Elements of logic

Front matter

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Preface

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 Encyclopaedia 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 con-

IV PREFACE.

ciseness of his expression, still give to his work the greatest circulation. Among so many endeavours the author would venture to express the hope that his little manual may find its special purpose and mission : it is short ; it is explanative of all the difficult points so often left to confuse a student ; the arrangement is simple, and much that in a larger treatise would be 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 ; 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 " Devey's

PREFACE. Y

Logic,'" (Bolm's series), ('^ Aristotle s Post mid Prior Analytics,'' (Bohn's translation); NeiVs Art of Reasoning ;'' ^-'Blahey's Historical Sketch of Logic;" " Lord Bacon's New Organon ; Arnauld (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 or CONTENTS.

CHAPTEB L

PAGE

Section 1. Logic; the meaning of the term and the scope of the Science 13

2. Sources of Error 14

3. Logic and Philosophy 16

4. Objection to Logic as an Art 19

5. Natural Logic 21

6. Systematic forms of Error 22

7. Of Method 23

8. Analysis and Synthesis 26

9. Analysis and Synthesis as applied to Logic . . .30 Proposed plan of Study : 1. An Analytical View of

Logic. 2. A Synthesis of Formal Logic. 3. A Historical View of Logic ' 31-32

Vm TABLE OF CONTENTS.

CHAPTER II. Analytical View of Logic

PAGE

Section 10. The reasoning process analyzed . . . .33 The Dictum of Ari&totle 36

CHAPTER IIL

A Synthesis of Logic.

Section IL Of certain operations and states of the mind in the process of Argument 40

Chapter IV

Section 12. Of Terms 45

13. Division of Simple Terms 47

14. Quantity and Quality of Terms 49

Chapter V

Of those operations in Logic which belate to Terms.

Section 15. Abstraction and Generalization 51

16. Species, Genus, and Differentia 52

17. Property and Accident 53

18. Of the different orders of Genera and Species . . 56

19. Realism and Nominalism 58

20. Definition of Terms 58

21. Nominal and Real Definitions 62

TABLE OF CONTENTS. IX

PAGE

Section 22. Rules for Definition .63

23. Division 68

24, Recapitulation . . 73

Chapter VI

Section 25. Propositions . 75

26, Propositions divided into Simple and Compound . . 79

27. Quantity and Quality of Propositions . . .81

28. Of the Distribution of Terms in Propositions . . 85

30, Of Opposition 94

31, Of the Matter of Propositions 96

32. Of Compound Propositions ...... 99

33. The New Analytic 103

Of lRRii:GULAR, Informal, and Compound Arguments.

Section 42. Of Abridged Syllogisms 147

43. The Sorites, or Chain Argument .... 151

44. Of the Epichirema 155

45. Of Hypothetical Syllogisms 167

CHAPTER X. Fallacies

Section 46. The Meaning and Comprehension of a Fallacy . . 170

47. Of Fallacies in dictione, or Formal Fallacies . . 172

48. Material, or Informal Fallacies 175

49. Verbal Fallacies 188

50. The manner of removing Ambiguity in Terms . . 201

51. The Fallacy of Probabilities, or the Calculation of

Chances 202

CHAPTER XL Section 53. Of certain modes in which Logic is applied . .211

TABLE or CONTENTS. XI

CHAPTER NIL

A Historical Sketch of Logic.

PAGE

Section 54. Division of the Subject 220

56. The Logic of Christianity 2.36

57. The Logic of Experimental Philosophy . . . 252

58. Logic in the Eighteenth and Nineteenth Centuries . 266

60. Conclusion 275

LOGIC.

Chapter I

(1.) Logic: the meaning of the Term and the scope of the Science,

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 (^oyoj,) so of all the sciences, none is less understood 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. As "Koyo^ means a ivord, some writers have supposed Logic to be simply the science of spoken or written words^ and have thus confounded it with Rhetoric and even with Grammar : others, considering a word to imply not simply the written symbol or the spoken sound, but also the expres- 2 (13)

sion of the tJiougJit, have supposed Logic to be the science of thought, and have thus confounded it Avith Intellectual Philosophy^ or the investigation of the laws of thought and mind : others still, and by far 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 labours of physical, metaphysical, and ethical philosophy.

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 labour.

(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 to explain the suhject-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

SOURCES or ERUOR. 15

called their views the true logic, and those of every other writer false. Others again have endeavoured, 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 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 labour easy as we proceed.

If we would see how important it is rightly to understand this fact of the ambiguity which the word Logic has produced in the minds of men, we 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. If, as we shall endeavour to demonstrate. Logic is the science which controls the universal and ultimate principle of reasoning, given to man, just as speech was 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 Pliilosoj^liy .

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 <-<• PMloso^liy ;'' but even the word ''Philosopher," adopted by a wise ancient* as a more modest title than 504)05, 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 pliiloso'pher means to pursue one of many intellectual pursuits, and Philosophy unqualified means everything or nothing.

And yet this vague and inexact term Philosophy, is the one which has been most frequently confoimded with Logic, and a want of clear definition and of a just understanding in the dispute, has led to the production of abominable, distorted, and monstrous systems,

* Pythagoras.

LOGIC AND PHILOSOPHY. 17

both of Philosophy and Logic, which have confused those desirous of learning, and deterred many from the difficult and perilous attempt.

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 G-reeks, upon which had been grafted all the pov^er 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 ivisdom ; and the art by w^iich 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.

In avoiding these errors, let us agree to regard Philosophy as the investigation of truth, as to its subject-matter, the process of finding materials, and of classifying and aggregating observations and experiments, and Logic, as the simple reasoning process by which we pass from truth to truth already found, and by which we guard against false arguments in such a passage.

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 'propositions and arguments — nor with their meanings, but only with the process of reasoyiing, i. e. passing from two hnoivn and achnoivledged judgments to a third which is derived from their combination. In general words, then, we may state a definition of the term. Logic is the Science and the Art of Reasoning.

Of these two terms. Science 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,

OBJECTION TO LOGIC AS AN AET. 19

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.

(4.) 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, and 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, 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 G-rammar and AritJimetie are not for such reasons condemned : their rules are an infallible test for 'pre-

20 LOO re.

cise speaJcing, 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 — is not absolutely requisite to excellence and success.

Many persons 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 w^hich 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 illogical religious creeds, monstrous social fallacies, false theories of government, w^hich are immediately made manifest by the simple application of Logic.

Nay more : since Logic is the one, universal princi-

NATURAL LOGIC. 21

pie of Keasoning, 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.

(5.) 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 this instinct of reason is in the main right, and originally, perfect in its kind ; but now, in the fallen condition of man, liable to be biassed 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.

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 system 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.

(6.) Systematic Forms of Error.

By a very common misuse of language, we hear such phrases as <■<■ mathematical reasoning j"' <-' moral reasoning^ " " si/llogistio reasoning, ' ' and ^ « inductive

OF METHOD. 23

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 professed 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 aipiply 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 which ever 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 measuringcentre of Logic, and apply its dicta before they can compute or use their gathered gains.

(7.) Of Method.

Method is the order and arrangement of facts to produce a certain result ; to establish new truth, to inv'estigate old, and to explain and teach both. It is derived from the Greek fisO'obov- which denotes the wai/ through which we arrive at a certain result.

Whatever steps are taken to make knowledge profitable, to reduce theory to practice, and to give clear and intelligible 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 Avhich 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, &c., we have a just representation of it, we proceed to observation and experiment, or induction ; and when by induction, or the laboured collection of many particular facts and examples, we have established general laws, we may then deduce from thejn any particular fact or facts, which it concerns us to know.

ANALYSIS AND SYNTHESIS. '2b

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 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.

(8.) 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 ivhat 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.

The third step w^ould be to show him how each part was made, and to let him see them all in minute detail lying together, according to some system, which should be preparatory to a reconstruction of the ship.

This process of successive steps is Analysis,"^ or a dissolution of anything into its elements.

In the investigation of any science, it is of primary

* avaXvoi — to Separate into elements.

ANALYSIS AND SYNTHESIS. 27

importance. Showing us at first the scope and design of the science, by systematic degrees it decomposes it into its elements, and prepares us for intelligent study of its many forms.

This operation shows us also the simplicity of science, and is evidently derived from the teachings of nature ; for while there are innumerable forms of animal and vegetable life, the analysis of nature which is constantly going on, shows but few parts or elements in all her works, and great simplicity of combination of the same elements in different proportions, to produce the most dissimilar forms and results. So all the sciences, physical, intellectual, and moral, while they assume many and varying forms, are in reality composed of a few simple elements of nature or mind, and this their analysis displays.

The analysis of physical science is of course the most exact of these processes, in proportion as the things of sense are easier to comprehend and fix than those of mind and spirit: in physics, this process of analysis is carried from the grandest class, such as kingdoms and high genera, to the observation and use of atoms and molecules inconceivably small, which are to constitute the basis-elements of a reconstructing process. Accurate analysis is a work of patient labour. Chance experiments have indeed occasionally produced great results, but this is an argument for, rather than against, careful analysis. Koger Bacon dis-

28 LCMuc.

covered a, ■fiiliuIiiatliiL!; powder when lie was not seeking it ; but, to be useful, this powder must cease to be a chance discovery; that is, it must be analyzed into nitre, charcoal., and hrimstoyie, so that, these constituents once known, we can make our fulminating powder at will. Science has never proceeded upon chance ; it moves safely cnly when it moves by invariable but ever-extending laws.

Incomplete analysis has done more to establish and perpetuate error, than even blind superstition. For it was in the face of the latter that Copernicus and Galileo established the true theory of the heliocentric system ; while before their time, the incomplete, false, and arbitrary analysis of astronomy, and the belief in stellar influences, which a just analysis would liave destroj^ed, led all the writers, from the time of Ptolemy, to build a false system of celestial mechanics ; and thus to clog the wheels of true science.

The process of analysis having been completed, we come naturally to Synthesis. "^^

Having taken to pieces, we proceed to the other task of rebuilding : carefully examining each different element as they all lie before us, until we understand thoroughly the material of which it is made and its construction, we proceed to adjust it to its place in the structure : piece by piece, perhaps slowly and pain-

'^ ivvrWrjiiL — to place together.

ANALYSIS AND SYNTHESIS. 29

fully, we build the ship, until ai length it is complete : nor is the labour yet finished ; we launch it upon the waters, spread its sails to the wind, and see it in practical and successful movement, and then we may account ourselves acquainted with the structure, and able to build its like whenever called upon to do so.

This operation is called Synthesis ; it is evident that it is also continually going on in nature in the reproduction out of crude materials of the many forms of complicated existence.

Many writers, in investigating a science, begin with this latter process, entirely neglecting the former ; but it is so evident that the analysis of a science gives large and valuable lessons preparatory to its synthesis, or real study for ourselves, that most modern treatises on science have adopted and followed this order of instruction. It may then be safely stated that in any science the true synthesis can only be proportional to a vigorous and just analysis, and there have consequently been rules laid down for proceeding to consider any science or art in pursuance of this method.

The rules for Analysis may be reduced to these : —

1st. Not to believe any general scientific statement without proof: that proof determined by the just principles of evidence.

2d. To divide every scientific dictum into as many parts or elements as shall be necessary to resolve it.

3d. To make a methodical arrangement of these elements in order that we may understand them clearly and the relation which they bear to each other.

Having done this, the corresponding rules for Synthesis are : —

1st. To use such terms to express the elementary parts as are free from ambiguity.

2d. In combining these, to assume only such clear principles or axioms as cannot be contested by any persons.

3d. To prove, by demonstration, all the conclusions at which we arrive, in the employment of the terms and axioms used.

These remarks upon analysis and synthesis, as the two vital functions of Method in investigation, and as the two necessary instruments of all scientific study, are designed for general application. A proper and constant application of the rules of analysis and synthesis would cause great advancement in our studies, and would go far to insure us from error, however rapid that advancement might be. But we have placed the subject of Method in this place, because we design to use it in application to the study of Logic itself; for, as a science to be studied. Logic comes under the rules which have been just laid down.

(9.) Analysis and SyntJiesis as applied to Logic,

Now, let us employ this method in investigating the science of Logic.

PROPOSED PLAN OF STUDY. 31

That we may study the subject profitably, making each step a preliminary to the due understanding of the successive steps, we propose to divide the entire subject into the following special considerations : —

1. AN ANALYTICAL VIEW OF LOGIC.

In this we regard the science in its aim and its workings, and after thus showing its design and its scope, we analyze or dissolve it into its different parts, showing what those parts are which effect by their combination the purpose designed.