Elements of logic

Preface

The work here undertaken differs somewhat in its scope and design from systems of Logic which have hitherto been given to the world. The Aristotelian Logic is simply the method of deduction; and. as such, it is complete. Subsequent works, in so far as they have been strictly logical, have closely copied the great master, and have confined themselves to an exhibition of the deductive principles and processes. Now, the deductive method comprehends merely the laws which govern inferences or conclusions from premises previously established. These premises may, in their turn, be inferences from other premises, and so on, to a certain extent ; and just so far this method ,4s all sufficient. But it is evident that the evolution of premises and conclusions, and conclusions and premises, must have a limit. There must be premises which are not conclusions from other premises, but which arise in some other way. Now, a complete and adequate Logic ought to exhibit this other way likewise : it ought to inform us how the most original premises arise, and upon what basis they rest.

IV PREFACE.

Other methods indeed have been abroad in the world, but without being systematically propounded as parts of Logic. Thus the Platonic philosophy really contains a Logical dev^lopement of the most original forms of human thought, springing out of the intuitive faculty* And the Novum Organum of Bacon contains a logical exposition of the method of establishing first principles through the observation of phenomena.

Both Plato and Bacon have had many able disciples and expounders ; and both are daily coming out into a broader and clearer light, not as opponents, but — » to adopt the thought of Coleridge — as the opposite poles of one great and harmonious system.

The present attempt, therefore, is to make out the system of Logic under its several departments ; and to present it not merely as a method of obtaining inferences from truths, but also as a method of establishing those first truths and general principles which must precede all deduction.

With all humility, I acknowledge my indebtedness to the great thinkers who have preceded me. I have of course read as well as thought ; and my thinking and reading are naturally blended together. With this acknowledgment, may I be permitted to go on with my work, without stopping to note narrowly in my own mind, or to remark to my reader, when I am drawing from original, and when from other sources ? I ought perhaps, in justice to myself, to remark that the entire

PREFACE. V

plan of this work was struck out several years since, and different portions of it written before Professor Whewell's and Mr. Mills' elaborate and suggestive works had fallen under my eye.

That Logic really embraces all the parts which I hare assigned to it, I think will fully appear in the sequel. It is that branch of philosophy which expounds the laws of the Reason as the faculty of truth and reality.

The view which I have taken of Logic, will justify the prolegomena. I give the Introduction to Philosophy in General, in order to point out the relative position and importance of Logic in a philosophical system. And I give the Preliminary View of the Reason, because, since this is the faculty which reasons or logicizes, I deemed that such a view, if given both clearly and briefly, would be satisfactory in this place.

1*

Part I. Introductory View Of Philosophy In General

PAGE

Section I. Definition of Philosophy ..... 3

II. Distinction between the Phenomenal and the Me-

taphenomenal ........ 12

• III. Of the Reality of the Metaphenomenal . . 16

IV. The Objective and the Subjective ... 21

V. Reason and Sense 28

VI. Sensualism and Transcendentalism ... 31

VII. Ideas and Laws ....... 39

VIII. Primary and Secondary Phenomena ... 47

IX. Antecedence in Time and in Necessary Existence. 49 X. Ideas the Last Authority *of all Judgments or

Knowledges . 53

XI. Divisions of Philosophy :

I. Metaphysics 59

Comprehending

Psychology 60

Dynamics 62

Anthropology 63

Ontology 64

II. Nomology; comprehending

The Morale 69

Esthetics ib.

Somatology 71

Logic 72

Vlll CONTENTS.

PAGE

Sec. XII. Of the Relations between Philosophy and the Sciences and Arts] 75

Geometry 78

Sciences of Discrete Quantity . . 80

Natural Science 81

Conditional and Unconditional Science . 84

Art 88

XIII. Reason, the Organ of Philosophy ... 92

XIV. Criteria of a True Philosophy .... 97

Part II. Preliminary View Op The Reason

Section I. General Introductory Considerations respecting

II. Outline of the Ideas and Functions of the Reason.

III. Explication of Ideas ■

IV. Explication of the Functions of the Reason . .

Part III. Logic Proper

119 128 133

Book I. Primordial Logic

Section I. Geperal Laws of the Evolution of Ideas . . 141 ] II. Metaphysical Ideas ; comprehending

I. Subject and Objective Exteriority . . 145

II. Time and Space 146 J

III. The Infinite and the Finite . . . 149 !

IV. Ctuantity ib.

V. duality 155

VI. Relation 157

VII. Modality 163 i

CONTENTS. IX

PAGE

f. III. Nomological Ideas ; comprehending

I. Law 167

II. Matter and Spirit 168

III. Perfection * 170

IV. Right and Wrong ib.

V. Freedom and Responsibility ... 173

VI. Personal Identity ..... ib.

VII. Immortality 174

Vf II. The Beautiful, comprehending

Symmetry 177

Grace 178

Regularity, Uniformity, Variety . . ib.

Determinate Form 179

The Sublime 180

Melody 181

Harmony " ib.

IX. The Useful 187

X. Centralization and Diffusion . . . 188 XL Affinity and Repulsion .... 189

XII. Life. 190

XIII. Polarity 191

XIV- Instinct . ib.

XV. Regularity, Uniformity, Variety, Symmetry, and Determinate Form . . . 192

XVI. Identity, Difference, Resemblance . . 193 . • XVII. Design, Final Cause, Means, and End. 196

XVIII. Truth 197

XIX. The Philosophical Idea. ... 199

XX. Intuition . . . a . . . . 201 XXL Involution and Evolution ... ib.

XXII. Analysis and Synthesis . . . 204

IV. Primary Sensuous Cognitions, or Cognitions of

the Exterior Consciousness .... 210 V. Primary Subjective Cognitions, or Cognitions of

the Interior Consciousness .... 213

VI. Axioms 215

Metaphysical Axioms ...... 217

Nomological Axioms 219

VII. Of the Characteristics of Axioms in general . 226

VIII. General Relations of Axioms .... 231

IX. Definition 235

IX. Inductive Logic

PAGE

Introduction 241

Causes and Laws. . . . . . . 244

The Human Reason, as related to the Objective

World 252

General View of Classification .... 255 Principles determining the Induction of Phenomena in Classification . . . . . 258 Distinction between a General Fact and an Absolute and Fixed Law 269

The Logic of General Fact 276

Principles of Elimination :

I. General Difference with Uniform Agree-

ment in One Point . . . . 281

II. General Agreement with Uniform Differ-

ence in One Point . . . . . 283

III. Elimination by Corresponding Quantities

and Intensities 285

IV. Elimination of the Terms of a Sequence, in order to determine which is the Antecedent and which the Consequent . . 287

Inductive Logic of Universal and Necessary

Laws 29G

The Logic of Art 308

Book III. Deductive Logic

Section I. Introduction .

I II. Analysis of Propositions

III. Of Propositions, as opposed to each other

IV. Of the Conversion of Propositions. V. Propositions constructed into Syllogisms

VI. Of Moods and Figures

VII. Of the Reduction of Syllogisms .

VIII. Of Modal, Hypothetical, and Disjunctive Propo

sitions

CONTENTS. XI

[ PAGE

Sect. IX. Hypothetical Reasoning ..... 350

X. Of the Dilemma 355

XI. Of the Sorites 358

XII. Application of the Deductive Formula. . . 361

XIII. Of Fallacies.

Fallacies of Deduction 370

Comprehending

I. Fallacies in the Formula .... 371

II. Fallacies in the Matter .... 373

1. Ambiguous Middle ib.

2. Fallacies relating to the Connection be-

tween the Matter of the Premises and

that of the Conclusion .... 376 Fallacies of Induction ; comprehending

I. Fallacies of Observation .... 387

II. Fallacies of determining General Facts . 390

III. Fallacies in Inducting Laws . . . 392 Fallacies in respect to Intuition .... 393

Book IV. Doctrine Of Evidence

Section I. Nature of Proof 397

II. The different kinds of a priori and d posteriori

III. Of the Nature of the Relation between Antecedents

and Consequents 407

IV. Of Degrees of Evidence 410

V. Of Testimony 424

VI. Circumstantial Evidence 430

VII. Argument from Progressive Approach . . 437

t YlH. Proving by Example 440

IX. Reasoning from Experience 445

X. Reasoning from Resemblance and Analogy . 448

XL Demonstrative Proof 457

[XII. Calculation of Probabilities and Chances . . 458

ERRATA.

N. B.— The Author regrets the following Errata, which have crept into these sheets while passing through the press ; and as a few of them are important, he begs the reader at once to make the necessary corrections with his pen. Page 17, line 15 from the top, after perception, substitute a comma for the period.

" 18, line 8 from the top,/or entered, read enter.

u 20, line 2 from the top, after materialism, substitute an interrogation point for the period.

" 31, line 2 from the top, for the, read their.

" 35, line 3 from the bottom,/or conveying, read conceiving.

" 45, line 10 from the bottom, dele of, after possible.

" 57, line 11 from the top, for phenomena, read phenomenon.

" 65, line 13 from the bottom, /or omnipotence, read omnipresence.

" 79, line 1 at the top,/or positivity, read positively.

" 79, line 6 from the top, for comes, read come.

" 80, line 11 from the bottom,/or formula, read formulae.

" 81, line ,,15 from the top, dele of, after ideas.

" 82, line 1 at the bottom,/or formula read formulae.

" 96, line 5 from the top, after temple, substitute a semicolon for the period.

" 103, line 5 from the top, after errors, dele to, and insert before.

" 186, line 6 from the bottom, for laid, read lain.

" 200, line 12 from the top, for quick, read quiet.

" 258, line 8 from the top, after unity, substitute a period for the mark of exclamation.

" 329, line 10 from the bottom,/or universal premises, read universal positive premises.

" 371, line 15 from the top, for there can be ground, read there can be not ground.

" 373. In the formula on .this page in the minor premiss, substitute X for Z ; and in the conclusion, substitute Z for X.

mvt *.

INTRODUCTORY VIEW

OP

PHILOSOPHY IN GENERAL.

Part I. Introductory View

OP

PHILOSOPHY IN GENERAL.

SECTION I.

DEFINITION OF PHILOSOPHY.

The term Philosophy in common usage has obtained an indefinite and often an improper application. When employed alone, and without relation to any specific subject, it is generally supposed to refer to natural science : and thus a Treatise, or Essay, or Lecture, on Philosophy, would be expected to embrace something relating to Mechanics, Astronomy, Chemistry, Electricity, or Magnetism.

Some undoubtedly would go beyond this ; and regard the term in its higher applications, as expressing something in relation to the doctrines of the intellectual and moral powers : or they would simply identify it with Metaphysics, a term no less vague and obscure to common apprehension.

It is to be expected that the affirmation will at first appear to many, paradoxical, that Mechanics, Astronomy, Chemistry, &c. are not branches of Philosophy : but in the end it will appear perfectly just. Philosophy indeed holds a close and most important relation to these sciences : they are grand results of philosophy ; but they are not philosophy itself. And even Metaphysics, general and comprehensive as it is, does not comprehend all philosophy — it only forms one of its important divisions.

In defining philosophy, we may go on to say, that it is the Scientia Scientiarum — " the Science of Sciences ; as its object is to explain the principles and causes of all things existing; and to supply the defects of inferior sciences, which do not demonstrate, or sufficiently explain their principles."* Or we may call it the " Science of the Universal and the Absolute." But this is not enough. It would be like defining Astronomy as the " Science of the Heavens." A definition may be just, and yet by reason of its dry, general, technical, and elaborate form of expression, may fall short of the true end of all definition, viz., to lead the intelligence to a clearer insight and a more perfect comprehension.

Philosophy is a word formed from the Greek *«Xocro(pia. It primarily expresses a mental affection — a love of knowledge or of wisdom.

It cannot be questioned that such an affection is inherent in the human mind. It appears in feeble infancy — it stimulates the activities of the busy prattling child — it forms the wakeful earnestness and joy of youth — it stirs nobly in manhood — it decays not with the decay of age. It is a moving spirit even in savage life, and shows man, when i lowest, as still above the brute. This impulse to know,- f\

* Ed. Ency.

PHILOSOPHY IN GENERAL. O

this restless curiosity, is connected with the whole development of humanity in Science, Arts, Government, and Religion. Co-existent with this love of knowledge is the love of external action. Hence, the development of humanity appears not only in the cultivation of the intelligence and the consequent unfolding of the sciences ; but also in the construction of implements and machinery, and in the changes and improvements wrought upon the face of Nature. The eager love of knowledge, and the no less eager love of action — the impulse to know, and the impulse to no — these are elements spontaneously at work in human nature, and may be appropriately termed philosophical elements.

Let us conceive of that period when the Heavens and the Earth were finished, and man was created and placed in the Earth its inhabitant and lord. Then he had the same faculties which he now possesses ; and the Earth was under the government of the same physical laws which govern it now ; but his faculties were undeveloped, and science and art had not yet appeared ; and the Earth, whatever modifications it might be capable of, stood as it came from the hand of the Creator, in uncultivated beauty. But man, as he walks abroad upon the Earth, with all the endowments of intelligence and feeling, observes the Heavens and the Earth, exercises thought, generalises, and forms conclusions. What is working within him, impresses its form upon all outward things : — the forest is levelled, and cultivated fields appear ; the mountain and the valley feel the touch of his hand, and put on new appearances ; he opens a way across rivers, and covers the ocean with fleets; where rivers are wanting, he creates them ; he digs into the crust of the Earth, and brings up minerals and appropriates them ; he calls into being a thousand useful arts ; he scatters over the face of the Earth convenient habitations, and crowds them together into cities. But not only does he change the face of the Earth, and put to his uses its various materials — he also establishes government, administers law, and awards justice : he speaks eloquence into being ; poetry born in his heart, is expressed in flowing numbers ; he perfects sound into music ; he takes the chisel, and from the marble quarry spring up forms whose beauty is divine ; and majestic temples, which seem born with them as their k fit habitation : he takes the pencil, and dipping it in the colours of heaven, imitates every form of life, and advances beyond Nature herself : he affirms, reasons, and believes ; draws out pure abstractions from his thought ; advances into Nature, and searches out laws for her phenomena ; and thus builds up systems of science : he invents a method of analysis, and, in the laboratory, compels Nature to reveal her more secret processes ; and, not content with this world, the light of heaven, which has lighted him to his labors here, he seizes upon as his minister, and makes it reveal to him the worlds from whence it has travelled. Still more — from these finite forms, he ascends up to the Infinite : he is a worshipper of God, and an expectant of immortality.

" Imagine a being who had been present at the earliest days of the universe, and of human life ; who had seen the external surface of the Earth, as it came forth from the hands of Nature, and looked upon all the beauty of those ancient times ; who had seen the beautiful forms which Nature presented, and heard the melodious sounds which she then uttered ; in a word, a being who had been a spec- J tator of the first exhibition of the primitive world, and who should return at the present day amidst the prodigies of our industry, our institutions, and our arts ; would it not seem to him in his astonishment as if he no longer recognised the ancient dwelling-place of man; as if beings of a superior order had transferred their abode to the Earth and had metamorphosed it ?"* Or contemplate an epitome of the whole mighty development of mind in a single individual, appearing first on the shore of this world a feeble infant, and in less than a century assuming the character of a Newton, a Leibnitz, a Milton : and as an illustration of the changes made in the condition of the world by human invention and skill, take the history of Mechanics, of the Needle and the Telescope.

In contemplating these developments and changes, what enquiry springs up, yea, irresistibly springs up, in the mind ? Do we not ask, how all this came to pass, and why the developments and changes came up under these particular forms ? Do we not ask, why did man change the face of the Earth? Why did he create government? Why did he give birth to science and art ? Where and how did the development of his mind begin ; and how did it proceed ? What are the laws of his thought, the grounds of his knowledges and beliefs, the forms of his reasonings, and the methods of his investigations ? What are the laws of his emotions and passions ? What are the capacity and force, and what the laws of his will ?

Enquiries like these evince the workings of the philosophic

spirit : they are found under some form, in some degree in every human mind. Few indeed take in that whole field of enquiry, which embraces the complete development of humanity : but whether in the child, or in the adult, in the savage, or in cultivated man, you perceive questionings after the origin and reason of things — after efficient and final causes — an earnest prying of the mind into something beyond mere visible and tangible forms, you there perceive the workings of the philosophic impulse — the ^jXotfopia. This is the dawn of philosophy. The impulse to know and to do, the elements of philosophy spontaneously at work in the mind, lead forth the developments and changes above mentioned. The enquiry after the causes and reasons of these developments and changes, after they have in any degree taken place, is the higher form of the 'pjXoo'opja, and leads forth the mind to the construction of philosophy as a system. Under the first form, the mind appears intent upon its objects, thinking, feeling, doing, and making its inherent energies to appear in external effects. Under the second form, it turns back upon itself, that is, makes itself its own object by an act of reflection, and finds out its own reach and limits, its own aims and laws.

*jXotfo<pia, from expressing the impulse to know and the consequent causal activity of man, and from expressing, after the development of humanity has taken place, the impulse to seek after the laws and principles which have governed this development, comes to express these laws and principles themselves. These laws and principles, like the simple desire of knowledge, act spontaneously in the development of humanity. They are in the highest sense philosophical elements of our being, inseparable from it, and energizing as a plastic power within, and as such distinguishable from philosophy as an expressed system without, laid down in books, or in the lectures of the schools. The first of course gives birth to the second, as thought gives birth to language.

In that early period of humanity to which we have adverted, it could not exist as a developed system : it was then in man as a light and a power, under which he thought and acted, but upon which he did not reflect : Thus the idea of the useful, led him to change the face of nature and to originate the ordinary arts: The idea of justice, led him to constitute government and law : The idea of the beautiful, led him to the creations of painting, sculpture, music, and poetry : The inherent laws of his intelligence, guided him in his reasonings ; he believed, because he could not disbelieve, and faith appeared in him like a sublime and divine instinct : When he looked out upon the phenomena of the world, he assigned them causes, because he could not think of them without this relation : And from finite being, his mind necessarily rose up to the conception of the Infinite Being — he became a worshipper under the energy of a spontaneous and irresistible idea.

At length reflection began — when it began we know not, but its beginning was the birth of philosophy as a system developed and recognised. By the act of reflection or selfconciousness, the mind turns back upon itself, and makes itself the object of its own contemplations. All the phenomena of the mind, are presented in the field of its consciousness ; — the sensations which are caused by the external world — the affirmations of the reason — the volitions — must all alike appear there, in order to be known. There is an ordinary consciousness which belongs necessarily to every man ; but reflection is a special and voluntary consciousness, and thence called a philosophic consciousness, which appears ! only when the mind becomes the object of its own observation by an act of Self-determination.

Now in the exercise of this philosophic consciousness, the mind questions itself respecting the grounds of its knowledge and its faith — respecting the forms of its thinking, and the modes of its investigation — respecting the grounds of its decisions in arts, morals, government, and religion : it makes those very enquiries which we recognize in ourselves, when, reviewing the progressive development of humanity, we are struck with wonder and admiration at what man has accomplished, and at what man has himself become. The results of these enquiries form systematic philosophy.

Let us sum up here the preceding observations, so as to present a succinct definition.

1. Philosophy, from ^iXofrtxpfa, expresses the inherent de- ! sire of knowledge in the human mind ; and as closely connected with this, the desire of action. Under the impulse of these desires man begins to acquire knowledge ; and to exert his causality in appropriating the materials supplied him from the earth — in working in various arts, and in modifying the face of nature.

2. After a time he begins to reflect* upon the development of his mind, the facts he has observed, and the works of his own power and skill : and now the $i\o<focpia or love of knowing, takes a new direction and impels him to search out the causes, laws, and forms of the various development of his own being.

3. These causes, laws and forms really existed subjectively, inseparable from himself, before he began to mako them the object of his thought and curious enquiry : and they, as the first principles of his being, and as governing its manifestations, are the substantial elements of philosophy.

4. These first principles of his being are known through reflection or self-consciousness ; and when stated methodically, under proper divisions, and with clear definitions and expositions, form Didactic Philosophy.

The term $t\o<fo$ia, which at first expressed only the desire of knowledge, or love of truth spontaneously working in the human mind, is thus employed to express all the grand results of this high and glorious impulse.

Section II. Distinction Between The Phenomenal And The Metaphenomenal

Consciousness is the common field of all our mental activity. All our sensations, our perceptions, thinking, and reasoning, our imaginations and fancies, our emotions, passions, determinations, and volitions, alike appear and are recognised here. These affections of our being are not the movements of an insensate mechanism : we know them in their going on, and we know ourselves as the subjects of them.

Now there is an important distinction to be drawn here. The distinction between the immediate objects of consciousness, and those objects which, although known, or at least supposed to be known, yet lie without the sphere of consciousness. The immediate objects of our consciousness are phenomena, and these only are phenomena ; while those objects which, by supposition, lie beyond immediate consciousness, are metaphenomenal.

What are the immediate objects of consciousness, or of what are we immediately conscious ? This is the first enquiry.

Let us begin with our sensations. The sensations are affections of our inner being, and unquestionably are the immediate objects of consciousness. But there are many perceptions and judgments which come up to view in connection with the sensations, which, together with their objects, are entirely distinct from the sensations. The bare sensations are those of color, of sound, of fragrance, of taste, of touch, of heat and cold, of titillation, and of pain and pleasure. In these are contained what are commonly called the secondary qualities of matter : but this designation cannot be made from the bare sensations. We have in the sensations mere internal experiences, or movements of our own inner being. We are not conscious of matter, distance, space, substance, or cause ; — we are conscious of sensations oniy. We may be conscious of the action of other faculties of our being, affirming or perceiving the existence of body, distance, space, substance, and cause ; but the bare sensations are no such affirmation or perception. I think it must be plain to every mind that will reflect a little, that if we had only the sensations above mentioned, we should have no knowledge of an external world whatever. The same conclusion must be drawn with respect to the primary qualities of matter. These are extension and resistance. But resistance, to immediate consciousness is only an internal experience, and extension only a repetition of this experience. There is nothing in this experience to give us a knowledge of any thing external: time, space, substance, and cause, are not contained in a mere inward experience, a mere modification of our own being. In the primary qualities, therefore, we have no immediate consciousness of an external world. It thus appears, in general, that we have an immediate consciousness only of certain affections or modifications of our own being. What immediately appears to us, what we immediately know, are these affections. These are truly the pJieno?nenaL If there be an external world, — if there be substance, space, time, and cause, — they are not phenomenal or immediately recognised in the consciousness, nor do they come directly from the sensations.

Let us suppose, then, that we have faculties by which we can know an external world, and by which we can know substance, time, space, body, and cause, either through the sensations or independently of them ; then, with respect to these faculties, the enquiry arises also, what are the immediate objects of consciousness ?

The faculties themselves are not the immediate objects ; nor are the objects perceived, and the truths affirmed the immediate objects : simply the acts of these faculties are the immediate objects of consciousness. Thus in perceiving any external object, as a house or a tree, I am not immediately conscious of the house or the tree, but of sensations of color, and of the act of perceiving. The external object does not come into my consciousness, but only the sensations and perceptions, and these are simply movements of my own being. Indeed, my own being, as a substance endowed with faculties of feeling, knowing and willing, is not immediately presented to my consciousness : I am conscious only of certain phenomena, and of acts of judgment connecting the phenomena with external objects and internal faculties.

In processes of deep thinking and reasoning, the same holds true. In studying out some mathematical theorem, for example, the recondite mathematical relations, — the necessary and absolute truths are not immediate objects of consciousness ; — but the acts of attention, the acts of thinking and reasoning — the modifications of my own being in order to know and comprehend, and in knowing and comprehending. The mathematical relations, the necessary and absolute truths, do not come into consciousness as phenomena, — the acts and modifications of my own being are the phenomena, while the relations and truths are metaphe. nomenal.

Again, God is invisible : He is neither as a substance addressed to the senses ; nor is he manifested to the consciousness as a modification of our interior being ; but still, if known at all, he must be known by these modifications : He is not the phenomena of consciousness, but known through them.

Here, then, we have the broad and clear distinction between the phenomenal and the mefaphenomenal. Sensations, emotions and passions, acts of perceiving, judging, reasoning and imagining, acts of choice and volition — these, as the immediate objects of consciousness, are phenomenal ; but the causes of sensation, emotion, and passion, the objects and truths perceived, affirmed, or deduced, the objects of the imagination, of choice and volition — these, not being the immediate objects of consciousness, are metaphenomenal.