Logic in Its Application to Language

Front matter

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Preface

If the term Logic be a misnomer, the reason for its use lies in the contrast between the practice of the ordinary grammarians and the logicians. Of the former, many admit that the nature of terms and copulas, along with the structure of the proposition, is a matter which lies within their own jurisdiction. On the other hand, there are plenty of logicians who treat everything anterior to the syllogism as phenomena, not of Logic, but of Language. The practice, however, nowhere, or but rarely, coincides with the theory. Look in an ordinary grammar for anything about propositions, and, in ninety-nine cases out of a hundred, you will look in vain. It is in the books upon Logic that you will find them. At the present moment I remember but one grammar written in English, and written for the practical purpose of teaching a foreign language rather than with a strictly scientific view, wherein the truly grammatical phenomena of the structure of propositions are exhibited. This is Dr. Lee's Hebrew Grammar ; and even here the notice is short, and appears no earlier than the first page of the Syntax. Throughout the Etymology no word about propositions is spoken. I repeat, however, that in thus limiting the grammars that treat of a proper grammatical Logic, I speak from memory. There may be many others. Nevertheless — whether many or few, they bear but a small proportion to those which relegate the subject to the domain of the logician.

And he always supplies them. Yet they are not his own wares ; and he would manifestly and advantageously disencumber his subject of more than one unnecessary appendage if, presuming the gram-

a 2

VI PREFACE.

marians to have cultivated their own domain up to its true boundary, he supposed, on the part of his reader, a knowledge of Terms, Copulas, Propositions, Names, and the like, and began his own subject where the preliminaries supplied by another ended.

Enough, however, of the remarks upon the title of the work. The work itself is by no means an ambitious one. Saving the sections upon the convertibility of the pronoun, and those wherein the connotation of Names is quantified, it contains next to nothing of original matter. The importance, however, of these I place high, especially as elements in the Natural History of Language.

This is a sea upon which, if I consulted my inclinations only, I would willingly launch. But the mass of detail is enormous, whilst the principles of criticism that should regulate its construction are but faintly foreshadowed. Nevertheless, whenever such a Natural History is attempted, the remarks just alluded to will find their place.

So far as they do this the present treatise contains materials connected with the advancement rather than the mere diffusion of knowledge. In all other respects, however, it is educational rather than scientific, advertising and promulgating what is known rather than investigating and illustrating the unknown.

The line of study to which it is more especially preparatory, so far as it deals with Logic per se, is easily seen, inasmuch as it manifests itself transparently through the names of the auchors most especially quoted, and the nature of the (perhaps) over-abundant extracts. These point to the writers

PREFACE. Vll

who, above all others, have within the laAt few years carried Logic beyond the point where its revivers (by whom I mean the school to which Archbishop Whately has been the Coryphaeus)' left it — Mill, in his System of Logic ; De Morgan, in his Formal Logic ; Boole, in his Laws of Thought ; and Sir William Hamilton, in his DiscussioTis on Philosophy and his edition of the Works of Reid.

I repeat the statement that the present treatise is written for young students. And here the title Logic has its disadvantage. To many it conveys the idea of something subtle, metaphysical, difficult, sophistical, and the like ; something useless, or worse ; something quite as difficult as profitable — difficult, at least, to students of an early age and uncultivated understandings. To those who think loosely enough to think thus, the idea of boys being employed upon what they may choose to call chopping Logic must be ridiculous.

Be it so. I wish the name were more popular. Popular, however, or unpopular, it is one with which even the unlearned are acquainted. That Logic is neither nonsense nor sophistry I shall not attempt to show. I shall only ask how far it is difficult — difficult for young students, too difficult for being taught in schools.

Many of the studies of youth are held to be adapted to the youthful capacities not so much because they are more or less easy, but because they happen to be taught. When such is the case, the particular branch of education is not taught because it is easy but is easy because it is taught. . Where there are many teachers, methods of instruction improve, simply from the practice of

VU1 PREFACE.

communicating knowledge being general Opinions upon points connected with it become interchanged. Errors have a tendency to become exploded. Ideas are ventilated ; the result being that subjects lose much of their difficulty when they lose their novelty.

This is not the case with Logic and its allied subjects. There is no trained body of teachers, no series of explanatory books, no Logic made easy.

The exact time of life for the study of elementary Logic is not to be given in years and months. The age, however, at which ordinary grammar, as it is usually taught, is understood is the time of life at which anything conveyed by the forthcoming pages can be understood also. How far the meaning of such words as Substantive, Adjective, Noun, Concord, and the like, along with the so-called rules of Orthography, Etymology, Syntax, and Prosody, is actually understood, teachers in schools and classes know better than I. They have, doubtless, too good reasons for teaching them, even when not understood ; as is too often the case.

Now what I hold respecting the logical part of Language as compared with Grammar as usually taught is this —

1. That, as far as the thing taught is to be understood, Terms and Copulas are no whit more unintelligible or difficult than Nouns and Verbs.

2. That if the memory is to be appealed to without the understanding, the appeal may as well be made for Logic as for Grammar.

This means that where Grammar can be taught, Logic can be taught also, the one subject being in

PREFACE. IX

reality no harder or more inaccessible than the other.

The real amount of thought is much the same on both sides; indeed, the thought is of the same kind. It results in the analysis of what we say or write, and the observation of what we think. The terminology certainly is the easier in Logic. The logical terms remarkable for either their length or exotic origin are only three in number — Categorematic, Syncategorematic, and Hypercategorematic; and these may (at first), by a little management on the part of the teacher, be dispensed with. Of the remainder, the list is but short. It consists of —

Subject,

Concrete,

Predicate,

Abstract,

Copula^

Denotation,

Term,

Connotation,

Proposition,

Summum Genus,

Substance,

Infima Species,

Attribute,

Subaltern, and a few others less distantly removed from the language of common life. Will any one say that these are more difficult of either explanation on the part of the teacher, or remembrance on the part of the learner, than the longer and more technical list, consisting of names like —

Article, Adverb,

SubstaD ti ve, Preposition,

Adjective, Conjunction,

Noun, Interjection,

Pronoun, Copulative,

Verb, Disjunctive,

Participle, Indicative,

X PKEFACE.

Imperative, Potential,

Infinitive, Conjunctive,

and the like ?

If Logic be too difficult for beginners, Grammar is too difficult also.

It is submitted, however, that the real difficulties lie in the facts already alluded to, viz. the slight extent to which the subject has been made a branch of early education ; the intrinsic difficulties of the subject being but small.

The sections whereof the numbers stand in parentheses (56), need not be attended to at the first reading.

Part I. Propositions

PAGE

§ 1. Statements, Assertions, Declarations, or Propositions . . . ... . ... .1

§ 2. Two parts, members, or constituent elements necessary to the structure of Propositions. — The

two Somethings 6

§ 3. The third Part, Member, Element, or Constituent

of Propositions — the word is . . .9

§ 4. It is coming 10

§ 5. Loaves are dear, <fcc 11

§ 6. I am coming, &c 11

§ 7. A Proposition consists of three Parts, and no fewer 12

§ 8. Apparent exceptions 13

§ 9. A Proposition consists of Three Parts, and no more.

— Apparent exceptions 15

§ 10. Propositions Affirmative or Negative . . .16 § 11. Special names of the three Parts, Members, Elements, or Constituents of a Statement, Assertion, Declaration, or Proposition — Subject, Predicate,

Copula 18

§ 12. Order of the three Parts, Members, or Elements, of

a Proposition — Copula in the middle . . .19 § 13. General name for Subject and Predicate — Term . 21 § (14.) Remarks on the Copula. — Apparent absence of a

Predicate 22

§ (15.) Remarks on the Copula. — Division between the several Parts of a Proposition. — Incidence of the Negative Element! — Negative Predicates (?) .23 § (16.) Differences between the logical and philological

view of Propositions 27

§ 17. Questions 31

XU CONTENTS.

PAGE

§ 18. Question s of appeal 33

§ 19. Commands 34

§ 20. Grammatical Propositions of three kinds— declaratory, interrogative, and imperative . . .35 § 21. Practice in columns. — Words capable of forming,

by themselves, Terms 35

§ 22. Practice in columns. — Words capable of forming

Predicates, but not capable of forming Subjects 37 § 23. Practice in columns. — Words capable of forming

both Subjects and Predicates . . . .39 § 24. Practice in columns. — Words capable of forming

both Predicates and Copulas .... 40 § 25. Practice in columns. — Words capable of forming

only parts of Terms 42

§ 26. Propositions Universal or Particular . . .46

§ 27. Many-worded Terms 49

§ 28. Many-worded Copulas. — Negative element compound 57

§ 29. Propositions isolate or connected — Therefore . 57 § 30. Propositions isolate or connected — Because . . 60 § 31. Propositions isolate or connected — If — And . . 60 § 32. Propositions isolate or connected — As (or since),

FOR, THEN 61

§ 33. Propositions isolate or connected — But . . 62

§ (34.) Sketch of the structure of the Ordinary Syllogism

— its mechanism 62

§ (35.) Structure of the Ordinary Syllogism. — Combination of Propositions. — Mood . . . .71

§ (36.) Structure of the Ordinary Syllogism. — Combinations of Terms. — Figure 75

§ (37.) Structure of the Ordinary Syllogism. — Combinations of Propositions and of Terms considered together. — Mood and Figure . . . .77

§ (38.) Structure of the Ordinary Syllogism. — White. —

Socrates. — Some 80

§ (39.) Structure of the Ordinary Syllogism. — Quantity

or Extent of the Predicate . . . .83

§ (40.) Operations on the Ordinary Syllogism — Strengthening and Weakening .... 85

* (41.) Operations on the Ordinary Syllogism — Conversion and Reduction 86

CONTENTS. XI11

PACM

§ (42.) Structure of the Syllogism illustrated by treating its Terms as the Names of Glasses. — Is equivalent tO INCLUDED IN 87

§ (43.) Structure of the Syllogism. — Symbolic Representation of Terms by means of Letters . . 89 § (44.) Propositions Categoric or Hypothetic . . .96

§ (45.) Mnemonics 97

§ (46.) Analysis and Synthesis 101

§ (47.) Rationale of the Ordinary Syllogism. — Its Terms viewed as the Names of Classes. — The dictum de

OMNI ET NULLO . 104

§ (48.) Rationale of the Ordinary Syllogism. — Its Middle

Term viewed as a Measure 108

§ (49.) Rationale of the Ordinary Syllogism. — Its Terms viewed as expressive of the co-existence of certain Attributes 109

§ (50.) Rationale of the Ordinary Syllogism. — The Middle Term always in the Premises, and never in the Conclusion Ill

§ (51.) The Place of the Middle Term in the several

Figures.— The Figures four in Number . .114

§ (52.) The Moods.— Mood aSid Figure.— A Real and Rational Relation of the Middle Term essential to the Perfection of the Syllogism . . . .118

§ (53.) The Mnemonics. — What is meant by their Consonants. — Reduction 122

§ (54.) The Middle Term, as Contained and Containing.

— Perfection of the First Figure . . . 129

§ (55.) Contained and Containing capacities of the Middle Term. — Predicates Containing, Subjects Contained, Terms 130

§ (56.) Imperfection of the Second Figure. — The Middle

Term not really Middle 132

§ (57.) Imperfection of the Third Figure.— The Middle

Term not really Middle 133

§ (58.) Imperfection of the Fourth Figure. — The Middle

Term not rationally Middle .... 133

§ (59.) Recapitulation 135

§ (61.) The Ordinary Syllogism called Aristotelian . 138

§ (62.) Certain Aristotelian Syllogisms over-strong . 140

b

XIV CONTENTS.

PAGE

§ (63.) Certain Aristotelian Syllogisms over-strong. — Conclusions a fortiobi 143

§ (64.) Syllogisms in which both the Premises are Particular 144

§ 65. Two, or more, Propositions disguised as one . . 146 § 66. Propositions as Parts of Terms .... 147 § 67. Extent to which Language consists of Propositions.

—Extracts 148

PAET II.

NAMES. § 69. Names, Individual or Common .... 158

§ 70. Individual Names, Singular 160

§ 71. Individual Names, Proper 161

§ 72. Common Names also called General . . . 162

§ 73. Collective Names 162

§ 74. Individual Names essentially Singular . . . 163 § 75. Individual and Common Names. — Names of Persons and Places 164

§ 76. Individual and Common Names. — Necessity and

Usefulness of Common Ones. — Extract . .167 § 77. Common, General (Generic), and Subaltern Terms . 168 § 78. Individual and Common Names. — Degrees of Generality. — Generic 173

§ 79. Individual and Common Names. — The Extremes.

— Infima Species and Individuals . . .174 § 80. Individual and Common Names. — The Extremes.

— Summa Genera and the Universe . . .175 § 81. The Universe. — Positive and Negative Names. —

Non-effective Negative Names . . . .177 § 82. The Universe.— Its Limitations .... 180 § 83. The Universe. — Negative Names effective when it

is limited. — Contraries 181

§ 84. Negative Names. — Opposites. — Privatives . .182 § (85.) I and Not-L— Ego and Non-Ego . . .184 § 86. Substance and Attribute. — Abstract and Concrete . 188 \ 87. Substance and Attribute 189

CONTENTS. XV

PAGE

§ 88. Concrete Names the Names of Substances. — Abstract, the Names of Attributes . . . .193 § 89. Abstract Names of different Degrees of Generality 194 § 90. Abstract Names, how far Individual . . . 195 § 91. Attribute — why a better Term than Quality — Attribute of a Quantity 196

§ 92. Attribute of Relation 199

§ 93. Convertible Names 201

§ 94. Notation (or De-notation) and Con-notation. — Individual Names not Connotative ... 204 § 95. Notation, &c. — Common Names connotative. — Characteristics, or essential Attributes . . . 209 § 96. Difference of view respecting the characteristics of

Classes 211

§ 97. Relation between Names and Classes. — The Class

growing out of the Name 212

§ 98. Relations, &c. — The Name growing out of the

Class 214

§ 99. Classification 214

§ 100. Definitions 217

§ 101. Classification by Type 219

§ 102. Equivocal Names 220

Part III. Parts Of Speech

§ 104. Parts of Speech. — Number, Criteria, &c. . . 223 § 105. Parts of Speech. — Number of them . . . 223

§ 106. Parts of Speech.— Criteria 224

§ 107. Parts of Speech. — Criterion, the Place of a Word

in a Proposition. — Categorematic, Syncategore-

matic, and Hypercategorematic Words . . 225

§ 108. Categorematics, <fcc 226

§ 109. Categorematics 227

§ 110. Categorematic Words Subjective or Predicative . 227 § 111. Categorematic Words Nominal (Subjective) and

Quasi-Nominal (Predicative) .... 228 § 112. Names. — Convertible or Inconvertible. — Pronouns

or Substantive 230

XVI CONTENTS.

PAOB

§ 113. Pronouns Names of Substances. — How far Individual .230

§ 114. Pronouns the Names of Substances. — How far Common 233

§ 115. Pronouns the Names of Substances. — Simply Notative (Denotative). — The Attribute they denote

that of Relation 234

. 236 . 237 . 239 . 241

§ 116. Pronouns as compared with Proper Names § 117. Pronouns as compared with Adjectives . § 118. Pronouns as- compared with Abstracts . § (119.) Criticism. — Use of the Word Noun . § (120.) Criticism. — Plurality and Non-plurality of Attributes 243

§ 121. The Attribute of Quantity.— Quantity a Relation . 246 § 122. The Attribute of Quantity. — Cardinals and Ordinals ......... 247

§ 123. The Article 249

§ 124. The Substantive 254

§ 125. The Adjective 255

§ 126. The Adjective. — Its relation to the Participle and

the Verb. — States and Actions .... 255

§ 128. The Participle 261

§ 130. Prepositions 263

§ 131. Conjunctions 264

§ 132. Yes and No 265

§ 133. Interjections . 266

§ 134. Inflection . 266

§ 135. Inflection.— Number 270

§ 136. Inflection.— Gender 270

§ 137. Inflection.— Gender.— Of Pronouns . . .271 § 138. Inflection. — Degrees of Comparison . . . 271 § 139. Inflection of Verbs. — Conjugation . . . 272

§ 141. Determination of Forms by Inflection . . . 274

§ 143. Pronouns and Participles as compared with Substantives and Adjectives 276

§ 144. Recapitulation 277

" 145. Place of the Article 280

16. Development of Inflections. — Conclusion • . 218

LOGIC AND PHILOLOGY.

PAET I. pbopositions.

Statements, Assertions, Declarations, or Propositions.

§ The first subject that requires to be considered is the nature of statements, assertions, declarations, or propositions.

In order to understand what is meant by a proposition, let us suppose that two persons are talking together.

They talk about something. Let us suppose that they talk about bread.

Bread being the something concerning which they talk, what is it that they say about it?

Let us suppose that they say that it is dear.

They then make the statement, declaration, or assertion, that bread is dear, and this statement, declaration, or assertion, is, in the language of logicians and grammarians, a proposition.

Let us now suppose their conversation to have been heard by some third person, and reported to a fourth, and that the two, on their part, talk it over after the following fashion : —

DIALOGUE.

A. What was said by the two men you saw just now ?

B. A great deal. They talked together more than an hour.

A. What did they say?

B. More than I can remember. I only know that they talked about something or other. One of them talked about bread.

A. What did he say?

B. Something that I did not quite understand, but which was contradicted by the other.

A. What did he say?

B. Something that the other disapproved of.

A. So all that you can tell me is, that they talked about something ?

B. Aye ! and that something was bread.

A. And that they said something about it?

B. They said a good deal about it ; and as fast as one said something one way, the other said something another way.

A. Did either of them say that it was dear f

B. Yes.

A. And did the other say that it was cheap t

B. He did.

So end the two conversations which four imaginary speakers have made for the sake of illustrating the nature of a proposition. We might have made two serve our purpose. Four, however, make the matter somewhat clearer. We might, indeed, have done with only one, for it requires no grfeat stretch of the imagination to suppose a single person talking to himself Or writing ; in either of which cases he would be in a condition to form propositions. For the sake, however, of giving all the prominence possible to the essential and fundamental character of the proposition, the Dramatis Person© were raised to the number of four.

Which of these speakers is right, and which wrong ? The one* whose statement, assertion, declaration, or proposition, is true, is right ; and the one whose statement, assertion, declaration, or proposition, is untrue, is wrong. Common sense tells us this. There is a reason, however, for asking the question. It suggests the fact that propositions are, at least, of two kinds, either true or false ; the men who make them being right or wrong accordingly.

Which, then, of the two statements, assertions, declarations, or propositions, is true, and which untrue? This is a question which we cannot answer, inasmuch as we do not know what particular bread is talked about, and, even if we did, we might not, ourselves, know the price of it. All we know is, that two persons, speaking about bread, make different statements.

But these statements are opposite, and contradictory to one another. Hence, we may fairly say, that, as both cannot be true, one of them must be the contrary, or untrue. Even this, however, is more than we are justified in asserting ; inasmuch as we are by no means certain that they both talk about the same bread. We have a notion that they do ; nevertheless, this notion is very far from

B2 being a certainty. We have only learnt a part of the conversation, whereas, if we had had the whole, the result might have been that the bread which was declared cheap was the bread of one year, the bread which was declared dear, the bread of another. We need not, however, go further in this question ; for it is not the price of bread that we are investigating, neither have we any interest in the comparative merits of the statements of our two speakers. Both may be right, inasmuch as they may be talking of different breads; or both may be wrong, inasmuch as bread may have been neither dear nor cheap, but moderate in price ; or one may have been wrong, and the other right. We do not, however, care which of the two it was. Yet the price of bread is seldom or never a matter of indifference to either us or any one else. We may not, perhaps, either make or sell, but the chances are strongly in favour of our either buying it. or consuming it. Besides this, the political economists tell us, that the price of bread enters into the price of everything else. So that the question is anything but an indifferent one.

The fact, however, is, that the case before us is not one of either domestic or social economy at all ; but merely an illustration drawn from those departments of inquiry for another and a very different investigation ; an investigation which we have undertaken, not as millers, or bakers, or buyers of bread, or economists of any kind, but as grammarians; and it is only with the eye of a grammarian that we look upon such sentences as the one under notice.

All propositions must be either spoken or written by some one. They cannot make themselves ; neither are they self-existent. They are made in" words by some one who uses language.

What do they convey ? At the first view of this question, we are inclined to answer that they convey a fad. Yet this is not the case. A speaker may as easily put an incorrect statement in the shape of a proposition as a correct one. He may as easily say gold is not yellow, which is contrary to feet, as gold is yellow, which is a true and real fact.

Propositions, then, by no means convey facts : that is, they by no means necessarily and essentially do so. They may do so, but they do not do so on the strength of their being propositions.

Do they convey the belief, on the part of the speaker, that what he asserts is a fact ? Not exactly ; though something like it. The same person who has said gold is yellow, may, immediately afterwards, and in the very next breath or sentence, say gold is not yellow. He cannot be said to believe both these assertions.

What a proposition conveys is this. It conveys what the speaker chooses to pass off as his belief ; so that it may give us something in which he really believes, or it may give us something that he does not believe in at all.

EXAMPLES.

1. Man is mortal. — This is true.

2. Man is jive-headed. — This is false.

3. Man is Tnan. — This is true, and something more. It is so true that it is unnecessary to be stated. It is a truism.

4. Somebody is nobody. — This is not only false, but impossible.

5. Bread is dear. — This, in the mouth ,of a person who believes, when he utters it, that bread is actually dear, is a real belief, and, if the price be actually high, it is a true fact. Again —

6. Bread is dear. — This, in the mouth of a person who believes, when he utters it, that bread is really cheap, is a simulated, or pretended belief even if it be true as a statement.

All which instances serve to show that truths, falsehoods, truisms, wilful perversions of feet, mistakes, and, even, impossibilities, may form equally unimpeachable propositions ; the proposition being considered only in respect to its grammatical character.

Two parte, members, or constituent dements necessary to the structv/re of Propositions. — The two Somethings.

§ If we have clearly seen what is not essential to the structure of a proposition, we shall all the better understand what is essential to it.

There must be two somethings — the something we speak about, and the something we say concerning it.

In order to form an estimate of the value of these two somethvngs, let us try to form a judgment, or express some act of belief by a sentence (if so it can be called) in which one of them is wanting. We shall find that it is no easy operation.

Suppose, for instance* that I say the swn. Here there is a distinct object before me, and before the person whom I address. But here the matter ends. We have a conception, an idea — each of us; but we have nothing more. What about the sun ? What about its properties or its powers ? Nothing whatever. What is said about it ? Nothing. What is believed about it ? Nothing. What is disbelieved about it ? Nothing. There is no assertion made concerning it — nothing affirmative, nothing negative, nothing false, nothing true, nothing that I maintain, nothing that I deny, nothing that I pretend to believe in, nothing that I pretend to disbelieve in. How can there be 1 What can I say of it ? What can I compare it to ? What can I say it is ? What can I say it is not ? Suppose I make one of the simplest of all possible assertibns, and say the sun is exhstmg y or the sun exists. Even here there are two elements, or parts, one denoting swi and the other denoting existence. Suppose I say the sv/n, is the sum. There are two somethings even here. Both (it is true) are expressed by the same word; and that makes the proposition a truism. Nevertheless, the parts, members, elements, or constituents of the sentence are two, and the sentence itself is a statement, assertion, declaration or proposition, consisting of two somethings, though not of two different somethings.

A truism, however, is the rarest kind of proposition. It will be well for the world when mistakes and untruths are equally so. In these, as well as in the ordinary statements of fact, the two somethings are different. Contrast with sentences like —

Bread is bread,

Water is water,

Man is man, &c,

such propositions as —

Bread is dear, Bread is cheap, "Water is scarce, Water is abundant, Man is mortal, Man is immortal, Summer is coming, Summer is departing, Winter is cold, Life is shorty Life is long, Life is uncertain.

In each of all these sentences, and in each and all of the thousands that could be framed like them, the two questions that suggest themselves have different answers.