an introductory text-book of logic 1000011061

8/12/2019 An Introductory Text-Book of Logic 1000011061

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OQf I

AN INTRODUCTORYTEXT-BOOK OF LOGIC

BY

SYDNEY HERBERT MELLONEM.A. LOND., D.Sc. EDIN.

AUTHOR OF ' STUDIES IN PHILOSOPHICAAND CONSTRUCTION,' ETC.

WILLIAM BLACKVVOOD AND SONSEDINBURGH AND LONDON

MCMII


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be


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PREFACE.

IN the present volume the author's aim has been toprovide a text-book at once elementary and philosophical. More specifically, he has endeavoured, in thefirst place, to give an accurate exposition of the essentials of the Traditional Logic ; in the second place,to connect the traditional doctrine with its Aristotelian

fountainhead, not only because of the value and clear

ness of Aristotle's own treatment (as compared withlater accretions), but in order to make various doctrinesand phrases intelligible, which in the ordinary text-bookare simply shot from a pistol as it were ; in the thirdplace, to show the open door leading from the traditional doctrine into the more modern and more strictlyphilosophical treatment of the subject. The book isintended to stop short of giving what is supplied in MrBosanquet's Essentials of Logic (not to mention largerworks), but to lead on naturally to that and to aserious study of Modern Logic.


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VI PREFACE.

A text-book constructed on this plan seems to correspond closelyto the treatment of the subjectrequiredby the course of instruction for the ordinaryDegree inmany of our Universities and Colleges.

The author's plan has certain difficultieswhich he hasat least endeavoured to avoid. The chief of these isthe danger of leaving an unbridged gap between thetraditional or formal and the philosophicalarts of thebook. To some extent the author found that thisdifficultyas diminished by keeping as close as possibleto the Aristotelian exposition,hich is in itself thoroughly philosophical.By treatingthe formal part ofthe subjectin this way, the gap seemed almost to disappear. For the rest, the most practicallyonvenientcourse seemed to be to indicate,n the earlier chapters,by footnotes or otherwise,those pointsat which morefundamental questionsarise ; and in a concludingchapter, to bringthese references togetherand developthem.The author hopes that he will at least be found to haveavoided a mistake too common in books of this kind :of making the treatment of the traditional Logic perfunctoryor even inaccurate ; of expounding it de hauten bas, so to speak,leavingon the student's mind theimpressionthat it is not worth his attention a mistakeequally serious from the educational and the philosophical point of view. It is hoped also that some freshness will be found in the choice of examples andillustrations,s well as in other respects. If Logicseems trivial to the student,the fault is not necessarilyin Logic; it may be because the student's range of know-


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PREFACE.

logical mistakes. Some of its doctrines are freely criti

cised in the following pages ; but the present writer fully

concursin the general acknowledgment of its real

suggestiveness and value.

S. H. MELLONE.

HOLYWOOD, BELFAST,

Augiist 1902.


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CONTENTS.

CHAPTER I.

THE GENERAL AIM OF LOGIC.

1. Provisional definition of Logic2. Scope of Logic .. *'3. Stages in its history ..- 24. Logic and Language .5. Judgment as the fundamental fact of Thought6. Judgment and Proposition

Inference

10. The process of Thought is continuous

CHAPTER II.

THE NAME, THE TERM, THE CONCEPT, AND THELAWS OF THOUGHT.

1. Name and Term

2. Concrete and Abstract Names

3. Singular, Common, and Collective Names .4. Positive and Negative Names .5. Relative and Absolute Names .6. The logical Concept ; connection between changes of Con

notation and of Denotation.

7. Limits of Connotation .8 Every Term has both Connotation and Denotation

.

9. Laws of Thought


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X CONTENTS.

10. Three fundamental Laws 3911. Law of Identity ...... .o12. Law of Contradiction ..... 4I13. Law of Excluded Middle 4314. Law of Sufficient Reason .... 46

CHAPTER III.

THE PROPOSITION, THE OPPOSITION OF PROPOSITIONS,AND THE FORMS OF IMMEDIATE INFERENCE.

Part i. The LogicalProposition.i. Propositionnd Sentence ; Kinds of Propositions; Quantity

* 502. Modality of Propositions;Propositions as Analytic and

Synthetic ..... -53. Compound Propositions . . _84. Expression in LogicalForm . . 62

Part ii. Oppositionof Propositions.5. Possibilityf the class interpretationf Propositions 696. Distribution of Terms .7- Four kinds of Opposition . . ^

Part iii. Immediate Inference.8. Elementaryprocesses ....9. Conversion ...

10. Obversion . .11. Contraposition12. Inversion13. Other forms 91

CHAPTER IV.

THE IMPORT OF PROPOSITIONS AND JUDGMENTS.

1. Four views2. Predicative interpretationclass interpretationequational

^

view .3. Attributive view4- Comprehensive view; Quantification of the Predicate5. Compartmental view6. Implicationof Existence in


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CONTENTS.

CHAPTER V.

MEDIATE INFERENCE AND THE ARISTOTELIAN SYLLOGISM.

1. Mediate distinguishedfrom Immediate Inference . . US2. A typicalSyllogism; its Premises, Major, Minor, and Middle

Terms II83. Rules or Canons of the Syllogism . I234. Figures and Moods of the Syllogism . I315. Determination of Valid Moods J356. Characteristics and Examples of fig.i. J387. Fig. ii . . 1428. Fig.iii. . . 449. Fig. iv. . . . J45

10. Superiorityf fig.i.; Reduction to fig.i. . 14611. Abridged and conjoined Syllogisms . JS212. Expression in Syllogisticorm . . I57

Note. A new Notation . l64

CHAPTER VI.

THE PREDICABLES, DEFINITION, AND CLASSIFICATION.

Part i. The Predicables.1. Aristotle's view ..... -1652. Genus, Diiference,Proprium, and Accident . . 1673. Traditional view .... l69

Part ii. Definition.4. Object of Definition .... I7I5. Rules of Definition . J736. Nominal and Real Definition ; Genetic Definition ; Legal

Definition . ... .176Part iii. Classification.

7. Definition and Classification . .1818. Natural and Artificial Classification . .1829. LogicalDivision . J

10. Dichotomy . .187Part \v. The Categoriesr Predicaments.

11. Aristotle's viewNote. Real Kinds ...- J93


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Xll CONTENTS.

CHAPTER VII.

CONDITIONAL ARGUMENTS AND THE VALIDITYOF THE SYLLOGISM.

1. Conditional Propositions ..... 1962. Conditional Arguments ..... 1983. HypotheticalSyllogisms ..... 1984. Expression in Categorical Form ; Mediate character of the

Inference ....... 2oo5. DisjunctiveSyllogisms ..... 2046. Dilemmas ....... 2067. Syllogismsinvolvingrelations other than that of Subjectand

Attribute ....... 2138. Mill's view of the Syllogism . . . . .216

Note A. On SyllogismsinvolvingNumerical Propositions . 221Note B. Aristotle's Defence of the Syllogism . . 222

CHAPTER VIII.

THE GENERAL NATURE OF INDUCTION.1. Induction as the discoveryof major premises . . 2242. Aristotelian Induction ; Scholastic Induction,Perfect

and Imperfect ...... 2283. The Aristotelian Enthymeme ..... 2344. The Aristotelian Paradeigma ..... 2415. Scientific aim of Induction ; Induction in Mathematics . 2456. Uniformityand Universalityf Causation . . .2517. Mill's view of Cause ...... 2558. Pluralityf Causes ...... 260

CHAPTER IX.THE THEORY OF INDUCTION OR SCIENTIFIC METHOD.

1. Observation and Experiment ..... 2642. Methods of Observation and Experiment . . . 2683. Method of SingleAgreement ..... 2694. Method of SingleDifference ..... 2735. Importance of the Negative Instance .... 2776. Double Method of Agreement .... 2787. Double Method of Difference . . . . .2818. Quantitative Methods ; Concomitant Variations ; Residues 2839. Double Method of Difference is fundamental so far ; Em

piricalaws 2g9


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CONTENTS. xiii

10. Method of Explanation ; Hypothesis . . 29111. Origin of Hypotheses .... 29912. Suggestionby Analogy . 30113. Conditions of a good Hypothesis . . 3 4

CHAPTER X.

FALLACIES.

1. Aristotelian Classification . 3*3I. Fallacies due to language

(1)Equivocation ... 3Z4(2)Amphiboly . 3*5(3)Composition . . 3l6(4) Division . 3T7(5) Accent 3*7(6) Figure of Speech . . . 318

II. Fallacies due to the thought rather than the language(1) Accident . 3l8(2) A dicto secundum quid and converse . . 318(3) IgnoratioElenchi ..... 32(4) Consequent . . . 322(5) Petitio Principii . 322(6) Non causa pro causa . , . 32S(7) Many Questions ..... 32S

2. Whately's Classification . 3253. Inductive Fallacies . ... 326

CHAPTER XI.

THE PROBLEMS WHICH WE HAVE RAISED.

1. Modern Logic; Logic as formal .... 3292. Jevons'sTheory of Inference ... 3313. Hamilton's Comprehensive view of Judgment . . 3344. Reference to Realityin Judgment .... 3365. Basis of Negation ... . 346. Generic and Collective Judgments .... 3437. Hypotheticaland DisjunctiveJudgments . . 3478. Deductive and Inductive Inference

. . 359. Logic and Psychology ... 353

Note ...... 356

INDEX .... 357


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CORRECTIONS AND NOTES.

PAGE LINE

21 21read

ovo^a. aopioroj/, indefinite name.

51 6 add that this meaning of Kanryopew is post-Aristotelian.

51 10 add that many Logicians prefer to identify conditional

with hypothetical propositions to the exclusion of dis

junctives.

53 1 6 for Some one read He.

56 19 add that the assertion of Impossibility forms an E proposition.

60 5 for who read though they.

145 8 from bottom, for three read these.

146 8 for simple readmere.


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AN

INTRODUCTORY TEXT-BOOK OF LOGIC.

CHAPTER I.


i. WHEN we begin the exposition of any science, it isusual to frame a definition of it. But the beginningis not the point at which we can give a completely satisfactory explanation of the ground to be covered or thenature of the questions to be asked. For the words inwhich such a definition would be expressed would notbe fully intelligibleuntil the student became acquaintedwith the study which it defines. Hence we shall notfor the present attempt any formal definition of Logic,beyond observing that to study Logic is to thinkabout thought, in order to distinguish between correct or valid and incorrect or invalid thoughts. Thus,we have to think about that which, in science and common life, we do not think about but use i.e., thoughtitself.

2. We have not said that Logic aims at distinguishing true thoughts, for this would suggest discovering


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2 THE GENERAL AIM OF LOGIC.

truths or facts, and would make Logic a name for allthe various sciences collectively,hich is absurd. Wehave said correct or valid thoughts; for these terms,especiallyhe former, suggest reference to a type orpattern, regarded as a rule or regulativerincipleo befollowed. Hence, far from givingus means by whichto discover new (particular)acts,the function of Logicis entirelyeneral. It shows that the thinking processis essentially the same, whatever be the particularsthought about. The process of calculation may beexplained in Arithmetic without regard to what thenumbers represent; and similarlythinkingmay be reduced to generaltypes which are the same in all particular applications.It is the aim of Logic to discoverthese types, and to show how to regulatethought bythem ; hence it deals with reasoning as a processcommon to all the sciences,without regard to theirsubject-matter. Only in this sense is Logic theScience of sciences ;and in this sense also, Logicdeals with the form and not the matter of thought.

3. The manner in which the subject has beenpresented in the more elementary works hitherto,depends partly on its history and the student willfind that a brief consideration of some of the chiefstages in that historywill clear up his generalidea ofthe logicalpoint of view.

The Greeks invented the very idea of Science,in thatsense of the word in which science is an Ideal, thepursuitof knowledge for the sake of knowing : and tothe Greeks also we owe the originand development ofLogic. Aristotle considered that logicalinquirieseganwith the disputationsf Zeno the Eleatic (towardsthe

1 The philosophicalspect of this definition will be considered inour concludingchapter, i.


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THE GENERAL AIM OF LOGIC. 3

end of the fifth century B.C.),ho found a number ofdifficultiesin the beliefs of common sense, and in thethen prevalent philosophicalonceptions,as to therealityof time, space, and motion ; the discussionsto which these arguments gave rise began to awakena conscious interest in methods of reasoning,n essentialpart of Logic. This interest was carried much furtherby the work of the Sophistsand of Socrates. TheSophists met a growing demand for means of enlarging and improving human nature, by givinginstructionin the arts and accomplishmentsuseful to a citizen inpracticalife. They gave specialttention to what maybe called the Art of Persuasion, in a wide sense. Thisinvolved the beginnings of Grammar, Rhetoric, andLogic, as distinct studies. Thus Logic first appears asthe art of arguing. The Sophists were more interested in persuasionthan in true instruction,in victoriesthrough verbal discussion than in scientific investigation. Some of them, such as Protagoras, werethorough Sceptics,denying the possibilityf knowledge.Socrates went with them in their interest in humanity ;but he was moved by an invincible faith that knowledgeof the truth is possibleor us all. His method of arriving at truth was so simple that its deep significanceis somewhat hidden. He observed that in ordinarythought people are much more sure of the particularobjectsto which a name belongs than they are of thequalitiesn the objects,n account of which the nameis given; thus, when we speak of such a thing as anoak-tree or a rose or a beautiful object, agood action it is more easy to bring forward actualinstances of these thingsthan to explainwhat we mean(what idea we have in our minds) when we use thename. But to arrive at consistencywith ourselves and


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agreement with others, we must not only be able topoint to the things; we must know the meaning, thethought, which the name expresses. Socrates considered that this could be done by comparing thethings,to ascertain the common qualitiesn accountof which they received a common name. His chiefcontribution to Logic, therefore,was to make peoplesee the importanceof Definition,s a means of knowing things. Plato made further contributions to theanalysisf the methods of discussion and scientific procedure ; but in Aristotle,these questionsgain distinctness and receive more suo a separate treatment.

Aristotle is the real founder of Logic as a science,forhe worked it out systematicallyn all its parts. Hisdoctrines are contained in six small but masterlytreatises,hich afterwards,n account of their affinity,were collectivelyeferred to as the Organon. Thetreatises of which the Organon consists are thefollowing

1. The Categories.This is a philosophicalntroduction to Logic.

2. De Interpretation(On Expression in Words).An account of terms and propositions.

3. Prior Analytics. An account of formal reasoning(seebelow, ch. v.)

4. Posterior Analytics. An account of the processesby which demonstrative or reasoned truth maybe obtained (asin Mathematics).

5. Topics. An account of reasoning in matterswhere complete demonstration is unattainable.

6. SophisticalDifficulties.n account of fallaciousarguments.

He founded a logicaltradition which has lasted to


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tion and explanationof Nature. In this work inquiryinto principlesof scientific method Roger Bacon(1214-1294)was a brilliantforerunner of writers muchlater in date. Francis Bacon, the Chancellor,carriedon the work, and wrote his Novum Organum in rivalrywith what he thoughtwas the Aristotelian system of Logic.It was natural that as this seemed to be a new beginningin Logic,a new name should be found for it; and duringthe nineteenth century,

Inductive Logic, s itiscalled,has received much attention. The most importantworksin which it has been developed are those of Herschel,Whewell, and John Stuart Mill.

Hence the usual treatment of Logic lays out the subjectin two branches. The firstof these is founded on the Logic-which the mediaeval writers developed out of such acquaintance with Aristotle as they possessed. This is usuallycalled Deductive Logic or Formal Logic. The seconddivision is the Inductive Logic of which we have spoken,which is often called Material Logic. So far as the distinction implies a difference in principlebetween the twokinds of knowledge, it has no foundation in the facts ofthought ; otherwise,there are advantages in not departingfrom it.1

4. Logic has to consider Language ; but only sofar as differences of expression in language are theembodiment of differences of type in the process ofthought. The word X6yo shad a double meaning inGreek : (a)the thought (/ )he word (orrather,phraseor sentence)which is the expressionof the thought,ratio and oratio. Aristotle distinguishedhese,callingthe former TOV lo-co,OV lv rfji/o^??,nd the latter TOV t n ;the inward and the outward logos. This ambiguityhas givenrise to a disputeas to whether Logic

1 The recent philosophicalevelopment of Logic will be referred to in our concludingchapter, I.


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has to do with thought or with language. Whately hasbeen referred to as holding the latter view. It is truethat when definingLogic he says that it is entirelyconversant about language ;but elsewhere he speaksof the processes of reasoning i.e.,processes of thoughtas the subject-matterf Logic. No other view canbe seriouslyaken ; but the stress which is laid on theverbal expressionf these processes varies in differentworks.

We cannot entirelyeparate the two aspects of theAoyos; for,while thought is priorto language,thoughtcould make no progress without embodying itself inlanguage. As soon as we have an idea there is anirresistibleimpulse to giveit bodilyshape in a word.

The thought is purelyinward and in a sense abstract ;the word has an external existence as a sound or awritten symbol, and is therefore a thing of sense ; butthe thought would dissolve again were it not stereotypedin a word. Hamilton (Logic,ol. i. p. 138) has illustrated this reciprocaldependence as follows. An armymay overrun a country, but the country is only conquered by the establishment of fortresses;words arethe fortresses of thought. And in tunnellinghrougha sandbank it is impossibleo proceed until the presentpositionis made secure by an arch of masonry ; wordsare such arches for the mind.

Questions connected with the foregoing,and deservingof the student's attention,are, the extent to which languagemay be a hindrance, as well as a help,to thought ; and thereason why spoken language has become universal ratherthan gesture language. And we may remark, in passing,that Grammar, dealing with the thought - structure oflanguage, lays stress on the other side of the \6yo ;,theoutward expression. Hence Grammar has been called a concrete Logic.


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5. We shall find a convenient centre from whichto start if we ask What is the simplesttype of'thoughtwhich may be either true or false? Evi-;dently this cannot be less than a singleassertion orIstatement of fact,affirmative or negative. Let us calla thought of this kind a Judgment ; and the expression of it in language a Proposition. It would be wellif the term proposition could be kept for theJudgment expressed so as to bring out its logicalcharacter i.e.,xpressed in a grammaticallycompletesentence, with subject and predicate; but commonusage is too strong, and we must take the term asmeaning the sentence which contains (or,as containing) a Judgment, whether it is properly formulated(seebelow) or not.

Not every judgment is naturally expressed in the formof a complete proposition a singleword, e.g., Fire maysuffice to express a judgment. The judgments of childrenare often of this kind.Again, every \6yos (sentence)is significant,ut only

such as can be true or false are assertive'1'1(Ar.De Intcr-pretatione,iv.) In other words, not every sentence is aproposition; thus, go away is not a statement of fact,the notion of truth or falsityoes not belong to it. Eventhe enunciative sentence contains emotional elements overand above the mere judgment ; e.g.,there's the door mayexpress much more than a judgment concerning the place,c., of the door. Just as Fire contains a judgment,but a great deal besides.

The Judgment may be called the Unit of Thought ;for all our deliberate thinkingconsists in making statements or assertions,nd if we are to have truth orfalsitye must have at least a judgment. 6. Any judgment may be resolved into two relativelysimplerelements,which for the present we will


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vaguely call ideas. An idea by itself cannot be eithertrue or false ; it must enter into a judgment first. Anexample of this is, that ' unicorn ' means something,but is not true or false until affirmation or denial of itsexistence is added (Ar.De Int. i.) This does not meanthat judgments are built up by putting togetherideasthat were separate. Whether we can even entertain asignificantdea as such without judging,or at leastframing possiblejudgments on the basis of that idea,is very doubtful. In Logic we may assume that ideasexist only as elements in the judgment.

We have a correspondingrelation in the proposition.A proposition affirms or denies something of somethingelse : e.g., Some useful metals are becoming rarer.The Subject is that about which the assertion is made(i.e.,some useful metals ); the Predicate,that whichis asserted (i.e.,are becoming rarer ).It is a standing convention in elementaryLogic to express the statement which is made, by the verb is or is not (are orare not); and the predicateof a propositionis alwaysunderstood to be expressed in a form admittingof theuse of this verb,which is called the Copula (i.e.,n ourexample, Some useful metals arc things which arebecoming rarer ). The subjectand predicatere theterms (termini,limits)f the proposition and we shall -understand by a term, any word, phrase,or sentencewhich is standing as the subjector predicateof a proposition.A Term which is not in its place in a propositionwe shall call a name.

Just as every sentence is not a proposition,o everyword is not a term. A term will be either a noun, an adjective,r a participle,r some word, phrase, or sentenceequivalentto one of these. Words which arc not terms aredistinguishedas syncategorematic, while terms are called


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categorematic, from the Greek Kcn-nyoptw,I predicate. A syncategorematic word may become a term in a proposition which makes some statement about its use as a partof speech : e.g.) When is an adverb, and sometimes aconjunctionalso.

The student must remember that there is no separateexistence in thought (no third idea coming between thesubjectand predicate)corresponding to the separate existence of the copula in the typicalproposition, is P.

7. Judgments may be combined into reasoningsorinferences. What is an inference? To infer is toarrive at a truth not directlythrough experience,butas a consequence of some truth, or truths alreadyknown ; as when I see a circle of stones, and inferthatthey were arrangedby human hands ; or when I believethat nothing proceedingfrom a pure moral intentioncan be utterlycondemned, and that some deviationsfrom the common rules of moralityhave proceededfrom this source, and accordinglyinfer that those deviations are not to be altogetherondemned. J. S. Milldefines inference thus : We start from known truths toarrive at others reallydistinct from them. The truthsfrom which we start are the premises, that which wereach is the conclusion. Both Mill and Whately pointout that the chief work of practicallife is concernedwith drawinginferences in this sense.

Hence we have three main divisions of LogicI. The doctrine of Terms, leadingon to that of the

ideas, the element in the Judgment towhich the Term corresponds.

II. The doctrine of the Judgment.III. The doctrine of Inferential Thought. 8. We have seen that Ideas are not priorto Judgments ; for a Judgment is not built up by putting

separate Ideas together. Ideas are distinguishable


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THE GENERAL AIM OF LOGIC. II

though not separate elements in a Judgment. If weconsidered only this fact,we could hardlyrecognisethedoctrine of Ideas as a separate part of Logic. ButIdeas which have been formed by Judgment and areproducts of Judgment, may be prior to further Judgments ; and in consideration of this,e must admit thejusticeof treatingideas first as if they could exist independently in the mind. It is the same with Terms.In the originof language the sentence is priorto theword, and the parts of speech were originallyentences ; but we may give separate logicalreatment toTerms apart from Propositions,f we remember that inlivingspeech the Term only exists as a part of a Propositionexpressed or understood.

This statement of the relation between the three divisions of Logic differs from what Jevons and some otherwriters say. Jevons speaks thus: Simple apprehension isthe act of mind by which we merely become aware of something,or have a notion, idea, or impression of it broughtinto the mind. The adjectivesimple means, apart fromother things ; and apprehension, the taking-hold by themind. Thus the name or term ( iron ' makes the mind thinkof a strong and very useful metal, but does not tell us anything about it,or compare'.itith anything else. . . . Jiidg-ment is a different action of mind, and consists in comparing together two notions or ideas of objectsderived fromsimple apprehension,so as to ascertain whether they agreeor differ, And similarly,he continues, when we havealreadymade judgments, a third activityf mind may comein and combine them into processes of argument or reasonings. According to Jevons' account, the three activities ofmind, apprehension,judgment, reasoning, are three different kinds of operation,which simply come after oneanother. The later forms use the finished products of theearlier ; but knowledge is made to resemble a process ofadding part to part from the outside. This view of thelogicalprocesses of the mind, and of the growth of know-


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ledge, is fundamentally a mistake ; the further the studentpursues the study of modern logic the more clearly he willsee that it is so. The point of view adopted in modern logicis, that in the formation of ideas, in judgment, in reasoning,we have not three separate processes but a development orexpansion of one and the same process ; and the full significance of this statement will be seen at a later stage. We

may add that the statements made earlier in this chapterimply that there is no such thing as simple apprehensionas Jevons defines it. We apprehend or mentally takehold of an idea, only by making judgments about a thing;we form the idea of iron through the judgments that it ishard, heavy, malleable, c., and the idea of ironis a product of such judgments.


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14 THE NAME, THE TERM, THE CONCEPT,

words which can serve as a term, but is considered without specialreference to its use in a propositionas aterm.

Aristotle had already remarked that the Term (8pos,terminus) is not something out of which a propositionisbuilt up, but that into which a propositionis analysed,as its subjector predicate (Prior Analytics,I. i).1 Allthat Logic has to do with terms is to distinguishtheirvarious kinds, so far as these throw lighton the process ofthinking. Now if we take the Aristotelian conception ofthe Term as always either subjector predicateof a proposition, a great deal of what English logicianssay about terms and some of them, especiallyJevons, use theword in a loose sense as equivalentto names or words or phrases falls outside Logic. It belongs to Grammaror Rhetoric, or to specialsciences. Hence when dwellingon the distinctions usuallygiven,we shall speak of names as above defined, and not of terms ; for only one of thesedistinctions is of primary logicalimportance that between singular and general, which is the only one that appliesstrictlyo logicalterms, as parts of a proposition. We mayarrange the various distinctions of names as follows :

1 In De Interpretatione,h. i.,Aristotle seems to give morecountenance to the view that the judgment is a combination orseparation, rwOeffis or Staipecns,f concepts,s though it were built


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AND THE LAWS OF THOUGHT. 15Two other distinctions,of positive and negative,relative and absolute, will be mentioned because some

interestingnd important logicalconsiderations arise out ofthem.

2. Our first division is into abstract and concretenames.

Mill explainsa concrete name as the name of anobject or thing viewed as possessingattributes;nabstract name, as the name of an attribute (aquality,property, or action)iewed apart from the objectto whichitbelongs. The ground of this distinction in the use ofnames lies in the fact that we may think of thingsashaving attributes i.e.,qualitiespredicatedof them,when the names by which we signifythe things areconcrete; or we may think of the qualitiesapartfrom their attribution to things,when the names bywhich we signifythem are abstract. The distinctionconcerns the use of names ; for some names maybe used now as abstract, now as concrete. Hencebefore we can determine to which of the two classesany term belongs, we must consider a propositionrstatement in which it is contained. Thus, all adjectivesare concrete; for an adjectivecan be a logicaltermonlywhen standing as the predicatef a proposition,if it is not predicatedof a noun it must be prefixedtoa noun. This will make the noun a concrete term, andthe adjectivewill share this character with it : thelightof certain stars is coloured

Abstract names are generallymarked by a suffix :whiteness, manhood, hospitality. A phrase or

up out of them ; but this is for the specialpurpose of urgingthatonly the judgment, as distinguishedrom the concept, can havetruth or falsehood.


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sentence may be an abstract term : that this rumour isfalseis evident on the face of it. The names of attributes are sometimes used to signifynstances of theiroccurrence, and then they must be considered as concrete names : unpunctualitys irritating. n this connection,Mill refers to the apparent use of abstract namesin the plural but the name of an attribute can be described as common and put in the pluralnumber, onlyin so far as it can be regardedas varying,s being itselfthe subjectof attributes ; and then it becomes a concretename. A purely abstract name e.g., colour when itmeans simply colouredness cannot be used in theplural. When we speak of colours we use the termas a concrete which has different attributes or varieties.Hence the distinction of abstract and concrete has nofixitys appliedto names ; a name may pass from oneclass to the other.

Some names which are used in two senses may beabstract in one, concrete in the other e.g., introduction (the opening of a discourse, the act of introducing). This is an example of an equivocal orambiguous term. We cannot make a separate class ofnames out of these, as Jevons and others do, callingthem equivocal or ambiguous names ; for each ofthem is reallytwo or more names. Thus, vice(meaning an immoral action)is a different name from vice (themechanical instrument).

3. Concrete names are ordinarilydivided intosingular,common, and collective ; and although sucha classification reallyimpliestwo principlesf division, since collective names may be either singularr common, there is some practicalonvenience in following it.

(a) A singular name can denote only a singleobject,


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AND THE LAWS OF THOUGHT. I?

as long as its meaning does not change. All propernames belong to this class. If the singularame isnot a proper name, it is always indicated by a demonstrative,r by an equivalentxpressionivingthe objecta definite positionn time or place.

The followingare singularnames which are not propernames : the writer of the letters of Junius, the year inwhich Queen Victoria died, the present Government,the earth, the largestplanetof the solar system ; and

all names introduced by singulardemonstrative adjectives, this, that, c. A proper name may be described as a particularisedemonstrative. It is a mark used for thesake of distinguishingne particularbject,nd not (atfirst)for what it means. It may have almost no meaning whenfirstapplied(seebelow, 8).

There is great vagueness in the explanation of singular names in logicaltext-books,through neglectto noticethat the characteristic of such names is to specifytheobjectby limitingit or individualising it in space andtime.

(b)A common name is applicableithout change ofmeaning to a number of objects,which resemble oneanother in some characteristic features or aspects, calledin Logic attributes. When a name is thus applicableto every one of a class in turn, it is said to be distrib-utively used. The name is appliedto the individualsbecause theyhave in common certain attributes. Theseattributes are what the name means ; togetherthey formwhat is called the connotation of the name, or theintension or content of the idea; and the objectstowhich it is applied constitute the denotation of thename, or the extension of the idea. Thus the denotation of the name man consists of the wholegroup or class of beings which this name denotes that

B


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1 8 THE NAME, THE TERM, THE CONCEPT,

is, which it points out and distinguishesfrom othergroups ; and the name is applicableto each memberof the group. The connotation of the same nameconsists of the attributes by which all these beings aredistinguished,the attributes constitutinghumanity.Or, to give a mathematical example, the connotation ofthe name circle may be accepted in the form inwhich Euclid states it; while its denotation consistsof all the cases of motion, form, c., which are circular.

It has been objectedthat in names such as unicorn,dragon, we have connotation,but the attributes which

are signifiedo not exist,and therefore we have nodenotation. But by denotation we do not mean onlyexistence in the real world ; existence in any kind ofworld which is being spoken of as the subjectof discourse is sufficient e.g., the ideal world, or the worldof heraldryor folklore. Hence every common namehas both connotation and denotation,and is in shortthe name of a class. It is none the less a classname even if there is only one instance to whichit is applied; for if it signifiesertain characteristicattributes of the thingwhich it denotes,it ispotentiallycommon; the sun is an instance of this. On theother hand, the class denoted need not be numericallydefinite or limited ; it is known by the attributes,ndany instance of these, whether a known or an unknown instance,constitutes a member of the class.At a later stage of our present discussion,e shallconsider the connotation and denotation of singularnames ( 8).

Names of materials,the so-called homogeneousnames, are in a doubtful position. Names such aswater, wood, iron, are singulars used of the


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AND THE LAWS OF THOUGHT. 19

mass as a whole, but common as applicablen the samesense to different portionsof the mass. Aristotle hadalready noticed this (Topics,I. ch. vii.)The case ofwater from the same well differs from the usual case ofobjectsbeing members of the same class only in thatthe degree of resemblance between the objectsis higherin the former.

(c)A collective name is the name of a group ofsimilar thingsregardedas a whole, the name not beingapplicableo the things taken one by one. Collectivenames may be singular,s, the British Army in SouthAfrica, the present House of Commons ; or common,as a committee, a library. Where a name may beused in both ways, the collective and distributive meanings must be carefullydistinguished.Thus the name committee is used distributivelys being applicableto each one of the many different groups formed in themanner, and with the object,which the name signifies.But as appliedto any particularne of these groups, itsuse is not distributive but collective ; it cannot be givento each or to any member composing the group, butonly to all the members together.

This distinction is of great importance ; and the neglect ofit may lead to serious fallacies or mistakes in reasoning.The word all, for instance,may be used either collectivelyor distributively all men may mean any man, or allmen together i.e.,he human race as a whole. And what istrue of all collectivelyay not be true of all distributively,r vice-versa. It is not easy to givesimple exampleswhere the distinction covers a reallydeep difference of meaning,for such cases usually occur in the discussion of difficultquestionsin ethics or philosophy. Consider Kant's dictum,ought implies can. We may interpretthis in the sensethat man is capable of realisingevery ideal which he iscapable of presenting to himself. Understood distribu-


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tively,his means that each man is capable of being anddoing everythingwhich he sees that he ought to be and do.Understood collectively,t means that though you or I maynot always be able to do everything which we see that weought to do, yet the human race can, in the course of time,realise every genuine ideal which any man is capable ofconceiving.

Some logicians e.g., Hamilton, followed by DrFowler treat collective names as alwayssingular thecommittee, the library, the regiment are treated asthe true collective terms, while committee, library,regiment are ordinarycommon terms. 4. Another division of names is into positive and

negative.Positive names imply the presence, negativeames theabsence,of a given attribute. Sometimes two different

words are used to express the two implicationssometimes the negative name is formed from the positivebya prefix.

Positive names. Negative names.Light. Darkness.Gratitude. Ingratitude.Agreeable. Disagreeable.Manly. Unmanly.

The negative name, as Mill points out, does notimply mere negation,but the presence of some otherquality;in each of the above instances the negativename impliesthe presence of an actual qualitywhich isthe opposite of the one excluded. Hence, as Jevonssays, it is often a matter of accident whether a positiveor negative name is used to express any particularnotion.

This leads us to a distinction which is of the highest


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between them the universe of discourse, not the wholeuniverse of thought and existence. Thus, white and not white are contradictories in the world of colour;and only those thingswhich may have colour must be eitherthe one or the other. Sometimes we have a pairof nameswhich themselves denote a particularsphere ; British and Alien are limited to the sphere of human beings, andwithin that sphere would be considered as contradictories,fthe view to which we have referred is to be accepted. Butit is preferableo keep to the older view and take the contradictory in the widest possiblesense, as this brings outmore forciblythe nature of pure logicalcontradiction. Wemay interpretthe pure contradictoryin such a way that itinvolves no logicalabsurdity. We need not, for instance,use the name not-man as meaning all things togetherwhich are not man, that is,we need not use it collectively.We may use it distributively,s being applicableto anything which is not man : it is exactlytherefore what Aristotlecalled it an indefiniteame. If we try to express itsdenotation, we must think, not of a chaotic mass of themost different things together,but of either this,or this,or this,or ... and so on indefinitely,hrough everythingwhich is not denoted by the original term. Those whotake the narrower view of contradictorynames, explaincontrary terms as representingoppositeswithout exhaustingbetween them the particularsphere of reference or universeof discourse ; thus, white and black are contraries inthe world of colour.

According to our view, contraries do not exhaustbetween them the universe of thought and existence;and the oppositionhich they express is of various kinds.The type to which Aristotle restricts the name of contrary opposition is the relation of thingswhichstand furthest apart among those of the same genus (Categories,h. vi.,and elsewhere);s white and black, virtuous and vicious. A more generalcase is incompatibility,.e.,the opposition of qualitieswhich cannot be possessed by the^same thing in the


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same way, as round and square, one andmany, red and green ; while red and round, large and square, c., are perfectlycompatible. The oppositionf positiveand negativenames approachesmore nearlyto that of contradictorynames. In those,the formation of the words indicatesthat the oppositionis one of the presence and absenceof a certain quality. Names which indicate contrastedclasses,British and foreign, male and female,c., arc analogous to positivend negativenames; and

these are a frequent type of contrary opposition. Butthe different kinds of oppositionwhich pairsof contrarynames express, depend on the thingsdenoted by thenames, and our understandingof the oppositiondependson our knowledge of the things. Logic can give nogeneralaccount of all the types of contrariety.Hencecontrary oppositionis real or material, while contradictoryoppositionis formal,

5. Names may also be divided into relative andabsolute.

A relative name has been defined as denoting anobjectwhich cannot be thought of without reference toanother object,or can only be thought of as part of alargerwhole. But in this sense, there are no non-relative or absolute names. Everythingis related toother things,even on a superficialiew; and if weimagine ourselves to be knowing or investigatingtsconnections as completely as possible,root and all,and all in all, its relations to other thingswould befound to have increased in extent and complexity,hefurther our knowledge had penetrated.

Hence every conceptionwhich we form is relative tosomething else ; whenever we think of a thingwe aredistinguishingt from other things. We think of a


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table,and the table is at once opposed at least tovacuity,f not to other articles of furniture. In thissense, every name is relative. It is possible,owever,to distinguish relative names in a narrower sense, asMill has done. A name is relative,hen over andabove the objectwhich it denotes,it impliesthe existence of another objectderivingits denomination fromthe same fact which is the ground of the first name :e.g., father,child, both terms implyingthe facts ofparentage; king, subject, oth implyingone of themodes of government. Such pairsof names are calledcorrelatives.

6. Let us now characterise more preciselyhe kindof idea which we use in judgment.

Why do we express our thoughts at all? Becausethought forms a common ground in which differentminds can meet, and which affords them a means ofmutual understanding. Every judgment gives information ; it pointsoutwards by means of languageto otherminds, to whom, actuallyr in imagination,t is alwaysaddressed. Hence when we express a judgment in theform of a proposition, is P, there are two conditionswhich the terms must fulfil:

(a) Each term ought to have the same meaning forthe mind using it,at one time,as it has at every othertime ; otherwise it would not be the genuine identification of a thought;

(b) Each term ought to have a meaning for otherminds beside the one which judges,otherwise no information is conveyed; and it ought to have identicallythe same meaning for all these various minds, forotherwise the information conveyed is confused ormisunderstood.

Thus we see that the meaning of a term in judging,


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is not and cannot be the privatepossessionof any onemind. But so far,we have grasped only one aspect, soto speak,of the meaning. It is not only identical inmeaning for each individual mind and identical in meaning for different minds ; it is also the thought of thesame object,whoever may think it; in other words, italways means the same thing. Thus when I speak ofthe earth, the British Constitution, Englishwriters on Logic, A library, c., c., in eachcase I refer to something real which I am thinkingabout, but which continues to be what it is and meanwhat it means whether I am thinkingabout it or not ;and I intend the same reference to be understoodwhenever I use the words. For this reason, the logical term has also been described as an identicalreference.

In the case of common terms, the identical referenceis to the common qualitiesf the objects to which thename is applicable.Common terms signify universalwhich is formed usuallyby comparison; and the generalidea of the pointsin which the thingsresemble one another is fixed by the common term. Consider,for example, the two well-known heavenlybodies called Jupiterand Sirius. Bringingthem into comparison, I observethat they agree in being small, bright,shiningbodieswhich rise and set and move round the heavens withapparentlyequal speed. By minute examination,however, I notice that Sirius givesa twinklingr intermittentlight,hereas Jupitershines steadily. More prolongedobservation shows that Jupiterand Sirius do not reallymove with equal and regularspeed,but that the formerchanges its position upon the heavens from night tonight in no very simple manner. If the comparison beextended to others of the heavenlybodies,I shall find


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26 THE NAMK, THE TERM, THE CONCEPT,that there are a multitude of stars which agree withSirius in givinga twinklinglightand in remaining fixedin relative positionto each other,whereas several otherbodies may be seen which resemble Jupiterin giving asteadylight,and also in changing their positionfromnightto nightamong the fixed stars. I have now formedin my mind the generalidea of fixed stars by bringingtogethermentally a number of objects which agree ;while from several other objectsI have formed thegeneral idea of planets This example, from Jevons,illustratesin a simplecase the formation of a universalby comparison.

We may illustrate the process also by reference to a fewof the general qualitiesof bodies. Among the qualitieswhich our sense of sightreveals to us, there is a group connected by an obvious resemblance to which we give the nameof colour. It is not easy to explainpreciselyhat is common to all the different colours,unless we are acquaintedwith the psychology and physiology of visual sensation,and the physicaltheory of light; nevertheless we are convinced that theyhave something in common, and we refer tothis by the general idea named colour. Similar observations apply to the general idea of brilliancy. Again, theuniversal property of Gravitation,hich is common to all thedifferent degrees of heaviness, is named weight ; andsimilarlywith density. Now to take a more complexcase. Metals, such as gold, silver,copper, lead, c., resemble one another in certain definite ways ; each of themhas colour of one kind or another, each has some degreemore in one case, less in another of brilliancy,eight,anddensity: hence the universal, metal, includes the generalideas, some kind of colour, some degree of brilliancy,fweight,and of density. If we pursue the subjectscientifically,e have of course to include the ideas of other qualities in the universal ^., that metal is an element, is agood conductor of heat and electricity. nce more, weobserve that some animals walk, others fly,and so on ; that


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some breathe through lungs, others through gills,othersthrough the skin; that some produce young alive, otherslay eggs, others multiply by division. Hence we form theuniversals, locomotion, respiration, reproduction,which are included in the general idea animal, somekind of reproduction,f respiration,nd of locomotion.When the general idea or universal meaning is defined with precision,it is called a concept.

We will now compare the relation between changes ofconnotation and changes of denotation in terms whichare related /.^, which denote related kinds of things.The connotation of the term ship is definite enoughfor an illustration. Increase the connotation to steamship ; what change have we made in the denotation ?Obviously there are fewer steam-ships than ships.Increase the connotation to screw steam-ship ; thedenotation is further decreased. We may arrange suchrelated terms in a series of increasingconnotation anddecreasing denotation, or vice-versa: Ship, Steam- ship,Screw steam-ship,Iron screw steam-ship,British ironscrew steam-ship. Here the connotations form an increasingseries,the denotations or applications diminishing series. Hence the followingrule is given : Asconnotation increases, denotation decreases ; as denotation increases, connotation decreases. The rule appliesonly to terms which can be arranged in a classifi-catory series. This impliesthat the connotations ofthe terms are fixed, and accepted as practicallydequate (see 7, ad finem); and that the terms arcarranged in a series, in ascending or in descendingorder of divisions and subdivisions. The rule is sometimes wrongly stated, and is so exposed to objectionswhich are reallyirrelevant. Jevons states it as thoughit appliesto the same term. If so, the rule might fail


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in two ways. We might,through increase of knowledge,expand the connotation of a term without decreasingits denotation ; and we might find new individualsto which the term is applicable without decreasingthe connotation e.g., increase of populationdoes notchange the meaning of man. But the rule wasnever meant to apply to what happens to a singleterm through increasingknowledge or increasingumber of individuals.

The best illustrations of the law are found in thesciences of classification. Thus, the adequate definitions of Dicotyledon,Thalamiflorcc,anunculacecz, Ranunculus,Ranunculus ficariaform an increasingseries ;the applicabilityf these terms is a diminishingseries.The older logiciansere fond of the followingillustration,which has therefore acquired a certain historicimportance:

Connotation least,denotation highest.Beings

(i.e.,nythingexisting, beings in general)material beings

(i.e.,atter in the widest sense)organic material beings

(i.e.,he whole world of life,animal and vegetable)Sentient organic material beings

(i.e.,nimals)Rational sentient organic material beings

(i.e.,en)This Man.

Connotation highest,enotation least.In this case each term is predicable of the following


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3O THE NAME, THE TERM, THE CONCEPT,

that of being an element to all metals. As we shall see(ch.VI. 2),this is equivalentto saying that the newqualitymust not be a Definition or a Proprium ; itmust be a Differentia.

7. The next necessary questionis as to the limits ofconnotation.

The traditional view is that the connotation consistsof a perfectlyefinite group of attributes which areneither more nor less than sufficientto mark off a classfrom all other classes. These attributes are expressedin the definitionf the term. On this view of connotation some importantlogicaldistinctions depend, as thatbetween verbal and real predication(ch.III. 2).But what the student has to notice is the implicationthat to each term there belongs a fixed and definitemeaning. This is a logicalideal rather than a psychologicalfact ; and for this reason many of the rules ofthe Aristotelian Logic seem artificial,they are notintended to have reference to the shiftingonnotationsof many of our ordinary terms. Logically,it is ourbusiness to make the meanings of our terms definite,and to keep them so, changing them only when a realadvance in knowledge requires it. Thus, in Plato'stime the connotation of the term sun was thebrightestf the heavenlybodies which move round theearth. This clear and definite idea had to be changedto what we now mean by the sun in consequenceof advancing knowledge. The connotation of a termshould be made clear and distinct,nd then remainfixed as long as possible,being revised only whenrevision is inevitable.

How littleattention is paid to this logicalrequirementin the ordinaryaffairs of life was shown by Locke in avigorouspassage in his Essay concerningHuman Under-


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standing(Bk.III. ch xi.) He that should well consider the errors and obscurity,he mistakes and confusion,that are spread in the world by an ill use ofwords, will find some reason to doubt whether language,as it has been employed, has contributed more to theimprovement or hindrance of knowledge amongst mankind. How many are there that, when they wouldthink on things,fix their thoughts only on words,especiallyhen they would apply their minds to moralmatters ; and who then can wonder if the results ofsuch contemplations and reasonings, whilst the ideasthey annex to them are very confused and very unsteady,or perhaps none at all, who can wonder, Isay, that such thoughts and reasoningsshould end innothing but obscurityand mistake, without any clearjudgment or knowledge ? This inconvenience in an illuse of words men suffer in their own privatemeditations ; but how much more manifest are the discordswhich follow from it in conversation,discourse,andarguments with others. For language being the greatconduit whereby men convey their discoveries,reasonings,and knowledge from one to another ; he thatmakes an ill use of it,though he does not corrupt thefountains of knowledge which are in thingsthemselves ;yet he does, as much as in him lies,break or stop thepipes whereby it is distributed to the public use andadvantage of mankind.

The only remedy for this condition of things is torealise clearlywhat are the ideas for which words stand,and to take care that for each term there shall always bethe same definite idea.

Some logicianshave proposed to give a wider meaningto connotation, and to understand by it,all the knownqualitiesf the thing,or (ifthe term denotes a class)all


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the known qualitiescommon to the members of theclass. But with the growth of experiencend knowledge,we usuallyfind that many of these known qualitiesreunessential,and some are insignificantrom every pointof view, and we simply leave them out of account informing our idea ; hence they do not form part of theconnotation. It is sufficientif the connotation includesthe important or essential attributes. The connotation of man does not include an idea of thepeculiarshape of the ears, of the capacityfor laughter,and other known qualitiesommon to the class.

There is a third possiblemeaning of connotation,that it is all the qualitiesf the thing(orclass),hetherknown to man or not. The word is not employed inthis sense, for it would introduce fundamental confusioninto Logic. If we assume that Tennyson's well-knownlines on the flower in the crannied wall express aphilosophicaltruth, that the complete and perfectknowledge of the flower would involve the knowledgeof what God and Man is, then, usingconnotationin the sense that we now speak of,God, Man, and thewhole universe would be part of the connotation of theflower. But complete and perfectknowledge is anideal so far beyond our present attainment,that we haveno rightto say what it would or would not imply.

Our result is therefore as follows. The questionforLogic is never what a name means for you or me, butalways what it ought to mean. And what it ought tomean must be somethingdefinitelyixed,the idea of theimportantqualities or, expressingthis in other words,the qualitiesn account of which the name is given,andin the absence of which it would be denied. Our idea ofthese depends on our knowledge of the thingsreferred toby the name, and will change as that knowledge grows ;


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AND THE LAWS OF THOUGHT. 33but the connotation of the term can never be used tosignifynythingmore than what we actuallynow.

8. We have now to examine the question,hetherevery term has both connotation and denotation.1

We saw in 2 that some terms at least have bothkinds of meaning. The denotation consists of theparticularnstances to which the term is applicable.The connotation is the general idea of the attributeswhich are exemplifiedn the particularnstances. Theconnotation is logicallyhe primarymeaning,the denotation is the secondary; for if we wish to refer to objects,otherwise than by pointingwith the finger,e must doit by means of the connotation of their name ; theconnotation determines the denotation ; and when weare asked to define a term, we know that we are toexplainitsconnotation. This is fullyadmitted by Mill ;for althoughhe says that the term signifieshe subjects[itsdenotation]irectly,he attributes indirectly,edoes not mean that the fact has any logicalsignificance*It is not always a fact ; and when it is so, it is becausewe have no sufficientlyxact ideas correspondingtomany of the terms which we use, and so find it easierto think in denotation. Here we have a psychologicalfact,which is logicallyserious defect of thought.

Now from 6 we see that not only some but allterms have the two kinds of meaning : every name hasa primary meaning, the universal,the connotation, theintension,r content ; and it also refers to actual orpossibleinstances of the content.

This terminologyhas unfortunatelyeen reversed byMill. He divides terms into connotative and non-connotative : but he means by a connotative term,

1 This discussion has specialeference to Mill's views, as set forthin Book I. ch. ii. 5 of his Logic.

C


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one which denotes a subject,nd impliesan attribute,as all common terms do ; while a non-connotative termis one which signifiessubjectonly, or an attributeonly. He then proceedsto argue that proper names andabstract names are non-connotative, ince the formersignifyubjectsonly,the latter attributes only. But thewhole question,which is thus raised,has been throwninto confusion by the ambiguityof the word connota-tive ; for Mill uses it of terms whose primarymeaningis denotative,in our sense of the word; terms whichdenote a subjectand imply an attribute. This use ofthe word connotative is a revival of a scholastic use,1which should be remembered only to be avoided. DrFowler adopts Mill's view as to abstract and propernames ; but his terminology is consistent with thatwhich we have already explained. He divides termsthus : (a)those which are both connotative and denotative ; (b) those which are connotative only (calledbyMill non-connotative i.e.,bstract terms); (c)thosewhich are denotative only (calledy Mill non-connotative i.e.,roper names).

Practically,herefore,the question is this : whethernames of attributes as such have connotation withoutdenotation,and whether proper names have denotationwithout connotation. Let us take the former case first.

It is said that a name such as colour, signifyingmere attribute,as no denotation. But as long as weconsider a term by itself,n detachment from a proposition,we cannot see what is reallyinvolved in its meaning. When considered in its place in a proposition,the name of an attribute expresses substantiation of theattribute ; the abstract is transformed into the concrete(cf. 3). This is obvious when the term occurs in the

1 On this historical point,see Professor Minto's Logic,pp. 46,47.


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plural: a coat of many colours1''; different sizes maybe had. And it is true even when the term is used ina purely abstract sense: colour (i.e.,olouredness ingeneral),extension,density,are propertiesf bodies ; red is the complementary colour to green Abstractterms of this kind have no plural; and hence theconnotation and denotation coincide.

It is said,again,that proper names have no connotation. This question does not concern singularnames,in all of which the two sides can be distinguished.Many of them are speciallyonnotative : the honourable member who brought forward the present motion.

Settingthese aside,it is not to be denied that whenwe hear a proper name mentioned by itself,n detachment from a proposition,hen (a)itgivesus no information as to the qualitiesr characteristics of the person orplace,unless we are acquainted with him or it already;names like Dartmouth, Oxford, which signifyparticularsituations,nd personal names which are supposedoriginallyo have signifiedhe occupation of the individual bearing them, have long ceased to have anysuch meaning, (b)And when we know the qualities,c., of the individual denoted, then when the propername is changed, the new name tells us nothing different from the old : 1 we may contrast this with whatis signifiedby changing the name of a thing fromvegetable to animal. (c)Also it is the fact thatthe proper name is, as a rule, not given in order tosignifyny attributes ; in the case of a child,it couldnot be meant to signifyattributes which are mostlydeveloped after the name is given. Hence we aretold that the name comes to suggest a number of these

1 The case of a woman changingher name on marriage seems theonly importantexception.


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36 THE NAME, THE TERM, THE CONCEPT,qualities,o any one who hears it and is acquaintedwith the person who bears it. But it is given not tosignifyhe qualitiesut to identifyhe individual.

Hence the questionis,whether what is suggestedby aproper name does or does not correspond to what ismeant by a common term or an ordinarysingularerm.Mill and some others maintain that there is no analogy;there is a difference of function so complete as to justifyus in saying that proper names have

no significationin the strict sense of the word. Against this,e maintain that the proper name has no fixed or co?istantbut an acquiredconnotation. When used in a proposition i.e.,hen used in the concrete as the designationof a definite individual the name acquiresmeaning inthe strict sense, not merely suggestions or associations. The whole peculiarityf proper names consistsnot in having no meaning, but in the fact that their use(asthe identification of a particularindividual)reventsthe meaning from becoming general.

The main proof of our positionconsists in the factwhich Mr Bosanquet has pointed out (EssentialsfLogic,p. 92). The convention of usage, which prevents a proper name from becoming general i.e.,rombeing cut loose and used simply for its meaning isalways on the pointof breakingdown. This actuallytakes place when the meaning which a proper nameacquired while it was used as a designationfor a particular individual,s made general,and the name is usedas a type: A Don Quixote, a Daniel, a secondDaniel, a Solon, a Croesus, a Nero, a CaesarBorgia. And as a matter of fact there are numerousexceptionsto the statement which we admitted, that aproper name has no fixed meaning. Any name whatever impliesn existence of some kind ; and if we know


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38 THE NAME, THE TERM, THE CONCEPT,The result of this discussion is that the general con

clusion of 6 remains unshaken ; every name has bothconnotation and denotation. The two kinds of meaning belong to every significanterm.

9. The subjectto which we will now pass is closelyconnected with the relation of terms to their concepts(thesubjectof the present chapter),nd the relation ofthe concepts to one another in a judgment (thesubject of the two followingchapters).What are calledthe Laws of Thought have a reference to both theserelations.

The word law is not without ambiguity. Most writerson Logic have distinguishedwo chief meanings. Inone sense of the word we speak of Laws of Nature,which are generalstatements of what uniformlyhappens.A singleexceptionto such a law would make it nolonger a law of Nature. In another sense, a law is aprecept or rule laid down by some authority, an injunction or command addressed to persons who arecalled on to obey it but have it in their power to disobey. This use of the term is exemplified in suchphrasesas law of the land, law of conscience. Theauthorityremains independentlyof its violation by individuals. When speaking of a Law of Thought, weuse the term mainly in this second sense. Men constantlyfall into errors and confusions in their thinking,and so disobey the laws of thought,although as arule they do not do so consciouslyr deliberately.

The Laws of Logic,then,set up a standard to be followed. They may be compared with the laws of Grammaras regards correct speakingand writing. The scienceof Ethics also endeavours to formulate a standard,consistingf laws of rightconduct which are far from beingconstantlyrecognisedin life. Hence Logic has been


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called the Ethics of Thought. The student will alreadyhave observed the applicabilityf this title. In dealinglogicallyith the concept,for instance,our main businessis not to inquirewhat kind of Universals are formed inthe average mind, as a matter of fact,and what are theprocesses of thought which lead to their formation ;we begin to formulate and shall formulate more fullyin the sequel an ideal of what the Universal oughtto be. This is the characteristic of logicaltreatmentthroughout.

In this way we have answered the over-discussed question,whether Logic is a Science or an Art. A mere Art would bea body of practicalrules,having no scientific connectionamong themselves ; gathered, perhaps, from haphazardexperience,r gathered from very various object-matters,s the art of music. But Logic is first a Science, a systematic body of doctrine,of theory, and then a science whichaims at distinguishingorrect principlesof thought. Hencemany logicianshave described it as both a Science and anArt; e.g., Mill in his Examination of Sir W. Hamilton'sPhilosophy,speaks of Logic as the art of thinking,whichmeans correct thinking, and the science of the conditionson which correct thinkingdepends. Logic may be definedas a practical,r better,as a normative or regulative,science.

10. In a wide sense, the phrase Laws of Thoughtmeans all the generalprinciplesr types of Thought (seech. I. 2) which we treat of. In a narrower sense,it signifiesertain fundamental principleshich lie atthe basis of inference.

Since the time of Aristotle,three such principlesavebeen made of fundamental importance. The first ofthese was not explicitlytated by him. It was subsequentlyknown as the Law of Identity, and assumedthe form : a thingis identical with itself ;A is A.The second principle,fterwards called the Law of Con-


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tradiction,1as thus stated by Aristotle : the propositions A is B and A is not B cannot both be truetogether The third law, now known as the Law ofExcluded Middle, was formulated by Aristotle thus : ofthe two propositionsA is B and A is not B, one mustbe true and the other false.

ii. As it stands,the Law of Identity,A is A,does not giveus any information. It may, however, beinterpretedo as to make it a genuine principlenwhich the very life of Thought depends.

(a)We have seen that in actual thinkinge requireterms to identifyur thoughts. The Term identifies a universal meaning ( 6). The Law of Identityhasan importantapplicationo this relation. Let A denoteanythingthoughtabout, any more or less defined ideawhich is distinguishedrom other ideas so far as to beindicated by a singlesymbol in language,a name orterm, M. Then to say that A is A means that Mmust always stand for the same A, the same fordifferent minds and for one mind at different times.Terms must have fixed meanings, each clear in itselfand distinct from others. If the meaning of a termis changed, it should be done deliberatelynd for asufficient reason.

(V)In another sense, the principleeans that what istrue must be consistent with itself;nd this is one ofthe necessary tests of truth. This principleas laiddown by Aristotle,hough he does not attempt to cast itinto the form of a Law of Identity(An.Prior.,i.32) :All truth must be consistent with itself in everydirection. Aristotle is here thinkingspeciallyf theconsistencyof a conclusion or consequence with the

1 Sometimes referred to, more appropriately,s the Law of Non^contradiction,


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premises; but the principleay be made universal. Ifany system of doctrines or set of statements is true,they must be consistent among themselves.

The dictum that only little minds burden themselveswith the effort of attainingto a rigidconsistency,xpresses atruth which has a practicalnd not a logicalbearing. Wemust not sacrifice ideas which contain truth because wecannot make them self-consistent in the precise form inwhich we have them before us. It is possibleto be assured-through a power of judging (not logicallyjudging)which is developed by life and experience that certain ideasare fundamentally true, while yet we cannot exhibit theirconsistency in a satisfactorylogicalform. To sacrifice truthin such cases for the sake of a rigidlogicalconsistency,issimple or rather complex folly. Yet this does not alter thefact that, so far as the ideas are true, to that extent they areself-consistent.1

12. The Law of Contradiction, that the propositions A is B and A is not B cannot both be truetogether,is another aspect of the Law of Identity,ndcorrespondsto it in meaning.

(a) Just as the principleof Identity secures theidentical reference of a term to a meaning, so the principleof Contradiction secures the same result by forbidding a term to be diverted to another meaning in thesame discussion or discourse. While we are treatingfone subject,e must fix the meanings of our terms, andkeep to the same meanings.(V) Just as the principleof Identitydeclared thatall parts of truth must be self-consistent,o the principleof non-contradiction declares that the different parts oftruth cannot be incompatibleith one another. We mayillustrate this by referringo the manner in which certaintypes of philosophicaloctrine have been maintained.

1 The philosophicalspects of the Law of Identitywill be furtherconsidered in ch. XI. 8 2.


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If we find a thinker maintaining as essential parts of hissystem the following doctrines : (i) we know, with thehighest degree of certainty,that the Reality which liesbehind the phenomena of mind and matter is unknowable,and (2)we know with the highestdegree of certaintythat itexists,that it is infinite,ternal,the Cause of all things,andmanifested in all things: then, by mere comparison of theideas employed, we see that the system is fundamentallyinconsistent. Realityis declared to be altogether unknowable,and also to be knowable in certain important respects.Both statements cannot be true.

If,again,we find it maintained that the Association ofIdeas is a law of connection among the units of whichthe mind is composed, which are distinct sensations ;that, by this law, a present sensation may revive anotherone with which it was experienced at some former time, wefind the doctrine wrapt in inconsistencies when we ask,What happened to the second sensation in the intervalbetween its first experience and its revival? Here themind is firstdeclared to be only a series of sensations,eachof which disappears to give place to the next; then themind is declared to be such that a sensation when itdisappears can leave behind a permanent effect or tracewhich can come up into consciousness. Both these viewscannot be true.

If,once more, a scientific man denounces with vigour theassumption of a controllingdesigning Power at work in theproduction of certain natural events, and yet allows himselfto speak as if Nature were a Power acting with a purpose, and is unconsciouslyinfluenced by this very idea inhis explanation of natural facts,then we may bring the samecharge. On the one hand it is maintained that no naturaleffects are produced by a superhuman designingPower; andon the other hand, that some effects are so produced.

The inconsistent doctrine or statement may alwaysbe reduced to the one fundamental form, of attemptingto make the propositions A is B and A is not B true together. In this form the principleis stated byAristotle (Metaphysics,V. iii.) It is impossiblethat


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the same predicateshould both belong and not belongto the same thing at the same time and in the same wayA thing may have different qualitiest different times,as in the changes in a person'scharacter ; and it mayhave a quality in one respect, and not have it inanother, as in the celebrated shield that was gold onone side and silver on the other ; but these facts do notconflict with the law of Contradiction as Aristotle statesit. Aristotle pointsout that the denial of this principlewould be the denial of the very possibilityf thinking.

13. The law of Excluded Middle says that of thetwo propositions A is B and A is not B, one mustbe true and the other false. In this form the principlewas laid down by Aristotle ; and the student will observeits close connection with the principlesf IdentityndContradiction as regardsthe meanings of terms and theconsistency of propositions.he applicationof theprinciples plainin proportionas A and B are exactlydefined. If we are in doubt as to where one thingbegins and another ends, we are in doubt as to thepreciseapplicationf our principle.This may happenin cases where we do not find a perfectlydefinite limitto an event in space or time e.g., when something isin the act of occurring,we seem unable to say, either it has happened or it has not happened. Thesun may

be just rising without having risen or not having risen. But as soon as we have attacheda precisemeaning to rising, n the case of the sun, e.g., if we make it mean that the actual globe is visibleabove the true horizon, then the law of excludedmiddle is applicable.When we are speakingof naturalqualitiesuch as heat, which always have degrees,thenagain we cannot say that a body must either be hot or not be hot until we know that some definite


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degree of heat is signifiedy that word. And in thecase of the great divisions of Nature, which seem toshade off into one another, as animal into vegetable, and vegetable into inanimate matter, wemay be in doubt as to the applicationof the law ofexcluded middle to an individual on the borderline ofone of these divisions ; we may not be able to sayeither that it is an animal or that it is not an animal,it may seem to be something between the two. Butthis results from our imperfectunderstandingof whatanimal life reallyis ; the greater the lightwhich isthrown on this problem,the smaller the extent of thedoubtful borderland,of thingswhich seem neither in theclass of animal life nor outside it.

Sometimes the law of excluded middle has beenquestioned through a mere confusion. The contrastwhich the law of thought makes, is between two propositions one of which simply denies or contradictsthe other, between an affirmative and a negativeproposition,This water is hot, this water is not hot,

This paper is white, this paper is not white,This line is longer than that, this line is not longer

than that, This opinionis simplytrue [i.e.,rue without qualificationr limitation],this opinionis simplynot true. In each of these pairsof propositions,neand one only must be true ; there is no third alternative.But it is not uncommon to apply the law to a pairof propositionswhich affirm contrary predicatesof anobject,nd to say (takinghe last of the above examples)that either this opinion is simplytrue or it is simplyfalse. Here there may be a third alternative, t maybe a mixture of truth and error. Similarly,etweenwhite and black, hot and cold, greaterthan, and less than, in each case there are other


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46 THE NAME, THE TERM, THE CONCEPT,only must be true. The second and third laws give aprogressivenfolding of the implicationsof the first.

14. Since the time of Leibniz an importantprinciplehas been introduced in Logic and placed by the sideof the three laws of which we have spoken. It is calledthe law or principlef Sufficient Reason, and is usuallystated thus : For everythingthere is a sufficient reasonwhy it is so rather than otherwise. In this principletwo different laws of thought are brought together,which must be distinguished,nd, for the purposes ofelementary Logic,carefullyseparated.

(a)The first principletates that for every proposition which is held to be true, there must be reasons forregardingit as true, arguments which may be broughtin support of it. It must be capableof being shownas the conclusion from certain premises. In otherwords, every judgment, when questioned,expands intoan inference. This does not apply to the propositionswhich state the laws of thought ; they cannot beproved by argument, from premises to conclusion,they cannot be, in this sense, inferred for all argumentand all inference depends upon them.

The principlethat every judgment justifies itselfby expanding into an inference, is reallypart of awider principle,that all parts of our knowledge, sofar as they are true knowledge, are connected together. We know that any statement, once admittedto be true, may have a modifyingeffect upon any otherportion of our knowledge. All the current scientific,theological,nd philosophicalontroversies afford abundant illustrations of this fact ; and it is a fact,becauseevery judgment is at bottom connected with everyother one. We cannot show this connection, in manycases ; but most of the controversies alluded to consist


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in the endeavour to discover the connection betweendifferent parts of knowledge, the results of differentsciences. It has been said,for instance,that Man'splacein Nature has been the cause cclcbre of the nineteenth century. And when we have succeeded in reconcilingdifferent results,e find that they mutuallysupport one another.

(b)The second principleincluded under the Lawof Sufficient Reason states that for every event in thereal world there must be a cause, without which theevent could not happen. This is properlydescribed asthe Law of Universal Causation ; and we shall have toconsider it later,along with other principlesf InductiveLogic. These also are Laws of Thought, principleson which knowledge depends, and the trustworthinessof which is to be granted if not only knowledge butthought itself is to be possible.

We have stated the principlesof Contradiction and excluded Middle as they were formulated by Aristotle,whohad in view two contradictory propositions contrastedwith one another. Later logiciansstated the laws in theform a thing cannot be both A and not A, a thing-must be either A or not A. * Here, instead of two contradictory propositions,e have a pair of contradictoryterms opposed to one another. Aristotle did not use thenomen indefinitum not A. These later statements ofthe principlesare of course true ; but they have not thelogical significanceof Aristotle's statements, for they donot express what formal inconsistencyor contradiction is. Not A is a purelyindefinite term ; and though we call itthe contradictory term to A, the relation between these two

1 The followingvariations are sometimes found : for the Law ofContradiction, a thing cannot both be and not be ; a thingcannot be other than itself, A cannot be not A. And for theLaw of Excluded Middle : a thing must either be or not be.


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48 THE NAME, THE TERM, THE CONCEPT,does not give us the meaning of the logicalact of contradiction. Contradiction takes place only between propositions; and only when one propositionaffirms a predicateand the other simply denies it of the same subject. And ofsuch propositions,oth cannot be true, while one must betrue and the other false.

EXERCISE I.

The followingare selected questionson the subjectsdealtwith in this chapter :

1. What is the logicaldifference,f any, between Substantives and Adjectives? [L.]

2. Describe the nature of Collective terms, examining inparticularany difficultiesin distinguishinghese and Generalterms. [C.]3. Explain what is meant by the Connotation of a name.Has it any connection with the etymology of the name?[C]

4. Is there any distinction to be drawn between Singularand Proper Names ? What views are or may be held asto their being mere unmeaning marks ? [L.]

5. Explain the distinction between Concrete and Abstractterms. Does this distinction correspond to that betweenSubstantives and Adjectives? May differences of quantitybe recognised in the case of Abstract terms ?

6. Are there any terms without Connotation or withoutDenotation? How far has controversy on this questionarisen from the ambiguity of the word connotation ?[StA.]

7. Give a careful explanationof the nature of RelativeTerms. [L.]

8. Distinguish between Positive and Negative names.What ambiguity is there in the use of such a name asnot- white ? [C]

9. Which of the usual divisions of terms do you conside

an introductory text-book of logic 1000011061

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