENTIALS OF LOGIC 
 
 40. Law. — A law is the statement of a uni- 
 formity. The sources of knowledge being two, as 
 in Section 29, laws are of two kinds : intuitive, dis- 
 cerned by the intellect; inductive, based on observa- 
 tion by the senses. Intuitively discerned law, such 
 as the axioms of mathematics and of logic, being 
 known originally in the form of universal proposi- 
 tions, are thus the source of many subordinate laws 
 derived from them by deduction. Hence they are 
 called " primary laws." Inductively attained law, 
 such as the laws of sound and of heat, being based 
 originally on particular facts, may thus be explained 
 by higher and wider laws, until final explanation is 
 attained in universal laws beyond which the human 
 mind can not reach. These wide inductive uni- 
 versal, because they stand last in the order of at- 
 tainment are called " ultimate " laws. Though we 
 may be sure there are ultimate laws, we may not be 
 sure whether laws we have reached are those of 
 widest scope, whether they may not be included in 
 some other still wider. It would seem hardly pos- 
 sible to go further than Newton's Laws of Motion. 
 The Law of Gravitation is another notable example 
 of law that so far as we know, is ultimate. 
 
 41. Natural Law. — Inductive laws depend 
 upon and are formed in accordance with intuitive 
 principles; all concrete knowledge is cast in these 
 abstract forms. Even the axioms of pure mathe- 
 matics may be applied to definite numbers of con- 
 
RESULTS OF INDUCTION 171 
 
 crete things ; the laws of pure logic are useful only 
 when operative in actual thoughts ; the formal prin- 
 ciples of ethics do not guide conduct unless effec- 
 tive in the real act; the intuitive laws of causation 
 are of practical value only when connected with 
 particular causes. 
 
 Thus, the axioms of uniformity of Section 32 
 are intuitive, pure, formal, without content; but 
 when applied to the actual causes and effects of na- 
 ture, the resulting uniformities of concrete cases of 
 causation are natural laws. Natural law is expres- 
 sive of the uniformities in the sphere of causation, 
 and is logically opposite to moral law, which is ex- 
 pressive of the uniformities in the sphere of free- 
 dom; natural law declares what is in nature, moral 
 law commands what ought to be in conduct. Moral 
 law is obeyed or violated; natural law is neither 
 obeyed nor violated. When a rock is thrown up- 
 ward from the earth, the law of gravitation is not 
 violated, but a new cause, the energy of the mus- 
 cles, is put into operation according to its own law. 
 
 A miracle is not a violation of law. The Maker 
 of the Universe may use either a natural cause or 
 law unknown to us to work what we call a miracle, 
 or He may employ His creative power, itself the 
 cause of all causes. 
 
 The question of the possibility of resolving all 
 natural law into a single ultimate law, has been 
 much discussed. Whether or not we shall ever 
 
172 ESSENTIALS OF LOGIC 
 
 bridge the chasm between present multiplicity and 
 such a unity, may be doubted, but that there is such 
 unity we may be sure ; for, " In the beginning God 
 created the heavens and the earth." 
 
 42. Science. — The intuitive principles of 
 space and time, developed by deduction, give us the 
 pure science of mathematics; those of thought and 
 causation give logic, which is the pure framework 
 of every science. Sciences of facts and causes, de- 
 veloped according to the intuitive principles con- 
 trolling induction, but systematizing experiences, 
 give us such empirical sciences as physics and chem- 
 istry. Sciences which have intuitive knowledge 
 alone as their object-matter, are pure sciences; those 
 which deal with sensuous knowledge, according to 
 intuitive principles, to be sure, are empirical sci- 
 ences. 
 
 Pure sciences are necessarily deductive, for they 
 descend from the universal, directly known truths 
 of intellect. Empirical sciences are at first induc- 
 tive, and continue largely so, for they ascend from 
 individual facts to general laws; yet no sooner is 
 the first general law attained than the way is thereby 
 opened for deductions from it to new subordinate 
 laws or facts. As knowledge progresses, there- 
 fore, an inductive science becomes more and more 
 deductive. Theoretically, when all the laws of an 
 empirical science have been discovered, the science 
 would cease to be inductive, and be deductive only; 
 
RESULTS OF INDUCTION 173 
 
 but this theoretical case has not occurred, nor are 
 we likely to reach it. Astronomy, however, for in- 
 stance, has been developed largely by deductions 
 from the laws of gravitation and motion. There 
 are, therefore, no sciences that are always wholly 
 inductive. 
 
 The systematic arrangement in their proper re- 
 lation of all things knowable — principles, causes, 
 laws, and classes, is the goal of science. 
 

 
 
INDEX 
 
 Reference to Pages 
 
 Abstraction, 15 
 Affirmation, law of, 47 
 Agreement and Difference, joint 
 
 method of, 158 
 Agreement, method of, 154 
 Ambiguity, 123 
 Analogy, 148 
 
 Begging the question, 125 
 
 Causal basis for induction, 146 
 Causal basis assumed, 146 
 Causal basis proved, 151 
 Causation, 142 
 Cause, nature of, 143 
 Causes, combination of, 160 
 Chance, 149 
 Change, axiom of, 142 
 Classification, 28 
 Co-extension, 28 
 Combination, inference by, 77 
 Combination of causes, 160 
 Compound propositions, 54 
 Conception, 16 
 Concepts, 17 
 
 Conditional propositions, 105 
 Conditional syllogisms, 115 
 Contradictories, 46 
 Contraposition, 83 
 Contraries, 47 
 Contraversion, 83 
 Conversion, inference by, 79 
 Co-ordination, 27 
 
 Deduction, 75 
 Deduction, immediate, 76 
 Deduction, mediate, 86 
 Deductive method, 164 
 Definition, 38 
 Definition, rules of, 40 
 Denial, law of, 48 
 Dichotomy, 34 
 Difference, method of, ij 
 Discovery, 169 
 Disjunctive propositions, 
 Division, 32 
 Division, rules of, 34 
 
 107 
 
 Enthymemes, 90 
 Enumeration, 146 
 Epicheirema, 92 
 Episyllogism, 92 
 Exclusion, law of, 48 
 Extension and intension, 
 of, 17 
 
 Fallacy, 122 
 
 Figure and mood, 118 
 
 Forms of thought, 14 
 
 Generalization, 16 
 Genus, 30 
 
 Hypothesis, 161 
 
 Hypothetical propositions, 105 
 
 Illicit process, 88 
 Immediate inference, 77 
 
 law 
 
 175 
 
176 
 
 INDEX 
 
 Implied judgments, 76 
 Induction, results of, 169 
 Inductive inference, 139 
 Inference, kinds of, 75 
 Inference, nature of, 75 
 Intension and extension, 18 
 Intersection of notions, 27 
 Inversion, 83 
 
 Joint method of agreement and 
 
 difference, 158 
 Judgments, 52 
 
 Law, nature and kinds of, 170 
 
 Limitation, conversion by, 80 
 
 Logic a distinct science, 12 
 
 Logic defined, 1 
 
 Logic not an art, 11 
 
 Logic related to all science, 13 
 
 Major, minor, and middle terms, 
 
 87 
 Marks, kinds of, 24 
 Marks, nature of, 15 
 Mathematical propositions, 58 
 Mathematical syllogisms, 117 
 Misproof, 124 
 Moral law, 171 
 
 Natural law, 170 
 Notions, kinds of, 19 
 Notions, nature of, 15 
 Notions, relations of, 26 
 
 Obversion, 79 
 
 Polytomy, 34 
 Premises, 86 
 Probability, 149 
 Proof, 166 
 Proper names, 21 
 Propositions, 52 
 Propositions, conditional, 105 
 Propositions, disjunctive, 107 
 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Propositions, 
 Prosyllogism, 
 
 hypothetical, 105 
 individual, 58 
 kinds of, 54 
 methematical, 58 
 quality of, 55 
 quantity of, 56 
 relations of, 81 
 strict form of, 83 
 symbols of, 58 
 92 
 
 Quality of propositions, 55 
 Quantity of propositions, 56 
 Quantity, words showing, 57 
 
 Residues, method of, 160 
 Rules of definition, 40 
 Rules of division, 34 
 Rules of syllogism, 87 
 
 Science, 172 
 
 Scientific induction, 140 
 
 Sorites, 92 
 
 Species, 30 
 
 Subordination, 27 
 
 Syllogism, conditional, 115 
 
 Syllogism, incomplete, 90 
 
 Syllogism, mathematical, 117 
 
 Syllogism, nature and parts of, 
 
 Syllogism, rules of, 87 
 
 Symbols of propositions, 58 
 
 Term, meaning of, 18 
 Terms of syllogism, 87 
 Thought, nature of, 75 
 Thought, primary laws of, 46 
 Trichotomy, 34 
 
 Undistributed middle, 88 
 Uniformity, 144 
 
 Variation, method of, 156 
 Verification, 164 
 
 86 
 
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