Elements of logic, comprising the doctrine of the laws and products of thought, and the doctrine of method, together with a logical praxis

Front matter

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Preface

The present work is designed for learners. As a branch of science, the study of Logic commends itself by very special, not to say preeminent claims to all lovers of learning and liberal culture. But a leading motive in the preparation of this volume has been to furnish a needed help to the training of thought for effective communication in discourse. The first requisite for good speaking and good writing is the power to think well ; and to a good thinker, the study of Logic as the science of Thought bears the same relation as the study of mathematics to a good civil engineer.

The plan of the work has been determined by this governing design. The aim has been to develop the science in strict method. From the determination of the single radical principle of Thought, its Laws and the forms of its Products have been methodically evolved ; and the Doctrine of Method with the Exercises is but the end and result toward which the unfolding of the Doctrine of the Elements of Thought has steadily tended. The barbarous terminology of the Scholastic Logic, shown by Sir William Hamilton to be as erroneous as useless, is discarded, except so far as seemed necessary for understanding the forms in which it has entered and modified general literature. The Exercises are prepared for the help of the teacher, rath or than to be used just as they are presented,

IV PREFACE.

except, perhaps, in small classes, where free conversational discussion and criticism are practicable, and in private study. For large classes there may be found necessary special adaptations of the material here furnished, which may be used to suggest other exercises or to furnish opportunity of ready selection.

The hope that this object of training for effective thinking, and especially with reference to the construction of Discourse, may be better accomplished than through other published treatises on Logic, has been one principal inducement to prepare the present work. But some new things will be found to characterize it, which, if approved and accepted as valuable contributions to the advancement of the science, may, of themselves, justify this address to the public.

These contributions are in part to be found in the following particulars, to which the attention of the cultivators of the science is particularly solicited.

1. The rigid reduction of Thought to its one essential principle — that of Identity.

2. The unfolding of the Laws and of the forms of the Products of Thought under this principle, and the validating of each of them by it.

3. The formal derivation of the Concept and of the Eeasoning from the primitive product, of Thought — the Judgment — under the principle regulative of all Thought — that of Identity.

4. The determination of the reciprocal relations and distinguishing characteristics of Concepts in respect of their peculiar Quantities, and of the relations of Concepts to Language.

PREFACE. V

5. The more exact discrimination of the Thought-process itself from its object-matter or datum.

6. The determination of the different kinds of Wholes in which Thought may proceed, and the discrimination of those founded in the matter or datum to Thought from those which are the pure product of Thought itself.

7. The full development of the relationship of Part to Complementary Part as one of the two relationships in which all Thought proceeds, equally primitive and necessary with that of Whole to Part ; this last being the only one recognized hitherto by logicians, who have, by unavoidable consequence, been obliged to give a one-sided and therefore essentially imperfect and unsatisfactory development of the whole science, and either to exclude the consideration of Inductive Reasoning altogether or to give an entirely erroneous and pernicious presentation of it.

8. The formal grounding of all Induction, so far as a process of Thought, on this relationship of Part to Complementary Part, with a full unfolding of its laws, its forms, and its uses.

9. The more exact exposition of Logical Disjunction, of the grounds of distinction between Contradictory and Contrary Oppositions, of Modality and its distinctions, and of Necessary and Contingent Truth.

10. A new classification of Reasonings, — the logical consequence of modifications of logical doctrine already indicated.

11. A new system of Logical Methodology, more precisely defined as the Doctrine of the Conditions of Thought in order to perfect science.

12. A Logical Praxis, comprising copious exercises sep-

VI PREFACE.

arately arranged for each of the forms of the various products of Thought,

A free use has been made of the elaborations of Sir William Hamilton, who, however defective and imperfect his system appears in his posthumous lectures, has done more for the science, it may perhaps be said without extravagance, than all that has been done for it since the times of Aristotle. In some cases, where his language has been used, it has been modified and changed to make his teachings correspond to those that are peculiar to the present work. These borrowings are indicated by the usual quotation marks without more special reference, and without any discrimination of Hamilton's free borrowings from German writers, or of the changes made in his statements. The intended uses of the book as a text-book seemed to forbid the incumbering of the text with such special references, while this general acknowledgment will enable any critical reader to ascertain the extent to which these borrowings have been carried.

Chapter II. The Laws Of Thought

§ 10-14. The Four Laws of Thought : — 1. Of Identity ; 2. Of Contradiction ; 3. Of Disjunction ; 4. Of Exclusion 21-25

§ 15. Quantity in all Thought . . . . . 25, 26

CHAPTER in.

THE WHOLES IN THOUGHT. LOGICAL POSTULATE.

§ 18. Hamilton's Postulate 29, 30 viii CONTENTS.

Chapter IV

THE PRODUCTS OF THOUGHT. — I. JUDGMENTS.

PAGB

§ 19, 20. Judgment defined and explained . . . 31-35 § 21, 22. Terms :— Subject; Predicate . . . 35-38

§ 23. The Copula 38, 39

§ 24. Division of Judgments 39-47

§ 25, 26. — 1. As to Quality : — Affirmative ; Negative ;

Disjunctive 48-51

§ 27. — 2. As to Modality : — Assertory ; Problematic ;

Apodictic 51, 52

§ 28. — 3. As to Degree of Identity : — Identical ; Partial ; Tautological . . . . 52, 53 § 29, 30. — 4. As to Character of Terms : — Categorical; Hypothetical; Hypothetico-Disjunct-

§ 31. — 5. As to Logical Quantity : — Extensive ; Intensive 56, 57

§ 32. — 6. As to Kind of Whole : —Integrate ; Substantial ; Causal 57,58

§ 33. Judgments in relation to one another . . . 58-61

CHAPTER Y.

THE PRODUCTS OF THOUGHT. — II. CONCEPTS.

§ 34-38. Formation and Essential Nature of Concepts 62-65 § 39. Relations to Objects and to Language . . . 65-72 § 40-44. Quantity of Concepts : — Extensive and Intensive . 72-78

§ 45-50. Relations of Concepts in Extension . . 78-86

§51-54. Relations of Concepts in Comprehension . 86-90

Chapter VI

THE PRODUCTS OF THOUGHT. — III. REASONINGS.

§ 55-58. Nature, Denominations, and Divisions of Reasonings . 91-94

§ 59-65. Immediate Reasonings : — Conversion ; Quantitative Restriction ; Modal Restriction ; Transference; Disjunction; Composition 94-102

CONTENTS. IX

PAGE

§66-70. Categorical Syllogisms : — Deductive; Inductive 102-118

§ 71-77. Conditional Syllogisms : — Ponent and Tollent ; Hypothetical; Dilemma ; Disjunctive . . . . . . . . 118-128

§78-80. Polysyllogism : — Epichirema ; Sorites . . 128-131

Chapter IV. Methodology Of Beasonings

§110. Probation and Investigation . 183,184

§111. Objective Law of Reasonings .... 184,185 §112-124. Subjective Law 185-206

X CONTENTS.

PAET III.

LOGICAL PRAXIS.

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I. Exercises in Judgments . • . . 207-214

II. Exercises in Concepts 214

III. Exercises in Reasonings 214-222

Appendix A. Induction 223-227

" B. Origin of Language . . • ,227-231

INTRODUCTION.

DEFINITION OF LOGIC.

§ 1. Logic is the Science of the Laws of Logic de _ Thought as Thought. fined -

The name, Logic, is derived from Aoyos, which word in Greek had a twofold meaning, denoting both thought 0rigia of and the expression of thought. To avoid the Name - ambiguity thus arising, Aristotle limits the term, when applied to thought, by the definitive rbv eo-w — that within the mind ; and when applied to the expression of thought, — to speech, by the definitive rbv efoo — that without.

It has been a point much discussed whether Logic is a science, or an art, or neither, or both. " Plato and L ic a gci _ the Platonists received it as a science ; but with ence * them Dialectic was coextensive with the Logic and Metaphysics of the Peripatetics taken together. By Aristotle himself, Logic is not defined. The Greek Aristotelians, and many philosophers since the revival of letters, deny it to be either science or art. The Stofcs, in general, view r ed it as a science ; and the same was done by the Arabian and Latin schoolmen. In more modern times, however, many Aristotelians, all the Pamists, and a majority of the Cartesians, maintained it to be an art ; but a considerable party were found who defined it as both art and science. In Germany, since the time of Leibnitz, Logic has been almost universally regarded as a science."

By a science, is meant only a branch of knowledge, un- 1 folded in systematic method. It would seem superfluous to attempt a formal vindication of the claims of Logic to be thus regarded.

The object-matter of Logic is Thought, strictly so called, its Object- as tne product of the Discursive Faculty, other- Matter. w j se ca u ec [ the Faculty of Comparison, the Understanding, and by Hamilton, the Elaborative Faculty. This term, thought, has been used to include any act of consciousness, whether a cognition, a feeling, or a volition. It has been more commonly used to include any act of the Intelligence — any cognitive act. But as the object-matter of Logic, it is used in a still more restricted meaning to denote only an act of the Discursive Faculty — the Faculty of mediate cognition. Logic, accordingly, takes no account of the faculties of original cognition — the Presentative Faculties of Perception, Self- Consciousness, and Intuition ; nor of the Faculties of Representative Knowledge — Memory and Imagination. The range of Thought proper, then, is far more limited than the bounds of the Intelligence, as a department of mental activity coordinate with the feelings and the will. And of the several Faculties of the Intelligence, it is restricted to the operations of but one — the Discursive Faculty, or Faculty of Comparison.

The distinctive nature of Thought may be indicated in a general way thus : The Faculties of original cognition first, as a condition to the exercise of Thought, present to the mind one or another of their several objects. These objects, as apprehended, become, as cognitions, the materials upon which the Faculty of Thought then commences its operations. If, for example, the Faculty of Perception present any object, as a Tree, the object is first apprehended vaguely and simply by itself. But as the attention is concentrated upon it, it is apprehended as standing in certain relations — either in external relations to other objects which with it make up a certain sphere of knowledge to us, or in internal relations to some of its own parts or properties.

The object, thus viewed in relation to the object without or to the part or property within, is said to be thought. Before, the tree was simply perceived — known simply in itself; now it is known relatively to something else — to some object external to itself, or to some internal part of itself: for instance, externally, as distant from some other external object ; or, internally, as broadly-branched, as covered with foliage, as fruit-bearing, or as having some other property or character. Thought, then, is a cognition, not immediate and irrelative, as is a perception, an intuition, an imagination, but mediate and relative — a cognition of an object as related to something else. We think the tree, when we apprehend it as distant, as branching, and the like — as having some attribute.

Logic, thus, as the science of Thought, is limited to a single department of our cognitive functions — to the function of relative cognitions. Its more precise nature will be exhibited in the sequel.

§ 2. The utility of Logical Science may be estimated from the inherent excellence and interest of the utility of Science itself, and from its value as a Mental Dis- L ° S1C " cipline and Instrument of Knowledge.

Objectively, as a science to be acquired and understood, Logic claims a twofold consideration. First, in ( a ) objectrespect of its object-matter, Human Thought, s^rice of As no science presents more commanding induce- Thou s ht - ments to its investigation and study. The mechanism of Thought, its parts, its springs, its movements, its products, its guides and principles, — no subject certainly possesses a prior claim to the consideration of Thought itself than this its own mechanism. All science, all our systematic, methodical knowing, is the product of Thought. Thought introduces into the Temple of Truth. The first truth we gain is given us by Thought, and all subsequent truth is equally her gift. Perception and Self-Consciousness give us objects of knowledge, furnish the rude materials of Thought. But their products are, in themselves, but the most meagre, vaguest cognitions.

They are only impressions. It is the prerogative of Thought to attribute to these vague impressions reality, to determine their relations to the universe of truth around, to mark the inner properties which characterize and qualify them.

It is under the prompting and guidance of Thought, indeed, that Perception itself moves on from the most indeterminate observations to full and definite cognitions. Without the aid of Thought, it stumbles and falls at the very threshold of knowledge. The keenest eye and the most laborious delving in the earth can at best uncover but little of the story of the antediluvian world. Out of a single fragment of a fossil, geological Thought reads a voluminous history of life, habits, conditions, laws, belonging to ages before the flood. The mere observer might sweep his eye over volumes of an ancient language, and be little wiser as to its history and connections, its laws and structure ; while a single page furnishes all the conditions necessary to enable the disciplined Thought of the philologist to determine all. The great part of astronomical facts, of such as are attainable without Thought, were known to the early Oriental shepherds. Thought, out of those few observations, has constructed that magnificent structure of modern astronomy. Indeed, human Intelligence would be little elevated and expanded above and beyond that of the brute without the Faculty of Thought. By the comparative excellence of the object-matter of Logical Science may we, thus, estimate its own importance and value.

But Logic presents another peculiar attraction, as a Pure 2. As Pure Science. Its matter lies in the mind itself; and Science. ft treats only of that which is necessary in that

matter. It has this feature in common with Mathematical Science. They both found themselves upon the operations of the same faculty — the Discursive Faculty, which, if viewed in its essential characteristics, and exclusively of its conditions and accessories, is simply an identifying faculty, ever and only recognizing the same and the different. In

Mathematical Science, its identities are those which are found only in the forms in which Being enters into our experience — the forms of Space, and Time, and are only those of the equal, the more and the less, in magnitude and number. In Logical Science, the identities in Being itself, as it comes into our experience, — the same and the different there, are in addition brought into view. Now, as only what transpires within its own realm can be accepted by Thought as strictly necessary, as what is given to thought must be ever taken only as given, — must be assumed, and so viewed as only problematical — all necessary matter lies in thought ; and as Logic, like Mathematics, takes into view only the necessary in thought itself, it is, as conversant only with the necessary, a Pure Science. Mathematics and Logic are, thus, as the only sciences of pure thought, the only sciences of necessary truth. No other science possesses properly the character of necessary matter, except so far as pure thought enters into and characterizes it ; and wherever, in whatever department of knowledge, pure thought enters, there is necessary truth. There is here discovered an eminent incidental utility of Logical Science that it enables us to discriminate readily what is necessary from what is at best but contingent in any department of knowledge, while it claims to itself all those distinctive attractions and excellencies which properly belong to Pure Science.

Subjectively, however, as Instrument of Knowledge and of Mental Discipline, Logic claims the highest con- (t>) Subject-

., ' . ^ c ' .° & ive Utility

sideration as a useful science. of Logic.

It is, indeed, in a certain restricted sense, only a Formal Instrument of Knowledge. It can of itself effect no new discovery in the field of matter from which it derives the conditions of its operations. We cannot begin with our thought, and out of that evolve being — construct sciences of the world external to thought. It is but gross self-imposture to assume a mere form of thought, an empty formula, and then, out of this, educe outward, objective reality. It is no function of

Thought, of itself to amplify any science in respect to the proper object-matter of that science. So far as it attempts this, it invades the territory of the Presentative Faculties, and its attempts are suicidal. . •

Still, Logic is true Instrument of Knowledge. It prompts

1. As Aid to an( l guides the proper Presentative Faculties. Discovery. Except as these lead on to Thought, and except as Thought elaborates their rude and indeterminate cognitions, they themselves seem to lose spring and motive to exertion. They are, to a great extent at least, blind, also, and need to be directed as to the proper objects which they are to apprehend and to present to Thought. How much of modern astronomical discovery has been prompted and guided by Thought ? Certain relations in the solar system, obtained by pure, scientific Thought, indicated the existence of planetary worlds here or there in space ; and the telescope, guided by these indications of Thought, brought the unknown worlds into view. Indeed, a large proportion of the new discoveries that are made in the progress of every science have originated in what have been vaguely called analogies, which have been furnished by Thought. And it is the province of Logic to unfold the laws that govern these analogies, determine their conditions, test their soundness and validity.

Further, all proper science is the product of Thought, and

2. As Builder lies wholly within the domain of the Discursive of Science. F acu i ty f fl^ human Intelligence. The cognitions of Perception, as already remarked, are vague and indefinite ; the cognitions of the pure Reason, or, as it has been called, the Regulative Faculty, are equally without limitation and without relation. Science is relative and defined cognition. It is the proper province of Logic to acquaint us with the laws of all science, or all relative cognition, and thus, in the intelligent application of these laws, to conduct us to assured knowledge.

While Thought deals only with cognitions, with what is already in the mind, and thus, strictly speaking, originates no material knowledge, we must not take in too narrow an application the truth that it is but the Formal Instrument of Knowledge. Mathematics, like Logic, is a Formal Science, yet our knowledge of the heavenly bodies has been chiefly furnished to us by Mathematics. The facts given in observation are comparatively meagre. Astronomy has in fact made most of its growth since the time of Kepler and Newton, and that growth has been effected chiefly by mathematicians, not by observers. What Mathematics is to the outer world, Logic is to the inner world of truth. Neither can do anything for any object of science, till the object is given to it ; neither can start forth and from its own underived and unacquired resources construct any system of knowledge. But matter being given it in very meagre amounts, and each, in its sphere, can build up vast structures of true knowledge ; for the essential qualities of any object of knowledge are very few in comparison with the relative. While the observed attributes increase arithmetically, the relations of thought increase with the rate of permutation and combination. When a fragment of a bone was presented to Cuvier, he was enabled in thought to read in it the size, age, habits, the specific characteristics of the animal to which it belonged. So Thought, out of a fragment of fact, interprets rich and vast treasures of truth through its relations, internal and external. It is true that Logic is not Thought ; it is true, also, that men think without Logic. So Mathematics is not Astronomy ; and men can compute without arithmetical rules. But how extremely limited is all such computation, all such thought ; and at best how uncertain are its results, and even although correct, how little assurance do these results give to the ignorant calculator and thinker ? The absolute impotence of Logic, of Thought, to construct a science in any department, without the matter of that science being previously given in experience, is now every where recognized. Not so distinctly recognized is its dependence on the other faculty or source of knowledge — the

Regulative Faculty — the Reason — Common Sense. But if not its absolute impotence, still its impotence to any thing valuable or worthy, is just as real without the ideas of the Reason, as without the facts of experience. Of what worth would science be to us, even were it possible, that proceeded independently of our ideas of Space and Time ; of Being, Substance, Cause ; of Truth, Beauty, Rectitude, and Goodness ? Logic can venture forth not one step in safety, or in promise of attaining any worthy result, except as these great ideas of the Reason guide and animate, as its processes are upon and through these fundamental data of the Intelligence. But in turn, these grand ideas are of little worth to us, except as Thought apprehends them, scans them in their manifold relations, and then determines and indicates these relations.

Logic, indeed, is not Thought ; it is only Thought applied to Thought ; the science of Thought, or still more precisely, the science of the necessary in Thought. But this very limitation of Logic suggests its immeasurable utility to the spirit of man, whose dignity consists so much in Thought. If Logic is not Thought, it yet presides over Thought, and prescribes its function and its sphere. It preserves us, thus, from illusions and phantoms, which are for the most part occasioned by the confounding of experiences and thoughts ; and the consequent imposition of thoughts for objects.

Logic, moreover, opens the way for Thought, and by presenting occasions, calls it forth into exercise. It teaches how it may fasten upon an object of experience, or an idea of the Reason ; trace out its relations ; determine its properties, its conditions, its bearings. The chief obstacle to thinking is ignorance how to think. Matter enough is given in every outlook upon the external world, in every glance turned inward upon our mental experience, to provoke and to sustain endless thought. Thought does not go forth as this gate of occasion opens to it, because it does not see. Logic opens its eyes upon the relations in their diversity, through which it may go forth to its work.

Logic, further, completes and perfects Thought. Thought necessarily remains feeble and immature, except as it is developed and matured by Logic. As Mathematics enables Thought to carry its computations to indefinite limits, and to pace off the measureless skies, while the savage can only compute but several scores, and can measure only where the foot can tread ; so Logic not only carries Thought forward in every particular direction to its remotest bounds, but also carries it over the entire field of its explorations, so that no part shall be overlooked.

Logic is useful, also, in correcting our knowledge. It has been justly termed a medicine of the mind, as it 3. as Correchelps to purge it from errors which impair and tive of Error, vitiate its healthful activity. It does not directly heal the imperfection or error that may have crept into its operations at the original presentation of its matter. But when, by its sure procedure, it discovers that the original datum as presented to it has led to results that are not in harmony with its already ascertained truths, or that involve contradictory relations, or that do not admit of being perfectly brought under the complete and necessary conditions of thought, by detecting the fact of error and its probable source, it guides and helps to the needful correction by the proper presentative faculty; precisely as Mathematics, although like Logic a purely formal science, can show that there is error somewhere in the original measurement, or the running of the lines of a survey, if the bearings and distances as given will not admit of being plotted into a bounded field, and may indicate also, possibly, where the error originated, so that it may be corrected by new survey.

Logic, still further, is of eminent utility in furnishing the proper assurance of Truth. If it is much to know, 4 Ag as _ it is often more to know that we know ; to be rea- surin s truth - sonably assured that what we accept as true is indeed true, as verified by the only possible criteria of truth within the reach of the human mind. Confidence in the correctness of the procedures of Thought, confidence in the validity of the results of Thought, is one of the leading conditions of success in all thinking. To be in doubt whether we are on the road to truth, whether we are in possession of the requisite means of attaining it, whether what we at last have reached is the truth we seek, is very mental imbecility. It is the prerogative and proper function of Logic, as the Science of the Laws of Thought, to remove the grounds of such doubt, to indicate and so to assure as certain the way to truth, and to impart credibility to the results of Thought. It is true that, in large departments of our knowledge, what we know can have at best but the character of probable truth, never that of absolute certainty. But it is the part of Logic to point out just where the lines that separate probable from absolute certainty run, and also to discover just where the contingency in imperfect knowledge attaches ; the nature, the source, the extent, the means, if any, of removal of all that impairs our knowledge. Such is the assurance that Logic gives to our thinking.

" But it is not only by affording knowledge and skill that 6. As in- Logic is thus useful ; it is perhaps equally con- Se°UndCT- ducive to the same end by bestowing power. The standing. retortion of thought upon itself — the thinking of thought — is a vigorous effort, and, consequently, an invigorating exercise of the Understanding ; and as the Understanding is the instrument of all scientific, of all philosophical speculation, Logic, by preeminently cultivating the understanding, in this respect likewise vindicates its ancient title to be viewed as the best preparatory discipline for Philosophy and the sciences at large.

" But Logic is further useful as affording a Nomenclature 6. As af- °f tne l aws D y which legitimate thinking is goven r tmc Sa No-~ erne< ^? an( l °f tne violations of these laws, through menciature. w hich thought becomes vicious or null.

" Words do not give thoughts ; but without words, thoughts could not be fixed, limited, and expressed. They are, there-

IISTTRODUCTION. 11

fore, in general, the essential condition of all thinking worthy of the name. Now, what is true of human thought in general, is true of Logic and Rhetoric in particular. The nomenclature in these sciences is the nomenclature of certain general analyses and distinctions, which express to the initiated, in a single word, what the uninitiated could (supposing, what is not probable, that he could perform the relative processes) neither understand nor express without a tedious and vague periphrasis ; while, in his hands, it would assume only the appearance of a particular observation, instead of a particular instance of a general and acknowledged rule. To take a very simple example : there is in Logic a certain sophism, or act of illegal inference, by which two things are, perhaps in a very concealed and circuitous manner, made to prove each other. Now, the man unacquainted with Logic may perhaps detect and be convinced of the fallacy ; but how will he expose it ? He must enter upon a long statement and explanation, and after much labor to himself and others he probably does not make his objection clear and demonstrative after all. But between those acquainted with Logic the whole matter would be settled in two words. It would be enough to say and show that the inference in question involved a circle, and the refutation is at once understood and admitted. It is in like manner that one lawyer will express to another the ratio decidendi of a case in a single technical expression ; while their clients will only perplex themselves and others in their attempts to set forth the merits of their cause. Now, if Logic did nothing more than establish a certain number of decided and decisive rules in reasoning, and afford us brief and precise expressions by which to bring particular cases under these general rules, it would confer on all who in any way employ their intellect — that is, on the cultivators of every human science — the most important obligation. For it is only in the possession of such established rules, and of such a technical nomenclature, that we can accomplish, with facility, and to an adequate extent, a criticism of any work of reasoning. Logical language is thus, to the general reasoner, what the notation of Arithmetic, and still more of Algebra, is to the mathematician. Both enable us to comprehend and express, in a few significant symbols, what would otherwise overpower by their complexity ; and thus it is that nothing would contribute more to facilitate and extend the faculty of thinking, than a general acquaintance with the rules and language of Logic."