Elements of logic : designed as a manual of instruction

Front matter

Class~fiC \ O ft Book ■( — 14"

CoEyright'N

COPYRIGHT DEPOSIT;

Preface

TO THE REVISED EDITION.

In obedience to the public demand, the publishers have spared no expense in giving to this volume a new and more attractive form. The author has, on his part, revised it carefully, and added much important matter, some of it embodying the valuable suggestions of instructors who have been using it for many years. Parts of the subject have received fuller illustration. Parts have, after careful deliberation, been omitted, and a chapter has been added on the Fundamental Laws of Thought or First Principles of Reason. The plan and divisions of the work remain the same. As many and apparently conflicting views have been taken of the meaning, genus and scope of Logic, as a branch of Philosophy, it seems proper to say that much of the diversity is nominal ; that, with differences in name, most treatises admit the same functions of words, conceptions, propositions and arguments, and that the chief antagonism arises from an undue exaggeration of the place and value of certain functions in the reasoning process. This remark is made in the interest of those who are deterred by the apparent antagonism of systems from the study of a science most of the details

4 PREFACE TO THE REVISED EDITION".

of which are the same in all systems ; the body of logical doctrines recognized by all logicians do not refuse to combine harmoniously in one system.

In the present edition the author has availed himself of the voluminous and exhaustive treatise of Sir William Hamilton, in which, together with the expression of his peculiar views and criticisms, some of which may be dissented from, the functions and the history of Logic have been set forth with great acuteness and erudition. This has led the author to slight modifications of the system of Whately, but none that will affect the general importance and soundness of his views. The numerous more recent treatises on the science have also been examined.

It is confidently hoped by the author and the publishers that the favor so continuously displayed towards this work ever since its appearance fifteen years ago will be increased by its additional value and its clear and attractive form ; and that a subject frequently regarded as both abstruse and vague will be commended, by the clearness and simplicity of its treatment, to many who have been heretofore doubtful of its utility.

H. C.

The Lehigh University, August 1, 1872.

PREFACE

TO THE FIEST EDITION.

The following treatise has been written in the hope that it may supply, in some degree, a real want. For several years the author was a teacher of Logic in the Military Academy at West Point, where the subject was thoroughly studied by the aid of Archbishop Whately's text-book.

How much a manual was needed before that work appeared may be known, from the significant fact that, as soon as it was published as an article in the Encyclopedia Metropolitana, it was eagerly caught at by the community of teachers, and. used, unaltered, as a book for college instruction, on both sides of the Atlantic.

Since the publication of that article many have attempted the preparation of a manual which should have the instruction of classes as its original design ; but the soundness of Whately's views and the conciseness of his expression still gave to his work the greatest circulation. Among so many endeavors the author would venture to express the hope that his little manual may find its special purpose and mission. It is short ; it is explanatory of all the difficult points so often left to confuse a

1* 5

6 PREFACE TO THE FIRST EDITION.

student ; the arrangement is simple, and much that in a larger treatise would be 1 of necessity included is here omitted, so that what the student learns in the limited time of a college term he may learn well, and retain in his memory as a basis for further investigations. To some persons it may seem too much simplified j but let it be remembered that it is a manual for youth, and that its only aim is to teach them the Elements of Logic as the foundation of all reasoning.

The basis of the work is " Whately's Logic" ; many of the examples are taken directly from that ; so many, indeed, that the acknowledgment is here made for them all, and for much that is excellent in arrangement and in expression. As the clear expounder of Aristotle, and the originator of much that is valuable, Whately must stand at the head of the Logicians of this age. The author would refer specially also to the material assistance obtained from " Levey' s Logic" (Bonn's series); "Aristotle's Post and Prior Analytics" (Bonn's translation); "Neil's Art of Reasoning;" "Blakely's Historical Sketch of Logic;" "Lord Bacon's New Organon; Arnaidd (Logique de Port Royal) ; J. Bentham's "Book of Fallacies." . From Neil a few of the examples have been taken.

Besides these, he has consulted a great number of works, the aid derived from which is so general that they do not require special mention.

University of Pennsylvania, July, 1857.

Table Of Contents

CHAPTEE I.

Logic, the Meaning op the Teem, and the Scope of the Science.

PAGE

Section 1. Of the term Logic 13

2. Sources of Error 14

3. Logic. and Philosophy 15

4. Logic and Ehetoric 17

5. Objection to Logic as an Art 18

6. Natural Logic 20

7. Systematic forms of Error 21

8. Of Method 22

9. Analysis and Synthesis , 23

10. Analysis and Synthesis as applied to Logic , 27

1. Analytical View. 2. Synthesis 27

3. Historical Yiew , 28

CHAPTEE II.

Analytical Yiew of Logic.

Section 11. The Eeasoning process Analyzed 29

The Dictum of Aristotle.. 31

CHAPTEE ILL

A Synthesis of Logic.

Section 12. Of certain operations and states of the Mind used in

the process of Argument „. 35

TABLE OF CONTENTS.

PAGE

1. Apprehension . 35

2. Judgment 36

3. Seasoning 37

CHAPTEE IV.

Section 13. Of Terms 39

14. Division of Simple Terms 40

15. Quantity and Quality of Terms 42

CHAPTEE V.

Or those Operations which Eelate to Terms.

Section 16. Abstraction and Generalization 44

17. Species, Genus and Differentia 45

18. Property and Accident 47

19. Of the different orders of Genera and Species 48

20. Eealism and Nominalism „ 50

21. Definition of Terms 51

22. Nominal and Eeal Definitions 53

23. Eules for Definition 54

24. Division 58

25. Eecapitulation 62

CHAPTEE VI.

Section 26. Propositions 63

27. Simple and Compound 66

28. Quantity and Quality of Propositions 67

29. Of the Distribution of Terms in Propositions 70

30. Conversion 73

Illative Conversion — 76

31. Of Opposition 78

32. Of the Matter of Propositions , 79

33. Of Compound Propositions 81

34. The New Analytic 84

TABLE OF CONTENTS. 9

CHAPTEE VII.

PAGE

Section 35. Of Arguments 87

36. Of the Syllogism 88

37. Logical Axioms. , 89

CHAPTEE VIII.

Of Figure and Moods.

Section 38. Figure.. 95

40. Of Eeduction 107

41. Indirect Eeduction Ill

42. dotation of the Syllogism 113

CHAPTEE VLX.

Of Irregular, Informal and Compound Arguments.

Section 43. Of Abridged Syllogisms 118

44. The Sorites 121

45. The Epichirema 124

Conditional 126

Disjunctive 130

The Dilemma 132

CHAPTEE X.

Fallacies.

Section 47. The Meaning and Comprehension of a Fallacy 137

48. Fallacies in dictione 138

Errors in the Premisses 142

Petitio Principii 142

Arguing in a Circle 142

Non causa pro causa 143

Errors in the conclusion , 145

10 TABLE OF CONTENTS.

PAGE

Irrelevant conclusion 145

Argumentum ad rem, etc 148

Changing the point in dispute 148

Fallacy of Objections , 149

50. Verbal Fallacies 150

1. Etymology 152

2. Interrogations 153

3. Amphibolous Sentences 154

Causes of Ambiguity 155

51. The manner of removing Ambiguity , 160

52. The Fallacy of Probabilities 161

53. Popular Fallacies 163

CHAPTEE XI.

The Fundamental Laws^of Thought or First Principles op Reason.

1. Identity 167

2. Contradiction 168

3. Excluded Middle , 168

4. Reason and Consequent 168

CHAPTER XII.

Section 54. Of certain modes in which Logic is applied 173

Intuition, Induction, Deduction...., 173

Argument a priori, a posteriori, a fortiori 176-178

The Investigation and Discovery of Truth 178

1. Observation 179

2. Hypothesis 179

3. Induction 179

4. Theory 180

Of the Nature and Kinds of Evidence 180

Consciousness 180

Sensation , 180

Analogy 181

Induction 181

Testimony ,.... 181

TABLE OF CONTENTS. 11

CHAPTER XIII.

A Historical Sketch of Logic.

PAGE

Section 55. Division of the Subject 182

1. Aristotle. 2. Christianity and Logic. 3. Bacon and the rise of Inductive Science. 4. The Present System.

The Categories 188

58. The Logic of Experimental Philosophy 200

59. Logic in the 18th and 19th centuries 209

60. Categories and Classification...., 211

61. Conclusion 217

Appendix

Examples for Praxis , 218

Chapter I. Logic: The Meaning Of The Term And The Scope Of The Science

(1.) Of the Term Logic.

Logic is directly from the Greek Aoyr/.rj, feminine of the adjective Xoyr/.og, and implies ^ruaryj [i-q or riyvt] — science or art. The adjective is from the noun logos. As, of all the Greek words which have been transferred to our English speech, none is vaguer and more subtle in its meaning than the word logos (Xoyoq), so, of all the sciences, none has been less clearly defined, both as to its meaning and its scope, than the science of Logic, the name of which is taken from that word ; and, in consequence, no term is more erroneously applied and more frequently misapplied than the name itself.

Logos means both thought and speech, and the earlier writers distinguish it as being both that in the mind and that without. Combining these, logos came to mean discourse, and hence some writers have supposed Logic to be simply the science of spoken or written language, thus confounding it, in part, with Rhetoric, and even with Grammar; others, considering discourse to imply not simply the written symbol or the spolcen sound, but also the expression of the thought, have more correctly supposed Logic to be the Science of the Laws of Thought, and, as such, a branch of metaphysics, or the science which investigates the workings of the mind ; others still, and by far 2 13 the greater number, regarding it as a union of language and thought in the deduction of truth, have claimed that it had to do with the subject-matter of scientific investigation, and have thus erred more widely than all by confounding Logic with the labors of physical, metaphysical and ethical philosophy rather than an instrument for the service of them all, as it really is.

It seems necessary, then, at the beginning of a treatise on this subject, to define the meaning of the word, and the true scope of the science, before we undertake its study — to rid ourselves, as it were, of the mists which surround us, before we can even see clearly the field in which we are to labor.

(2.) Sources of Error.

Many accurate thinkers have confused the minds of students by producing books which, while they contain a just view of the logical system itself, attempt at every step, as has been said, to explain the subject-matter upon which this system is employed, and which forms no part of it; while many others, adopting strongly the views of those who have initiated so-called systems of logic, have, as partisans, carried forward from period to period old errors and old perplexities ; and, themselves ignorant of the subtleties which surround them, have called their views the true logic, and those of every other writer false. Others again have endeavored, in an amiable but unscientific spirit, to harmonize all the schemes of the philosophers, and to call the result, full of error and inexactness, the system of Logic.

There are, indeed, in the systems of the great philosophers many parts that are mutually dependent, and true science will be found to harmonize with itself everywhere. But since there is also error in them all, no mere greatness of name should exempt from the scrutiny and exposure of error.

We must take care to distinguish between the different functions of the intellect, so as to call things by their right

LOGIC AND PHILOSOPHY. 15

names — not including in the name Logic what belongs to Physics or Metaphysics, but laying down at the outset the limits and province of that system which we wish to designate by the word Logic. If we can do this we shall have accomplished very much at the beginning, and shall find our labor easy as we proceed. s

If we would see how important it is rightly to understand this fact of the ambiguity of the word Logic, as frequently employed, w T e need but look for a moment at the errors into which modern philosophers have fallen when speaking of the Logic of Aristotle as compared with the Logic of Bacon. This has been fostered by the fact that w T hile Aristotle set forth his logical views in his Organon, Bacon produced a Novum organum or new organon. If, as w r e shall endeavor to demonstrate, Logic is the science which controls the universal and ultimate principle of reasoning, given to man, just as speech w T as given to him, by a beneficent Creator, then it is not Aristotle's Logic, nor Bacon's Logic, but a single universal Logic, given to man as the rule of his reason, which must be intelligible and harmonious wherever and by whomever it is used.

(3.) Logic and Philosophy.

In this consideration another word plays a prominent part. The word which has been pressed into service, to denote the peculiar progress of great minds in the domains of Truth, is "Philosophy ;" but even the word "Philosopher," said to be adopted by a wise ancient* as a more modest title than aoifwq, as the sages of Greece were called, has been productive of great confusion. "Philosophy" has been made to stand for a thousand sciences, and to preside in the kingdoms of mind, morals, and physics, until to be a philosopher means to pursue one of many intellectual pursuits, and Philosophy unqualified means everything or nothing.

* Pythagoras.

And yet this vague and inexact term Philosophy is the one which has been most frequently confounded with Logic, and a want of clear definition and of a just understanding in the dispute has led to the production of inexact, distorted, and conflicting systems, both of Philosophy and Logic, which have confused those desirous of learning, and deterred many from the difficult and perilous attempt. In attempting to reach a clear division and definition of Philosophy and Logic, the followers of Plato asserted Logic to be a part— and the instrument — of Philosophy. The Stoics divided Philosophy into three parts, viz. : Physics or Theoretical philosophy; Ethics or Practical philosophy, and Logic, a subsidiary part, instrumental to the others.

Indeed both words, and the errors to which their use has led, indicate, at once, the yearning and the weakness of the human mind — the desire of man to investigate and systematize truth, combined with the obscurity and doubt which beset his investigations at every step.

The acuteness of the Greeks, upon which had been grafted all the j)ower and attainment of the Oriental world, could reach no clearer nomenclature than to call their studies and their inductions Philosophy — the love rather than the attainment of wisdom — and the art by which they reasoned from truth to truth, by which they progressed from parallel to parallel in the sea of doubt and uncertainty, Logic, the art of words or discourse, the very mention of which suggests a dubious question, and calls up, as it were, two opponents in considering it.

Without considering the numerous definitions, we may agree to call Philosophy a search for final causes, in accordance with a primary law of the mind, which demands a caui-fe for everything, and also in obedience to the tendency of all science to unity. This covers the investigation of truth as to its subject matter; the processes of collating and com-

LOGIC AND RHETOEIC. 17

paring material, and of classifying and aggregating observations and experiments.

Logic we shall consider the science which guides the operation of thought from simple intuitions and conceptions, through judgments, to the simple reasoning process, by which we pass from truth to truth already found, and by which we guard against fallacious arguments in the passage.

(4.) Logic and Rhetoric.

The exact line between Logic and Rhetoric is not always clearly drawn. The distinction between them may be thus stated : Rhetoric is the art of inventing, arranging and expressing thought in discourse, or, in brief, it is the Art of Discourse. Rhetoric finds terms, propositions and arguments ih the construction of discourse, and arranges and clothes them with language to produce a certain effect.

It is the province of Logic to test the Rhetorical operations, and particularly to declare of its arguments whether they are valid or invalid. Thus, in its relation to Rhetoric, Logic is a check and an ordeal ; an arbiter of the reason ; a detecter of what is false and fallacious.

In this view Rhetoric includes Grammar. Thus a discourse may be grammatically correct, and rhetorically elegant, and yet full of error as to its Logic.

Having thus seen that the name Logic is in a great degree arbitrary, and that we should not attain to an understanding of the subject, if we followed, even remotely, the etymology of the word, we repeat that Logic has to do neither with the words themselves — except as they are arranged into terms, propositions and arguments — nor with their meanings, except as related to reasoning, i. e., passing from two known and achioicledged judgments to a third, which is derived from their combination. With this explanation, then, we may state the definition of the term. Logic is the Science and tJie Art of Reasoning ; and reasoning is the ultimate process of thought in 2 * B its search for the True, the end proposed to us by our cognitive faculties.

Of these two terms, Scienee and Art, we remark that Art is in a critical sense more extensive than Science, since the practice of an Art implies the application of the principles of Science, while, on the other hand, Science might, indeed does, exist in its theoretic state without being put to practical use. The Science would be the investigation of the principles upon which the human mind is based in reasoning, and the Art the application of those principles to the establishment of practical rules for conducting the process. Logic may then be more simply defined the Art of Reasoning, and as such we shall consider it in these pages, less concerned about the composition of man's reason than about the practical laws and methods by which it works.

Before proceeding to explain the system of Logic, which has developed itself since the days of Aristotle, let us meet at the threshold some plausible objections which have been brought against the establishment of any system whatever.

(5.) Objection to Logic as an Art.

As man has been universally gifted with reason, by means of which he may combine his thoughts and arrive at just conclusions, and with language in which to communicate them, it is asserted that every man carries his own Logic within him, as the immediate gift of God.

All men reason, it is true, and many men are not aware of the logical process which they use ; and this has been made, even by men of acute minds, an objection against Logic ; for, they say, since men reason, and reason well, without rules, and without knowing the process, a system of rules must be unnecessary.

The objection is plausible, arid has been fruitful of evil. But as it is one which may be brought against many other arts as well as Logic, it may, we think, be most easily met

OBJECTION TO LOGIC AS AN AET. 19

and most clearly refuted by illustration. Many children speak with correctness and precision before they have any knowledge of Grammar ; and there are persons of wonderful powers in arithmetical computation who have never learned Arithmetic; but Grammar and Arithmetic are not for such reasons condemned : their rules are an infallible test for precise speaking and correct computation, and are thus guides to the weaker and slower intellects — and these constitute the immense majority of mankind — to keep them from formal error. So, too, in Music and Painting ; great geniuses arise in both Arts, but no one would contend that hard study, according to the established systems of the great composers and the great masters — established upon the true principle of voice and ear and eye — is not absolutely requisite to excellence and success.

Many persous of clear perceptive faculties, and who form and combine their judgments rapidly, may reason acutely and well without a system of rules ; but, in order to be certain of their correctness, others must have some invariable test ; on the other hand there are many, of quick but erratic minds, who reason with such dangerous sophistry that the most delicate logical tests alone can expose the fallacy, of which indeed they may not themselves be entirely aware. As such delicate tests have not been within the reach of the multitude, it is thus that men have become, for want of a popular knowledge of Logic, at once self-deceivers and deluders of mankind : have established illooical religious creed?, monstrous social fallacies, false theories of government, which are immediately made manifest by the simple application of Logic.

Nay, more : since Logic is the science which develops the one universal principle of Reasoning, applied alike to every branch of science, Exact or Inductive, it seems much more necessary that we should establish full and unerring rules for our guidance, and thus be kept, at every turn, from the manifold errors which arise from systems based upon such objections as those we have mentioned.

(6.) Natural Logic.

The natural laws which govern the human mind in its attempts to reason have been called by the opposers of Logical systems Natural Logic. We accept the name, and are ready to allow that, in following these laws, reason is right, and originally perfect in applying them ; but now, in the fallen condition of man, reason is certainly liable to be biased by prejudice, distorted by passion, or insidiously tempted into open error. Thus many men, who reason correctly on most subjects, are swayed, in one or more, by self-interest, partisanship, fashion, predominance of the imagination, and such like causes ; and thus men of equally clear minds in the main, from the same premises draw different conclusions, or establish the same conclusion by very different premises. Thus also the same man, at different periods of his life, or swayed by various circumstances, will reason differently ; and from such causes, it is evident that each man's natural Logic is not a sufficient guide for his reason. Besides, reason does not confine itself to the immediate conclusion flowing from these fundamental laws of reasoning, but is constantly drawing one conclusion from another. ]S"ow, in this process, reason certainly needs more than these natural laws to keep it from error.

Yet still it is from this natural Logic, or, rather, the concurrence of the right reason of many well-ordered minds, that the science of Logic has been deduced.

By a systematic observation of such minds, as they reason, taking care to remove all causes of error in each particular case, we establish rules for the reason, and are able to detect, by the application of these rules to other cases, every fallacious argument resulting from such causes of error.

There must have been reason before there could be a sys-

SYSTEMATIC FORMS OF ERROR. 21

tern of laws to govern it, just as we know there was language before Grammar was formed. It was to systematize this reason, to methodize this natural Logic, and particularly to guard against errors in the use of the reasoning powers, that a canon was prepared, and that a complete science of Logic has been formed.

We have spoken in general terms of the confusion and error which have grown out of the misapprehension of Logic. The more special phases of it are those resulting from an attempt to systematize these general erroneous notions.

(7.) Systematic Forms of Error.

By a very common misuse of language, we hear such phrases as " mathematical reasoning ," " moral reasoning," "syllogistic reasoning, " and "inductive reasoning ;" which would lead us to suppose that instead of one there were many kinds of reasoning. This is a fruitful source of error.

These so-called different kinds of reasoning are only applications of Logic to different subjects and different habits of thought. The Logic in each is the same ; the subject-matter alone is different.

It would seem unnecessary to dwell upon this point, but it has been so commonly misunderstood, and the error has been so disseminated by professional writers upon Logic, that it must be plainly stated and carefully remembered.

When we speak, then, of a good mathematician, we mean one who is able, most surely and rapidly, to apply Logic to the investigations of numbers and quantity. When we hear of a great theologian, we know that he has amassed much theological learning, and has applied Logic to it successfully. So, too, with other sciences.

In general, in whichever of the myriad fields of nature and mind ardent votaries may wander, however various the stores they may amass, they must all come back with their sheaves to the great measuring-centre of Logic, and apply its dicta before they can compute or use their gathered gains.

The value of Logic as a study is manifold. Not only is it an infallible test of argument, but it strengthens and disciplines the mind, giving it system and method ; and it has established a terminology of universal adoption and applicable to all its practical adaptations in science. Thus it gives uniformity to the investigation of all branches of science.

(8.) Of Method.

Method is the order and arrangement of facts to produce a certain result ; to establish new truth, to investigate old, and to explain and teach both. It is derived from the Greek fisffodou, which denotes the way through which we arrive at a certain result. Method is employed in every science, and plays a specially important part in Logic.

Whatever steps are taken to make knowledge profitable, to reduce theory to practice, and to give clear, distinct and connected ideas of science, constitute Method. The extension of the term Method, it is evident, will differ according to the subject to which it is applied.

The methods of investigation differ slightly for the different kinds of science, but may generally be classified under two heads, Analysis and Synthesis, of which the former is generally used in the private investigation of truth, and the latter for the purposes of instruction.

The successive stages in the discovery, progress and establishment of any science are three, viz. : the descriptive, the inductive (also called the experimental), and the deductive or exact stage.

As soon as, by the description of a science, the statement of its present condition, its wants, its unknown causes, etc., we have a just representation of it, we proceed to observation and experiment, or induction; and when, by induction, or the labored collection of many particular facts and examples, we

ANALYSIS AND SYNTHESIS. 23

have established general laics, we may then deduce from them any particular fact or facts which it concerns us to know.

These stages of investigation belong equally to the physical and moral sciences, with the slight difference in practice that the vagueness and complexity involved in mental, spiritual and social phenomena, which all belong to the moral sciences, require more delicate and subtle agencies to trace their laws than those of the natural world around us.

And the sources of experiment are not at all analogous. Here we are surrounded by apparent contradictions. The world of nature is changeable and shifting, and yet it is palpable to our senses ; the laws which govern it are mysterious and inscrutable, and yet they are constant ; the moral world, which is unchangeable and eternal,- is, when considered or examined by unaided reason, vague and obscure, and the abstract conclusions to which our inductions lead us, positive and incontrovertible as they are, are but few and unsatisfactory.

We shall have occasion to consider the subject of Method more in detail hereafter, but at present we design to apply it to the consideration of Logic.

We speak of the method of a single science, or a Method which is applied to all — as in that which leads to the Classification of the sciences. In either investigation the division of Method into Analysis and Synthesis is a just one, as both are used in either process.

(9.) Analysis and Synthesis.

To illustrate more clearly the nature of these two processes, let us take a familiar example. If we designed to teach a person how to make and use some complicated structure, as, for example, a ship, and if this person had never seen one, the first step in the process would be to show him the ship completely built and ready to proceed to sea, fully rigged, equipped and manned, that he might take in at a glance its finished appearance, and its ultimate design and use: in a word, that he might know what he was to learn to make. This would be the first lesson in ship-building. The next step would be to show it to him partially dismantled, or, in effect, to take it to pieces before his eyes, that he might see the parts of which it is composed, and their relative position in the structure.