An outline of the necessary laws of thought : a treatise on pure and applied logic

Preface

OME account of the exact position which this work pretends to occupy amidst a crowd of valuable treatises on the same subject, may not be an unfitting introduction to its pages. The system of Pure Logic or Analytic that has been universally accepted for centuries past, is very defective as an instrument for the analysis of natural reasoning. Arguments that commend themselves to any untaught mind as valid and practically important, have no place in a system that professedly includes all reasoning w^hatever ; and an attempt to reduce to its technical forms the first few pages of any scientific work, has generally ended in failure and disgust. The consequence has been that the more popular writers on Logic have begun to treat its strictly technical parts with a certain coyness and reserve. They have denied to the rules of the syllogism that prominent place once assigned to them, yet at the same time they have refrained from lejecting as cumbrous and unnecessary an instrument viu PEEFACE.

which did not subserve any practical end in their systems.

The present work is an attempt to enlarge the science of Pure Logic, so that it may be adequate to the analysis of any act of reasoning. How far it has attained its object ought to be decided by the application of its principles to many miscellaneous examples from different sciences ; and whilst I have rigorously and frequently applied this test to it for many years, I cannot hope that the partiality of an author will be a suiBcient guarantee of its pretensions, and therefore commend the same line of examination to any one who believes, with me, that a sedulous practice of logical analysis will richly reward the understanding with accessions of strength and clearsightedness. If the result should be the detection of many errors and omissions on the author's part, enough of matter may perhaps be left unshaken, to prove that Pure Logic is not the mere ojfficina veteramentaria — the warehouse of useless relics — it is too often taken for, but a practical system — an important branch of mental culture.

To Sir William Hamilton, of Edinburgh, whose death every student of philosophy may deplore as a personal loss, I am greatly indebted for valuable assistance, freely and generously afforded, at the cost of much time and trouble. There is no longer any feax that such an acknowledgment will be misconstrued into an admission that the present work only

PREFACE. IX

reports the opinions of that illustrious philosopher ; as he has himself recognized its claim to an independent position.* In truth, the extension of the syllogism, the enlarged list of immediate inferences, the doctrine of the three aspects of propositions, in Extension, Intension, and Denomination, and the grounds for rejecting the Fourth Figure of Syllogism, which serve, with other things, to give this little book its character, were worked out originally without assistance from any living author, from such materials as any student might command ; and it may perhaps be permitted me, without seeming to court a damaging comparison, to point out that the twelve affirmative modes of Syllogism in each figure, which here replace the much more limited number of the old system, are precisely those which Sir William Hamilton has found it necessary, on his own principles, to adopt. This will be an evidence to the reader that the alteration in question is not rash and arbitrary.

To Professor De Morgan, who has put forth, besides many excellent Mathematical Books and Essays, an elaborate and acute Treatise on Formal Logic, my best acknowledgments are due for his kind and patient explanations of certain parts of his system. Other obligations to him are notified in their proper places.

The Appendix on Indian Logic, by my friend Professor Max Miiller, of Oxford, whose philological prO'

* Sir W. Hamilton's Discussions in Philosophy, p. 126.

X PREFACE.

ductions have already made his name known ovei three continents, although they are but the first gatherings of a harvest rich in promise, is intended to call attention to the interesting resemblances between the Greek and Hindu systems, which have never yet received the consideration they deserve.

The favour with which this book has been received, has far exceeded the expectations of its writer. It is now adopted as a class-book in several places of education; and the careful revision of the present edition may perhaps have rendered it more fit for such a use.

W. T.

Table Of Contents

Inteoduction.

IICT. PAO>

1. Processes precede laws 17

Part I. Conceptions

46. Cognitions in general 91

47. Intuitions and Conceptions 93

48. Formation of Conceptions 94

49. Higher and Lower Conceptions 96

50. Genus, Species, Individual 97

51. Marks or Attributes 98

62. Extension and Intension 99

63. Determination 102

64. Three powers of Conception 102

55. Logical Division 103

56. Partition 107

67. Definition 107

{^S. Denomination 110

59. Privative Conceptions 112

60. Kelative Conceptions 114

61. Abstract and Concrete Representations 116

62. Nature of General Notions 116

65. Questions about Conceptions 124

<^. Summary 127

Part II. Judgment

67. Judgment defined 133

68. Doctrine of Relation in Judgments 134

69. The two Predicable-Classes 136

70. Definition explained 142

^ 71. Sources of Definition 143

L^ Table of Definition 145

72. Attribute 145

73. Common View of Relation 145

CONTENTS. Xui

■ECT. PAGB

74. Doctrine of Quantity 163

75. Doctrine of Quality 154

.ir_76. Doctrine of Modality 155

. 77. Distribution of Terms in Judgments 156

78. Table of all the Judgments i 160

79. The same, according to Sir W. Hamilton 162

80. Import of Judgments. Extension and Intension. Naming. 165

81. Explicative and Ampliative Judgments 168

Part III. Syllogism. Eeasoning

82. SyUogism 173

83. Immediate and Mediate Inference 174

84. Opposition and its Inferences 177

85. Conversion and its Inferences 182

*^^6. Inference by Privative Conceptions 185

87. Inference by Added Determinants 187

88. Inference by Complex Conceptions 188

89. Inference by Interpretation 188

90. Inference by Disjunctive Judgments 190

91. Inference by Sum of Predicates 191

^ 9 2. Concluding Remark. 191

93. Canon of Mediate Inference 192

94. Order of Premisses 199

95. The Three Figures , 201

96. Special Canons of the Figures 205

<97. The Fourth Figure 206

98. The Unfigured Syllogism 208

99. Modes of Syllogism 209

100. Table of Modes 209

101. A Mode of Notation 211

102. Equivalent Syllogisms 215

103. Sir W. Hamilton's Notation 218

104. Euler's Notation 220

105. Inference in Extension, Intension, and Denomination 222

106. Conditional Syllogisms 224

107. Disjunctive Syllogisms 230

108. Complex Syllogisms. Sorites 233

109. Dilemma 236

110. Incomplete Syllogisms 239

111. Prosyllogism and Episyllogism 240 xiv CONTENTS.

SECT. PAQB

Part IV. Applied Logic

112. Province of Applied Logic 245

113. Science 246

114. Criterion of Truth 247

113. Induction and Deduction 251

114. Search for Causes. Inductive Methods 254

115. Anticipation 266

116. CoUigation. Definition 269

117. Complete and Incomplete Induction 272

118. Degrees of Belief ." , 278

119. Syllogism, Deductive and Inductive 281

120. Employment of Defective Syllogisms 283

121. Syllogisms of Analogy 289

122. Syllogisms of Chance 293

123. Syllogisms of Classification 302

124. Nomenclature 304

125. Sources of Principles 306

126. Errors and Fallacies 309

127. Dealing with Errors 309

128. Method. Definition and Division 310

129. Subordinate Parts of a Science 312

130. Categories 313

131. Division of the Sciences 315

132. Conclusion 320

Appendix. On Indian Logic (by Professor Max Miillor) 325

LAWS OF THOUGHT.

Introduction

Alsxandee Aphkod.

LAWS OF THOUGHT.

mTRODUCTION.

VEE-Y process has laws, known or unknown, according to which it must take place. A consciousness of them is so far from being necessary to the process, that we cannot discover what they are, except by analyzing the results it has left us. Poems must have been written before Horace could compose an " Art of Poetry," which required the analysis and judicious criticism of works already in existence. Men poured out burning speeches and kindled their own emotions in the hearer's breast, before an Art of Rhetoric could be constructed. They tilled the ground, crossed the river or the sea, healed their sicknesses with medicinal plants, before agriculture, chemistry, navigation, and medicine, had become sciences. And wherever our knowledge of the laws of any process has become more complete and accurate ; as in astronomy, by the substitution of the Copernican for the Ptolemaic system ; in history, by a wiser estimate than our fathers had the means of forming, of civilization and its tendencies ; in chemistry, by such discoveries as the atomic theory and the wonders of electro-magnetism ; our progress has been made, not by mere poring in the closet over the rules already known, to revise and correct them by their own light, but by coming back again and again to the process as it went on in nature, to apply our rules to facts, and see how far they contridlcted or fell short of explaining them. Astronomers turned to the stars, where the laws they sought for were day and night fulfilling themselves before their eyes ; historians collected facts from the record<3 of different countries, watched men of many races, of various climates, differently helped or hindered, for there, they knew, the true principles of history were to be read ; and chemists, in the laboratory, untwisted the very fibres of matter, and watched its every pulse and change, to come at the laws which underlaid them. " Even geometry," says the great chemist, Justus Liebig, " had its foundation laid in experiments and observations ; most of its theorems had been seen in practical examples, before the science was established by abstract reasoning. Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ? "

§ 2. The same applies to Logic, or the science oj the laws of thought. The process of thought, or that active function of the mind by which impressions received from within or from without are described, classified, and compared, commenced long before the rules to which it adheres with unfailing strictness, had been drawn out. And though they do not devend on experience — i. e. their truth may be tried and made manifest without recurring to examples — still without experience, without the power of watching our own thoughts and those of others, there could never have been a science of Logic, which had its origin when some reflective mind, that had for years performed the various acts of thought spontaneously, began to lay down the laws on which they take place, or to give rules for repeating them at pleasure. The clearest reasoner cannot with propriety be called a logician, so long as he disputes spontaneously and without rule ; whilst the man with the humblest reasoning powers may lay claim to the title, in so far as he reasons according to laws, ascertained by reflection upon the process of thinking. If, for example, we call Zeno of Elea the inventor of Dialectic or Logic in Greece, it is not in virtue of his marvellous ingenuity in arguing against the possibility of motion, because this might have been the result of natural acuteness ; but because his arguments, all constructed upon one type, that of forcing his antagonists into an absurd position by reasonings drawn from their own views, seem to indicate the possession of a logical rule, the same which now has the name of reductio ad absurdum. He had reflected upon those modes of argument which his position led him to adopt spontaneously, and had formed a general rule or plan which assisted him in forming like argu* ments in future. Logic then, like Philosophy, of which it is a part, arises from the reflection of the mind upon its own processes ; a logician is not one who thinks, but one who can declare how he thinks. This important distinction, which has been too often neglected^ must govern all researches into the history of the science.

§ 3. Logic has been defined to be the science of the necessary laws of thovght. But this definition, the correctness of which shall presently be examined more particularly, requires a few words of general explanation. Our thoughts are formed indeed by laws ; and when we conceive, abstract, define, judge, and deduce, we put in practice so many ascertainable principles. But does Logic simply explain these laws in themselves, or contemplate them in their uses, as assisting and regulating our efforts in seeking after knowledge ? This distinction is analogous to that which is drawn between Anatomy and Physiology, the former of which simply examines what are the parts of the human frame, and the latter, the Science of Life, dwells upon the uses and developments of the parts : the one declares that I have a brain, and the other determines that it is the principal seat of passion, sensation, and reason ; and that it is weak in childhood, strong and constant in mature life, and subject to a gradual decay in age. It is competent to us unquestionably to consider the principles of thought under this twofold aspect of their nature and their employment. Thus, if we take a judgment; say, " The happiness of the human family will increase in pioportion to the increase of mutual love," and consider it in it^ own nature, we shall decide that it is a judgment correct in form, that certain other judgments may be gathered from it, that it has some qualities which may belong to a judgment, and wants others ; and so far we are only looking at the judgment in itself, by M^hat we know of the laws of judgment. But if we consider this example in connection with truth and knowledge, we are led to examine fm'ther, whether it is false or true, whether in forming it we fulfilled those conditions, of observation and reasoning, without which we have no right to expect a true result ; to what region of thought it belongs, and what is the method, be it testimony, deduction from principles, or observation of facts, by which judgments are to be obtained in that region. In the former case we only put in requisition what may be called pure Logic, which is defined to be the science of the necessary laws of thought in their own nature ; whilst the questions in the latter case belong to applied Logic, or the science of the necessary laps of thought as employed in attaining truth.

§ 4. But is this distinction worth preserving in our exposition of the science ? Many logicians, believing that they must undertake to teach men " the art of reasoning," do not attach aliy value to the laws of thinking, except in so far as the employment of them may help men to think, and so to enlarge their stock of truth ; that is, they do not regard pure Logic as a distinct branch of their subject. But there is one grand reason for the opposite course. Truth is a wide word, and denotes all that we can ever know of ourselves, the universe, and the Creator. The science which explains how the mind deals with truth, must be loose and indefinite, as its object-mat* ter is of infinite extent ; so that applied Logic can never attain perfect completeness and precision, because it can never affirm that it has shown how the mind deals with every part of truth and knowledge. But the laws of thought themselves are few in number, and lie, in examples of perpetual occurrence, under every thinking man's observation ; and therefore it may be declared with tolerable correctness when a full and accurate view of pure Logic has been taken. To secure that which we have completely mastered, it is desirable to keep it separate from that in which perfect completeness is hopeless ; and therefore we purpose to consider Logic under two distinct lights, first as a science of laws, and next as a science of laws applied to practice.

But here a caution is necessary (which we shall have to repeat in connection with the tiipartite division of pure Logic itself), that as the distinction is in a measure arbitrary, for the laws of thought are always put in force with a view to the attainment or communication of knowledge, it will be impossible to maintain it with perfect consistency throughout our labours. Occasions constantly arise when the line of demarcation becomes blurred and confused ; when the bare laws of thought cannot be explained without the mention of that truth, in the search for which they are always employed : thus, in treating of Definition, which is one form of judgment, we imply the existence of a person /or whom it is necessary to define a given notion that he may possess the true meaning of it, and be able to identify the things for which it stands. All that can be expected from us is, that, even if we find it necessary to repeat the m same truths in the two divisions, we do not desert our point of view, but explain the laws of thought, first mainly for themselves, and then mainly in relation to truth, which is the object of all thought and inquiry.

§ 5. Pure Logic (which is later in the order of discovery than applied, inasmuch as it is formed by abstracting from that more general science) takes no account of the modes in which we collect the materials of thought, such as Perception, Belief, Memory, Suggestion, Association of Ideas ; although these are all in one sense laws of thought.* Presupposing the possession of the materials, it only refers them to their proper head or principle, as conceptions, as subjects or predicates, as judgments, or as arguments. It enounces the laws we must observe in thinking, but does not explain the subsidiary processes, some or all of which must take place to allow us to think. Metaphysics is the science in which these find place ; but they also belong to applied Logic, because they are so many conditions under which the human mind acquires knowledge. Again, in pure Logic, the dif-

* " Now Tiniversal Logic is either pure or applied Logic. In the first we make abstraction of all empirical conditions, under which our understanding is exercised ; for example, of the influence of the senses — the play of the imagination — the laws of memory — the power of habit, of inclination, &c. ; consequently also of the sources of pre judices, nay, in fact, in general, of all causes out of which certain cognitions arise to us or are pretended to do so, since they merely concern the understanding under' certain circumstances of its application, and in order to know them, experience is requisite." — Kant's Critique, p. 58, Englisli transl. 1st ed. The ground here taken is different from that in the text. I do not say they are contingent, for memory, for example, enters into every act of thought ; but, that they are subsidiary ; thought is not complete without them, but at the same time thought is never complete with them alone.

ferent processes of the mind are regarded in their perfect and complete state ; whilst in applied, the im^ perfect faculties of man, the limited opportunities of observation, the necessity of deciding upon a question when the materials of a judgment are still insufficient, impose many limitations on the perfection of our knowledge. Thus, whilst pure Logic only treats of arguments that are certain and irrefutable, the most important duty of applied Logic is to determine under what conditions imperfect arguments, such as the Example, the Imperfect Induction, the Deduction from a proposition that is not truly universal, and some of the Rhetorical Enthymenes, can be fairly employed, and to show, that though these weaker forms are so many deviations from a perfect demonstrative argument, they are so far from superseding the perfect forms, that in reality each of them appeals to, and attests the cogency of, some perfect form, to which it strives, as it were, to conform itself. As we are anticipating, a very easy example must suffice to illustrate our meaning. Every one is perfectly certain of the truth of the proposition that men groio infirm and die ; of which we have been convinced partly by our own experience of men, and partly by the experience of others, delivered to us from all quarters, in the sober pages of the moralist as well as in the reckless lyrics of the reveller. Nor does our conviction of this truth permit itself to be distm-bed by the consideration, which is likewise undeniable, that the whole aggregate of this experience does not in itself warrant any statement having all mankind for its subject : that even supposing the decadence and death of every man in times past had been observed, which is utterly inconceivable, at any rate there are many now living upon whom the common doom has not passed, and whose cases therefore cannot enter into the sum of our experience.

In a word, we have concluded from an experience that inany men have become infirm and died, the much wider truth that all men do so ; and this is warrantable in the given case, and we are right in rejecting upon the faith of it an assertion, unless supported by evidence that transcends experience, that one man has not died, such as we have in the fable of the Wandering Jew, or a proposal to obviate death in future, such as was involved in the search of the alchemist for an Elixir of Life. But that this mode of argument from a particular to a universal, from some to all,, is not valid in itself, is evident from applying it to another case, in which it is absurdly false — some meii are tall, therefore all men are tall : and the only form perfectly indisputable in itself would be, " the men whom we have observed have all died, and these men are all men, that is, the only men, therefore all men die," which from the nature of this case cannot be employed. But applied Logic first shows that this perfect argument is the measure of the validity of the other ; that our conclusion is only true if we can say, not indeed "these men are ail men," which is impossible, but the equally general proposition, " These men are {as good as) all men ; " thus conforming really to the perfectly conclusive argument ; and next, how and under what circumstances we can cpnform the incomplete to the complete enumeration, how some can ever be said to be as good as all for purposes of argumentation .

But it is time to proceed to examine the different parts of the definition of pure Logic, by showing that Logic is a science, rather than an art — that it is a science of the necessary laws or forms of thought — that it has thought rather than language for its adequate object-matter.

§ 6. Logic is a science rather than an art. This distinction between science and art is, that a science is a body of principles and deductions, to explain some object-matter : an art is a body of precepts, with practical skill, for the completion of some w^ork. A science teaches us to know, and an art to do ; the former declares that something exists, with the laws and causes which belong to its existence, the latter teaches how something must be produced.* An art will of course admit into its limits every thing which can conduce to the performance of its proper work ; it can recognize no other principle of selection. The painter may fail of perfect success from employing improper colouring materials, or a muddy and perishable varnish, as well as from incorrect drawing or ill-managed light and shade ; the lower defect or the higher is fatal to that perfect picture which he wishes

^ Ilepl jevEGiv T£Xi^V, '^fp^ to ov hntaTiJiiTj. Aristotle, An. Post. ii. iix. 4. By Science in the text is meant the speculative science of Plato and Aristotle ; by Art the practical science. Plato seems to use TEXVTi and sTnGTrifiT] as interchangeable terms (Tkeat. 146, c). Again [Politicus, 258, d. e.) he divides EiTLaT?jfj.aL into irpaKTLKal and yvua- TUial; the latter he would subdivide (260, b.) into critical, which end in judging mef?fily, and epitactical, which lead us to some practical result. See also Theoit. 202, d. Where Aristotle distinguishes between Science and Art, which is not invariably the case, he explains them as A^e have done in the text, adding only that the object-matter of Science is necessary or invariable ; that of Art, contingent and variable. See An. Post. i. ii ; Top. vi. viii. 1 ; Eth. Nic. vi. ii;

to produce. So that an art may contain precepts of a very dissimilar character; the painter must be taught Expression, Anatomy, and mixing of Colours ; the Rhetorician must learn to manage his thoughts, his hearers, and his hands, with equal dexterity. The science, on the other hand, having the object-matter for its touchstone, admits nothing except what relates directly to it ; and so a far greatei unity and simplicity naturally belongs to it. Geometry treats of nothing but the properties of space, because it is a pure science ; whilst the arts founded upon it, such as Land-surveying, must bring in such topics as inequalities of surface, use of instruments, and the like. The science of Musical Counterpoint teaches the theory of harmonic progressions, and nothing else ; but the musician's art, in which it is employed, must add the knowledge of instruments and their compass, of the human voice, even sometimes of the powers of a particular singer. Now in the popular meaning of the word Logic, no doubt the notion of an art is more prominent ; to be able to reason better, and to expose errors in the reasoning of others, is supposed to be the object of this study.* But those writers who have followed out this view have been compelled to go over too wide a field for any one system. Logic must be the widest of all arts or sciences ; because thinking, which is its object-matter, belongs to all the rest ; it is ars artium, the art which comprehends all others, because its rules apply to every subject on which the human

* Upon the historical view of the question, whether Logic is an Ajt or a Science, most valuable remarks will be found in a paper by Sir William Hamilton. Edinburgh Review, 115, p. 202, seq.

mind can be engaged. If then it is to be taught as an Art, it should contain specific rules for reasoning or thinking in every region of thought ; it must propose to itself nothing less than to enable men of the most various capacities to apply a set of principles to effect the work of thinking correctly, under all circumstances. And the consequences are, an enormous expansion in the first instance, from the huge mass of heterogeneous materials ; and a consciousness of incompleteness in the second, since it is impossible to suppose that so vast a work has ever been completely achieved. Works in which the attempt has been made often contain a chapter on Scriptural Interpretation, and perhaps another on Forming a Judgment on Books : — can it be supposed that the precepts under either of these heads can be complete ? The one is an epitome of all Theology, and the other, it might be said, of all wisdom. Now Logic may be unquestionably an art or a science ; but it seems that all we can do is to lay down the principles of the science and leave each student to form for himself his own art, to teach himself how to employ these principles in practice. In this way we may attain something like completeness in a moderate compass, and may escape those incessant shiftings of the boundaries of the art, which are inevitable where men have to select a finite number of precepts out of infinite knowledge.

§ 7. Those who represent Logic as both art and science are accustomed to assume that all arts, possessing the principles of correspondent sciences, teach their application to practice, so that art is but science turned to account. In the case of Logic this is not very far from the truth ; but as a general statement it is false, for it overlooks that notion of unconsciousness which is commonly involved in Art. Shakspeare is admitted to be a consummate artist, but no one means by this that his plays were composed only to develop a certain express theory of Dramatic Poetry, such as Coleridge, Horn, or Ulrici have since founded upon them. No : the man of science possesses principles, but the artist, not the less nobly gifted on that account, is possessed and carried away by them. " The principles which Art involves, science evolves. The truths on which the success of Art depends, lurk in the artist's mind in an undeveloped state, — guiding his hand, stimulating his invention, balancing his judgment, but not appearing in the form of enunciated propositions." * And because the artist cannot always communicate his own principles, men speak of his " happy art," as if it were almost by chance or hap that his works were accomplished ; f and it was the fashion of the last century to speak of Shakspeare himself as a wild, untutored chUd of genius, not even to be named as an artist, because in truth his plays wanted dramatic science and were not obedient to' the law of the dramatic unities. So that the praise of being a good logician, or of having a logical mind, is sometimes awarded where there is little or no acquaintance with the science of logic. An understanding naturally clear, and a certain power of imitation, will enable the