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LOGIC.



PAET FIRST.



DEDUCTION.



ALEXANDER BAIN, LL.D.,

PROFESSOR OF LOGIC IN THE UNIVERSITY OF ABERDEEN.



LONDON:

LONGMANS, GREEN, & CO.
1879.



j<ING AND PO., f^INTEF^S,



PREFACE.



THE present work aims at embracing a full course of Logic,
both Formal and Inductive.

In an introductory chapter, are set forth such doctrines
of psychology as have a bearing on Logic, the nature of
knowledge in general, and the classification of the sciences ;
the intention being to avoid doctrinal digressions in the
course of the work. Although preparatory to the under-
standing of what follows, this chapter may be passed over
lightly on a first perusal of the work.

The part on Deduction contains the usual doctrines of
the Syllogism, with the additions of Hamilton, and a full
abstract of the novel and elaborate schemes of De Morgan
and Boole.

The Inductive portion comprises the methods of induc-
tive research, and all those collateral topics brought for-
ward by Mr. Mill, as part of the problem of Induction ;
various modifications being made in the manner of state-
ment, the order of topics, and the proportion of the hand-
ling. The greatest innovation is the rendering of Cause
by the new doctrine called the Conservation, Persistence,
or Correlation of Force.

Mr. Mill's view of the relation of Deduction and Induc-
tion is fully adopted, as being the solution of the otherwise
inextricable puzzle of the syllogism, and the means of
giving unity and comprehensiveness to Logic.



iv PREFACE.

A separate division is appropriated to the Logic of the
Sciences, with the view of still further exemplifying the
logical methods, and of throwing light upon various points
in the sciences themselves. The review comprises all the
theoretical or fundamental sciences Mathematics, Physics,
Chemistry, Biology, and Psychology ; the sciences of Classi-
fication, or Natural History ; and two leading Practical
sciences Politics and Medicine.

The department of Definition is, for the first time,
brought under a methodical scheme, and rendered of co-
ordinate value with Deduction and Induction, as a branch
of logical method. The modes of defining, as a generalizing
process, are given under two canons, a positive and a
negative ; and attention is called to the chief obstacles
uncertainty in the denotation of words, and the gradual
transition of qualities into their opposites.

In discussing Fallacies, I have canvassed the grounds
for the usual practice of detaching the violations of logical
rules from the exposition of the rules themselves ; and
have endeavoured to show that the only portions of the
subject proper to reserve for separate handling, are the
Fallacious tendencies of the Mind, and Fallacies of Con-
fusion, As these are subjects of great moment, and admit
of wide illustration, both are considered with some minute-
ness.

None of the controversies in the subject are overlooked ;
but it has been deemed advisable to separate them from
the main body of the work. In an Appendix, are em-
braced the various Classifications of the Sciences, the Pro-
vince of Logic, the Classification of Nameable Things, the
Universal Postulate, the meanings of Analysis and Syn-
thesis, the Theories of Induction, the Art of Discovery,
and the maxims of Historical Evidence.

To adapt the work to an elementary course of Logic,



PREFACE. V

the parts to be omitted are the Additions to the Syllogism,
the Logic of the Sciences, and the chapters in the Appen-
dix. The junior student, or the candidate for a pass
examination, without attempting to master or commit these
reserved portions, might yet find their perusal of service
in understanding the rest.

There is a general conviction that the utility of the
purely Formal Logic is but small ; and that the rules of
Induction should be exemplified even in the most limited
course of logical discipline. I would suggest that an in-
creased attention should be bestowed on Definition and
Classification, with reference both to scientific study and
to matters not ordinarily called scientific.

As I may be open to the charge of presumption in
appearing as a rival to Mr. Mill, I will venture the remark,
that an attempt to carry out still more thoroughly the
enlarged scheme of logical method, seems the one thing
hitherto wanting to the success of his great work.

ABERDEEN, March, 18/0.



TABLE OF CONTENTS.



INTRODUCTION.

FAOB

1. Logic briefly characterized, ..... 1

PSYCHOLOGICAL DATA OF LOGIC.

2. Logic, under every view, involves the workings of the mind, 2

Discrimination or Relativity.

3. To make us feel, there must he a change of impression ;

which makes feeling two-sided, ib.

4. Also, in Knowledge, there are always two things, . . 3

Agreement or Similarity.

5. An impression repeated, after an interval, gives a character-

istic shock, ...... ib.

Knowledge as conjoining Difference and Agreement.

6. Knowledge is Discrimination and Identification comhined.

Retentiveness is also necessary, .... 4

Knowledge is of two kinds, called Object and Subject.

7. The External and tho Internal world contrasted, . . ib.
Knowledge as (1) Individual and Concrete, or (2) General and Abstract.

8. General Knowledge is the agreement of individuals, . ib.
Dispute as to the Character of General Knowledge, called also Abstract

Ideas.

9. Views as to Abstract Ideas : Realism ; Oonceptualism, . ib.

Our idea of an Individual a conflux of Generalities.

10. The Perception of an Individual unites many generalized

impressions, ...... 7

11. The speciality of a concrete Individual is to be definite, . ib.

12. Presentation and Representation explained, ... 8

13. Names of Individuals are combined from names of generals, ib.

The intellectual function of Agreement, or Similarity, as the basis
of Seasoning

14. Reasoning, in every form, is Assimilation, . . ib.

Origin of our Knowledge in Experience.

15. Both matter and mind are known through our consciousness

or Experience, ...... 10



Vlll CONTENTS.

PAOB

16. A certain portion of our knowledge has been said to be intu-

itive : Force, Space, Cause, Substance, . . . ib.

The nature of Belief as applied to the controversy respecting the origin of
Knowledge.

17. The natural tendency is to believe too much, . . 12
Nothing can be affirmed as true, except on the warrant of experience.

18. We must set aside instincts, and accept experience alone, .

19. We know whatever affects any of our sensibilities, . 14

FIRST PRINCIPLES OF LOGIC.

20. Enumeration of Logical First Principles, . . . ib.

Principle of Consistency Necessary Truth.

21. What is affirmed in one form of words must be upheld in

another, . . . ... 16

22. The 'Laws of Thought' Identity, Contradiction and Excluded

Middle, . . . . . .16

First Principles of Deduction.

23. Application of a general proposition to a case under it, . 18

24. Statement of the Axiom of Deduction, ... 19

25. Deduction supposes the Uniformity of Nature, . . ib.

First Principles of Induction.

26. Inferring from a fact known to a fact unknown, . . 20

27. Uniformities of Succession come under the Law of Causation, ib.

28. Causation as the Persistence or Conservation of Force, . 21

NATURE AND CLASSIFICATION OF KNOWLEDGE.

29. Knowledge defined : Involves Belief, whose criterion is Action, 22

30. Knowledge must be true, ..... 23

31. Knowledge is either Particular or General, . . . ib.

32. Nature's repetitions the basis of generality, . ib.

33. We are to strive after the highest degree of generality, . ib.

34. The perfect form of knowledge is SCIENCE. Search for the

true, . . . . . . 24

35. Science especially aims at generality, ... ib.

36. Each separate science has a distinct department, . . ib.

37. A Science has an order of topics, . . .26

38. The Classification of the Sciences accords with these proper-

ties, ....... ib.

39. The Sciences are divided into Abstract and Concrete, . 'ib.

40. The ABSTRACT Sciences classified, . . . . 27

41. The CONCRETE Sciences, ..... 28

42. The PRACTICAL Sciences, . . , . . ib.

43. A Practical Science supposes an End, ... 29

VIEWS OK THE DEFINITION OH PROVINCE OF LOGIC.

44. Logic as the Art and Science of Reasoning, ... 30

45. The term ' Reasoning' too narrow, .... ib.

46. Logic defined ' the Science of the Laws of Thought,' . ib.

47. ' The Science of the operations of the understanding in the

pursuit of Truth,' ..... 3 1

48. Truths are (1) immediate, or intuitive, (2) mediate, or in-

ferred, ..... 32



CONTENTS. 1*

PAO.

49. Defined, by Mill, as the estimation of Evidence, . 34

50. Scope of Logic as viewed in the present work, . . ib.

DIVISIONS OF LOGIC.

51. In the investigation of Knowledge there are four cardinal

operations, .... .



52. Observation. Why this is not a part of Logic,

53. Definition. A leading department of Logic,

64. Induction. The largest portion of scientific enquiry

55. Deduction. Contains the forms of the Syllogism,



BOOK I.

NAMES, NOTIONS, AND PROPOSITIONS.



ib.
38
40
ib.



CHAPTER I.

NAMES OB TERMS.

1. The truths considered in Logic are expressed in Words.

Language not necessary to Knowledge, . .. 42

2. Knowledge conveyed in language takes the form of Proposi-

tions, ....... 44

3. Motives for commencing Logic with an examination of

Names, ... . ... 45

4. A Name is a mark to enable a thing to be spoken about, . 46
, 6. Names for Logical purposes have regard to GENERALITY and

to RELATIVITY, ...... 47

6. According to GENERALITY, Names are Singular or General, ib.

1. Meanings of the two kinds, ..... 48

8. General names are said to be Connotative, ... 49

9. Hamilton's distinction between Extension and Comprehension, 50

10. The last result of generality is the Abstract Name,

11. The second group of Names is connected with RELATIVITY, 54

12. Positive and Negative names. A ' universe ' supposed in each

case of contrariety, ..... 55

13. A universe containing but two members, ... 57

14. When the universe contains more than two members, the

contrariety is diffused, . . . . ib.

15. Verbal forms for expressing negation, ... 68

16. The Negative of a real property or thing is also real, . ib.

17. The Special Relationships give birth to numerous relative

terms, . . ..... 60

18. The meaning of every object grows with the extension of its

contraries, .... . . ib.



X CONTENTS.

CHAPTER II.

CLASSES, NOTIONS, OE CONCEPTS.

HP

1. The generalization of single properties as opposed to general-

ized couples, ...... 61

2. Many classes are based on a single point of community, . 63

3. Classes formed on more than one, but yet not many, points

of community, ...... ib.

4. Classes grounded on a large and indefinite number of features.

Bands, ....... ib.

5. Classes are of higher or lower Generality. Genus and Species.

Grades in Natural History, .... 64

6. Every class has its Correlative class or classes, . . 66

THE NOTION UNDER THE GUISE OP THE PROPOSITION.

7. Many propositions are wanting in the reality of affirmation.

Fallacies thence arising, ..... J.

8. When a class has several attributes in common, it may lead

to unreal propositions, ..... 68

9. In the Natural Kinds, verbal predication may be confounded

with real, ....... 69

10. The Definition has the form without the reality of predication, 71

11. The Definition of a word exhausts the properties connoted

by it, . . . . . . . ib.

12. In Natural Kinds, a purpose may be served by unexhaustive

definitions, ...... 72

13. The Five Predicates bring out the distinction between verbal

and real predication, ..... 73

14. Definition by the Genus and the Difference, ... 74

15. The defining attributes of a thing are called essential attri-

butes, ....... ib.

16. The Predicable, called Proprium, belongs to real predication ;

it flows from the subject, ... ib.

17. The Accident or Concomitant is something distinct, and does

not flow from the subject,

18. Separable and inseparable Concomitants, . . 77



CHAPTER III.

PROPOSITIONS.

1. Propositions classified under Generality and under Relativity.

Extension and Comprehension of Propositions. The term

' Judgment ' used to designate propositions, . . 78

EXTERNAL FOHM OP PROPOSITIONS.

2. Propositions are either total or partial ; expressed as differ-

ense in QUANTITY, ..... 81

3. Propositions are either affirmative or negative ; a distinction

in QUALITY, ...... 83



CONTENTS. XI



4. Words and phrases of negation, .... 84

5. Propositions are either Simple or Complex, a distinction only

partly logical, ...... 85

6. The logical complex propositions are the Conditional and the

Disjunctive, ... #.

7. Four classes of Propositions arising out of Quantity and

Quality together ; their symhols, . . .86

8. By quantifying the predicate, Hamilton proposes four addi-

tional forms, ...... ib.

9. By a more thorough-going expression of contraries, De Morgan

adds new forms, ...... 90

Opposition of Propositions.

10. The opposition of Contraries, .... 92

11. The opposition of Contradictories. The Square of Opposition, 93

12. Modal Propositions, ...... 99

IMPORT OB MEANING OF PROPOSITIONS.

18. The classification according to Import, prepares for Induc-

tive Logic, ....... 100

14. The meaning of a proposition according to Hobhes, . ib.

15. A proposition said to refer something to a class, . . 101

16. Modes of arriving at the highest generalization of Proposi-

tions, ....... 102

17. The ultimate affirmations are Co-existence, Succession, and

Equality or Inequality, . . . t b.

18. Propositions of QUANTITY, or Mathematics, predicate equality

or inequality, ...... 103

19. The Sciences of Quantity are Deductive. Their Logical

department is DEDUCTION, . . . .16.

20. Propositions of CO-EXISTENCE are, first, Order in Place, . ib.

21. The second form of Co-existence is Co-inherence of Attri-

butes, ....... ib.

22. Under SUCCESSION falls, first, Order in Time, . . 105

23. The second mode of Succession is Cause and Effect. Existence

not a regular predicate, ..... 106

EQUIVALENT PROPOSITIONAL FORMS IMMEDIATE OR APPARENT INFERENCE.

24. Modes of Equivalence. In what sense called Inference, . 107

25. A Universal Proposition and its constituent Particulars, . 108

26. Greater and Less in Connotation or Comprehension, . . ib.

27. Obversion, Formal, ...... 109

28. Obversion, Material, . . . . . .111

29. Conversion. (1) Simple Con version. (2) Conversion by Limi-

tation. (3) Conversion coupled with Obversion, . . 113

30. Hypothetical Inference. Improperly treated as Syllogism, . 116

31. Conditional Propositions, and their equivalence, . . 117

32. Disjunctive Equivalence, ..... 119

33. The Dilemma, ...... 121

34. Synonymous Propositions, ..... 123

EXERCISES ON PROPOSITIONS, INCLUDING NOTIONS.

Aspects of the Proposition summarized. Examples, . . 125



OOK II.

DEDUCTION.



CHAPTER L
THE SYLLOGISM.

PAO

1. The Syllogism the fully expressed form of Deductive In-

ference, ....... 133

2. The Syllogism contains three Terms, . . .134

3. The Syllogism contains three Propositions two Premises and

the Conclusion, . . . . . .135

4. Syllogisms are divided into FIGURES, according to the posi-

tion of the Middle Term, . . . . . 136

6. Each Figure has distinct forms, called Moods. Detail of the
syllogistic forms according to Figures and Moods. The
First Figure contains the regular or standard forms.
Order of the Premises, . . . . .138

6. Mnemonic Lines of the Syllogism, . . . .147

7. Canons of valid reasoning. The usual mode of stating

them, ....... 148

8. Hamilton's Canons, . . . . . .161

9. The rules of the syllogism as separate canons for each

Figure, .'..... 152

10. Selection of the valid moods, .... 153

AXIOM OP THE SYLLOGISM.

11. Form of the Axiom called Dictum de omni et nullo, . . 155

12. Form expressed by Nota notce est nota ret ipsius, . . 156

13. The Proof of the Axiom is uncontradicted experience, . 159

14. Hamilton's statement of the Axiom for Informal Eeasoning, 160

15. For the Figured Syllogism, . . . . . ib.

16. Thomson's amendment of Hamilton's first form, . . 161

17. De Morgan's view of the Axiom, . . . .162

18. Supposition that the common axiom (the Dictum") follows

from the Laws of Thought, .... ib.

19. The special canons of the Syllogism deduced from the Axiom, 163

20. Axiom of Equals, and the argumentum a fortiori, . . 164

EXAMPLES OF THE SYLLOGISM.

21. Application of the theory and the forms of the Syllogism, . 165

22. Procedure for dealing with confused reasonings, . . ib.

23. Eeference of arguments to the standard forms of Deduction, ib.
Examples, .... 166



CONTENTS.

CHAPTER II.
KECENT ADDITIONS TO THE SYLLOGISM.

PAO

HAMILTON'S ADDITIONS. Hamilton's extensions of the theory and
the forms of the syllogism are chiefly based on the Quanti-
fication of the Predicate, and on the full development of
the two modes of Quantity Extension and Comprehen-
sion, ....... 178

Da MORGAN'S ADDITIONS. Theory of the Copula. Extension
of Syllogistic forms through the increase in the funda-
mental propositions. Tests of validity and rules of infer-
ence. Opponent forms. The cumular and the exemplar
modes of signifying Quantity. The Numerically Definite
Syllogism. Distinction of the Figures. Comparison with
the Aristotelian scheme, ..... 182

BOOLE'S ADDITIONS. Signs and symbols employed in Reasoning.
Expression of the Proposition. How far the rules of
common Algebra apply to the symbolical expression of
notions and propositions. The symbols and 1. Expres-
sion of classes and their contraries. Expression and
equivalence of complex attributes. Definitions. Real
Propositions, and their negatives. Immediate Inferences.
Secondary Propositions (hypotheticals, &c). Examples
of the symbolical derivation of equivalent forms Clarke's
'Demonstration of the Being and attributes of a God,'
and Spinoza's argument for Pantheism. Conversion.
The SYLLOGISM.



CHAPTER III.

FUNCTIONS AND VALUE OF THE SYLLOGISM.

1. The peculiarity of the Syllogism that the conclusion does

not advance beyond the premises differently viewed.

The Syllogism charged with petitio principii, . . 207

2. The major premise may be divided into two parts the in-

stances observed and the instances inferred, . . 208

3. In affirming a general proposition, real Inferenceis exhausted, 209

4. The true type of reasoning is inference from Particulars to

Particulars, ...... it.

5. When, from certain particulars, we can infer to another par-

ticular, we may make the inference general, . . 210

6. Deductive Inference described as Interpretation, . . ib.
1. Advantages of embodying all possible inferences in a formal

generality, . . . . . .212

8. Use of the syllogism in presenting for separate consideration

the parts of an argument, . . . . .213



XIV



CONTENTS.



CHAPTER IV.



TRAINS OF REASONING AND DEDUCTIVE

SCIENCES.

1. A chain of syllogisms, .....

2. The inference from particulars to particulars holds in a chain

of reasoning, ......

3. The Deductive Sciences are those where the labour mainly

consists in carrying out inductions hy the discovery of
minors, .......

4. A Deductive is opposed to an Experimental determination, .



FAOB

214
215



216
218



CHAPTER V.

DEMONSTRATION. AXIOMS. NECESSARY TRUTH.

1. Demonstration has its sources in Induction, . . 219

2. The chief argument against the Inductive origin of first

principles is that these are necessary, . . . 220

3. Meanings of Necessity. I. Certainty. This would apply to

Inductive truths, ...... ib.

4. II. Implication, or Self-consistency, . . .221

5. Necessary truths, in this sense, are admitted when the lan-

guage is understood. They are not, however, intuitive, . 222

6. III. Necessity as the inconceivability of the opposite, . 223

7. The Nature of Axioms. The fundamental principles of the

Deductive Sciences are called Axioms, . . . 224

8. The two chief Axioms of Mathematics are Inductive truths, ib.

9. The Axioms of the Syllogism repose upon experience,

10. There is a primitive tendency to believe the Law of Causation,

which experience adapts to the facts . . .

11. Underlying all these axioms, is the Uniformity of Nature, . 227



APPENDIX.



^-CLASSIFICATIONS OF THE SCIENCES.



BACON'S Classification,

D'ALBMBKRT,

ENCYCLOPEDIA METROPOLITANA,

NEIL ARNOTT,

AUGUSTS COMTE, .

HERBERT SPENCER,

Criticism of Spencer's scheme,



229
230

ib.
231

ib.
232
236



CONTENTS. XV
B. THE PROVINCE OF LOGIC.

PAQ

Mansel's severance of Formal Logic from Material Logic. His

positions examined, . . . . .241

Field of Theoretical Logic, on an enlarged view of the Province, 246

Meanings of Form and Matter, ..... 248

Mathematical Reasoning the best example of Formal Reasoning, 249

Analogy of Logic and Mathematics, .... 250
Verification essential to all Formal Reasoning, . . .251

The Logical processes are essentially Material, . . ib.

Deduction and Induction are continuous operations, . . 252

Logic a Practical Science. Value of rules of Induction, . 253

C ENUMERATION OF THINGS.

Different modes of dividing the Totality of Things, . . 255

Relativity fundamental, . . . . . . ib.

I. The deepest of all Relations is OBJECT and SUBJECT, . ib.

II. OBJECT analyzed, ...... 256

III. SUBJECT, ....... 257

IV. Attributes common to Object and to Subject : Likeness

and Unlikeness, Quantity, Co-existence and Succession ;

or in brief, QUANTITY, SUCCESSION, and CO-EXISTEKCB, . ib.

V. Attributes special to the OBJECT : Extension, Resistance,

Colour, Touch, Sound, Odour, Taste, Heat and Cold, besides
molecular properties that elude the senses, . .259

VI. Attributes special to the SUBJECT -.Feeling, Will, Thought, 261
VIL SUBSTANCE, not the antithesis of Attributes, but the essen-
tial or defining attributes, . . . .262

Mill's enumeration of Nameable Things, . . . 263

The Categories of Aristotle, ... ib.

D. THE UNIVERSAL POSTULATE.

All Demonstration must repose on something undemonstrable, . 266

Modes of stating the Primary Assumptions : Laws of Thought, 267

Hamilton's Testimony of Consciousness, .... ib.

Spencer's Inconceivability of the Opposite, . . . 268
There must be at least two Primary Assumptions. (1) The Pos-
tulate of CONSISTENCY. (2) An assumption relating to

EXPERIENCE, ...... 272

Nature's Uniformity our ultimate guarantee. It cannot be

proved, but may be variously stated, . . . 273

E ARISTOTELIAN AND SCHOLASTIC FALLACIES.

Aristotle's Enumeration of Fallacies, .... 275

The usual arrangement in Manuals of Syllogistic Logic, . 278

The Axiom of the Syllogism

Supplementary Note, . . . 279



1. LOGIC may be briefly described as a body of doctrines
and rules having reference to Truth.

The functions of Logic will be afterwards given with par-
ticularity and precision. For the present we remark that it
concerns the Truth of things, no matter what the subject be.
While in one aspect it is theoretical, in the prevailing aim it is
practical.

In this introductory chapter we are to consider the following
topics.

(1) The Psychological data or groundwork of Logic.

(2) The First Principles of Logic.

(3) The Classification of the Sciences.

(4) The different views of the Province of Logic.

(5) The Divisions of Logic.

PSYCHOLOGICAL DATA OF LOGIC.

2. Logic, under every view, involves frequent references
to the laws and workings of the mind ; and the more so
the more we extend its province.

In the common Logic of the Schools, the Syllogistic or
Deductive Logic, explanations are usually given of the intel-
lectual processes named Perception or Simple Apprehension,
Abstraction or the formation of concepts or notions, Judgment
or the laying down of propositions, and Reasoning or the
drawing of inferences or conclusions from premises.

In the Inductive Logic, an enquiry is instituted into our



2 PSYCHOLOGICAL DATA OF LOGIC.

idea of Cause ; in connection with which, notice is taken of
the controversy respecting the Origin of our Knowledge in
the Mind, namely, as to whether it be wholly derived from
experience, or whether any portion of it fas Cause, the Axioms
of Mathematics, &c.) be intuitive, instinctive, or innate.

It is considered a part of Logic to set forth the theory and
the limits of the Explanation of phenomena ; for which pur-
pose a reference must be made to the structure of the mental
powers. This was the avowed aim of Locke, in his Essay on
the Understanding, one of the greatest contributions to the



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