A treatise on logic; or, The laws of pure thought; comprising both the Aristotelic and Hamiltonian analyses of logical forms, and some chapters of applied logic

Preface

THE revival of the study of Logic, at least in England and America, as an important element of a University education, dates only from the publication of Dr. Whately's treatise on the subject, little over thirty years ago. Yet so much has been accomplished for the advancement of the science during this short period, that this treatise, with all its excellences, must be admitted to be now as far behind the times as were the compilation by Aldrich, and the meagre compendium by Dr. Watts, the use of which it superseded. Dr. Whately lived long enough to be able to appropriate to himself the epigrammatic boast, that he had labored so effectually as to render his own work useless. Without the interest which was awakened in the study of the science by the publication of his book and the discussions which it excited, it is not too much to say that many of the valuable works upon Logic, which have appeared during the last thirty years, either would not have been written, or would have lacked some of their most interesting and important features. Sir William Hamilton's own labors in this department, by which he certainly accomplished more for the science than has been done by any one man since Aristotle, began with an elabo-

IV PREFACE.

rate article on Dr. Whately's treatise in the Edinburg Review, a paper which, as he has himself declared, contains the germs of all his subsequent discoveries. Besides what Hamilton has accomplished, the publications within this period of Professor Mansel, Dr. Thomson, Mr. De Morgan, Mr. Boole, Mr. J. S. Mill, and a host of others, have given an entirely new aspect to the science. Among recent American works upon Logic, honorable mention ought to be made of those bj Mr. Tappan, and bj Dr. W. D. Wilson of Geneva.

The only hope that this volume may be found to be of some use consists in the fact, that, as I was the last to enter the field, I have been able to profit by the labors of my predecessors. Certainly it could not have been written without their aid, and one of the chief objects held in view in the preparation of it has been to gather together, and digest into system, their several improvements and elucidations of the science. At the same time, the work would not have been carried on in the same spirit in which they began it, if I had not ventured respectfully to dissent from some of their doctrines, and even to present some opinions which will very likely be found to have no other merit than that of originality. As Le Clerc remarks, in introducing his own lucid and thoughtful compendium of the science to the reader's notice, "5t, in hacce Logica, nihil esse novi, aut pleraque 7iova dixerim, lector em perinde fcfelleroy

When Dr. Whately wrote, it was not so frequent a practice as it has since become for English scholars to profit by the labors of their German brethren, and hence some of the greatest deficiencies of his book. It cannot be said that the study of Lps^ic ever declined in the schools of Germany, as

PREFACE.

it did in those of France, England, and this country. Upheld for a time by the genius of Leibnitz and the indefatigable industry of Wolff, it was at last reduced to rigorous system, its boundaries were fixed, and its relations to Psychology and Metaphysics accurately determined, by the master mind of Kant. Though this great Metaphysician prepared no distinct work upon the subject, the volume relating to it which passes under his name being a mere compilation from his loose notes by Jasche, the science has profited more by his labors than by those of any other Continental writer of modern times. Indeed, the publication of his " Criticism of Pure Eeason" formed hardly less an era in the history of Logic than in that of Metaphysics. In one respect, it is true, it had an injurious influence, as it established the practice, which has since become wellnigh universal in Germany, of modifying the doctrines of this science in order to furnish a basis on which might be erected any peculiar scheme of speculative Philosophy. Since Kant's time, a multitude of treatises upon Logic have been published by German writers, about half of them having no other purpose than that of preparing the way, and furnishing the materials, for some extravagant speculations in Metaphysics. This mode of treatment was carried to an outrageous extent by Hegel, who labored to break down altogether the boundary that had been established by Kant, and whose elaborate work, bearing the name of Logic, is a mere perversion and caricature of that science, as it is metaphysical from beginning to end. Even Trendelenburg, who has contributed more than any other person to the rapid decline of Hegelianism in Germany, is not free from blame in this respect, his very able work, Logischc TJiitermchimgeny

VI PREFACE.

being devoted in great part to building up a philosophical system of his own.

But the very prevalence of this abuse in Germany furnishes an additional motive for the study of the subject. A key to German Metaphysics can be obtained only by a thorough mastery of the principles and the terminology of Logic. To some persons, perhaps, this consideration may not have much weight, as they will object, that it is of little use to be able to open the door, if the room contains little more than rubbish. Still I cannot but believe — and the opinion is founded on considerable experience as an instructor in both departments — that a fair knowledge of Logic is a natural, and even an indispensable, preparation for the successful pursuit of Psychology and Metaphysics; — may I not add, of any philosophical speculations whatever? It appears certain, that the University lectures of Kant, Fichte, Schelling, and Hegel could not have been made even intelligible, much less instructive, to hearers who had not previously acquired at least the elements of Losrical science. Hence the multitude of manuals and text>books upon this subject, which have appeared in Germany during the last three quarters of a century, many of them having passed through numerous editions, and each betraying very plainly the particular system of Philosophy to which it was intended to serve as an introduction. Some familiarity with the principles of Logic appears essential for a thorough comprehension even of the metaphysical doctrines of Sir William Hamilton, which, both in their philosophical and theological bearings, seem likely to exert a considerable influence over English and American minds for many years to come.

PREFACE. VU

Hamilton's "Lectures on Logic" are marked with the inevitable defects of a posthumous publication, the larger portion of which was probably never intended by the author to be given to the public ; and though very ably edited by Professor Mansel and Mr. Veitch, they present a mass of crude material from which a knowledge of the peculiar doctrines of the writer cannot be extracted but with considerable difficulty. Indeed, the " Lectures," which form the body of the book, were evidently prepared in great haste, when the author's appointment to the Professorship in this department, in 1836, obliged him to collect at short notice the materials for an extended course of instruction. He appears to have met this sudden call by hurriedly translating a series of extracts from the most approved German text-books, especially those of Krug, Esser, and Bachmann, merely interpolating here and there some of the comments, corrections, and additions which could not fail to occur to so rich a mind as his, while traversing so broad and familiar a field. These Lectures, containing only a glimpse of one feature of the peculiar system which has since become identified with his name, he seems to have repeated from year to year, during his whole period of office, with no material enlargement or alteration of the manuscript, though doubtless inserting, from year to year, many extemporaneous expositions of his corrections of the leading doctrines of Logical science, as these occurred to him at successive periods. The whole transaction seems to me to affi)rd an instructive comment on the futility of what is called the Professorial mode of teaching, which has always prevailed in the University of Edinburgh, and which consists in getting up very

Vlll PREFACE.

hastily a course of lectures during the teacher's first year of office, and repeating them, parroWike, from year to year, without any regular use of a text-book or manual of instruction. If such lectures contain anything really valuable, in addition to what is already before the world, they are apt very soon to find their way to the press ; if they are 'of little worth, they are almost sure to be repeated, with little alteration, to one class after another, and with as little profit to the hearer as exercise to the reader. It may be doubted whether the most fertile and best-trained minds, at least in the speculative sciences, are capable of preparing every year an entirely new course of lectures, without either filling them with crudities and truisms, or lapsing into paradox and extravagance, such as have too frequently characterized the productions of German Professors.

With all his amazing activity of mind and prodigious erudition, Hamilton appears to have been either too indolent, or too critical of his own labors, to be able, without great delays, to digest his materials into a shape fit for publication. He was not an adept in the very low, but very necessary, art of book-making. But for his controversy with Mr. De Morgan, I doubt whether he would ever have worked up into form as much as he did of his " New Analytic of Logical Forms," the publication of which was promised as far back as 1846. Stimulated by opposition, however, though impeded by ill-health during the later years of his life, he appears to have labored strenuously, after the lastmentioned date, to fulfil this promise. Death surprised him long before he had completed his preparations ; and out of the mass of fragmentary materials which were found among his papers, with

PREFACE. UC

some aid from the few critical and controversial articles that he had already printed, his editors pieced together, with great difficulty, the imperfect view of his improved system of Logic, which appears as a long Appendix to the volume of his Lectures. The manuscripts which they selected and arranged were judiciously printed just as he left them, and with very little editorial comment. The reader must gather from them as best he may, always keeping in view the date attached to each fragment, a connected view of Sir William Hamilton's latest doctrines upon the subject. This posthumous work has at least one odd characteristic, as the body of the work and the Appendix flatly contradict each other, by giving opposite views of the science to which they relate.

These are the sources whence I have endeavored to collect the materials for a general survey of the science of Logic in its present state, embracing what is common to all systems, and a review of most of the questions relating to it which are still open to discussion. Among English authors, after Sir William Hamilton, I have been chiefly indebted to Professor Mansel ; for without the aid afforded by his Prolegomena Logica, and the notes and supplementary matter appended to his edition of Aldrich, of which Hamilton justly remarks that la sauce vaut mieux que le poisson, this book would have cost me much more labor, and yet would have wanted what are now its best claims to notice. I have also derived much help from the excellent " Outline of the Laws of Thought," by Dr. Thomson, the present Archbishop of York. Among the German writers, besides all whose names have been already mentioned, I have made profitable use of Kiesewetter,

X PREFACE.

Fries, Beneke, Dressier, and Drobisch, besides consulting a host of others. Of the earlier logicians, it seems to me that Burgersdyck, with the annotations of Heereboord, gives the clearest account of the science as it was taught in the schools before the influence of Descartes and Locke began to be felt; and that the Port Royal "Art of Thinking," of which an admirable translation, with Notes and an Appendix, by Mr. Baynes, has recently been published, is far the best of the treatises on the subject which were in use during the eighteenth century. Throughout the work, I have kept constantly in view the wants of learners, much of it having been first suggested while attempting to expound the science in my own classroom. My highest ambition will be satisfied if it should be found to be of use to other teachers.

Cambbidge, March, 1864.

Contents

CHAPTEE I.

Pagb

Psychological Introduction ....•••!

Chapter II

The Form distinguished from the Matter of Thought . • 31 Universal distinguished from Special Logic . . . .34

Divisions of the Science ....... 36

Utility of the Study of Logic .38

CHAPTER III. These Axioms reduced to one Principle .... 48

This Principle explicated into three Axioms . . . .49

Analytic distinguished from Synthetic Thought ... 52

The Principle of Synthetic Thought explicated . • . .53

Hamilton's Postulate of Logic 55 xu

CONTENTS.

Chapter IV. 62 66 70 , 72 75 77 84 86 90

The Elements of a Concept

The twofold Quantity of Concepts . .

First and Second Intentions . . .

The Relation of the two Quantities to each other

Infinitated Concepts .....

The Quality of Concepts ....

The Standards of Nominal and Real Definition

The Relations of Concepts ....

The Laws of Homogeneity and Heterogeneity

Definition and Division 93

CHAPTER V. The Doctrine of Judgments

The Nature of the Copula ....

The Predicables and the Categories .

The Quantity of Judgments, Aristotelic Doctrine The Quality of Judgments, " "

Quantity as afiected by Quality, " "

The Relation of Judgments ....

Conditional Judgments ....

The Hamiltonian Doctrine of Judgments Explication of Propositions Into Judgments .

CHAPTER VI. JEquipoUence or Infinitation . . . . . . 152

Hamilton's Doctrine of Conversion 160

Conspectus of Judgments and Immediate Inference, Aristotelic

Doctrine 166

Hamilton's Doctrine of Opposition and Integration . . 168

CONTENTS.

XIU

CHAPTER VII. Thb Doctbinb of Mediate Inference : the Abistotelio Anai^

TSis OF Syllogisms 174

The Canon of Categorical Syllogisms . . This Canon explicated into Six Bales Dictum de omni et nuUo ....

Figure and Mood .....

Redaction to the First Figure . . .

The Mood of a Syllogism . . .

The Technicalities of Redaction exemplified Conditional Syllogisms ....

Disjunctive Syllogisms ....

Dilemmas or Hypothetico-Disjunctives Defective and Complex Syllogisms . .

Sorites

Conspectus of the Aristotelic Doctrine of Syllogisms

CHAPTER VIII. The Hauiltonian Docteinb of Syllogisms .... 228

Analytic and Synthetic Order of Enouncement . . . 228

Reasoning in the two Quantities 234

The Doctrine of the Figures 239

The Unfigured Syllogism ....... 244

Hamilton's System of Notation or Symbolization . . . 246

The Number of Moods increased by Quantifying the Predicate . 251

The worse Relation of Subject and Predicate . . . 253

Hamiltonian Table of Moods ....... 256

Falsity of the Special Rules demonstrated .... 259

Applicability of the diflFerent Figures to Deduction and Induction 261

Conditional Syllogisms reduced to Immediate Inferences . . 264

Chapter IX

Fallacies in dictione improperly so called .... 269 Division of Formal and Material Fallacies . . . .271 Syllogisms of more than Three Terms ; Ambiguous Middle . 272

XIV

CONTENTS.

Undistributed Middle ; Composite and Divisive sense Illicit Process of the Major and Minor Terms The Sophism of Eubulides, the Liar Sophisms respecting the Quality of the Reasoning Violation of the Canons of Hypothetical Eeasoning Material Fallacies ; petitio principii . , , Fallacy of the Impossibility of Motion . Ignoratio denchi ...,.,.

Argumentum ad ignorantiam i . . .

Non Causa pro Causa; post hoc, ergo propter hoc . Ignava Ratio . ... . , . , Achilles and the Tortoise .....

Chapter X

Science formed by Analysis and Synthesis . . . Classification in Science .......

The Relation of Cause and Effect ....

Necessary Cognitions a priori ......

These Cognitions not mere Laws of Thought . . Elements of our Concepts of Individual Objects . . The preliminary Classifications of Science . . . Science advances through the improvement of Classifications Failure of the attempts made to classify the Sciences .

CHAPTER XI. Demonsteative Reasoning and Dbductivb Evidence , . 351

Demonstration applicable to mere Concepts, not to Real Things 352

Why Mathematical reasoning is demonstrative . . . 353

Mathematical evidence not a mere perception of identity . . 359

Distinction between Pure and Applied Mathematics . . 361

The Conclusion not deduced from the Major Premise . . 362

The only New Truth is that enounced in the Subsumption . 364

Particular facts not learned, but proved, by Reasoning , , 367

Difierent classes of Major Premises ..... 371

Technical terms used in the Construction of Science . . . 374

CONTENTS. XV

CHAPTER XII. Ikdttction akd Analogy 376

Want of Universality in the Sumption fatal to strict Beasoning 376

Induction and Analogy are means for discovering Truth . . 380

Difference between them illustrated ..... 381

Analogy is Aristotle's Seasoning from Example . . . 382

Analogy leads only to Probable Conclusions . . . 383

Induction presupposes the correctness of previous Classifications 385

Uniformity of Nature the basis of Induction . . . 383

This Maxim not an Ultimate Fact 389

And not first obtained by Induction ..... 391

But derived from the Principle of Causality .... 395

What is Physical Necessity 400

All Induction proceeds by simple enumeration .... 401

A universal Logic of Induction cannot be established . . 403

A General Fact, a Law of Nature, and a Cause distinguished . 405

How a Law of Nature is discovered 409

Physical Causes proved by the Laws of Nature subsumed under

them 414

Induction discovers, the Law of Causality proves . . . 416

CHAPTER XIII. The Socbces of Evidencb and thb Causes of Ebbob . . 419

Intuition the basis of all Certainty 419

Intuition of external objects as external 421

Memory as a Source of Evidence ..... 423

The art of Writing an auxiliary to Memory .... 426

The experience of others a necessary aid ... . 427

Testimony distinguished from Authority ..... 428

And Veracity from Competency 430

Hume's Argument against Miracles examined .... 432

The Criticism of Tradition and Ancient Writings . . 433

The Theory of Probabilities 437

Moral Causes of Error 445

LOGIC.

Chapter I. Psychological Introduction

Intuitions distinguished from Concepts. — Mental Characteristics of Brutes. — Relations of Thought to Language.

THE beginning of all knowledge is in single acts of tlie Perceptive or Acqmsitive faculty, each of which relates immediately to an individual object or event. Such acts are called Intuitions or Presentations ; the former is the more generally received appellation. Each Intuition gives us a knowledge of its object so far only as this object is perceived now and here, and also as it is one, or undivided, though not necessarily indivisible. To recognize, or know over again, the object as similar to another tiling perceived on a former occasion or m a different place, or to analyze it into its parts or attributes, or to refer it to a class of tilings previously known, and thereby to give it a common name, requires the aid of a different alid higher power of the mind. In receiving Intuitions, the mind exerts no conscious activity whatever ; it is passively receptive of any impressions that may be made upon it, and does not in any way consciously react upon or modify those impressions. It is like a mirror reflecting the objects that are held up before it, perhaps giving distorted or unfaithful images of them on accomit of tlie imperfections of its own surface, but hav-

1 A ing no power to change or in any way affect them by its own will.

The impression made upon my mind by the portrait of a friend which I am now looking at, as it hangs before me, or by the sounds to which I am listening as they are struck upon a violin ; the image now present to my memory of the relative whom I have recently lost ; the picture of a waterfall in a wood which my imagination at this instant forms ; the consciousness which I have of the present state of my own mind ; — all these are Intuitions, as each one of them relates to a single object, and each is immediate^ — that is, it does not come through the intervention of any other state of mmd. But what is denoted by the word man^ sounds or waterfall, is not an Intuition, for it does not refer to one object only, but to many. Man, for instance, includes under it John, Thomas, William, and many others ; and it does not convey a complete image of any one of these persons, but only a partial representation equally apphcable to any of them. John, when considered simply as man, is not regarded as he really is, that is, as possessing all his individual attributes and peculiarities, but only as having those attributes which he possesses in common with all other men ; he is not viewed immediately, but only through the medimu of what is called a Concept, or ^Thought of what is common to many. These words, therefore, man, sound, waterfall, and all other common names, do not denote Intuitions, but Thoughts.

The Perceptive or Acquisitive faculty, through which we receive Intuitions, as it is a merely passive power, or a capacity of being affected in a certain way, constitutes what may be called the receptivity of the mind. The Thinking or Elaborative faculty, — i. e. the Understanding, — as it has no Intuitions of its own, but voluntarily reacts upon and modifies those received fi'om the Perceptive facility, comparing them with each other, and thereby combining

I them into one Thought, or disjoining them as dissimilar or incompatible, belongs to the spontaneity, or self-activity, of the intellect.

In the ordinary exercise of oiir faculties, Intuitions are so intemiingled with Thoughts, so quickly pass into them, and are so closely connected with them, that it is difficult to illusti'ate the distinction between the two by giving an example of an Intuition so isolated and peculiar that there will be no danger of confomiding it with any portion of a voluntary and more complex process of mind. But a good illustration may perhaps be foimd in the case, so frequently referred to, of a person bom entirely blind, and subsequently enabled by a surgical operation, for the first time, to see. Suppose that the first visual sensation given to such a person were that of a flash of red light. This sensation, it is evident, would be to him enthely peculiar or 8u% generis. He could not, at first, refer it to any class of things with which he was formerly acquainted ; he could not give it a name ; he could not analyze it into parts or attributes. He did not will to produce or to modify it ; it comes to him, so to speak, of its own accord. He could Tmoiv it, but not recognize it, as the presentation of an enthely new object, by which his mind was involuntarily affected in a new and surprising manner. Such, we may suppose, are the Intuitions of brutes ; and the faculty of Intuitions, as the Perceptive or Acquisitive faculty may be called, — a mere receptivity^ unmodified by any voluntary act of the patient, — is probably the most prominent of the few mental powers which brutes possess in common with man. In respect only to Intuitions produced in him by external causes, man has no advantage over the lower animals.

But although all our knowledo-e begins in Intuitions, it does not end vdth them. In man, the mere receptivity of mind is so soon modified by its spontaneity, — the mere Intuition so quickly passes into voluntary or consciously active

Thought properly so called, — that we can hardly tell where the one ends and. the other begms. To recur to the case just mentioned ; the moment the person who has now first received his sight begins to consider or reflect upon the new presentation that has thus been made to him, he probably, in a certain sense, recognizes it as a new sensation^ — that is, he refers it to a class of feelings with which he was formerly acquainted, as coming to him through the other senses, and which, as similar in some respects, though different in others, he has ranked together and called by one name, " sensations " or " feelino-s." Such recoo-nition is an act of Thought properly so called. It includes comparison of this Intuition with others, and a conscious discrimination of those respects in which it is similar to others from those in which it is unUke them. The Perceptive faculty gives us Intuitions of single objects, each of which is to us a distmct unit, having no connection or relation with anything else ; the Understanding, a higher faculty, gives us Thoughts, or enables us to analyze each thing into its parts or attributes, and thus to recognize its various points of resemblance and difference, and so to form classes of things. The former power furnishes the rude material — "the Matter," as it is technically called — of our knowledge ; the latter supplies " the Form," elaborating and disposing this rude material in a systematic way, or accorduig to regular laws, by tln^ow ing it into groups, so as to render it conceivable to Thought. Hence the Understanding has been called the unifying facidty, by which the many is reduced to unity.

If we look out of a window for the first time upon a landscape that is entirely new to us, the momentary glance gives us only an Intuition of the scene, or a confused knowledge of it as one whole, without any distinction of parts, and without recognition of any of these parts as former objects of knowledge. This is because the Understanding requires time to do its work. But if we dwell long enough upon the scene, first, we recognize (or know over again) one familiar set of objects, and call them trees ; then, other classes of objects previously kno^vn, and call them respectively buildings, rocks, hills, &c. Lastly, we consider the relations of these objects and classes of objects to each other and to similar objects fonuerly known, in respect to distance, magnitude, color, &c. , and are thus enabled to think the landscape as a whole. Tliis Thought contains a far more perfect knowledge than the Intuition, which was all that the senses gave us at the first momentary glance.

Now, how much is implied in the successive recognition of the component parts of this knowledge as objects previously known, and therefore appropriately designated by a famihar name ? Of course, as the landscape is supposed to be now seen for the first time, we do not recognize any individual tree, building, or hill in it as precisely the same object that we have formerly seen. We mean only that we recognize it as similar to some fonner objects of knoAvledge ; that is, having seen many objects wliich agreed with each other as similar in many of their parts, — as possessmg trunks, branches, and leaves, — we have formed them into one class, and called them trees. The object in the new landscape is then recognized, not as famihar in itself, but as belonging to a familiar class of tilings ; we do not recognize it as an Intuition, but as a Concept, — not as this tree, but as a tree. Conception is that act of the Understanding or Thinking faculty whereby we unite similar objects into one class by overlookmg their points of difference and forming their common attributes into one Concept or Thought, the name of which thus becomes the common name of all the individuals included in the class. Here, again, the unifying office of the Understandhig appears ; the Concept reduces the many to unity, — brings together many objects into one Thought or many attributes into one subject. Thus we are properly said to know many objects which we have never seen ; for, through hearing or reading descriptions of them, we have formed a right Concept of what they are, and thus are enabled to recognize — i. e. know them over again — and call them by their appropriate name, when we do see them. But this evidently is only mediate knowledge, and is more or less imperfect and inadequate, depending on the scantiness or fulness of the Concept. As Mr. Mansel remarks, a Concept " is not the adequate and actual representative of any single object, but an inadequate and potential representative of many." And again, " it is not the sensible image of one object, but an intelligible relation between many."

Concepts can never come to us from without, for the external world has no Concepts. It has not even Intuitions or Percepts, but only real objects, — that is, persons and things, and their marks or attributes. Every real object has an indefinite or comitless number of such attributes ; for, however long and careftJly we may observe it, we can never be sure that we have ascertained all its elements and quahties. Carry the chemical analysis of it one step further than before, or place it in new relations with other real objects, and it will manifest new properties or activities, the existence of which was formerly unsuspected. Observation, which proceeds by a series of Intuitions, can make known to us an indefinite number of these attributes, but can never exhaust them. Hence the knowledge which we can acquire by Intuition, though constantly increasing in ftilness and complexity, can never become complete, and is always attended with some uncertainty; as any conclusions that we form respecting the object may be vitiated by the presence of a quality or element of whose existence we were ignorant. Moreover, the limited compass and finite powers of the human mind cannot take in at once all even of those attributes whose presence is perfectly known. The image or representation of the object in our minds unmediately t becomes confused, when we attempt to make it grasp too much, or to comprehend, in truth, more than a very few of the known attributes. Giving up the attempt at completeness, then, we form a Concept of tlie object embracing comparatively few of its ascertained qualities, but selecting those which are most distinctive and essential, in order thereby more readily to discriminate it from other objects of a different class. Such a Concept is certainly incomplete, but it is clear in proportion to the narrowness of its dimensions. We can more easily grasp it in thought, and contemplate it at once in its entireness, because it has so little complexity. On the other hand, the lack of fuhiess is apt to render the boundaries of the Concept somewhat less distinct. Consequently, any object, so far as it is knoAvn only mediately^ or through such a Concept, is known only in a few of its leading attributes ; and it may even be doubtful whether another object, which resembles it in these attributes, but departs very widely fi'om it in others, ought to be ranked in the same class with it, and called by the same name, or not. If my Concept of tree, for instance, is limited to these few particulars, — a vegetable organism possessing a main trunk, branches, and leaves, — it will be doubtful whether many small plants ought to be called trees or shrubs. But if I attempt to enlarge the Concept by introducing more attributes, so as to distinguish tree fully from all other plants, the idea becomes cumbrous and confused ; we cannot so easily embrace it in a single act of thought.