Hegel's logic

Front matter

4 o

*> N A o_

V y • o

Preface

WHEN I promised Professor Morris to write this book (in 1883), I intended to throw together some of my previous studies on Hegel's Logic, with the addition of more or less new matter in the form of commentary and connecting introductions. I had worked pretty constantly on the subject of this logic — though mostly using the expositions of it which I found in histories of philosophy, rather than Hegel's own exposition — as a sort of center of all my thinking since the year I860, making, it is true, very slow progress. I had always cherished the project of writing some sort of commentary to the work, but did not think that I could prepare a worthy book for twenty years.

I soon discovered that if I were to place before the public an immature work on this subject I should find myself embarrassed at any time afterwards to obtain a hearing for the ripened views which I hoped to reach. I began, accordingly, to prepare a more thorough treatise, and to this end I set about a study of the entire scope and plan of the Hegelian Logic, and especially of its relations to other branches

VI PREFACE.

of knowledge and to preceding philosophic systems as well. I struggled for a long time with the preliminary question : how-to convey to a neophyte an idea of the province of such a system of "pure thought" — how, in short, to demonstrate the necessary existence of pure thought and show its significance in solving all problems. Such pure thought, could one demonstrate its existence as an element in all concrete problems, would furnish the formulae for the solution of all questions.

But these new investigations consumed much time. I gradually felt myself turning around from my attitude of faith in the Hegelian exposition, to an attitude of criticism. Formerl} I had trusted where I did not see — trusted tfyat I should see when I had gained more power of apprehension. Now I attacked what I could not verify with my present insight, and insisted on its falsity until it should demonstrate its truth. In this frame of mind I discovered many passages wherein it was evident that Hegel had introduced what he should call "external reflections," and many more wherein the "dialectic thread" w T as supposititious. For example, in the first chapter of The Phenomenology, his assumption of the Here and Now as the forms of immediate sense-preception would be seen to be necessary and exhaustive, had he called attention to the fact that time and space are the necessary forms of all sense-perception, as well as the logical conditions of

PREFACE. Vll

the existence of the sense-world. The immediately present objects of time and space are necessarily Now and Here. Such omission leaves the exposition apparently without exhaustive universality. It seems an accident that Hegel takes the now and here as the two forms. This is, of course, a defect only of the exposition, and not of the underlying insight of Hegel himself. We can see that he saw this exhaustiveness, but we can see also that he ought to have expounded it, but was held back by his desire to avoid "external reflection/' a desire that amounts to a "phobia" with Hegel. He strives always to make the object "unfold itself " (sick enhvickeln), and shrinks from expressing any idea until it comes obviously before us in consequence of objective dialectic.

This " objective dialectic" is the exhibition of the inadequateness and imperfection of a thought when it is assumed to be universally valid and true. Such a thought, if assumed in each of the forms of the absolute, namely, (a) as by itselfand independent ; (b) as in negative relation to itself as its own other, (c) in identity with itself in its other, will show up its imperfection and lead to a deeper thought which contains explicitly what the former thought has held only implicitly and has had to show dialectically as its contradiction.

This process, with the pure forms of experience — that is to say, with the categories underlying experience — gives us a sort of organon, or

Vlll PREFACE.

logic of ontology, containing in general formulae all the solutions to be found in experience.

Just as in the case of mathematics, the analytical solution given in the algebraic formulae is a general one and furnishes the pure form for all concrete or applied solutions ; so the " pure-thought" solution, according to this logic, develops what is essential in all solutions of particular cases ; for these particular cases are only applications of the pure-thought elements to limited spheres of conditions. Once master of the general solution, one can solve the practical questions that fall under it.

I must ask the reader to indulge me in further autobiographical reminiscences with the purpose of explaining what I have set forth as strictures on the Hegelian system.

As early as 1858 I obtained my first insight into this philosophy, in studying Kant's Critique of Pure Reason. I saw that time and space presuppose reason as their logical condition and that they are themselves the logical condition of what is in the world. Man, in so far as he is conscious reason, therefore transcends the world of time and space and is an immortal being, and possesses transcendental freedom also inasmuch as he is not conditioned essentially by the world — not essentially, but only in the expression or manifestation of his will, which expression he may altogether withhold. I saw also the necessity of the logical inference that the unity of time and space presupposes one absolute Reason. God,, freedom, and immortality

PKEFACE. IX

have therefore seemed to me to be demonstrable ever since the December evening in 1858 when I obtained my insight into the true inference from Kant's Transcendental JEsthetic. In 1859 I worked out my refutation of Sir William Hamilton's Law of the Conditioned, by proving the infinitude of space and showing that the supposed antinomy rests on confounding mental pictures with pure thought. The unpicturability of infinite space does not contradict its infinitude, but confirms it. In 1863 I arrived at the insight which Hegel has expressed in his Fur-sich-seyn or Being-for-itself, which I called, and still call " independent being." I did not obtain this insight by study of Hegel's logic, however, but rather by following out the lines of thought begun in 1858. This insight I supposed at the time to be specially that of Hegel, though I had not as yet read onetenth of his logic. But I discovered afterwards that it is the most important insight of Plato, and that Aristotle uses it as the foundation of his philosophy. It has in one form or another furnished the light for all philosophy worthy of the name since Plato first saw it. St. Thomas Aquinas presents it in the beginning of his Snmma Tlieologica. Leibnitz states it as the basis of his Monadology. But each thinker may claim originality, not only for his statement of it but also for the insight itself. For it cannot be borrowed from another, it is itself an original insight, because it is and must be a seeing at first hand of the necessity of all existence of

X PREFACE.

whatever character to be grounded in self-determined being. All dependent being is a part of independent being ; and all independent being is self-determined being. ~

The absolute is not, therefore, an empty absolute, an indeterminate being, but it is determined. It is not determined through another, but through itself. If there is no independent being there is no dependent being. If there is not self-determined being there is no being whatever.

It was a year or two later that I came upon a distinction between the true actual as totality, and the changeable real, which is partly actual and partly potential — in the process of change I saw that the full actuality is involved, partly affirmative as giving what reality there is to the phenomena, and partly negative as producing the change which negates the present real and actualizes in its place a new phase of potentiality.

It was in 1864 that I obtained an insight into the logical subordination of fate to freedom — the totality of conditions cannot have a fate outside it, but must be spontaneous in itself, and self-determined — hence all fate and all changes not spontaneous must be secondary and derivative from a higher source that is free. In 1866 I arrived at the first insight that is distinctively Hegelian and the most important apertju of Hegel's logic. I wrote this out in a letter to my friend Adolph E. Kroeger, an ardent Fichtean, whom I had discov-. ered and was endeavoring to proselyte for Hegel. I called it the distinction between comprehension

PREFACE. xi

(or Begriff), and Idea (Idee). It should really be the distinction that Hegel makes between negative unity or substantiality and Begriff or Idee. It is undoubtedly Hegel's highest thought. It is the insight into the nature of true being to be altruistic and to exist in the self-activity of others. It is the thought that lies at the basis of the doctrine of the trinity, though rather as a logical implication than as a conscious idea. It is also the highest goal of the Platonic- Aristotelian system — indicated in the assertion that God is without envy ( The Timaeus and The Metaphysics), also in the doctrine of the Good as the highest category.

This thought is not reached in its pure form by Plato or Aristotle, but rather in its ethical form — as it is the very fountain source of Ethics. Hegel's originality consists in seeing for the first time the pure-thought form of this doctrine. He names it Idee, to honor Plato as its first discoverer. For doubtless Hegel read into the Platonic doctrine of Ideas this pure thought. It must certainly be admitted that the attribution of the thought to Plato is correct, though with him it is not to be found stated adequately in its pure-thought form.

In 1866 I for the first time read through Hegel's larger logic, reading it in the English translation that had been made for myself and two other friends (George Stedman and J. H. Watters), by Henry C. Brockmeyer, in 1859 and 1860. I copied the work entire from the manuscript and am sure I read every word of it. But I am equally sure that I did not understand at the most any-

Xll PREFACE.

thing beyond the first part of the first volume and could not follow any of the discussions in the second and third volumes, or even remember the words from one page to another. It was all over my head, so to speak. I had of course made myself acquainted with the categories and sub-categories of the work years before through histories of philosophy, and was gradually learning to think something into them ; but I could make little of Hegel's deductions or discussions of them. This experience of my own, which lasted for years, is I presume the experience of other students of Hegel and also of students of any other system of deep philosophy. One has first to seize its general thought, its trend as a whole, and gradually descend to its details.

The translation which I copied out still exists, but has never been printed, any portion of it. Mr. Brockmeyer, whose acquaintance I had made in 1858, is, and was even at that time, a thinker of the same order of mind as Hegel, and before reading Hegel, except the few pages in Hedge's German Prose Writers, had divined Hegel's chief ideas and the position of his system, and informed me on my first acquaintance with him in 1858 that Hegel was the great man among modern philosophers, and that his large logic was the work to get. I sent immediately to Germany for it and it arrived late in the year. Mr. Brockmeyer's deep insights and his poetic power of setting them forth with symbols and imagery furnished me and my friends of those early years all of our outside

PREFACE. Xlll

stimulus in the study of German philosophy. He impressed us with the practicality of philosophy, inasmuch as he could flash into the questions of the day, or even into the questions of the moment, the highest insight of philosophy and solve their problems. Even the hunting of wild turkeys or squirrels was the occasion for the use of philosophy. Philosophy came to mean with us, therefore, the most practical of all species of knowledge. We used it to solve all problems connected with school-teaching and school management. We studied the "dialectic" of politics and political parties and understood how measures and men might be combined by its light. But our chief application of philosophy was to literature and art. Mr. Denton J. Snider, who entered our circle in 1866, has published his studies on Shakespeare, Goethe and Homer, and Mr. Brockmeyer has printed in the Journal of Speculative Philosophy his Letters on Goethe's Faust, and these will show sufficiently the spirit and methods of our studies in literature.

In 1873 I discovered the substantial identity of all East Indian doctrines. As early as 1856 I had begun to read oriental literature, but had not seized its essential spirit. I had looked for the same diversity of points of view that I was accustomed to in modern philosophy. Cousin's analysis of the oriental systems, as well as other histories of philosophy, had confirmed me in this mistaken path. But I undertook a thorough study of the Bhagavad Gita in 1872 and for the first time saw

XIV PREFACE.

that the differences of systems were superficial, and that the First Principle pre-supposed and even explicitly stated by the Sanscrit writers was everywhere the same, and that this is the principle of Pure Being as the negative unity of all things. In this I came to see Hegel's deep discernment which early in this century, in the dawn of oriental study, had enabled him to penetrate the true essence of Hindoo thought even in the Western wrappages in which the European first discoverers had brought it away. Hegel could perceive "the genuine oriental thinking through the English and French translations which interpreted the same into modern ways of philosophizing. Hegel's greatest apergu is the difference between the oriental and occidental spirit of thinking and doing.

It was in 1879 that I came to my final and present standpoint in regard to the true outcome of the Hegelian system, but it was six years later that I began to see that Hegel himself has not deduced the logical consequences of his system in the matter of the relation of Nature to the Absolute Idea. I have explained in the following work in many places this divergence of his system from the true doctrine of the Absolute Idea. But the wrong explanation of the use of Nature, strange to say, does not vitiate Hegel's theoiy of human life, and of the Christian church. His doctrine of the Trinity makes the Second Person, or Logos, to be Nature, whereas it should make the Logos to be eternally a Person like the First,

PREFACE. XV

and Nature should be the Processio of the Holy Spirit. But he rightly interprets the doctrine of the invisible Church as the body whose spirit is the Holy Spirit.

This defect in interpreting the Absolute Idea gives rise to a species of pantheism which says that the Absolute is real only in the process of Nature, and his personality actual only in historical persons. This is not Hegel's precise doctrine but it may be inferred from that part of it which makes Nature to be the Second Person of the Trinity.

11 This criticism on the system of Hegel, so far as I am aware, is a new one, and I am confident of its truth.

I will only add here that the interpretation of the doctrine of reflection, which I have discussed at length in treating of the second book of this Logic, is the result of many years' study, beginning with a series of expositions undertaken before the Kant Club, of St. Louis, in 1877-79, and continuing at intervals until 1887. In 1878-1881, I translated, with the assistance of Mr. James S. Garland, the entire • second volume of the Logic and published it, with a commentary to some portions of it.

This doctrine of reflection, I think, is the key to Hegel's dialectic, if anything may be called a " key " to it. It is the exposition also of what he calls the Universal {Das Allgemeine), and the notion or idea ( Der Begriff ). As such I respectfully invite the attention of all

XVI

PREFACE.

students of the philosophy of Hegel to it, and venture to express the hope that a new and fruitful road to Hegel's deeper thoughts may be opened by studying that portion of the Logic which expounds the relation of " determining reflection" to "external reflection."

W. T. HARRIS.

Washington, D. C, August, 1890.

Contents

PAGE

CHAPTER. I.— Philosophy and its Problem 1

Distinctions between science, art, religion and philosophy; enigma of the world the problem of evil; how a perfect being can create what is imperfect ; Oriental solution denies the real existence of evil ; the world is an illusion ; Greek thought sees in the world a manifestation of divine reason ; Christian thought finally explains imperfection through the procession of the Third Divine Person; religion a sort of institutional thinking ; philosophy a product of the thinking of individuals, free and without obedience to authority ; the contents of Hegel's great works ; his logic a discussion of the genesis of the categories of the mind; why these categories must be regarded as objective laws of being, as well as subjective forms of knowing.

CHAPTER II.— The Greek and German Philosophical Principles 22

Hegel the first to unite the Greek ontological results with the German psychological results ; Aristotle's self-active Reason at the basis of Christian theology ; what Plato meant by "Idea; 11 Fichte and Schelling give it the name of subject-objectivity ; the real significance of Kant's labors; the Greek solution turns on the idea of causality; Aristotle's four causes; ancient skepticism doubts the existence of objects; modern skepticism doubts our ability to know objects as they are ; ancient skepticism objective, modern subjective; nominalism the beginning of modern skepticism; Aristotle's "entelechy," and Plato's "Idea" the same as Hegel's "Begriff 11 or self-activity; Hegel's "Idee 11 what Aristotle calls a " second entelechy" and Leibnitz the "Monad of monads ; " Scholasticism arose to refute Moslem pantheism; adopts Aristotle's thought; how Christianity is the germ that at length produces subjectivity, at first as skepticism in nominalism and Hume's philosophy, and next as philosophy of the absolute in Kant

xvii xvm CONTEXTS.

and Hegel; Kant's subjective skepticism so thoroughgoing that it refutes itself and becomes a basis for objective ontology.

CHAPTER IIL— Hegel's Education and the influence of

his Contemporaries upon him 45

Early influences; discipleship of Schelling; study of Greek literature; Schelling' s constructive efforts in interpreting the deep thoughts of the mystics ; his insight into the substantiality of nature, which Fichte denied ; nature and mind the two poles and the Absolute Reason the identity ; Hegel adopts this view.

CHAPTER IV.— Hegel's Voyage of Discovery— Thing, Force, Law 57

When Schelling deserted his doctrine that Absolute Reason is the identity of nature and mind, and adopted the view that the absolute is an empty infinite devoid of :the characteristics of mind and nature, Hegel separated from him and continued to hold the doctrine of Reason as the Absolute; the Phenomenology his first work as independent thinker ; analysis of the Phenomenology; sense-certitude; Perception; how the unity and variety in things is to be explained: different hypotheses rejected and the idea of Force substituted for Thing as a more adequate conception of the reality; the dialectic of Force ; each force needs another to incite it; inciting and incited forces make a system of which the internal truth is law; self-differentiation and self -identification the truth at the bottom of the ideas of force and law; self -activity, therefore, the presupposition of all being: how Schelling came to lose this insight; Spinoza's Substance compared with HegersBegriff.

CHAPTER V.— Voyage of Discovery continued— Begriff

or Self-activity 74

Correlation of forces and the idea of law; Law presupposes self-activity: the use of the word Begriff or notion for self-activity misleading; with the insight into self-activity as the essence of the objective world, consciousness has become self-consciousness.

CHAPTER VI.— Voyage of Discovery continued— the ethical world 82

Self-consciousness manifests itself in history first by life and death struggles, out of which emerges the in-

CONTENTS. XIX

stitution of dominion and servitude ; the slave takes refuge in his inner self and formulates ethical codes ; out of an insight into ethics there grows a higher consciousness of the rationality of the world; the first step of insight into objective Reason is the interest in nature which observes and experiments; happiness, philanthropy, and virtue ; the establishment of institutions by man Hegel treats as the realization of spirit, i. e. the realization of a higher self than the individual ; distinction between self-consciousness, Reason, and Spirit ; Spirit or the personality of the social whole utters its will in the form of ethical and social laws and customs, and requires education to prepare for it; the individual is cultured by self-estrangement, he puts off his natural impulses and puts on habits of acting and thinking according to ethical forms, customs and usages ; culture enables him to see the rationality of the ethical ; but at first it destroys external authority and leads to revolution; the reign of terror; reaction in mysticism.

CHAPTER VII.— Voyage of Discovery continued— religion 103 Religion a higher activity of the soul ; personal relation to the Absolute; sketch of the history of religion ; evolution from nature-religion through art-religion to revealed religion or the religion that teaches that the Absolute reveals himself to his creatures and lifts them up into communion with himself; the doctrine of the Logos; God's knowing is willing or creating; the Logos creates the processio by recognizing his own derivation ; Christianity reveals an absolute entirely ethical.

CHAPTER VIII.— Voyage of Discovery concluded— Absolute Knowing 109

Since God's knowing is creating, the highest form of the human mind must be absolute knowing; defect of symbolic expression; philosophic form of knowing; the religion of a revealed God presupposes in man the power of knowing the absolute ; agnosticism presupposes pantheism ; it sets up an absolute devoid of attributes; revealed religion teaches a personal absolute; the nature of comprehension.

CHAPTER IX.— Hegel's Method ' 122

Hegel's method, that of tracing out the result of self-activity, which is his first principle ; cause contains as

XX C0KTE2s T TS.

its nucleus, self activity ; so does correlation of forces ; the pantheistic idea of substance is the second stage of thought and inseparable from the idea of the relativity of all things; but subject is the true substance according to Hegel ; the absolute is a Person.

CHAPTER X.— Pure Thought— Trendelenburg 1 s Objections 127

The beginning of Hegel's logic with the most elementary pure thought ; this is being, and all experience is a further determination of this idea ; Trendelenburg objects that Hegel names the ideas of pure thought by familiar words ; two parallel lines of thought, one of deduction and the other of recognition of what is deduced as identical with the contents of experience ; Trendelenburg therefore points out only an act of identifying pure thought results as the explanation of experience, but does not disprove pure thought itself.

CHAPTEE XI. — The three categories of Hegel's Logic— _

AN OUTLINE OF PURE THOUGHT 137

Being (Seyn), essence (Wesen), Idea (Idee), the three great categories of Hegel's Logic; immediateness, mediation, absolute mediation; isolated independence, dependence and relativity, concrete independence and self relation; empty indeterminateness, determination through others, self-determination ; mediation makes immediateness possible; the true being is self-mediated; the lower categories not adequate to express this truth; theosophy, correlation of forces; Emerson's Brahma; idea is self-activity; the Logos; the Trinity.

CHAPTER XII. — Hegel's absolute as the true beginning OF HIS SYSTEM . . . : 146

Three beginnings to a system of philosophy; being and thought are one in God's knowing: Hegel reached the insight into self-activity as the first principle of all things before he could begin his system.

CHAPTER XIIL— Analysis of Hegel's Begriff or Notion

AS SELF- ACTIVITY — UNIVERSAL, PARTICULAR AND SINGU- LAR 152

Self-activity contains the phase of universality as self-determining, and that of particularity as self-determined ; it is individual as a whole, or as particular elevated into universality; negative unity; the true actuality is not mere reality, but reality plus all its possibil-

CONTENTS. XXI

ities not yet realized; Plato's " Ideas " are true actualities of this kind ; Aristotle's " entelechies " the same ; the relation of Hegel's thought to Aristotle's; self-activity recognized in the forms of nutrition, sensation, , locomotion, thought, volition; Plato's "self-motion; " Aristotle's "active reason; " why the faculties of sense-perception and memory perish ; the outcome of pure thought is the idea of God ; analysis of the idea of true personal individuality ; explanation of the dual categories, such as cause and effect, thing and properties, by self -relation.

CHAPTER XIV.— Determinateness as Quality— Being. . . 166

The simplest possible thought, that of pure being; Hegel's definition of it as utter indeterminateness and emptiness identical with pure naught; thought thinking its own form devoid of content ; naught and being merely two words for the same empty idea ; hence the paradox of Hegel's idea of becoming as the unity of being and naught; becoming requires difference as well as identity, and this difference Hegel fails to show ; an attempt to show the real insight involved here ; the true thought of pure being is self-antithesis or becoming; Plato's statement of the dialectic; the moments of the becoming are beginning and ceasing rather than being and naught, and hence becoming cancels itself and determinate being results.

CHAPTER XV.— Reflection on the method of Hegel's FIRST CHAPTER 182

Hegel's beginning (pure being) is not a first principle but the farthest removed possible from it; whatever is proved true of pure thought must be true of objective realizations of it; the categories at the beginning are annuled through their own contradictions ; they have no " valid sphere ; " these logical categories not God's thought, but the human process of rising to the thought of the absolute; God's thought the Trinity.

CHAPTER XVI.— The category of determinate being or QUALITY 186

Reality and negation, the two threads of determinate being; each as containing the other is a somewhat opposed to another; somewhat as che first negation of negation; Hegel's repudiation of abstract indeterminate universals; his "absolute" an individual or personal being.

XX11 CONTENTS.

CHAPTER XVII.— Finitude 192

Dependence implies finitude or relativity; quality is the form of being in which somewhat depends on the other, and the other on another ; the subordinate categories of Being-in-itself and being-for-other, characteristic distinction, limit, destination, restraint and ought; ' why Hegel discriminates so many sub-categories in this place; outline of the dialectic process from pure being to being for-itself.

CHAPTER XVIII.— Infinitude 202

The infinite is the union of the somewhat and the other so that the somewhat is its own other ; Plato the first to discover the solution of the problem of the category of quality or finitude ; self-activity solves all its conditions ; infinitude is the quality of being for-itself, i. e. of independent being ; the infinite not empty of relations but self-related; dialectic transition from dependent being to independent being; quantity.

CHAPTER XIX.— Being-for-itself 207

Every whole a being for itself or independent; also a self-activity ; how the idea of one-ness arises ; negative unity; what Hegel means by " being-for-one ; " one of many ; each one composed of ones ; quantity is an aggregate of ones, each unit being also an aggregate.

CHAPTER XX.— The finite and the infinite— a commentary on Hegel's discussion of these ideas 212

The "other;" "in-itself ; " Hegel's order of treating the categories; finitude; agnosticism; Hegel's verbal quibbles; the ought and the restraint; destination and actual condition; the "ought" implies a synthesis of somewhat and other or the infinite ; ideality a very important category ; the erratum in Hegel's text— identi tat for ideelitat.

CHAPTER XXI.— Being for itself— a Commentary on Hegel's Discussion 228

The dialectic of being is a progression from being and naught as the extremes of a dualism to the insight which sees the negative to be only the activity of self-determination ; being-for-one; ideality of the qualitative moments; explanation of six moments that constitute the idea of the One according to Hegel ; why these six moments appear as independent and coordinate ; they constitute an analysis of self-activity; the atom

CONTENTS. XX111

and the void; Hegel's use of the terms repulsion and attraction misleading; divisibility essential to quantity.

CHAPTER XXII.— Quantity 242

Schelling's dictum, all determination is quantitative; in what sense it is true ; review of the dialectical progress from being to quantity; the sub-categories of quantity; tautological definitions of quantity; the contents of Hegel 1 s fourteen extensive notes on quantity; full discussion of his note on the Kantian antinomy of the limitation of the world in time and space; Kant's antinomy rather that of infinitude of space than of the world in space ; not a real antinomy after all, for its thesis and antithesis presuppose the same thought.

CHAPTER XXIII. —The relation of quantity to quality ELUCIDATED 257

Quantity the union of attraction and repulsion in the sense that Hegel uses these terms; attraction the predominance of ideality, and repulsion the predominance of " reflection-into-itself ;" quantity is self-determination with the self left out; the dialectic that leads out of quality to quantity really leads to the absolute idea at once— from the finite to the infinite, as Plato and Aristotle saw; Hegel takes next the most immediate phase of self-determined being and finds it to be quantity ; three points of view in which Hegel treats each category; what "indifference " means with Hegel; nominalism and realism; the general name stands for the determining process, and not for the particular individual nor for the abstract class ; the true actuality is this determining process; the deeper meaning of quantity as the most abstract concept of subject-objectivity or self-consciousness; the Logos thinks the processio as beginning with empty space and time ; quantity the form of self-determination without the substance of it; continuity and discreteness; sum and unity; arithmetical processes explained; extensive and intensive quantity ; dialectic of the transition from extensive to intensive quantity seemingly a verbal quibble ; the real thought underlying it, not stated by Hegel.