A treatise on logic, pure and applied

Front matter

iir;.:

t ,

Ygl, 150. Price is. 6{^.

II

?t^ Pneumatics ; for the use of Beginners, ^^V^ ToMLiNSON. Illustrated, Is.

^^^L^ Perspective for Beginners ; simplified for the use of Juve- <^£^ nilo Students and Amateurs in Architecture, Painting, &c. By George Pyns. Illustrated, 2s.

VIETXJE BROTHEES & CO., 1, Amen Corner, Paternoster Row.

m

m m

2£-— ^^HtTTTET BR0THEB8 & CO., 1, Amen Corner, Paternoster Eow. f^'l^ :

pl-^— = mt

'J? The^'Iollusca, a Manual of; or, a Eudimentary Treatise -i^^^c

7[t -^ Eecent and Fossil Shells. By S. P. Woodward, Associate of '^3'r^ ^

^^' "^^"ItS^^ne&n Society, Assistant in the Department of Mineralogy ^v^ sL"-

and Geology in the British Museum. Illustrated, 5s. 6d. ^^(^l

m

3tc

The Painter's Art, Eudiments of; or, a Grammar of Colouring applicable to Operative Painting, Decoratire Archi tecture, and the Arts. By George Field. Illustrated, 28, 'r^'l^*'

^ Painting on Glass, or Glass Staining, the Art of; com- ipy^i

^"^ prising Directions for preparing the Pigments and Fluxes, for c;^.^'

^ ^ laying tliem upon the Glass, and for Firing or Burning in the S^ -^y

iri Colours. From the German of Dr. Gessert. To which is added 5y?>(^''

?v» an Appendix on the Art of Enamelling, &c. Is. - )! ^1^ :

'^^ Painting on Glass, the Art of. From the German of '^v]^^

Fromberg. Is. Si-r^

The Law of Contracts for Works and Serrices. By IpQ-^^ David Gibbons. Is.

Clay Lands and Loamy Soils; comprising the Origin and "KiK^i

Chemical qualities of each variety of Land — Natural Properties of 33^-^*"

the Soils and Mode of Cultivation — Cropping and Value of the --^tv^/

Lands, and changes effected by mixing with Hot Lime. By Pro- V^yx*^

fessor Donaldson, la. ^\^^^<-

Music, a Eudimentary and Practical Treatise on. By t^^^,

Charles Child Spencer. 23. *^^^^

The Pianoforte, the Art of Playing, with numerous Exer- 45'^^

cises and Lessons, written and selected from the best masters, j^"^^

By Charles Child Spencer. Is. j3Cu^^

.C^ VIRTTJE BROTHERS & CO., 1. Amen Corner, Paternoster Eow. f'S^^^

TllEATISE ON LOGIC,

|uit mxa Ipplitb,

S. H. EM MENS, ESQ.

LONDON :

VIliTUE BE OTHERS & CO., 1, AMEN CORNER,

PATEENOSTER BOW. 186.5.

PEEFACE.

Little more will be expected from a work of the following description^ than that it should contain an intelligible and concise exposition of those facts and principles which form^ as it were^ the groundwork of logical science. Necessarily^ therefore^ it must be, for the most part, a compilation of such views as have obtained general acceptance, and can lay but little claim to any high degree of originality.

At the same time, I may be permitted to state that some features exist which serve to distinguish this Treatise from its numerous predecessors, and which will, I hope, prove of service to the student by inciting him to examine for himself such theories and principles as come under his notice. Those features to which I more particularly allude, are the reference of all so-called ^^ Immediate Inferences ^^ to the class of syllogisms j the grounds for an extended adoption of Aristotle^ s Dictmn ; the refutation of the charge that every syllogism involves a petitio principii ; the explication of the inductive theory in Applied Logic ; and, finally,

IV PKEFAOE.

the doctrine of classification^, by which every detail and branch of Logic is shown to exist in harmonious unison. And as these views are^ in a measure^ opposed to those contained in works of great repute^ I have appended to the body of this Treatise four Articles, wherein are set forth such arguments as I think sufficient to justify me in advancing the above-mentioned doctrines.

I also deem it advisable to state that it has been my endeavour to give this work as suggestive a character as possible j and^ therefore, although it belongs to a rudimentary series, professing to treat only upon the first elements of Logic, I am yet not without hope that it will be found a sufficient introduction to such comprehensive and elaborate treatises as those of Mr. Mill, Professor De Morgan,, and others. But while I have thus been compelled to satisfy myself in many cases with an enunciation rather than with a full investigation of certain doctrines, I still trust that, in the following pages, the student will find all that is really requisite to give him a fair, practical knowledge of Logic.

The chapter on Applied Logic is, I am sensible, but a mere sketch. As, however, to do justice to so vast a subject would require a great extension of the present limits, and would thus curtail the utility of this Treatise by enhancing its price, I have contented myself with directing the student^s attention to such points as are most important, both in theory and practice. For the same reason, nothing beyond the bare outlines is given of such new doctrines as I have here

TREFACE.

adopted; all further development of them beiog deferred to a future occasion.

I take this opportunity of acknowledging my many and great obligations to those writers upon Logic whose works I have consulted ; and although it may seem invidious to particularise^ yet as^ for reasons which will be found specified in their proper place, I have expressly referred to Mr. John Stuart Mill^ as being the advocate of certain opinions which are com.- bated in the following pages, I think it only just that I should here record my admiration for the profound philosophy and great attainments which are so apparent in the writings of that gentleman.

S. H. E.

London, January, 1865.

Contents

Page Introduction 1

Chapter I

An Inquire into the Various Members oe an Argument . . 7 »

CHAPTER ir.

Op Notions or Terms : —

§ 1. Simple-apprehension 14

2. Abstraction of Common -notions 16

3. Predicables, Extension, and Intension 18

4. Division of Common-notions 18

5. Positive, Negative, and Privative Te^'ms ...... 20

6. Definition 21

7. Names and their Divisions 22

8. Opposition of Terms 23

9. Structure of Terms 24

10. Conclusion and Recapitulation 24

Chapter III

§ 1. Formation of Judgments 27

2. Categorical Propositions 28

3. Hypothetical or Conditional Propositions 29

4. Disjunctive or Alternative Propositions 29

5. Quantity of Propositions 30

6. Quality of Propositions 30

7. Distribution of Terms 31

8. Relation of Terms 32

CONTENTS.

Pa2'e

9. Systematic Classification of Propositions 38

10. Table of Possible Propositions 'SS

1 1 . Interpretation of the Copula 34

12. On some other Properties of Judgments 85

13. Concluding Remarks 35

CHAPTER IV. Of Reasoning or Argument — Syllogisms

§ 1. Reasoning in General 38

2. Syllogisms — Inference 39

3. Opposition 41

4. Conversion 44

5. Coincident Junction 47

6. Mediate Inference formally expressed as such — its Divisions 48

7. The Fundamental Law of Mediate Inference 49

8. Of Figure * 54

9. Remarks upon the Four Figures 54

10. Of Mood or Mode 57

11. Table of Valid Syllogisms 58

12. Induction and Deduction 61

13. Extension and Intension 64

14. Denomination . 66

15. Syllogistic arrangement of Propositions 66

16. Conditional Syllogisms . 67

17: Disjunctive Syllogisms 72

18. The Dilemma 73

19. Incomplete Syllogisms 75

20. Complex Arguments, or Chains of Reasoning .... 76

21. Recapitulation 80

Chapter V

§ 1. Applied Logic in genera 84

2. Classification of Fallacies 85

3. Formal Fallacies 88

4. Material Fallacies — (^uarternio Terminorum 90

5. Material Fallacies — Premiss unduly assumed 95

6. Material Fallacies — Ignoratio Elenchi . Ill

CONTENTS. IX

CHAPTER VI . Page Of Logic as Practically Applied

§ 1. Introductory Remarks 117

2. Observation 119

3. Reflection —

2«. Of Induction J 31

3°. Of Deduction, Hypothesis, and A^erilication . . . 140

4«. Of Analogy 143

5^. Of Chance and Probability ]45

6°. Examples of Reflection —

a. The Discovery of Neptune 148

h. Kirchhoff's Researches on the Solar Spectrum . 150

Appendix

A On Judgments 155

B. On the so-called Immediate Inferences 159

C. On the Dictum de Omni et Nullo 163

D. On the Syllogism considered as a Petitio Principii . . . 166

I

LOGIC.

Introduction

Logic may be not inaptly described as the grammar of thought ; that is to say, it reveals and explains the principles according to which our judgments are formed, in much the same manner as grammar analyses the laws W'hich regulate the expression of our thoughts by means of speech. It will, therefore, be seen that Logic is a science of universal extent, inasmuch as wherever any process of reasoning is carried on, there will be found, in full operation, those mental laws which it is the office of Logic to examine and systematise. It does not, however, follow that every person who reasons is a logician, for it is only when a process of judgment is carried on in regular order, and according to the rules derived from a study of the science, that such an appellation could be justly bestowed. And, in Hke manner, it would be absurd to suppose that there can be no correct reasoning without a good knowledge of Logic; for, in order to perceive the error of such a view, we have only to consider for a moment the mode in which every science is formed. Take, for example, the science of astronomy : the heavenly bodies had been urged through space, by the operation of definite cosmical laws, for ages previous to the discovery of those laws by human philosophers, and it was the very fact of such motions being in progress, which led to the investigation of the principles concerned;

B

^ INTRODUCTION.

Thus, too, with regard to Logic : men had thought and reasoned according to certain laws, long before Aristotle, by observing and reflecting upon the various judgments which came under his notice, was able to enunciate the great fundamental truth upon which they were based. It is from considerations such as these that we speak of scientific discoveries, and not of scientific inventions ; for the latter term can only be applied to some new method of accomplishing a specific object, while the former is always used when we speak of any fresh law or principle, which, previously existing, has been brought to light by the exertions of the philosopher. Like, then, as Newton discovered gravitation, so did Aristotle discover the syllogism ; and, therefore, the notion that the use of the syllogism is merely one method of reasoning, is at once shown to be altogether erroneous. The truth is, that there can be no other process of forming a judgment, since every conceivable example of reasoning may, by the application of certain rules, be reduced to the syllogistic form.

From what has now been said, the true value of Logic will be easily discerned, and as its subject is one which lies at the root of all other sciences, its importance can hardly be overestimated. Its principal use is that it enables us to reason correctly, by furnishing us with various rules and standards Avherewith to test the validity of any argument that may be brought before us. And here it is requisite to guard against a very prevalent misconception ; I allude to the idea, that, by means of Logic, one may ascertain the truth or falsehood of any statement. The source of this error is to be found in the supposition that Logic is concerned with the subject of the various statements (technically, propositions) whose relations to each other it investigates ; whereas, in reality, it merely considers their form. Thus, the two propositions, ** Water is a fluid," and, " Evil is good," would by a logician be considered as precisely similar, although one of them is false^

INTRODUCTION. 3

and the other true. Again, the following argument or syllogism —

All fluids are poisonous,

Water is a flaid ; Therefore Water is poisonous,

is perfectly valid and correct, although the conclusion arrived at is false. To render this point quite j)lain and intelligible, let us adopt the following course : it w^as above stated that Logic merely considers the foriin and not the subject (or matter) of propositions ; accordingly, for all logical purposes, we shall not alter the nature of the propositions employed, if we substitute letters for the words we used to express the substances or notions of which we spoke. Thus, instead of *' water is a fluid," let us say ** A is B," and for " evil is good," let us put '^ is D : " we then see at once, that in both instances we use exactly the same kind of proposition. Again, let us similarly convert tlie syllogism : we have — All A's are B, C is an A; Therefore C is B; an argument which remains unalterable in form, no matter what ideas are expressed by the letters.*

This it is which confers such rigorous accuracy upon all the results and developments of Logic. Indeed, as Professor De Morgan has said. Mathematics and Logic are the two exact sciences. The primary doctrines of chemistry may require alteration as new combinations of the elements are brought to light ; the progressive theories of physiology are modified with every advance of microscopical investigation ; the glorious revelations of astronomy present an ever-changing aspect ; but Logic, like Mathematics, abides, eternal and immutable.

The preceding remarks will probably have pointed out to the reader that Logic is concerned with language as distin-

^ For further information as to form and matter see page 39 et seq.

4: INTRODUCTION.

guished from the ideas conveyed by the use of words ; but in order that the student may be well grounded in the fundamental truths of the science before he proceeds to study its details, I shall add some further observations upon this point. Language in its ordinary sense, that is, speech, is useful as a means of communication in two ways : it enables us to minutely describe, or, in other words, to analyse, our various ideas, and it also enables us to convey, by a single sound or sign, the combined impression of many particulars. Take, for example, this description :

" I gazed upon her form Transcendent, and upon her face which gleamed Pale through her tears, like some fair statue bathed In tlie cold moonlight ; and I marked the mute, Sad eloquence of that love-charged heart Which quickly heaved its alabaster veil In trembling fear."

Here gradually dawn upon us the many subjects of attention which exist in a single object, and it is only by means of a protracted analysis such as the above, that we are able to convey a complete idea of it. But then, again, we sometimes w^ish to express the notion of a numerous class of objects, in such a manner that the impression produced may serve for any one of them. Thus, suppose the objects were men, horses, cows, sheep, lions, &c. : we should merely confine our attention to those points in which they resembled each other, and should bestow a name upon this group of qualities, such as '* animal," by the use of which we might attain the desired end. This process is the reverse of the first, but at the same time is in a measure dependent upon it, for in order to ascertain the points of resemblance between various objects, a partial analysis is at all events necessary. Accordingly, Logic takes cognizance of both operations, and investigates the relations which subsist between them and the act of reasoning itself.

INTRODUCTION. 5

It has been said above that language enables us to convey, by a single sound or sign, the combined impression of many particulars. Now it is our ability to do this, which alone enables us to conduct a process of reasoning ; or otherwise we should find it impossible to judge of the relations between two ideas or objects — a condition which is evidently essential to an argument. One of the most curious proofs of this is afforded by deaf-and-dumb persons, who, when they have once been taught to speak by means of their fingers, are observed to use this means of recording their impressions, even when thinking alone. And it has been asserted, that '^ it will be found by any one who will question a deaf-mute who has been taught language after having grown up, that no such thing as a train of reasoning had ever passed through his mind before he was taught."*

We have hitherto considered Logic purely as a Science, but it is very frequently regarded as an Art, and perhaps it is this mode of viewing it which holds out the strongest incentive to the student. For it can only be the few who will voluntarily engage in the study of principles which, complete in themselves, give promise of no result beyond that delight which naturally arises from the consideration of organic symmetry and perfection ; the great majority being altogether occupied with the hope of turning their knowledge to some useful purpose. Therefore, in the following pages I shall endeavour to give as practical an effect as possible to the various laws of thought which we shall investigate ; and the student will thus find that Logic, instead of being merely an " ingenious recreation,'* is in reality a powerful aid to the prosecution of all other studies. Not that reasoning alone will suffice for the discoveri/ of truth, as to do this an extended observation of facts is indispensable ; but when we have collected a sufficient quantity of facts, we shall find that an

* Whately's *' Logic," p. 13.

D INTRODUCTION.

acquaintance with Logic will greatly assist us in deducing a correct inference.

I now trust that a tolerably clear notion has been gained of the nature and extent of Logic ; and in the next place I shall briefly describe the method of proceeding which I intend to adopt in my explanation of the science. First, then, it wnll be advisable to select some example of pure reasoning, and, having dissected it, to point out the various members of which it is composed, together with the principles which form, as it were, the framework of the structure. We shall thus obtain a bird's-eye view of the country before us, and we shall be able to advance without doubt or hesitation to the end of our journey. Accordingly, it will next become our duty to examine each branch separately and in detail, which being done, we shall proceed to the consideration of the various combinations formed by these branches, and so at length we shall be enabled to construct, or to analyse at pleasure, any train of argument, however extensive it may be. Here, strictly speaking, the study of Logic as such should terminate ; but in order that the utility of this treatise may be increased, I shall devote a chapter to the discussion of the several fallacies which are of most frequent occurrence, giving such rules for their treatment as have been found most effectual. The concluding portion of the work will consist of some remarks upon the proper application of Logic, with various illustrative examples.

Such is the course which I propose to take, and if the student be not dismayed by the shadowy anticipation of technical difficulties which have no real existence, he will find an ample reward for all his labours. A systematic regulation of his intellect ; a probe wherewith to examine the most mysterious doctrines of philosophy ; a wand before whose potent touch the stately fabric of deceit and fraud will disappear ; — these are bat a few of the benefits to be obtained by a study of Logical science.

A THEATISE ON LOGIC.

Chapter I. An Inquiry Into The Various Members Of An Argument

It lias already been stated that our first step towards a right understanding of Logic must be a strict examination of some definite argument. Now, as we are not all concerned with the subject of the reasoning, it will be the best plan for us to choose some example wdiich shall present us with the fewest and most simple ideas, so that we may devote our whole attention to the reasoning process^ and not be led aside by any extraneous matters. Accordingly, let us take for the subject of our investigation, the proof of Euclid's first proposition, which may be thus stated in arguments or syllogisms.

1. The radii of the same circle are ,.- «^- ..^

equal to one another, / y V

A and A B are radii of the ^ 4 -^'3 eJ

same circle BOD; \^ \ /' .•. A is equal to A B. *'*- --"- -'''*

2. The radii of the same circle are equal to one another,

B and A B are radii of the same circle A E ; .*. B is equal to A B.

3. Things which are equal to the same thing are equal

to one another, A and B are equal to the same thing (viz. A B); .*. A C is equal to B C.

Taking any one of the above syllogisms, we see that it is composed of three statements, among which this relation subsists : that if we admit the truth of the first two, we cannot

8 AN INQUIRY INTO THE

avoid admitting the truth of the last. This last statement is termed the conclusion ; the other two being called the premises. And here the question comes — why is it, that, having admitted the premises, we are compelled to admit the conclusion ? To answer this we must examine the constitution of each premiss, and ascertain whatever is implied thereby. Thus, in the first of the syllogisms given above, we find as a commencement, the following assertion or proposition: — '' radii of the same circle are equal to one another :'* w^here a certain property, viz., " equality," is asserted, or, in logical language, predicated^ of a group or class of objects, viz., ^* radii of the same circle." That is to say, *' equality " is a property common to every individual comprehended in the class. The second proposition is to this effect : — " A C and A B are radii of the same circle ;'* that is, w^e assert A C and AB to be individuals of that very class, concerning which we admitted that " equality " was common to every one of its members. Consequently we are compelled to admit that AG and A B possess the property of *^ equality," and this admission forms the conclusion.

Our mode of procedure has therefore been as follows : we first predicate something of a certain class of objects ; we then assert that certain individuals belong to that class; and lastly, we predicate the same thing of the individuals which we had predicated of the class.

Now suppose the syllogism had stood thus : ** Kadii of the same circle are not equal to one another ; A C and A B are radii of the same circle ; therefore A C is not equal to A B :" it would still be perfectly valid, for, having denied that a certain property is enjoyed by a class of objects among which we admit certain individuals to be, w^e must necessarily deny that those individuals possess the property in question.

We thus arrive at this axiom or law : ** Whatever is affirmed or denied altogether of any whole, may in like manner be affirmed or denied of any individual part belonging to, or comprehended in, that whole." Aristotle was the first who distinctly enunciated this great truth, and it is commonly known as '^ Aristotle's Dictum," or the ** dictum de omni et mdloJ'

VARIOUS MEMBERS OF AN ARGUMENT. »

It may at first seem strange that a statement so simple and obvious should be characterised as a great truth ; but a very little reflection will soon convince us that any law which is of universal extent and application, must be the more valuable according as it is the more simple ; and therefore it is with justice that Aristotle is honoured for having enabled us to explain the formation and examine the validity of any argument whatever, in so plain and satisfactory a manner. Another fact also which will appear improbable, is that the dictum may be universally applied ; that is to say, no syllogism can be valid or admissible unless it strictly complies with the requirements of the dictum, and in a later portion of this w^ork rules will be found by means of which it is possible to bring every specimen of reasoning to this test. Indeed, if we w^ould become thoroughly acquainted with the principles of logical science, we must invariably bear in mind the dependence of every train of thought upon the dictum of Aristotle.

But it is now time that we should revert again to our example of reasoning, and continue the division of each syllogism into its component parts. We have already seen that a syllogism consists of three propositions divided into the two premises and the conclusion ; we will now examine the propositions themselves more closely. In the statement ** radii of the same circle are equal to one another," we see three distinct portions : first, the subject of which we are speaking, and of w^hich something is predicated (that is, asserted or denied) ; secondly, the attribute or condition which is predicated of the subject; and thirdly, the sign of affirmation or negation. The technical names for these are, the subject, the predicate, and the copula.

In the proposition above quoted it will be observed that the ichole of the subject is spoken of; for when we say "radii of the same circle," w^e evidently mean every radius that could possibly be drawn. Accordingly, such a proposition is termed universal, as the predicate is universally applied to every part of the subject. But if we had spoken of a portion only of the subject, and had said " some of the radii of the same circle are equal to one another," we should have what is called a particular proposition, inasmuch as the predicate

B 3 f

10 AN INQUIRY INTO THE

is affirmed of some particular part of the subject, and not of the whole. Thus we see that propositions may be always divided into universal and particular, and this distribution is said to be made according to quantity.

Again, '' equality " is predicated affirmatively of ** radii of the same circle ;" the sentence is therefore termed an ajjirmatlve proposition : while if the predicate had been denied of the subject, thus, "radii of the same circle are not equal to one another," it would have been a negative proposition. We have, therefore, another system, by means of which to classify every possible proposition, and this distribution is called a division according to qualiti/.

And here w^e have introduced to our notice a very important branch of Logic, namely, division ; by means of which mental process we may at all times obtain a distinct grasp of any subject which occupies our attention. Indeed, this faculty would seem to be an inherent principle of our nature, for whatever may be the science, an attempt has always been made from the commencement, to properly classify and arrange its various subdivisions ; the best examples of such a course being found in such studies as Natural History, Comparative Anatomy^ &c. Accordingly, as Logic instructs us concerning the principles upon which alone a perfect division can be performed, it is an additional proof of the necessity which exists for an intimate acquaintance with that science.

We have now glanced quickly, but I trust intelligibly, at the structure of a syllogism and its component propositions. It remains that we should consider the nature of the materials of which the propositions are formed, having already discussed the mode of framing them together. The subject of the first proposition is, '^ radii of the same circle ;" and in saying this we speak of a class, the individuals of w4iich, though they may differ among themselves in many respects, yet have some features common to all. Thus, one radius of a circle will be unlike its fellows as regards position, but it will be exactly similar with respect to magnitude. So, when speaking of a given circle we mention its '* radius," we employ a name that may be apphed to any straight line whatever that is

VARIOUS MEMBERS OF AN ARGUMENT. 11

drawn from the centre to the circumference. Such a word is called by logicians, a common -name or common-tervi , because, as just stated, it is enjoyed in common by a multitude of objects. But if we proceed to the subject of the second proposition, we are met by terms which differ entirely from the preceding, viz., **AC and A B," the names given to individual radii. These of course can only be applied to a single object, and are consequently known as singidartermSy thus serving to distinguish the various members of a common-term.

Let us here pause for a moment to consider the results at which we have now arrived, and let us fully comprehend the purport of common and singular terms. We see that a common -term when applied to an object, merely indicates that it possesses certain properties which are shared in like manner by all the other constituents of a specified group. It is, therefore, evident that such a term or name belongs in reality not to an individual, but to a definite" combination of qualities which are found in it. And the mode in which a common-term is obtained, is by comparing a number of separate objects, observing the points wherein they agree, combining these points of agreement into one idea, and then giving this combination a name, so that at any future time we may be able to recall the idea without having the trouble to go through the same operations again. Thus, for example, men observed the properties of many natural bodies, and finding that a certain number refused more or less to alter their volume or shape, the name of solidity was conferred upon this property ; and, accordingly, whenever we hear the term " solid " applied to anything, we at once know that the body spoken of will resist a change either as to volume or shape. This process of combining various properties into one idea is called ahstraction, and is the reverse of that previously described, namely division ; for while the Litter is al ogether occupied in discovering the points of difference between various notions, the former exclusively deals with the points of resemblance.