Note that the page numbers are embedded in the source code. For example, "HL1_82b" means p. 82, in Book 1 of the Science of Logic.
§ 1. The complete transformation of philosophical thought in Germany has had little influence on logic.
§ 2. When a nation loses its metaphysics, its own pure essence is no longer a present reality in the life of the nation.
§ 3. Kantian philosophy was a justification for the renunciation of speculative thought.
§ 4. As if one could only learn how to digest and move about by studying anatomy and physiology.
§ 5. Once the spirit has reconstituted itself, all attempts to preserve an earlier culture are utterly in vain.
§ 6. Even those who are opposed to the new ideas have become familiar with them and have appropriated them.
§ 7. A new creative idea displays a fanatical hostility toward the entrenched systematisation of the older principle.
§ 8. Philosophy, if it would be a science, cannot borrow its method from a subordinate science like mathematics.
§ 9. Reason is negative and dialectical, because it resolves the determinations of the understanding into nothing.
§ 10. The development of all natural and spiritual life, rests solely on the content of logic.
§ 11. Logic is the first sequel to the Phenomenology, to be followed by the Philosophy of Nature and the Philosophy of Spirit.
§ 12. I have tried to remedy the imperfection of its treatment in the first edition.
§ 13. To exhibit the realm of thought philosophically, that is, in its own immanent activity.
§ 14. The forms of thought are, in the first instance, displayed and stored as human language.
§ 15. In physics,the category of force has become predominant, but more recently polarity has played the leading part.
§ 16. While logical objects may be thoroughly familiar to educated people it does not follow that they are intelligently apprehended.
§ 17. The forms of thought have been freed from the material in which they are submerged.
§ 18. The need to occupy oneself with pure thought presupposes that the human spirit must already have travelled a long road.
§ 19. It is customary, to include logic in the curriculum of youth, not yet involved in the practical affairs of life.
§ 20. In life, the categories are degraded to serve in the creation and exchange of ideas.
§ 21. It is our thinking that must accommodate itself to notions and our caprice ought not to want to mould them to suit itself.
§ 22. We cannot go outside our subjective thought, and just as little can we go beyond the nature of things.
§ 23. To focus attention on this logical nature which animates mind, moves and works in it, this is the task.
§ 24. Here and there in this mesh there are firm knots which give stability and direction to the life.
§ 25. The loftier business of logic is to clarify the categories and raise mind to freedom and truth.
§ 26. In its negation, the true is associated with limitation and finitude, its untruth and unreality.
§ 27. The merely formal categories concern only the correctness of the knowledge of facts, not truth itself.
§ 28. Content, divorced from form, cannot in fact be formless.
§ 29. No subject can be expounded with a strict immanent plasticity as thought in its own necessary development.
§ 30. This restriction to what is simple gives scope for the free play of caprice.
§ 31. Plato revised his Republic seven times over.
§ 32. The noisy clamour of current affairs and the deafening chatter leave little room for the passionless calm of knowledge of pure thought.
§ 33. The need to begin with the subject matter itself, without preliminary reflections, is felt most strongly in logic.
§ 34. Logic cannot presuppose any of these laws of thinking, for these constitute part of its own content.
§ 35. When logic is taken as the science of thinking in general, it is understood that its matter, must come from somewhere else.
§ 36. As thinking and the rules of thinking are supposed to be the subject matter of logic, these constitute its content.
§ 37. It is time that Logic received a completely changed shape.
§ 38. It is assumed that the material of knowing is present on its own account as a ready-made world apart from thought.
§ 39. Thinking is supposed to adapt and accommodate itself to the object.
§ 40. Thinking does not go out of itself to the object; this, as a thing-in-itself, remains a sheer beyond of thought.
§ 41. These views on the relation of subject and object bar the entrance to philosophy and must be discarded at its portals.
§ 42. Ancient metaphysics had a higher conception of thinking than is current today.
§ 43. Reflective understanding took possession of philosophy.
§ 44. This turn, which appears as retrograde step, is based on the elevation of reason into the loftier spirit of modern philosophy.
§ 45. If the forms of the understanding cannot be determinations of the thing-in-itself, still less can they be of the understanding.
§ 46. The forms of objective thinking have been removed only from the thing, but have been left in the subject.
§ 47. ... the nothingness of the thing-in-itself, this abstract shadow divorced from all content, and intended to destroy it.
§ 48. They are dead forms and the spirit which is their living, concrete unity does not dwell in them.
§ 49. The point of view from which logic is to be considered, how it differs from previous modes of treatment.
§ 50. I have exhibited consciousness in its movement from the immediate opposition of itself and the object to absolute knowing.
§ 51. The Notion of pure science is here presupposed as the Phenomenology of Spirit is the deduction of it.
§ 52. As science, truth is pure self-consciousness in its self-development.
§ 53. This objective thinking then, is the content of pure science.
§ 54. Logic is not a thinking about something — the necessary forms of thought are the content and the ultimate truth itself.
§ 55. One must discard the prejudice that truth must be something tangible.
§ 56. The determinations of thought have objective value and existence.
§ 57. The critical philosophy turned metaphysics into logic but the logical determinations were given an essentially subjective significance.
§ 58. The utter unworthiness of logic in comparison with other spheres cannot fail to strike the most superficial observer.
§ 59. Logic, as exhibited in the text-books, may be said to have fallen into contempt.
§ 60. The additions of psychological, pedagogic and even physiological material which logic received have been recognised as disfigurements.
§ 61. Logic is so dull and spiritless ... a childish game of fitting together the pieces of a coloured picture puzzle.
§ 62. Hitherto philosophy had not found its method.
§ 63. It is the inwardness of the content, the dialectic which it possesses within itself, which is the mainspring of its advance.
§ 64. The divisions and chapter headings are only of historical value. They do not belong to the content.
§ 65. Such preliminary definitions and divisions are in themselves nothing else but such external indications.
§ 66. The divisions which appear in this system are not intended to have any other significance than that of a list of contents.
§ 67. The negative which the Notion possesses within itself constitutes the genuine dialectical moment.
§ 68. Dialectic was held to be merely the art of practising deceptions and producing illusions.
§ 69. Dialectic is the grasping of opposites in their unity or of the positive in the negative.
§ 70. It is one thing for him who comes to logic for the first time, but another for him who comes back to it from these sciences.
§ 71. Only after acquaintance with the other sciences does logic cease to be a merely abstract universal and reveal itself as the universal which embraces the wealth of the particular.
§ 72. The system of logic is the realm of shadows.
§ 73. Thought becomes at home in abstractions and develops a power of assimilating in rational form all the various sciences.
§ 74. The general division here can only be provisional; the main distinctions which will emerge in the development.
§ 75. We are presupposing that the division must be implicit in the Notion itself.
§ 76. The quality of being right-angled, etc., by which triangles are classified, is not implicit in the Notion of triangle.
§ 77. In Logic the opposition in consciousness between a subject and an object is known to be overcome
§ 78. The determinations used on the pathway to truth, have lost their independent character and are now in their truth.
§ 79. Accordingly, logic should be divided primarily into the logic of the Notion as being and of the Notion as Notion.
§ 80. There results a sphere of mediation. This is the doctrine of essence.
§ 81. Objective logic would correspond in part to what with Kant is transcendental logic.
§ 82. Kant’s chief thought is to vindicate the categories for self-consciousness as the subjective ego.
§ 83. Consciousness embraces within itself the opposition of the ego and its object which is not present in that original act.
§ 84. If philosophy was to make any real progress, a consideration of the ego, of consciousness as such was necessary.
§ 85. The objective logic takes the place of metaphysics which meant to construct the world in terms of thoughts alone.
§ 86. The subjective logic is the logic of the Notion, no longer external but the subject itself.
§ 87. Logic has three parts: Being, Essence and Notion.
§ 88. What philosophy begins with must be either mediated or immediate, and it is easy to show that it can be neither the one nor the other.
§ 89. The principle of a philosophy does, of course, also express a beginning.
§ 90. What is the first for thought ought also to be the first in the process of thinking.
§ 91. The logical beginning appears either as a mediated result or as an immediacy.
§ 92. There is nothing in heaven, or in nature or in mind or anywhere else which does not equally contain both immediacy and mediation.
§ 93. In logic, the presupposition is that which has proved itself to be the result of that phenomenological consideration.
§ 94. Logic is pure science, that is, pure knowledge in the entire range of its development.
§ 95. All that is needed to rid oneself of all other reflections and opinions whatever, simply to take up, what is there before us.
§ 96. Pure knowing is only simple immediacy.
§ 97. Simple immediacy is itself an expression of reflection and contains a reference to its distinction from what is mediated.
§ 98. If no presupposition is to made, all that is present is that we propose to consider thought as such.
§ 99. The beginning therefore is pure being.
§ 100. Preliminary prejudices must be disposed of within the science itself where their treatment should be awaited with patience.
§ 101. Absolute truth must be a result, and conversely, a result presupposes a prior truth.
§ 102. The advance is a retreat into the ground, to what is primary and true.
§ 103. It is equally necessary to consider as result that into which the movement returns as into its ground.
§ 104. Hence the line of the scientific advance becomes a circle.
§ 105. This progress in knowing must be determined by the nature of the subject matter itself and its content.
§ 106. The beginning is neither arbitrary nor a provisional assumption, but is subsequently shown to have been properly made.
§ 107. If it were determinate, it would have been taken as something mediated.
§ 108. Here at the start, where the subject matter itself is not yet to hand, philosophy is an empty word.
§ 109. The determination of being so far adopted for the beginning could also be omitted, so that the only demand would be that a pure beginning be made.
§ 110. The beginning therefore contains both, being and nothing, is the unity of being and nothing
§ 111. In the beginning, being and nothing are present as distinguished from each other.
§ 112. Let those dissatisfied with being as a beginning, begin with the general idea of a beginning.
§ 113. This takes it for granted that everyone has roughly the same general idea of it.
§ 114. The beginning cannot be made with anything concrete, anything containing a relation within itself.
§ 115. What the subject matter is, that will be explicated in the development of the science, cannot be presupposed.
§ 116. Let those who are still dissatisfied with this beginning avoid these defects by beginning in some other way.
§ 117. Some begin with the ego, because the first truth must be something with which we are acquainted.
§ 118. But the ego is the most concrete of all things.
§ 119. The ego which formed the starting point is still entangled in the world of appearance.
§ 120. In logic we are concerned the determinate reality in thought of what is inner.
§ 121. This simple determination which has no other meaning, this emptiness, is therefore the beginning of philosophy.
§ 122. These preliminary were not so much intended to lead up to it as rather to eliminate all preliminaries.
§ 123. Being is first, as against another in general; second, immanently self-determining; third, abstract indeterminateness.
§ 124. Being is distinct from essence, for later in its development it proves to be in its totality, only one sphere of the Notion
§ 125. Being will posit itself in three determinations: quality, quantity and measure.
§ 126. With Kant these are supposed to be only titles for his categories though they are, in fact, themselves categories.
§ 127. Hitherto the determination of quantity has been made to precede quality, but the beginning is made with being as such.
§ 128. Measure is a relation, the specific relation between quality and quantity.
§ 129. Relation falls within the section Quality.
§ 130. Being is the indeterminate immediate.
§ 131. The first being is in itself determinate, and therefore, secondly, determinate being, thirdly, being-for-self.
§ 132. Pure Being has no diversity within itself nor any with a reference outwards.
§ 133. Nothing is the same determination, or rather absence of determination, and thus altogether the same as, pure being.
§ 134. But it is equally true that they are not undistinguished from each other, that, on the contrary, they are not the same.
Remark 1: The Opposition of Being and Nothing in Ordinary Thinking.
§ 135. Nothing is usually opposed to something; but is already thereby distinguished from a determinate something.
§ 136. Heraclitus brought forward the concept of becoming and said: being as little is, as nothing is, or, all flows, all is a becoming.
§ 137. Those who maintain that nothing is just nothing, are unaware that they subscribe to the pantheism of the Eleatics and Spinoza.
§ 138. Nowhere in heaven or on earth is there anything which does not contain within itself both being and nothing.
§ 139. What is in question is not such concrete something but only the pure abstractions of being and nothing.
§ 140. It is not a matter of indifference to it whether a certain other content with which it is in relation is, or is not.
§ 141. Kant said that being is not a determination of the content of a thing.
§ 142. Ordinary thinking transforms the abstract being and nothing which should be apprehended into a definite being and nothing.
§ 143. The concept of a determinate existence, says Kant, gains nothing by its being perceived.
§ 144. What is the first in the science had of necessity to show itself historically as the first.
§ 145. The reference back from particular finite being to being in its abstract universality is the first theoretical demand and the first practical demand too.
§ 146. The abstract definition of God, on the other hand, is precisely that his Notion and his being are unseparated and inseparable.
Remark 2: Defectiveness of the Expression 'Unity, Identity of Being and Nothing'
§ 147. The proposition: “being is the same as nothing” enunciates both determinations, being and nothing, and contains them as distinguished.
§ 148. The proposition contains the result, but the result is not itself expressed in the proposition.
§ 149. The deficiency is made good in the first place by adding the contrary proposition: being and nothing are not the same.
§ 150. The result which we have here before us is becoming, which is not merely the one-sided or abstract unity of being and nothing.
§ 151. The third in which being and nothing subsist must also present itself here, and it has done so; it is becoming.
§ 152. The challenge to distinguish between being and nothing also includes the challenge to say what, then, is being and what is nothing.
Remark 3: The Isolating of These Abstractions
§ 153. Transition is the same as becoming.
§ 154. We shall consider some of the results which appear when being and nothing are postulated in isolation.
§ 155. With Parmenides as with Spinoza, there is no progress from being ot absolute substance to the negative, to the finite.
§ 156. Jacobi recognised very clearly the insubstantial nature, the non ens, of abstraction.
§ 157. This abstract purity of continuity is the same as what the Indian calls Brahma, sitting for years on end looking at the tip of his nose.
§ 158. In this void, Jacobi says, he experiences the opposite of what Kant assures him he should experience.
§ 159. Is this still a synthesis if Jacobi omits precisely that which makes the unity a synthetic unity?
§ 160. Consciousness can make empty space, empty time, its object , but it does not stop at that; it goes beyond it.
§ 161. It is the thought of such indeterminates that is to be demonstrated as null.
§ 162. Because being is devoid of all determination whatsoever, it is not being but nothing.
§ 163. Being is posited only as immediate, therefore nothing emerges in it. But all the subsequent determinations are more concrete.
§ 164. That nothing is the result and should make the beginning (as in Chinese philosophy), need not cause us to lift a finger.
§ 165. The dialectic employed by Plato in treating of the One in the Parmenides is also a dialectic of external reflection.
§ 166. Being, taken as it is immediately, belongs to a subject, is something enunciated.
§ 167. Nothing, taken in its immediacy, shows itself as affirmative, as being.
§ 168. Just as little is seen in pure light as in pure darkness.
§ 169. The transition of being and nothing into each other is to be understood as it is without any further elaboration of the transition by reflection.
Remark 4: Incomprehensibility of the Beginning
§ 170. Let us consider the Kantian antinomy which proves that a beginning of the world, or of anything, is impossible.
§ 171. If the world, or anything, is supposed to have begun, then it must have begun in nothing.
§ 172. In this proof nothing is brought forward against becoming, or beginning and ceasing, against this unity of being and nothing.
§ 173. With the absolute separateness of being from nothing presupposed, then of course beginning or becoming is something incomprehensible.
§ 174. Tthere is nothing which is not an intermediate state between being and nothing.
§ 175. We call dialectic the higher movement of reason in which such seemingly utterly separate terms pass over into each other spontaneously.
§ 176. Becoming is the unseparatedness of being and nothing, not the unity which abstracts from being and nothing.
§ 177. Becoming therefore contains being and nothing as two such unities, each of which is itself a unity of being and nothing.
§ 178. Becoming is in this way in a double determination.
§ 179. They are not reciprocally sublated, but each sublates itself in itself .
§ 180. Becoming is an unstable unrest which settles into a stable result.
§ 181. Becoming is the vanishing of being and nothing; but at the same time it rests on the distinction between them.
§ 182. This stable oneness is being, yet no longer as a determination on its own but as a determination of the whole.
§ 183. Becoming, as this transition into the unity of being and nothing, is determinate being.
Remark: The Expression ‘To Sublate’
§ 184. To sublate constitutes one of the most important notions in philosophy which repeatedly occurs throughout the whole of philosophy.
§ 185. ‘To sublate’ has a twofold meaning in the language: on the one hand it means to preserve, to maintain, and equally it also means to cause to cease, to put an end to.
§ 186. It is remarkable to find that a language has come to use one and the same word for two opposite meanings.
§ 187. Being and nothing are the same; but just because they are the same they are no longer being and nothing, but now have a different significance.
§ 188. Through its quality, something is determined as opposed to an other, as alterable and finite.
§ 189. Determinate being falls into three parts: Determinate being as such, Finitude, Qualitative infinity.
§ 190. Determinate being as such, is first of all quality, as reality and negation.
§ 191. From becoming there issues determinate being, which is the simple oneness of being and nothing.
§ 192. It is not mere being, but determinate being [Dasein], there-being.
§ 193. Only that which is posited in a Notion belongs in the dialectical development of that Notion to its content.
§ 194. Determinate being is concrete.
§ 195. Determinateness has not yet severed itself from being.
§ 196. Determinateness thus isolated by itself in the form of being is quality.
§ 197. Quality, taken in the distinct character of being, is reality.
§ 198. Negation taken as mere deficiency would be equivalent to nothing; but it is a determinate being.
Remark: Quality and Negation
§ 199. Reality may seem to be a word of various meanings because it is used of different, indeed of opposed determinations.
§ 200. God was defined as the sum-total of all realities, and of this sum-total it was said that no contradiction was contained in it.
§ 201. Reality as thus conceived is assumed to survive when all negation has been thought away.
§ 202. If reality is taken in its determinateness, then the sum-total of all realities becomes a sum-total of all negations, all contradictions.
§ 203. Negation is as little an ultimate for philosophy as reality is for it truth.
§ 204. Spinoza grasped thought and being as attributes, as not having a separate existence, a self-subsistent being of their own.
§ 205. Negation stands directly opposed to reality.
§ 206. Quality is especially a property only where, in an external relation, it manifests itself as an immanent determination.
§ 207. Jacob Boehme's 'Qualierung' or 'Inqualierung' signify quality's own internal unrest by which it produces and maintains itself only in conflict.
§ 208. In determinate being its determinateness has been distinguished as quality, but there is distinction of reality and negation.
§ 209. This sublatedness of the distinction is determinate being's own determinateness, a something.
§ 210. Determinate being, life, thought, etc., determine themselves to become a determinate being, a living creature, a thinker (ego).
§ 211. Something is the negation of the negation in the form of being.
§ 212. Something as a becoming is a transition, the moments of which are themselves somethings.
§ 213. In this section, the negative determination contained in determinate being is developed.
§ 214. 1. Something and other are, in the first place, both determinate beings or somethings.
§ 215. Otherness thus appears as a determination alien to the determinate being
§ 216. Both are determined equally as something and as other, and are thus the same.
§ 217. The other is to be taken as isolated, as in relation to itself, abstractly as the other.
§ 218. The otherness, which is at the same time a moment of it, is distinct from it and does not appertain to the something itself.
§ 219. 2. Something preserves itself in the negative of its determinate being.
§ 220. Determinate being as such is immediate, without relation to an other.
§ 221. Being-for-other and being-in-itself are, therefore, posited as moments of one and the same something.
§ 222. Non-being is, in this unity of being and non-being, not negative determinate being in general, but an other.
§ 223. Being-in-itself has also present in it non-being itself, for it is itself the non-being of being-for-other.
§ 224. Being-for-other is negative determinate being which points to being-in-itself as to its own being.
§ 225. 3. Both moments are determinations of what is one and the same, namely, the something.
§ 226. People fancy that they are saying something lofty with the 'in itself'; but what something is only in itself, is an abstract determination.
§ 227. Things are called ‘in themselves’ in so far as abstraction is made from all being-for-other.
§ 228. In Being, the meaning of each opposite is complete even without its other; in Essence, the opposites are meaningless without one another.
§ 229. Determinateness reflected into itself is, therefore, again in the simple form of being, a Quality.
§ 230. The in-itself into which something is reflected into itself out of its being-for-other is no longer an abstract in-itself.
§ 231. 1. The quality of the essential unity of the in-itself in the simple something with its other moment, is the determination of the in-itself.
§ 232. The determination of man is thinking reason; by it he is distinguished from the brute.
§ 233. 2. The filling of the in-itself with determinateness is distinct from the determinateness which is only being-for-other.
§ 234. It is the quality of something to be open to external influences and to have a constitution..
§ 235. In so far as something alters, the alteration falls within its constitution.
§ 236. Determination and constitution are thus distinguished from each other.
§ 237. The first was only an implicit alteration belonging to the inner Notion; now alteration is also posited in the something.
§ 238. The transition of determination and constitution into each other is sublation of their difference, resulting in the positing of something in general.
§ 239. There is a single determinateness of both: this determinateness is limit..
§ 240. 3. Being-for-other is the indeterminate, affirmative community of something with its other.
§ 241. [a] Something, therefore, is immediate, self-related determinate being, and has a limit, in the first place, relatively to an other.
§ 242. The limit is simple negation or the first negation, whereas the other is, at the same time, the negation of the negation.
§ 243. Something is the limit relatively to another something, but the limit is present in the something itself.
§ 244. [b] The negative determinate being and the determinate being of the something fall outside each other.
§ 245. In accordance with this difference of something from its limit, the line appears as line only outside its limit, the point.
§ 246. [c] But further, something as it is outside the limit, the unlimited something, is only a determinate being in general.
§ 247. Something with its immanent limit posited as the contradiction of itself, directed and forced out of and beyond itself, is the finite.
§ 248. The being of something is determinate; something has a quality and in it is not only determined but limited.
§ 249. When we say of things that they are finite, we understand that non-being constitutes their nature and being.
§ 250. The thought of the finitude of things brings this sadness with it because it is qualitative negation pushed to its extreme.
§ 251. No philosophy or opinion will let itself be tied to the standpoint that the finite is absolute.
§ 252. This nothing is supposed to be only nothing.
§ 253. This contradiction is abstractly present simply in the circumstance that the something is finite, or that the finite is.
§ 254. Determination and constitution showed themselves as sides for external reflection.
§ 255. In order that the limit in something should be a limitation, something must at the same time in its own self transcend the limit.
§ 256. The ought therefore contains the determination in double form.
§ 257. The finite has thus determined itself as the relation of its determination to its limit.
§ 258. What ought to be is, and at the same time is not. If it were, we could not say that it ought merely to be.
§ 259. The limitation of the finite is not something external to it; on the contrary, its own determination is also its limitation.
§ 260. The finite as the ought transcends its limitation; its limit is also not its limit.
§ 261. Something has a limitation in so far as it has negation in its determination.
Remark: The Ought
§ 262. The ought has recently played a great part in philosophy, especially in connection with morality.
§ 263. 'You can, because you ought'.
§ 264. In the Ought the transcendence of finitude, that is, infinity, begins.
§ 265. The very fact that something is determined as a limitation implies that the limitation is already transcended.
§ 266. The sentient creature, in the limitation of hunger, thirst, etc., is the urge to overcome this limitation and it does overcome it.
§ 267. Leibniz said that if a magnet possessed consciousness it would regard its pointing to the north as a determination of its will.
§ 268. Reason and Law are not in such a bad way that they only ought to be.
§ 269. The ought as such contains limitation, and limitation contains the ought.
§ 270. The infinite is a fresh definition of the absolute; as indeterminate self-relation it is posited as being and becoming.
§ 271. Even so, the infinite is not yet really free from limitation and finitude.
§ 272. The infinite is (a) affirmative as negation of the finite, (b) the abstract, one-sided infinite, (c) the genuine infinite.
§ 273. The infinite is the negation of the negation, affirmation, being which has restored itself out of limitedness.
§ 274. It is the very nature of the finite to transcend itself, to negate its negation and to become infinite.
§ 275. The immediate being of the infinite resuscitates the being of its negation.
§ 276. Finitude is limitation posited as limitation; infinity is the nothing of the finite.
§ 277. The infinite posited over against the finite, in a relation wherein they are as qualitatively distinct others, is the spurious infinite.
§ 278. The finite remains as a determinate being opposed to the infinite; there are two worlds, one infinite and one finite.
§ 279. This contradiction develops its content into more explicit forms.
§ 280. As thus separated they are just as much essentially connected by the very negation which separates them.
§ 281. The infinite only emerges in the finite and the finite in the infinite.
§ 282. In this void beyond the finite, again there arises the void, in which a new limit, is encountered - and so on to infinity.
§ 283. The finite is finite only in its relation to the ought or to the infinite, and the latter is only infinite in its relation to the finite.
§ 284. The progress is a contradiction which is not resolved but is always only enunciated as present..
§ 285. The progress to infinity is only the perpetual repetition of one and the same tedious alternation of finite and infinite.
§ 286. The infinity of the infinite progress remains burdened with the finite as such, is thereby limited and is itself finite.
§ 287. In this alternating of the finite and the infinite, their truth is already implicitly present.
§ 288. The finite is only that which must be transcended, the negation of itself in its own self, which is infinity.
§ 289. The infinite and the finite viewed as connected with each other.
§ 290. This yields the decried unity of the finite and the infinite.
§ 291. The unity of the infinite which each of these moments is, is differently determined in each of them.
§ 292. The simple unity of the infinite and finite was falsified by the understanding; so too is the double unity.
§ 293. The unity of the finite and infinite is not an incongruous combination alien to their own nature; but each is in its own self this unity.
§ 294. Infinity is the negative of finitude, and hence of determinateness in general; the sublating of itself in the finite is a return from an empty flight.
§ 295. This is in itself self-relation, affirmation, but as return to itself, through the mediation which the negation of negation is.
§ 296. The infinite progress expresses the connection of terms which are also distinct from each other.
§ 297. Starting from the finite, the limit is transcended. We now have its beyond, the infinite, but in this the limit arises again.
§ 298. In the infinite, the beyond of the limit, there arises another limit which has the same fate, namely, that as finite it must be negated.
§ 299. Both finite and infinite are this movement in which each returns to itself through its negation.
§ 300. Since both the finite and the infinite are moments of the progress they are jointly the finite, and are equally together negated in it.
§ 301. As the infinite, they are the finite and the infinite, which are themselves in process of becoming.
§ 302. The image of true infinity becomes the circle, the line which has reached itself, closed and present, without beginning and end.
§ 303. It is not the finite which is the real, but the infinite. Thus reality is further determined as essence, Notion, Idea, and so on.
§ 304. The negation is thus determined as ideality; ideal being [das Ideelle] is the finite as it is in the true infinite.
§ 305. Ideality can be called the quality of infinity; but it is essentially the process of becoming, and hence a transition.
Remark 1: The Infinite Progress
§ 306. The infinite and the progress to infinity are the expression of a contradiction which is itself put forward as the final solution.
§ 307. Infinite progress is seen when one remains fixed in the contradiction of the unity of two determinations and their opposition.
§ 308. Infinite progress, the developed infinite of the understanding, is so constituted as to be the alternation of the two determinations.
§ 309. The resolution is not recognition of the equal correctness and incorrectness of the two assertions, but the ideality of both.
§ 310. Some placed the essence of philosophy in aswering the question: how does the infinite go forth from itself and become finite?
§ 311. To understand how to put questions presupposes a certain education, if one wants a better answer than that the question is idle.
§ 312. Expressions of sensuous conception arouse the suspicion that they spring from the level of ordinary conception.
§ 313. In the infinite this is expressed; it is the not-finite. The unity of the finite and infinite thus seems to be directly excluded.
§ 314. The infinite no more is than pure being is.
§ 315. The unity of the finite and infinite and the distinction between them are just as inseparable as are finitude and infinity.
Remark 2: Idealism
§ 316. The proposition that the finite is ideal [ideell] constitutes idealism.
§ 317. By the ideal [dem Ideellen] is meant the form of figurate conception and imagination, and what is simply in my conception.
§ 318. Determinate being is the sphere of difference, of dualism, the field of finitude.
§ 319. Being-for-self is first the One, secondly repulsion and attraction, thirdly, the alternation of repulsion and attraction.
§ 320. We have arrived at the general Notion of being-for-self. All that is now necessary to justify our use of the term.
§ 321. being-for-self is infinity which has collapsed into simple being.
§ 322. This moment expresses the manner in which the finite is present in its unity with the infinite, or is an ideal being.
Remark: The German Expression, 'What For a Thing' (Meaning 'What Kind of a Thing')
§ 323. “Was für ein Ding” — in other words that which is, and that for which it is, are one and the same.
§ 324. To call thought, spirit, God, only an ideal being, presupposes the standpoint from which finite being counts as the real.
§ 325. Eleatic Being or Spinoza's substance is the abstract negation of all determinateness. The idealism of Malebranche is more explicit.
§ 326. The Leibnizian idealism lies more within the bounds of the abstract Notion.
§ 327. The idealisms of Kant and Fichte, do not go beyond the ought, and remain in the dualism of determinate being and being-for-self.
§ 328. Being-for-self is the simple unity of itself and its moment, being-for-one.
§ 329. 1. negation in general, 2. two negations, 3. two that are the same, 4. sheer opposites, 5. identity as such, 6. relation which is negative and yet to its own self.
§ 330. The one is the simple self-relation of being-for-self in which its moments have collapsed.
§ 331. The one is a process of determining - and as self-relation it is an infinite self-determining.
§ 332. In its own self the one simply is; the one is not capable of becoming an other: it is unalterable.
§ 333. It is indeterminate but not, however, like being; its indeterminateness is the determinateness which is a relation to its own self.
§ 334. In this simple immediacy the mediation of determinate being, and all difference and manifoldness, has vanished.
§ 335. The one is the void as the abstract relation of the negation to itself.
§ 336. Being-for-self determined in this manner as the one and the void has again acquired a determinate being.
§ 337. The one in this form appeared as the atomistic principle, according to which the essence of things is the atom and the void.
§ 338. The void is the ground of movement only as the negative relation of the one to its negative.
§ 339. Physics with its molecules and particles suffers from this principle of extreme externality, just as does that theory of the State which starts from the particular will of individuals.
§ 340. The one and the void constitute the first stage of the determinate being of being-for-self.
§ 341. The one is a becoming of many ones.
§ 342. But this is not really a becoming, for becoming is a transition of being into nothing: the one, on the other hand, becomes only one.
§ 343. This repulsion is the positing of many ones but through the one itself. The second is the mutual repelling of ones presupposed as already present.
§ 344. The one repels only itself from itself, therefore does not become but already is.
§ 345. The ones are presupposed relatively to one another - supposed or posited by the repulsion of the one from itself.
§ 346. Plurality appears not as an otherness, but as a determination completely external to the one.
§ 347. The plurality of ones is infinity as a contradiction which unconstrainedly produces itself.
Remark: The Monad of Leibniz
§ 348. The Leibnizian idealism takes up the plurality immediately as something given and does not grasp it as a repulsion of the monads.
§ 349. The many ones have affirmative being external to them - the abstract void. But they are infinity posited in the immediacy of being.
Remark: The unity of the One and the Many
§ 350. The plurality is, in the first place, non-posited otherness, the limit is only the void, only that in which the ones are not.
§ 351. This mutual repulsion is the posited determinate being of the many ones.
§ 352. The being-for-self of the many ones shows itself as their self-preservation through the mediation of their mutual repulsion.
§ 353. The ones not only are, but they maintain themselves through their reciprocal exclusion.
§ 354. This reflection that the ones show themselves to be one and the same and indistinguishable, is a comparison made by us.
§ 355. The negative relationship of the ones to one another is only a going-together-with-self.
§ 356. Self-subsistence pushed to the point of the one as a being-for-self is abstract, formal, and destroys itself.
§ 357. It is an ancient proposition that the one is many and especially that the many are one.
§ 358. Repulsion is the self-differentiating of the one.
§ 359. Attraction belongs equally to each of the many ones as immediately present; none has any precedence over another.
§ 360. There is thus in the one one, the unity of repulsion and attraction in general.
§ 361. The difference of the one and the many is now determined as repulsion and attraction.
§ 362. Repulsion is indifferent to attraction which is externally added to it as presupposed. Attraction is not presupposed by repulsion.
§ 363. Repulsion is, although negative, still essentially relation.
§ 364. Not merely is repulsion presupposed by attraction, but equally, too, there is a reverse relation of repulsion to attraction.
§ 365. Each being a self-mediation, evident after closer consideration of them and brings them back to the unity of their Notion.
§ 366. That each presupposes itself is already implied in the relationship between repulsion and attraction, initially relative.
§ 367. Relative repulsion is the mutual repelling of the present many ones which are supposed to be immediately given.
§ 368. Attraction is the positing of the real one, in contrast to which the many in their determinate being are only ideal and vanishing.
§ 369. This self-presupposing of the two determinations each for itself, means that each contains the other as a moment within it.
§ 370. This being, in the determination it has now acquired, is quantity.
§ 371. The fundamental determination of quality is being and immediacy, in which determinateness is so identical with the being of something, that with its alteration the something itself vanishes.
§ 372. This unity is: [a] being only as immediacy; [b] determinate being; [c] being-for-self.
Remark: The Kantian Construction of Matter from the Forces of Attraction and Repulsion
§ 373. Attraction and repulsion, as we know, are usually retarded as forces.
§ 374. Kant, constructed matter from the forces of attraction and repulsion, or “set up the metaphysical elements of this construction”.
§ 375. Matter as it exists for sense perception is no more a subject for logic than space. But attraction and repulsion are also based on the determinations here considered.
§ 376. Later philosophers of nature gave the name construction to the most baseless concoction of unbridled imagination.
§ 377. Kant's method is analytical, not constructive. He presupposes the idea of matter, then asks what forces are required to maintain it.
§ 378. Kant remarks that the force of attraction just as much belongs to the concept of matter 'although it is not contained in it'.
§ 379. Kant from the start one-sidedly attributes to the concept of matter only the determination of impenetrability.
§ 380. Kant is chiefly concerned to banish the vulgar mechanistic way of thinking which stops short at impenetrability.
§ 381. These forces are only moments which pass over into each other.
§ 382. He defines attraction as a penetrative force by which one bit of matter acts directly on the parts of another even beyond the contact.
§ 383. It therefore follows, quite tautologically, that where repulsion is assumed to be not, there no repulsion can take place.
§ 384. Kant assumes further that 'through the force of attraction, matter only occupies space but does not fill it'.
§ 385. Forces through which bodies act on one another and are set in motion, are something quite different from forces supposed as [constitutive] moments of matter.
§ 386. The same opposition of attractive and repulsive forces is made by their more developed form of centripetal and centrifugal forces.
§ 387. Quantity is the determinateness which has become indifferent to being, a limit which is just as much no limit.
§ 388. The indifference of the limit and of the something to the limit, constitutes quantitative determinateness.
§ 389. Firstly, pure quantity is a compact, infinite unity which continues itself into itself.
§ 390. Secondly, this develops a determinateness which only an external one, quantum.
§ 391. Thirdly, quantum in a qualitative form is quantitative ratio.
§ 392. The ratio is only a formal unity of quality and quantity. Its dialectic is its transition into their absolute unity, into Measure.
Remark: Something's Limit
§ 393. In something, its limit as quality is essentially its determinateness.
§ 394. A magnitude is usually defined as that which can be increased or diminished; magnitude would thus be that of which the magnitude can be altered.
§ 395. Quantity is sublated being-for-self.
§ 396. Continuity is, therefore, simple, self-same self-relation, which is not interrupted by any limit or exclusion.
§ 397. In continuity, magnitude immediately possesses the moment of discreteness - repulsion.
§ 398. Quantity is the unity of these moments of continuity and discreteness.
Remark 1: The Conception of Pure Quantity
§ 399. Pure quantity has not as yet any limit or is not as yet quantum.
§ 400. It is this externality of continuity for the ones to which atomism clings and which ordinary thinking finds it difficult to forsake.
§ 401. It is the notion of pure quantity as opposed to the mere image of it that Spinoza has in mind.
§ 402. More specific examples of pure quantity are space and time, also matter as such, light, and so forth.
§ 403. Time is an absolute coming-out-of-itself, a generating of the one, and immediately the annihilation of it.
Remark 2: The Kantian Antinomy of the Indivisibility and the Infinite Divisibility
§ 404. It is the nature of quantity that gives rise to the conflict or antinomy of the infinite divisibility of space, time, etc.
§ 405. This antinomy consists solely in the fact that discreteness must be asserted just as much as continuity.
§ 406. The second of Kant's four (cosmological) antinomies deals with the antithesis constituted by the moments of quantity.
§ 407. Kantian antinomies remain an important part of the critical philosophy; they brought about the downfall of previous metaphysics .
§ 408. Kant wanted to give his four cosmological antinomies a show of completeness by the classification which he took from his schema of the categories.
§ 409. Kant did not take up the antinomy in the Notions themselves, but in the concrete form of cosmological determinations.
§ 410. Kant's conception of the antinomies is that they are 'contradictions which reason must necessarily come up against'.
§ 411. The Kantian antinomies contain nothing more than the categorical assertion of each of two opposed moments taken in isolation from the other.
§ 412. The relevant antinomy here concerns the so-called infinite divisibility of matter.
§ 413. To the simple, the atom, there is here opposed the composite, which is a very inferior determination compared to the continuous.
§ 414. Like the Kantian proofs of the rest of the antinomial propositions, this proof makes the detour of being apagogic.
§ 415. The main point, and in face of which all that precedes is completely superfluous, is mentioned by the way, in a parenthesis.
§ 416. The assertion that the parts are simple is only a tautology.
§ 417. The apagogical detour thus contains the very assertion which should result from it.
§ 418. We see the externality, that is contingency, of composition put forward as a consequence after it had already been introduced.
§ 419. The laboured, tortuous complexity serves no other purpose than to produce the merely outward semblance of a proof.
§ 420. The apagogical form is a groundless illusion.
§ 421. The apagogical proof begins with a proposition, but oddly enough immediately forgets it.
§ 422. The Kantian distinction between intuition and concept has given rise to a deal of nonsense.
§ 423. There is also involved here a clash between the continuity of space and composition; the two are confused with each other.
§ 424. Even the best microscopes and the keenest knives have not enabled us to come across anything simple.
§ 425. Neither taken alone has truth; this belongs only to their unity. This is the true dialectical consideration and the true result.
§ 426. Infinitely more ingenious and profound than this Kantian antinomy are the dialectical examples of the ancient Eleatic school.
§ 427. The solutions propounded by Aristotle of these dialectical forms merit high praise.
§ 428. The Kantian solution of the antinomy consists solely in the supposition that reason should not soar beyond sensuous perception and should take the world of appearance as it is.
§ 429. 1. Quantity contains the two moments of continuity and discreteness.
§ 430. Quantity is a concrete unity only in so far as it is the unity of distinct moments.
§ 431. 2. Immediate quantity is continuous magnitude.
Remark: The Usual Separation of These Magnitudes
§ 432. Space, time, matter, etc. are continuous magnitudes which possess the absolute possibility that the one may be posited in them.
§ 433. Continuous and discrete magnitude can be regarded as species of quantity.
§ 434. Discrete magnitude has first the one for its principle; secondly, it is a plurality of ones; and thirdly, it is essentially continuous.
§ 435. This limit, which is related to the unity and is the negation in it, is also, as the one, self-related.
§ 436. Since the one which is a limit includes within itself the many ones of discrete quantity, it equally posits them as sublated within it.
§ 437. Quantum, which to begin with is quantity with a determinateness or limit in general is, in its complete determinateness, number.
§ 438. Quantity is quantum, or has a limit, both as continuous and as discrete magnitude.
§ 439. The very nature of quantity is to be indifferent to its limit. But equally, quantity is not unaffected by the limit.
§ 440. This one is thus the principle of quantum, but as the one of quantity.
§ 441. Quantum completely posited in these determinations is number.
§ 442. Amount and unit constitute the moments of number.
§ 443. The number is not a plurality over against the enclosing, limiting one, but itself constitutes this limitation.
§ 444. The contradiction of number or of quantum as such within itself is the quality of quantum.
Remark 1: The Species of Calculation in Arithmetic; Kant's Synthetic Propositions a priori
§ 445. Spatial magnitude and numerical magnitude are regarded as two species, the former being a determinate magnitude just as much as the latter.
§ 446. Arithmetic considers number and its figures; or rather does not consider them but operates with them.
§ 447. Number has for its principle the one and is, therefore, simply an aggregate externally put together, devoid of any inner connectedness.
§ 448. The qualitative difference which constitutes the determinateness of number is that of unit and amount.
§ 449. Numbers can be produced in two ways, either by aggregation, or by separation of an aggregate already given.
§ 450. 1. After these remarks we proceed to indicate the species of calculation.
§ 451. The number produced by counting are in turn themselves counted.
§ 452. Kant considers the proposition: 7 + 5 = 12 to be a synthetic proposition.
§ 453. Counting is not determined by sensation which, according to Kant's definition of intuition is all that remains over for the a posteriors.
§ 454. Kant's assertion of the synthetic nature of the foundations of pure geometry is equally without any solid basis.
§ 455. Kant's notion of synthetic a priori judgements belongs to what is great and imperishable in his philosophy.
§ 456. The negative species of calculation corresponding to addition, subtraction, is the wholly analytical separation into numbers.
§ 457. 2. The next determination is the equality of the numbers which are to be counted.
§ 458. Division is the negative species of calculation with the same determination of the difference.
§ 459. 3. The two numbers related to each other as unit and amount are still immediate with respect to each other and therefore unequal.
§ 460. A graded instruction based on a logically formed division of the subject treats of powers before it treats of proportions.
§ 461. Philosophy must be able to distinguish what is an intrinsically self-external material.
Remark 2: The Employment of Numerical Distinctions for Expressing Philosophical Notions
§ 462. Pythagoras represented rational relationships (or philosophemata) by numbers.
§ 463. Number is the absolute determinateness of quantity.
§ 464. Number is at the same time the abstraction of the manifoldness of sense.
§ 465. The mind which rises above the world of the senses and contemplates its own essence, may therefore happen on number.
§ 466. When what is most alive are transposed into this element of pure self-externality, they become dead, inert determinations.
§ 467. The richer in relationships thoughts become, the more confused and meaningless becomes their representation in numbers.
§ 468. Thought is set its hardest task when the movement of the Notion through which alone it is the Notion, is denoted by numbers.
§ 469. In symbols the truth is dimmed and veiled by the sensuous element; only in the form of thought is it fully revealed.
§ 470. In the concrete philosophical sciences philosophy must take the logical element from logic, not from mathematics.
§ 471. Machines can perform arithmetical operations. So much for the idea of making calculation the means for educating the mind and stretching it on the rack in order to perfect it as a machine.
§ 472. 1. Quantum has its determinateness as limit in amount.
§ 473. The direct opposite of Extensive magnitude is not discrete but intensive magnitude.
§ 474. 2. The determinateness of something in terms of number does not require it to be distinguished from another numerically determined something.
§ 475. The limit of quantum passes over into simple determinateness.
§ 476. The degree is thus a specific magnitude, a quantum.
§ 477. 3. In number, quantum is posited in its complete determinateness; but as intensive quantum.
§ 478. None of the various distinct degrees is separate from the others but each is determined only through them.
§ 479. Degree is not external to itself within itself.
§ 480. The determinateness of intensive magnitude is, therefore, to be considered from two sides.
§ 481. Extensive and intensive magnitude are thus one and the same determinateness of quantum.
§ 482. The qualitative something makes its appearance, for the identity is the unity which is self-related through the negation of its differences.
Remark 1: Examples of This Identity
§ 483. Extensive and intensive quantum are usually distinguished in the ordinary conception of them as kinds of magnitude.
§ 484. In the conversion of the mechanical into the dynamic view, there occurs the concept of separately existing, independent parts.
§ 485. The other determinateness which occurs here is the quantitative as such.
§ 486. Number itself necessarily has this double form immediately within it.
§ 487. In the circle the one is called degree because the determinateness of any part of the circle derives from the many parts outside it.
§ 488. The magnitude of a more concrete object exhibits its dual aspects of being extensive and intensive.
§ 489. A higher degree of temperature expresses itself as a longer column of mercury.
§ 490. A larger surface can be coloured with a more intensive colour than with a weaker colour used in the same way.
§ 491. In the spiritual sphere, high intensity of character is bound up with a correspondingly far-reaching reality in the outer world.
Remark 2: The determination of degree as applied by Kant to the soul
§ 492. The determinateness of intensive quantum has been applied by Kant in a peculiar way to a metaphysical determination of the soul.
§ 493. The difference between extensive and intensive quantum is indifferent to the determinateness of quantum as such.
§ 494. A quantum, therefore, in accordance with its quality, is posited in absolute continuity with its externality, with its otherness.
§ 495. The one is infinite or self-related negation, hence the repulsion of itself from itself.
§ 496. Thus quantum impels itself beyond itself.
§ 497. Quantum alters and becomes another quantum.
§ 498. Finitude and infinity each acquire in themselves a dual, and indeed, an opposite meaning.
§ 499. Qualitative determinateness, as an immediacy, is related to otherness essentially as to an alien being.
§ 500. The progress to infinity is the expression of contradiction, here, of quantum as such.
§ 501. The infinite progress is only the expression of this contradiction, not its resolution; .
§ 502. The continuity of quantum with its other produces the conjunction of both in the expression of an infinitely great or infinitely small.
§ 503. This infinity which is perpetually determined as the beyond of the finite is the spurious quantitative infinite.
Remark 1: The High Repute of the Progress to Infinity
§ 504. The spurious infinite is commonly held to be something sublime, while in philosophy it has been regarded as ultimate.
§ 505. Kant at the close of the Critique of Practical Reason, .
§ 506. This exposition deserves praise mainly on account of truthfulness.
§ 507. Haller's description of eternity, called by Kant terrifying.
§ 508. This heaping and piling up of numbers is regarded as what is valuable in a description of eternity.
§ 509. Astronomers pride themselves on the sublimity of their science because it has to deal with an innumerable host of stars.
§ 510. To the infinity of outer, sensuous intuition, Kant opposes the other infinite.
§ 511. The ego in being thus alone with itself is, it is true, the reached beyond.
§ 512. Kant declares those exaltations to be unsatisfying for reason, which cannot stop at them.
§ 513. The ego in its self-determining proceeds to determine nature and liberate itself therefrom.
§ 514. Ego and non-ego or the pure will and the moral law, are presupposed as completely self-subsistent and mutually indifferent.
§ 515. The standpoint is powerless to overcome the qualitative opposition between the finite and infinite.
§ 516. In Fichte's Theory of Science, the first axiom is ego = ego.
§ 517. Only in the qualitative opposition does the posited infinitude emerge and the quantitative determination itself pass over into the qualitative.
Remark 2: The Kantian Antinomy of the Limitation and Nonlimitation of the World
§ 518. The Kantian antinomies are expositions of the opposition of finite and infinite in a more concrete shape.
§ 519. This antinomy concerns the limitation or non-limitation of the world in time and space.
§ 520. The antinomy is two simple opposite assertions: there is a limit, and the limit must be transcended.
§ 521. The other part of the proof which concerns space is based on time.
§ 522. The basis of the proof itself is the direct assertion of what was to be proved.
§ 523. The assumed limit of time is a now as end of the time already elapsed.
§ 524. In truth, time is pure quantity.
§ 525. The antithesis.
§ 526. The assumption is made that the world as an existence presupposes another conditioned existence in time, and so on to infinity.
§ 527. The proof regarding the infinity of the world in space is the same.
§ 528. Thesis and antithesis are nothing but the opposite assertions, that a limit is, and that the limit equally is only a sublated one.
§ 529. The solution of these antinomies, as of those previously mentioned, is transcendental.
§ 530. 1. The infinite quantum as infinitely great or infinitely small is itself implicitly the infinite progress.
§ 531. Quantum as degree is unitary, self-related and determinate within itself.
§ 532. But this is what quantum as such is in itself.
§ 533. Let us take the progress at first in its abstract determinations as we find them.
§ 534. The first sublation, the negation of quality as such whereby quantum is posited, is in principle the sublating of the negation.
§ 535. The infinite, which in the infinite progress has only the empty meaning of a non-being, is in fact nothing else than quality.
§ 536. Quantum is sublated quality; but quantum is infinite.
§ 537. Quantum as self-related as an indifferent limit in its externality and therefore posited as qualitative, is quantitative ratio.
Remark 1: The Specific Nature of the Notion of the Mathematical Infinite
§ 538. The introduction of the mathematical infinite has led to important results, but mathematics has not succeeded in justifying its use.
§ 539. Mathematics, being unaware of the nature of its instrument, is unable to determine the scope of its application.
§ 540. The science of mathematics can only defend itself by denying the competence of metaphysics.
§ 541. Mathematics finds a radical contradiction to that very method which is peculiar to itself and on which as a science it rests.
§ 542. Mathematics shows that results obtained by the use of the infinite agree with those found by the strictly mathematical method.
§ 543. Consideration of justifications and characteristics of the mathematical infinite I shall undertake at some length in this Remark.
§ 544. The usual definition of the mathematical infinite is that it is a magnitude than which there is no greater.
§ 545. It is the reflection that quantum is sublated, which is usually not made, and which creates the difficulty for ordinary thinking.
§ 546. Kant's finds the said definition does not accord with what is understood by an infinite whole.
§ 547. Kant objects to infinite wholes being regarded as a maximum.
§ 548. Kant's concept of infinite he calls truly transcendental.
§ 549. The character of the mathematical infinite and the way it is used in analysis corresponds to the Notion of the genuine infinite.
§ 550. The infinite quantum contains within itself first externality and secondly the negation of it.
§ 551. The Notion of the infinite as abstractly expounded here will show itself to be the basis of the mathematical infinite.
§ 552. A fractional number, 2/7 for example, is not a quantum like 1, 2, 3, etc., but is directly determined by two other numbers.
§ 553. The representation of infinity by a fractional number is still imperfect.
§ 554. Letters, the next universality into which numbers are raised, are only general symbols and indeterminate possibilities.
§ 555. The ratio first is a quantum, secondly, this quantum is not immediate but contains qualitative opposition.
§ 556. The fraction 2/7 can be expressed as 0.285714..., 1/(1 - a) as 1 + a + a2 + a3 etc..
§ 557. The series is itself infinite.
§ 558. The nature of this infinity of the series is the spurious infinity of the progression.
§ 559. In the infinite series, inexactitude is actually present, whereas in the mathematical infinite there is only appearance of inexactitude.
§ 560. The infinite series contains the spurious infinity.
§ 561. In the infinite series the negative is outside its terms which are present only qua parts of the amount.
§ 562. The existence of infinite series which cannot be summed is external and contingent with respect to the form of series as such.
§ 563. The terminological inversion with the fraction and its expression as a series, also occurs in the mathematical infinite.
§ 564. Spinoza opposes the concept of true infinity to that of the spurious.
§ 565. With Spinoza, substance and its absolute unity has the form of an inert unity.
§ 566. The mathematical example with which Spinoza illustrates the true infinite is the space between two unequal eccentric circles.
§ 567. The incommensurability which lies in Spinoza's example embraces in general the functions of curved lines.
§ 568. The expression 'variable magnitudes' is very vague and ill-chosen.
§ 569. In 2/7 or a/b, 2 and 7 are each independent determinate quanta and the relation is not essential to them.
§ 570. In an equation in which x and y are determined primarily by a power-relation, x and y as such are still supposed to signify quanta.
§ 571. In this concept of the infinite, the quantum is genuinely completed into a qualitative reality.
§ 572. This concept has been the target for all the attacks on the mathematics of this infinite, i.e. differential and integral calculus.
§ 573. Such an intermediate state, as it was called, between being and nothing does not exist.
§ 574. What is infinite is not comparable as something greater or smaller.
§ 575. The originators did not establish the thought as Notion and had to resort to expedients which conflict with their better cause.
§ 576. The thought cannot be more correctly determined than in the way Newton has stated it.
§ 577. Newton did what the scientific method of his time demanded, he only explained what was to be understood by an expression.
§ 578. Newton points out that final ratios are not ratios of final magnitudes, but limits.
§ 579. Carnot: by virtue of the law of continuity, the vanishing magnitudes still retain the ratio from which they come, before they vanish.
§ 580. The empirical reality is thereby raised above itself.
§ 581. The other form of Newton's exposition of the magnitudes in question is equally interesting, namely, as generative magnitudes.
§ 582. The conception of infinitesimals which is implicit in the increment or decrement itself, is inferior to the above determinations.
§ 583. In the science of mathematics there cannot be any question of such empirical accuracy.
§ 584. Euler insists the differential calculus considers the ratios of the increments, but the infinite difference as such is wholly nil.
§ 585. Lagrange's opinion is that the ratio of two magnitudes does not present any clear concept as its terms become simultaneously zero.
§ 586. In the actual application of the method of infinitesimals, the genuine Notion of the infinite cannot exercise any influence.
§ 587. The older analysts had little scruples but the moderns wish differential calculus to attain to the rigour of the proofs of the ancients.
§ 588. Some have attempted to dispense with the concept of the infinite, and without it to achieve what seemed bound up with its use.
§ 589. Fermat, Barrow, Leibniz and Euler, frankly believed that they were entitled to omit the products of infinitesimal differences.
§ 590. Newton had an ingenious device to remove the arithmetically incorrect omission of the products of infinitesimal differences.
§ 591. Other forms Newton employed in derivations are bound up with concrete meanings of the elements relating to motion.
§ 592. Newton made the mistake because he omitted the term of the series containing that power on which the specific problem turned.
§ 593. The procedure is made to depend on the qualitative meaning.
§ 594. Carnot gives a most lucid exposition of what is essential in the ideas referred to above.
§ 595. Lagrange reverted to Newton's original method of series to be relieved of the difficulties inherent in the idea of the infinitely small.
§ 596. The demonstrated qualitative character of the form of magnitude in the infinitesimal, is found in the category of limit of the ratio.
§ 597. The very expression 'limit' implies that it is a limit of something.
§ 598. The idea of limit is supposed to have the advantage of avoiding the inconsistency here involved.
§ 599. [Continuous or fluent magnitude enters with the consideration of the external and empirical variation of magnitudes.]
§ 600. We shall discuss the confusion which the conception of approximation currently used in expositions of the calculus.
§ 601. The so-called infinitesimals express the vanishing of the sides of the ratio as quanta.
§ 602. The limit here does not have the meaning of ratio; it counts only as the final value.
§ 603. The increments or infinitesimals have been considered only from the side of the quantum which vanishes in them.
§ 604. Analogous is the assumption that infinitely small parts of the same whole are equal to each other.
§ 605. Propositions are put forward as results of calculus, without enquiry whether by and in themselves they have a real significance.
§ 606. Much has been accepted as proof for no other reason than that the result was always already known beforehand.
§ 607. The empty scaffolding of such proofs was erected in order to prove physical laws.
Remark 2: The Purpose of the Differential Calculus Deduced from its Application
§ 608. The so-called application, presents greater difficulties, but also the more interesting side; the elements of this concrete side are to be the object of this Remark.
§ 609. The method of the differential calculus shows on the face of it that it was not invented and constructed for its own sake.
§ 610. The nature of the infinitesimal is the qualitative nature of determinations of quantity which are related to each other as quanta.
§ 611. The specifically qualitative character of quantity is first indicated in the quantitative relation as such.
§ 612. The core of the whole business is the actual procedure in the mathematical solution of a certain group of problems.
§ 613. (a) Equations in which any number of magnitudes (here we confine ourselves to two) are combined into a qualitative whole.
§ 614. The magnitudes have simply and solely the character of variables such as occur in the problems of indeterminate analysis.
§ 615. The difference between variables in calculus, is that at least one of those variables is found in a power higher than the first.
§ 616. (b) We have now to indicate what is the interest on which the treatment of the equation is focused.
§ 617. The sole point of importance here is the qualitative determinateness of the terms.
§ 618. The binomial: xn = (y + z)n = (yn + ny(n-1)z + ... ).
§ 619. The object is an equation, ym = axn.
§ 620. The representation of these functions of potentiation of a variable is taken as a sum complex within itself.
§ 621. The increment is supposed to be not a quantum but only a form, the whole value of which is that it assists the development.
§ 622. For what purpose are such functions sought.
§ 623. The answer follows directly and automatically from the nature of the matter.
§ 624. The appearance of arbitrariness of the differential calculus is clarified by awareness of where its application is permissible.
§ 625. For the determination of its moment we shall take the simplest example from equations of the second degree.
§ 626. The equations between these lines and the co-ordinate are linear equations.
§ 627. The first discoverers could only record their findings in a wholly empirical manner.
§ 628. The power forms in the equation are reduced to their first functions. But the value of the terms of the equation is thereby altered.
§ 629. Lagrange rejected this pretence and took the genuinely scientific course.
§ 630. I must also mention the tangential method of Descartes, if only for its beauty and its fame.
§ 631. The final equation obtained in this way is the same as that obtained by the method of the differential calculus.
§ 632. The omission of the constant has the meaning that the constant plays no part in the determination of the roots if these are equal.
§ 633. To differentiate denotes that differences are posited. In integration, on the other hand, the constant must be added in again.
§ 634. Another important sphere in which the differential calculus is employed is mechanics.
§ 635. The erroneous assumption that 2at is part of the motion regarded as a sum, gives the false appearance of a physical proposition.
§ 636. The motion represented by the equation s = at2 we find, says Lagrange, empirically in falling bodies.
§ 637. The application of the differential calculus to the elementary equations of motion does not of itself offer any real interest.
§ 638. The aim has been to make prominent and to establish the simple, specific nature of the differential calculus and to demonstrate it.
§ 639. The other part of the problem of the calculus appears in connection with its formal operation, namely the application of the latter.
§ 640. The problem now is to determine which of the moments determining the subject matter is given in the equation itself.
§ 641. The differentiation of an equation of several variables yields the differential coefficient, not as an equation but only as a ratio.
§ 642. The usual method makes the matter easy for itself by using the idea of the infinitesimal difference.
§ 643. The rectified arc stands to a certain function given by the equation of the curve, in the relation of the original function to its derivative.
§ 644. It is the derived function which in integral calculus is given relatively to the original, which has first to be found by integration.
§ 645. It is superficial to say that the integral calculus is simply the converse problem of the differential calculus.
§ 646. Lagrange did not smooth over the difficulties of its problems simply by making those direct assumptions.
§ 647. Lagrange's rectification of curves provides an insight into the translation of the Archimedean method into modern analysis.
§ 648. The idea of the infinitesimal occurs in Archimedes' method, as well as later in Kepler's treatment of stereometric objects.
§ 649. In these methods the affirmative aspect as such which is veiled by the merely negative determination fails to be recognised.
§ 650. Each mode of calculation has as its subject matter a specific determinateness; so too has the differential and integral calculus.
§ 651. Differential and integral calculus has a more particular interest in common with series: to determine the coefficients of the terms.
Remark 3: Further Forms Connected With the Qualitative Determinateness of Magnitude
§ 652. The infinitesimal of the differential calculus is, in its affirmative meaning, the qualitative determinateness of magnitude.
§ 653. From the analytical side, the different power determinations appear in the first place as only formal and quite homogeneous.
§ 654. The sole interest of this procedure is to determine the points and the lines into which the lines and planes have been resolved.
§ 655. It is the need to have recourse to the infinitely small, which constitute the greatest difficulty.
§ 656. It will now be evident how the qualitative element here considered differs from the subject of the previous Remark.
§ 657. The alleged pure summation does in fact include a multiplication.
§ 658. Representing planes as sums of lines is also often employed when multiplication as such is not used to produce the result.
§ 659. The area of a circle bears the same proportion to the area of an ellipse, as the major axis does to the minor axis.
§ 660. The criterion for Cavalieri's method of indivisibles referred to above equally is justified by it.
§ 661. This leads us to reflect on the difference which exists with respect to that feature into which the determinateness of a figure falls.
§ 662. Cavalieri means to distinguish what belongs to the outer existence of the continuous figure from its determinateness.
§ 663. This form of coincidence is a childish aid for sense perception.
§ 664. With parallel lines and with parallelograms there enters another factor.
§ 665. Tacquet asked which line, in the calculation of conical and spherical surfaces, should be taken as the basis.
§ 666. These objections have their origin in the idea of the infinite aggregate of points of which the line is supposed to consist.
§ 667. The affirmative meanings, in the various applications of the infinitely small in mathematics, remain in the background.
§ 668. The introduction of the infinite which is meant to remove the difficulty only serves to aggravate it and prevent its solution.
§ 669. The infinite quantum as the unity of both moments, of the quantitative and qualitative determinateness, is a ratio.
§ 670. In the ratio, quantum is no longer merely indifferent but is qualitatively determined as simply related to its beyond.
§ 671. This relation is itself also a magnitude; the quantum is not only in a ratio, but it is itself posited as a ratio.
§ 672. Ratio as such is direct ratio; indirect or inverse ratio; and in the ratio of powers, becomes measure.
§ 673. It only remains therefore to expound the abstract Notion of these ratios.
§ 674. 1. In the direct ratio the determinateness of either quantum lies reciprocally in the determinateness of the other.
§ 675. 2. The exponent is any quantum; but it is self-related in its own externality and a qualitatively determined quantum.
§ 676. The exponent is this difference as a simple determinateness, i.e. it has immediately within it the significance of both.
§ 677. 3. The two therefore constitute strictly only one quantum.
§ 678. The exponent ought to be the complete quantum, since the determination of both sides coincides in it.
§ 679. The ratio as now before us is the sublated direct relation.
§ 680. In the inverse ratio the exponent as quantum is likewise immediate and is any quantum assumed as fixed.
§ 681. The ratio is so determined that the amount as such is altered relatively to the other side of the ratio, to the unit.
§ 682. 2. We have now to consider more closely this qualitative nature of the inverse ratio, more particularly in its realisation.
§ 683. In conformity with these determinations, each of the two moments has its limit within the exponent.
§ 684. This continuity of each in the other constitutes the moment of unity through which they are in ratio.
§ 685. The exponent is a limit of the sides of its ratio within which they increase and decrease relatively to each other.
§ 686. 3. The outcome of this, however, is the transition of the inverse ratio into a different determination from that which it had at first.
§ 687. The ratio is now specified as the ratio of powers..
§ 688. 1. The quantum has reached the stage of being-for-self.
§ 689. The exponent of this ratio is no longer an immediate quantum as it is in the direct ratio and also in the inverse ratio.
§ 690. 2. The ratio of powers appears at first to be an external alteration to which any quantum can be subjected.
§ 691. The quality of quantum as the posited difference of itself from itself is simply this: to be a ratio.
§ 692. 3. But with the positing of quantum in conformity with its Notion, it has undergone transition into another determination.
§ 693. At first, then, quantity as such appears in opposition to quality.
§ 694. This is the truth of quantum, to be Measure.
§ 695. The remark to be made here concerns the intrusion of quantitative forms into the pure qualitative forms of thought in philosophy.
§ 696. There is just as much to be said against powers as against all symbolism whatever philosophy.
§ 697. Philosophy needs no help from the world of sense or products of the imagination in its own peculiar province.
§ 698. The use of numbers, the mathematical infinite, and suchlike is nothing more than a convenient means of evading the task of grasping the Notion.
§ 699. Abstractly expressed, in measure quality and quantity are united.
§ 700. Thirdly, we now have self-related externality.
§ 701. Kant did not apply triplicity to the genera of his categories, but only to their species which, alone he called categories.
§ 702. With Spinoza, the mode is likewise the third after substance and attribute.
§ 703. In Indian pantheism, Brahma (abstract thought) progresses through Vishnu, particularly in the form of Krishna, to a third form, Siva.
§ 704. The mode itself is declared to belong essentially to the substantial nature of a thing.
§ 705. Mode has the specific meaning of measure. Spinoza's mode, like the Indian principle of change, is the measureless.
§ 706. Measure in its more developed, more reflected form is necessity.
§ 707. Measure, having realised its own Notion, has passed into essence.
§ 708. At first, measure is only an immediate unity of quality and quantity.
§ 709. Natural science is still far from an insight into the connection between quantities and the organic functions on which they depend.
§ 710. In the realm of spirit there is still less to be found a characteristic, free development of measure.
§ 711. Qualitative quantity in the first place an immediate, specific quantum.
§ 712. 1. Measure is the simple relation of the quantum to itself, its own determinateness within itself; the quantum is thus qualitative.
§ 713. All that exists has a measure.
§ 714. Measure as a standard is a quantum arbitrarily assumed as the intrinsically determinate unit relative to an external amount.
§ 715. Immediate measure is a simple quantitative determination.
§ 716. Quantitative determinateness is twofold: that to which the quality is tied and that which can be varied without affecting the quality.
§ 717. Because quantum is posited as the external limit which is by its nature alterable, and so alteration requires no explanation.
§ 718. 2. The sudden conversion into a change of quality of a change which was apparently merely quantitative attracted the attention of the ancients.
§ 719. Does the pulling out of a single hair from the head produce baldness?
§ 720. The contradiction which results is not a sophism, for such contradiction is not a sham or a deception.
§ 721. What is refuted is the error of one-sidedly holding fast to the abstract determinateness of quantum.
§ 722. Quantum, as an indifferent limit, is the aspect of an existence which leaves it open to unsuspected attack and destruction.
§ 723. 3. Measure in its immediacy is an ordinary quality with a specific magnitude attaching to it.
§ 724. This is first a rule, a measure which is external with reference to mere quantum.
§ 725. Comparison is an external act, the unit itself being an arbitrary magnitude.
§ 726. Measure is a specific determining of the external.
§ 727. Something, in so far as it is a measure within itself, has the magnitude of its quality altered from outside itself.
§ 728. Intensive, and extensive quantum is the same quantum , once in the form of intensity and again in the form of extension.
§ 729. The strictly immanent qualitative form of the quantum is solely its determination as a power.
§ 730. Remperature is a quality in which these two sides of external and specified quantum are distinguished.
§ 731. 1. The qualitative, intrinsically determinate side of the quantum exists only as a relation to the externally quantitative side.
§ 732. 2. In measure there enters the essential determination of variable magnitude, for measure is quantum as sublated.
§ 733. Magnitude, simply as magnitude, is alterable.
§ 734. The two sides thus related have, in keeping with their abstract aspect as qualities generally, some particular significance.
§ 735. The direct ratio is reduced to the merely formal determination which has no existence except as an intellectual abstraction.
§ 736. These kinds of motion, no less than their laws, rest on the development of the Notion of their moments, of space and time.
§ 737. It is a great service to ascertain the empirical numbers of nature, but an infinitely greater service to make them moments of a law.
§ 738. 1. In the form of specified measure, the quantitative element of both sides is qualitatively determined.
§ 739. The immediate qualities also belong to measure.
§ 740. 2. It is still with reference to the specific measure an externally given quantum.
§ 741. 3. Measure has now acquired the character of a specified quantitative relation which, as qualitative, has in it the ordinary external quantum.
§ 742. Measure is now determined as a correlation of measures which constitute the quality of distinct self-subsistent somethings — or things.
§ 743. Self-exclusive and self-subsistent measure are one with each other, and self-subsistent measure enters into a negative relation with itself.
§ 744. Measures are no longer merely immediate but self-subsistent, because they have become relations of measures which are themselves specified.
§ 745. Something is immanently determined as a measure relation of quanta which also possess qualities.
§ 746. The exponent is the specific quantum of the something.
§ 747. As purely quantitatively determined, the compound would be a mere addition of the two magnitudes.
§ 748. Not only is one of the qualitative sides posited as alterable but measure itself.
§ 749. (1) If two things forming a compound body owed their natures to a simple qualitative determination, they would destroy each other when combined.
§ 750. (2) This combination with a number of others which are likewise measures within themselves, yields different ratios.
§ 751. It seems that a self-subsistent measure which forms a series of exponents with a series of such measures, is distinguished from another measure.
§ 752. Those measures which yield a series of exponents of the ratios between the members of that series, are in themselves self-subsistent measures.
§ 753. 3. In this form there is a return to the particular way in which quantum is posited as self-determined, i.e., as degree.
§ 754. The individual note is the key of a system, but again it is equally an individual member in the system of every other key.
§ 755. In elective affinity as an exclusive, qualitative correlation, the relationship is rid of this quantitative difference.
§ 756. Neutralisation is not only the form of intensity; the exponent is essentially a measure determination and therefore exclusive.
Remark: Berthollet on Chemical Affinity and Berzelius's Theory of it
§ 757. Chemical substances are the most characteristic examples of measures which are characterised solely by their relationship to other measures.
§ 758. The law of the chemical affinities of acids and alkalis states that if two neutral solutions are mixed resulting the products are neutral.
§ 759. Berthollet modified the general conception of elective affinity by the concept of the activity of a chemical mass.
§ 760. Berzelius in his Textbook of Chemistry.
§ 761. Berzelius, himself makes use of the conception of degrees of affinity.
§ 762. Affinity is reduced to a quantitative difference.
§ 763. Chemical affinity has been distinguished from elective affinity.
§ 764. If the experimental method has been the guiding star in the theory of proportions, then mixing with the corpuscular theory, a desert lying away from the path of experience, forms all the greater contrast with it.
§ 765. Every chemical action is at bottom an electrical phenomenon.
§ 766. It is just this kind of metaphysics which is proclaimed and echoed too with the greatest pretension.
§ 767. The problem would be to recognize the exponents of the ratios of the series of specific gravities as a system based on a rule.
§ 768. When substances are combined, there occurs also a neutralisation of the specific gravities.
§ 769. The last determination of the measure relation was that being specific it is exclusive.
§ 770. The relation to itself of the measure relation is distinct from its externality which represents its quantitative aspect.
§ 771. They form in this way a nodal line of measures on a scale of more and less.
§ 772. Here we have a measure relation, a self-subsistent reality which is qualitatively distinguished from others.
§ 773. People fondly try to make an alteration comprehensible by means of the gradualness of the transition.
Remark: Examples of Such Nodal Lines; the Maxim, ‘Nature Does Not Make Leaps’
§ 774. The system of natural numbers already shows a nodal line of qualitative moments which emerge in a merely external succession.
§ 775. Qualitative nodes and leaps occur in chemical combinations when the mixture proportions are progressively altered.
§ 776. It is said, natura non facit saltum [there are no leaps in nature].
§ 777. In thinking about the coming-to-be of something, it is assumed that what comes to be is already sensibly or actually in existence.
§ 778. With the expansion of the state and an increased number of citizens, the laws and the constitution acquire a different significance.
§ 779. Magnitude is that side of determinate being through which it can be caught up in a seemingly harmless entanglement which can destroy it.
§ 780. The abstract measureless is the quantum as such which lacks an inner significance.
§ 781. This transition of the qualitative and the quantitative into each other proceeds on the basis of their unity.
§ 782. The alteration is only change of a state, and the subject of the transition is posited as remaining the same in the process.
§ 783. Measure is, in the first instance, only the immediate unity of quality and quantity as an ordinary quantum which is, however, specific.
§ 784. This process is equally the progressive determination of measure in its realisation and the reduction of measure to the status of a moment.
§ 785. Being is the abstract equivalence in which there is supposed to be as yet no determinateness of any kind.
§ 786. what has thus been determined as qualitative and external is only a vanishing determinateness.
§ 787. This determination of indifference is posited within the indifference itself and how the latter is therewith posited as being for itself.
§ 788. 1. The reduction of measure relations which at first ranked as self-subsistent measures, establishes their common substrate.
§ 789. At first it is essentially the merely quantitative external difference which is present in it.
§ 790. The difference is present, further, as two qualities, one of which is sublated by the other.
§ 791. each side is in its own self an inverted relation. As formal, this relation recurs in the two distinct sides.
§ 792. 2. As this indifference, being is now the specification of measure no longer in its immediacy, but measure as developed.
§ 793. The determinations come into immediate opposition and this develops itself into a contradiction.
§ 794. 3. Each quality enters within each side into relation to the other.
§ 795. There can be no question of a quantitative difference or of a more of the one quality.
§ 796. This unity has for its result not the unity which is merely indifferent, but that immanently negative and absolute unity called essence.
Remark: Centripetal and Centrifugal Force
§ 797. The relationship of quantitative difference of two factors determined qualitatively, is applied to the elliptical motion of the celestial bodies.
§ 798. All that can properly be required of a theory has been accomplished; but to reflective understanding this did not appear sufficient.
§ 799. It is evident that it would be an alien force which effected this reversal.
§ 800. The same has been applied to the forces of attraction and repulsion to explain the different densities of bodies.
§ 801. With Spinoza, attributes, thought and extension, then the modes too, the affections are introduced quite empirically.
§ 802. It is the dissolution of measure, in which both moments were directly posited as one.
§ 803. This reflection of differences into their unity is not the product of the subjective thinker, but it is their very nature to sublate themselves.
§ 804. The process is not a transition, nor an external alteration, but its own self-relating which is the negativity of itself.
§ 805. The determinations are no longer simply affirmative as in the sphere of being, but a sheer positedness.
§ 806. Implicit being has vanished and its unity is this simple self-relation only as a result of the sublating of this presupposition.
§ 807. The truth of being is essence.
§ 808. When this movement is pictured as the path of knowing, then this beginning, appears to be an activity of knowing external to being.
§ 809. But this path is the movement of being itself.
§ 810. Essence is in this way only a product, an artefact.
§ 811. Essence is neither in itself nor for itself; what it is, it is through an other.
§ 812. But essence as it has here come to be, is what it is, through a negativity which is not alien to it.
§ 813. Absolute essence in this simple equality with itself has no determinate being.
§ 814. In the whole of logic, essence occupies the same place as quantity does in the sphere of being.
§ 815. Essence stands between being and Notion, and its movement is the transition from being into the Notion.
§ 816. At first, essence shines or shows within itself, or is reflection; secondly, it appears; thirdly, it manifests itself.
§ 817. Essence is first reflection; secondly, we have essentialities; thirdly, essence passes over into Appearance.
§ 818. This immediate being is the unessential but secondly, it is illusory being; thirdly, reflection.
§ 819. Essence is sublated being.
§ 820. But at the same time, being, as contrasted with essence, is the unessential.
§ 821. The distinction of an essential and an unessential side in something has its origin in a third
§ 822. The immediate that is still distinguished from essence is in and for itself a nullity.
§ 823. 1. The being of illusory being consists solely in the sublatedness of being, in its nothingness.
§ 824. Illusory being is all that still remains from the sphere of being.
§ 825. Thus illusory being is the phenomenon of scepticism.
§ 826. 2. Illusory being, therefore, contains an immediate presupposition, a side that is independent of essence.
§ 827. It is the immediacy of non-being that constitutes illusory being.
§ 828. The nothingness which yet is and the being which is only a moment, constitute the moments of illusory being.
§ 829. Illusory being is essence itself in the determinateness of being.
§ 830. Illusory being is the negative that has a being, but in an other, in its negation.
§ 831. Illusory being, therefore, is essence itself, but essence in a determinateness.
§ 832. Essence in this its self-movement is reflection.
§ 833. Illusory being is the same thing as reflection; but it is reflection as immediate.
§ 834. Essence is reflection, the movement of becoming and transition that remains internal to it.
§ 835. Becoming is essence, its reflective movement, is the movement of nothing to nothing, and so back to itself.
§ 836. Reflection is first positing reflection. Secondly, it is external reflection. But thirdly, it is determining reflection.
§ 837. Illusory being is nothingness or the essenceless; but this nothingness or the essenceless does not have its being in an other.
§ 838. This self-related negativity of essence is just as much sublated negativity as it is negativity.
§ 839. reflection is the movement of nothing to nothing and is the negation that coincides with itself, self-negating equality.
§ 840. Reflection is the movement that starts or returns only in so far as the negative has already returned into itself.
§ 841. Reflection-into-self is essentially the presupposing of that from which it is the return.
§ 842. Reflection finds before it an immediate which it transcends and from which it is the return.
§ 843. The reflective movement is to be taken as an absolute recoil upon itself.
§ 844. Reflection is itself and its non-being.
§ 845. Since Reflection has a presupposition and starts from the immediate as its other, it is external reflection.
§ 846. External or real reflection presupposes itself as sublated.
§ 847. External reflection therefore presupposes a being.
§ 848. External reflection is the syllogism in which the two extremes are the immediate and reflection-into-self; the middle term connects the two.
§ 849. The externality of reflection over against the immediate is sublated. Reflection is thus determining reflection.
§ 850. Reflection is usually taken in a subjective sense as the movement of the faculty of judgement beyond an immediate conception.
§ 851. That reflection to which Kant ascribes the search of the universal of a given particular is clearly also only external reflection.
§ 852. The immediate determinations of being are more readily granted to be transient, relative; but the reflected determinations count as essential.
§ 853. 1. External reflection starts from immediate being, positing reflection from nothing.
§ 854. What is posited is consequently an other, but in such a manner that the equality of reflection with itself is completely preserved.
§ 855. 2. Positing is now in unity with external reflection; Positedness is thus a determination of reflection..
§ 856. It is the equality of reflection with itself that possesses the negative only as negative, that enables the negative to persist.
§ 857. By virtue of this reflection-into-self the determinations of reflection appear as free essentialities floating in the void.
§ 858. Essence does not go outside itself; the differences are simply posited.
§ 859. 3. It is positedness, but as reflection-into-self it is at the same time the sublatedness of this positedness.
§ 860. Reflection is the showing of the illusory being of essence within essence itself.
§ 861. Essence is at first pure identity; secondly, difference, external or indifferent difference — diversity, or opposed diversity — opposition; thirdly, as contradiction, opposition reflected into itself, and ground.
Remark: A = A
§ 862. These propositions ranked as the universal laws of thought that are absolute in themselves and incapable of proof.
§ 863. Identity is enunciated in the proposition: everything is identical with itself, A = A.
§ 864. But a determinateness of being is essentially a transition into its opposite.
§ 865. Since they are enunciated as universal laws of thought, they still require a subject of their relation.
§ 866. These propositions are defective in that they have for subject, being, everything.
§ 867. The several propositions which are set up as absolute laws of thought are, opposed to one another.
§ 868. If everything is identical with itself, then it is not different, not opposed, has no ground.
§ 869. 1. Essence is simple immediacy as sublated immediacy.
§ 870. 2. This identity-with-self is the immediacy of reflection.
Remark 1: Abstract Identity
§ 871. Thinking that keeps to external reflection, fails to attain to a grasp of identity, or of essence, which is the same thing.
§ 872. 2. This identity is, in the first instance, essence itself, not yet a determination of it.
§ 873. Non-identity is absolute in so far as it contains nothing of its other but only itself, that is, it is absolute identity with itself.
§ 874. Identity, therefore, is in its own self absolute non-identity.
Remark 2: First Original Law of Thought
§ 875. A = A is, in the first instance, nothing more than the expression of an empty tautology.
§ 876. By clinging to this unmoved identity which has its opposite in difference, it becomes a one-sidedness which has no truth.
§ 877. Confirmation of the absolute truth of the law of identity is based on experience; for anyone admits that it is self-evident.
§ 878. Identity only in union with difference, occurs in every experience.
§ 879. Nothing will be held to be more boring and tedious than conversation which merely reiterates the same thing.
§ 880. Identity, instead of being the unmoved simple, is the passage beyond itself into the dissolution of itself.
§ 881. If the appeal is to be made to what experience shows, then it shows that this identity is nothing.
§ 882. The other expression of the law of identity: A cannot at the same time be A and not-A, has a negative form, the law of contradiction.
§ 883. The law of identity itself, and still more the law of contradiction, is not merely of analytic but of synthetic nature.
§ 884. The law of identity which purports to express merely abstract identity in contrast to difference as a truth, is not a law of thought, but rather the opposite of it.
§ 885. Difference is the negativity which reflection has within it.
§ 886. 1. This difference is difference in and for itself, absolute difference, the difference of essence.
§ 887. 2. Difference in itself is self-related difference; as such, it is the difference not of an other, but of itself from itself.
§ 888. Identity, having entered into the determination of difference, has not lost itself in it as its other, but preserves itself in it.
§ 889. 3. Difference possesses both moments, identity and difference; both are thus a positedness, a determinateness.
§ 890. 1. Identity falls apart within itself into diversity.
§ 891. Diversity constitutes the otherness as such of reflection.
§ 892. The moments of difference are identity and difference itself.
§ 893. 2. In diversity, as the indifference of difference, reflection has become, in general, external to itself.
§ 894. Thus the reflection that is implicit, and external reflection, are the two determinations into which identity and difference, posited themselves.
§ 895. This external identity is likeness, and external difference, unlikeness.
§ 896. 3. External reflection relates what is diverse to likeness and unlikeness.
§ 897. The diverse are from one side like one another, but from another side are unlike; in so far as they are like, they are not unlike.
§ 898. This holding apart of likeness and unlikeness is their destruction.
§ 899. The comparer goes from likeness to unlikeness and from this back to likeness, and therefore lets the one vanish in the other.
§ 900. Likeness and unlikeness, as moments of external reflection and as external to themselves, vanish together in their likeness.
§ 901. Diversity, whose indifferent sides are just as much simply and solely moments of one negative unity, is opposition..
Remark: The Law of Diversity
§ 902. Diversity, like identity, is expressed in its own law; each is valid on its own without respect to the other.
§ 903. All things are different, or: there are no two things like each other.
§ 904. To say everything is different from everything else is superfluous, but that no two things are completely alike, expresses more.
§ 905. This proposition that unlikeness must be predicated of all things, surely stands in need of proof.
§ 906. Likeness and unlikeness, are different in one and the same thing. This has therefore passed over into opposition..
§ 907. But the tenderness for things, whose only care is that they do not contradict themselves, forgets that the contradiction is not thereby resolved but merely shifted into subjective reflection.
§ 908. In opposition, the determinate rejection, difference, finds its completion. It is the unity of identity and difference.
§ 909. Identity and difference are the moments of difference held within itself; they are reflected moments of its unity.
§ 910. Positedness is likeness and unlikeness; these two reflected into themselves constitute the determinations of opposition.
§ 911. This self-likeness that contains unlikeness is the positive; and the unlikeness that contains likeness, is the negative.
§ 912. The positive and the negative are thus the sides of the opposition that have become self-subsistent.
§ 913. Each is only the opposite of the other, the one is not yet positive, the other is not yet negative, but both are negative to one another.
§ 914. The two sides are merely different; each side is of such a kind that it can be taken equally well as positive as negative.
§ 915. The positive and negative are not only something posited, but their positedness is taken back into each.
§ 916. The positive is the not-opposite, the sublated opposition.
§ 917. The negative is not the immediate negative but the negative as a sublated positedness, the negative based positively on itself.
§ 918. The positive and negative are therefore not merely implicitly positive and negative, but explicitly and actually.
Remark: Opposite Magnitudes of Arithmetic
§ 919. The positive and negative as it is employed in arithmetic does not avoid insoluble difficulties and complications.
§ 920. In the first instance, +a and -a are simply opposite magnitudes.
§ 921. a is not merely the simple unity forming the base but, it is the reflection of the opposites into themselves.
§ 922. According to the first aspect, +y - y = 0.
§ 923. The opposites certainly cancel one another in their relation, so that the result is zero.
§ 924. The opposites are not only a single indifferent term, but two such.
§ 925. Capital, even if its respective determinations of assets and liabilities nullified each other, remains first, positive capital.
§ 926. a, when it bears no sign, is meant to be taken as positive.
§ 927. When positive and negative magnitudes are added and subtracted, they are counted as positive or negative on their own account.
§ 928. This becomes more evident in multiplication and division.
§ 929. The negative here is the intrinsically opposite as such, but the positive is an indeterminate, indifferent sign in general.
§ 930. The negation of negation is the positive.
§ 931. 1. Difference as such contains its two sides as moments.
§ 932. One is the positive, the other the negative, but the former as the intrinsically positive, the latter as the intrinsically negative.
§ 933. The self-subsistent determination of reflection that contains the opposite determination is contradiction.
§ 934. Difference as such is already implicitly contradiction.
§ 935. The positive makes itself into the relation of a non-being.
§ 936. This is the absolute contradiction of the positive, but it is immediately the absolute contradiction of the negative.
§ 937. The positive is only implicitly this contradiction, whereas the negative is the contradiction posited.
§ 938. The negative is the whole opposition based on itself, absolute difference that is not related to an other.
§ 939. 2. Contradiction resolves itself.
§ 940. The result of contradiction is not merely a nullity.
§ 941. The sides of opposition destroy themselves in that they determine themselves as self-identical.
§ 942. The sublating of positedness is not again a positedness, but is a uniting with itself, the positive unity with itself.
§ 943. 3. According to this positive side, opposition is not only destroyed but has withdrawn into its ground.
§ 944. Thus essence as ground is a positedness, something that has become.
§ 945. The resolved contradiction is therefore ground, essence as unity of the positive and negative.
Remark 1: Unity of Positive and Negative
§ 946. The positive and negative are the same. But it is not an external comparison that should be drawn between them any more than between any other categories.
§ 947. Superficial thinking does not consider the positive and negative as they are in and for themselves.
§ 948. Even a slight experience in reflective thinking shows that when one moves forward, the positive has secretly turned into a negative.
§ 949. But the negative also has a subsistence of its own apart from this relation to the positive.
§ 950. The opposition between positive and negative is chiefly that the former is supposed to be objective, and the latter subjective.
§ 951. Error is a positive. But ignorance is either indifferent to truth and error, or a negative that contains a positive direction within it.
Remark 2: The Law of the Excluded Middle
§ 952. The so-called law of the excluded middle: something is either A or not-A; there is no third.
§ 953. This law implies first, that everything is an opposite, is determined as either positive or negative.
§ 954. The law of the excluded middle is also distinguished from the laws of identity and contradiction considered above.
Remark 3: The Law of Contradiction
§ 955. Identity, difference and opposition, have been put in the form of a law, still more should Contradiction, into which they pass as their truth, be enunciated as a law.
§ 956. It is one of the fundamental prejudices of logic that contradiction is not so essential a determination as identity.
§ 957. In the first place, contradiction is usually kept aloof from things, from the sphere of being and of truth generally.
§ 958. As regards the assertion that there is no contradiction, that it does not exist, this statement need not cause us any concern.
§ 959. Internal self-movement proper, instinctive urge in general, is nothing else but the fact that something is the negative of itself.
§ 960. If the contradiction in motion is masked for ordinary thinking, contradiction is immediately represented in the determinations of relationship.
§ 961. Though ordinary thinking everywhere has contradiction for its content, it does not become aware of it, but remains an external reflection which passes from likeness to unlikeness.
§ 962. In the end the sum total of all realities simply becomes absolute contradiction within itself.
§ 963. Every concrete thing, every Notion, is essentially a unity of distinguished and distinguishable moments, which pass over into contradictory moments.
§ 964. Essence determines itself as ground.
§ 965. Essence, in determining itself as ground, is determined as the non-determined; as self-sublating, self-identical essence.
§ 966. Essence, in determining itself as ground, proceeds only from itself.
§ 967. Reflection is pure mediation in general, ground is real mediation of essence with itself.
§ 968. Ground is first, absolute ground; Secondly, it is a determinate ground; Thirdly, ground presupposes a condition.
Remark: The Law of Ground
§ 969. Ground, like the other determinations of reflection, has been expressed in the form of a law: everything has its sufficient ground.
§ 970. The determination of reflection, in so far as it withdraws into ground, is a first, an immediate determinate being in general.
§ 971. The determinateness of essence as ground is therefore twofold, that of ground and the grounded.
§ 972. This mediation of the ground is therefore the unity of the pure and the determining reflection.
§ 973. The determinations of reflection ought to be self-subsistent; but their self-subsistence is their dissolution.
§ 974. To form belongs in general everything determinate.
§ 975. Form is the completed whole of reflection.
§ 976. The question cannot be asked, how form is added to essence, for it is essence's own immanent reflection.
§ 977. Essence is the indeterminate for which form is an other. As such, it is determined as formless identity; it is matter..
§ 978. Matter is the differenceless identity which is essence, the other form, the real basis or substrate of form.
§ 979. 1. If abstraction is made from every determination, from all form of anything, what is left over is indeterminate matter.
§ 980. Matter must therefore be formed, and form must therefore materialise itself.
§ 981. 2. Hence form determines matter, and matter is determined by form.
§ 982. Form and matter presuppose one another.
§ 983. Form as self-subsistent is, besides, the self-sublating contradiction.
§ 984. Matter is also not determined, since form sublates its own self-subsistence. But matter is self-subsistent only as against form.
§ 985. This, which appears as activity of form, is also no less a movement belonging to matter itself.
§ 986. The activity of form and the movement of matter are the same, save that the former is an activity, whereas the latter is a movement.
§ 987. Form, in so far as it presupposes a matter as its other, is finite. It is not ground but only the active principle.
§ 988. The unity of form and matter, which is formed matter, but which is at the same time indifferent to form and matter, these being sublated and unessential determinations. It is content.
§ 989. What was previously the self-identical comes under the dominance of form and is once more one of its determinations.
§ 990. The content is, first, a form and a matter which belong to it and are essential; it is their unity.
§ 991. The content is, secondly, the identical element in form and matter, so that these would be only indifferent external determinations.
§ 992. The content of the ground is the ground that has returned into its unity with itself.
§ 993. The ground has thereby simply converted itself into determinate ground.
§ 994. The ground has a determinate content. The determinateness of the content is the substrate for the form.
§ 995. In this content, the determinateness of the ground and the grounded over against one another has at first vanished.
§ 996. The substrate of the determinations which are form and content are themselves one and the same identity.
§ 997. There is nothing in the ground that is not in the grounded, and there is nothing in the grounded that is not in the ground.
§ 998. The ground and the grounded are each the whole form, and their content is one and the same.
Remark: Formal Method of Explanation From Tautological Grounds
§ 999. The sciences, especially the physical sciences, are full of tautologies of this kind.
§ 1000. To answer ‘Why is this person going to town?’, ‘Because there is an attractive force in the town’ is sanctioned in the sciences but outside them is counted absurd.
§ 1001. Since the ground is derived from the phenomenon, the phenomenon flows smoothly and with a favourable wind from its ground.
§ 1002. They premise as ground what is in fact derived, and then place in the consequents the ground of these supposed grounds.
§ 1003. At the same time hear it repeated that we do not know the inner nature of these forces and matters themselves.
§ 1004. The relation of ground and grounded comes to be an external form imposed on the content.
§ 1005. When we ask for a ground, we demand that the content of the ground be a different determination from that of the phenomenon.
§ 1006. Apart from this content of the ground, the grounded now has its own distinctive content and is the unity of a twofold content.
§ 1007. In the real ground relation, what is present is twofold.
§ 1008. The self-identical form of the ground, that the something is essential, and on the other hand, posited, has vanished.
§ 1009. An external ground brings the content into combination and determines which is ground and which is posited by the ground.
Formal Method of Explanation From a Ground Distinct From That Which is Grounded
§ 1010. Gravity, which is the ground for a house standing, is no less also the ground for a stone falling.
§ 1011. Before Nature can be the world a multiplicity of determinations must be externally added to it.
§ 1012. If in one case a determination is present as ground of another, it does not follow that this other is posited in another case.
§ 1013. Because each is a one-sided ground, and none of them exhausts the subject; none is a sufficient ground, that is, the Notion.
§ 1014. 1. In real ground, ground as content and ground as relation are only substrates.
§ 1015. The resultant ground-relation is therefore the complete ground relation.
§ 1016. 2. The ground-relation has thus determined itself more precisely in the following manner.
§ 1017. The two somethings are therefore the two distinct relations of the content which have been brought to view.
§ 1018. The ground-relation of the determinations of the content in the second is thus mediated by the first, implicit relation of the first.
§ 1019. 3. Real ground shows itself to be the self-external reflection of ground.
§ 1020. The total ground-relation has determined itself to be conditioning mediation..
§ 1021. 1. Ground is the immediate, and the grounded the mediated.
§ 1022. Condition is, therefore, first, an immediate manifold something. Secondly, this something is related to another.
§ 1023. 2. Something is not through its condition; its condition is not its ground.
§ 1024. 3. The two sides of the whole, condition and ground, are indifferent and unconditioned in relation to each other.
§ 1025. Each of the two relatively unconditioned sides is reflected into the other.
§ 1026. Condition is an immediate determinate being; its form has the two moments, positedness and the in-itself.
§ 1027. Ground is equally the whole itself.
§ 1028. What is present is simply only one whole of form, but equally only one whole of content.
§ 1029. The two sides of the whole, condition and ground, are therefore one essential unity, equally as content and as form.
§ 1030. It is the fact's own act to condition itself and to oppose itself as ground to its conditions.
§ 1031. The absolutely unconditioned is the absolute ground that is identical with its condition.
§ 1032. The other side of this reflective movement is the ground-relation as such, determined as form over against content.
§ 1033. When all the conditions of a fact are present, it enters into Existence.
§ 1034. This is the tautological movement of the fact to itself, and its mediation by conditions and ground is the vanishing of both.
§ 1035. The truth of grounding is that its reflection into another is its reflection into itself.
§ 1036. Essence must appear.
§ 1037. Since essence is ground, it gives itself a real determination through its reflection.
§ 1038. Appearance is that which the thing is in itself, or its truth.
§ 1039. What appears manifests what is essential, and this is in its Appearance.
§ 1040. Whatever is, exists. The truth of being is to be, not a first immediate, but essence that has emerged into immediacy.
§ 1041. Existence is the immediacy that has emerged from the sublating of the mediation by which ground and condition are related.
§ 1042. Proof is, in general, mediated cognition. The various kinds of being demand or imply their own kind of mediation.
§ 1043. The proofs of the existence of God adduce a ground for this existence.
§ 1044. The comprehension of God's existence has been declared unprovable and knowledge of it only an immediate consciousness.
§ 1045. Existence, then, is not to be taken here as a predicate or as a determination.
§ 1046. Existence is negative unity and a being-within-self; it therefore determines itself immediately as an Existent and as thing.
§ 1047. The existent something is thus a thing..
§ 1048. The thing is distinct from its Existence just as something can be distinguished from its being.
§ 1049. 1. The thing-in-itself is the existent as the essential immediate which has resulted from the sublated mediation.
§ 1050. Reflection, too, as determinate being that mediates itself through other, falls outside the thing-in-itself.
§ 1051. The thing-in-itself has colour only in relation to the eye, smell in relation to the nose, and so on.
§ 1052. 2. Now this other is reflection which, determined as external, is first, external to itself and determinate manifoldness.
§ 1053. The thing-in-itself is therefore identical with external existence.
§ 1054. The thing-in-itself is self-related, essential Existence.
§ 1055. 3. This external reflection is a relating of the things-in-themselves to one another, their reciprocal mediation as others.
§ 1056. Quality is the immediate determinateness of something, the negative itself through which being is something.
§ 1057. Properties are the determinate relations of the thing to another thing; property exists only as a mode of relationship between them.
§ 1058. Through its properties the thing becomes cause, and cause is this, that it preserves itself as effect.
§ 1059. The thing-in-itself is not a substrate devoid of determinations, but is present in its properties as ground.
Remark: The Thing-in-itself of Transcendental Idealism
§ 1060. The thing-in-itself as such is nothing else but the empty abstraction from all determinateness.
§ 1061. For transcendental idealism this external reflection is consciousness and falls in me, the subject.
§ 1062. Subjective idealism is contradicted by the consciousness of freedom, according to which I know myself as the universal.
§ 1063. The thing-in-itself essentially possesses this external reflection within itself and determines itself endowed with properties.
§ 1064. The thing-in-itself essentially exists; the external immediacy belongs to its in-itself or to its reflection-into-self.
§ 1065. These many different things stand in essential reciprocal action their properties.
§ 1066. Things fall only within the continuity which is property; as extremes having a continuing Existence apart from this property, they vanish.
§ 1067. Property, the relation of the self-subsistent extremes, is the self-subsistent itself. The things are the unessential.
§ 1068. The transition of property into matter is that performed on sensible matter by chemistry when it represents properties of colour, &c, as colouring matter, &c.
§ 1069. The necessity of postulating that properties are in truth matters, has resulted from properties being the essential element of things.
§ 1070. Though the thing as this thing is a complete determinateness, this determinateness in the element of unessentiality.
§ 1071. Property is not only an external determination but an intrinsic Existence.
§ 1072. The thing consists of an unessential combination of self-subsistent matters, indifferent to their relation in the thing.
§ 1073. Matters circulate freely out of or into 'this' thing; the thing itself is absolute porosity without measure or form of its own.
§ 1074. The thing is determined as an external collection of self-subsistent matters.
§ 1075. Existence has reached its completion; the truth of Existence is to have its being-in-self in unessentiality - Appearance.
Remark: The Porosity of Matters
§ 1076. The thing is considered to have properties, whose subsistence is the thing, but these are regarded as matters whose subsistence is not the thing.
§ 1077. The usual excuse to evade the contradiction of the independent subsistence of a number of matters is the smallness of the parts.
§ 1078. The contradiction is partly subjective, stemming from pictorial thinking, and partly objective, stemming from the object.
§ 1079. Recent expositions in physics show that a certain volume takes up the same amount of steam whether it is empty of air or filled with it.
§ 1080. Existence is the immediacy of being to which essence has restored itself again.
§ 1081. Existence as essential Existence is Appearance.
§ 1082. Something is only Appearance, but the reflection by virtue of which it is this, is its own.
§ 1083. The fact is that Appearance is the higher truth.
§ 1084. Appearance is accordingly the unity of illusory being and Existence.
§ 1085. These determinations as well as their relation remain self-equal in the flux of Appearance; this is the Law of Appearance..
§ 1086. The world of Appearance is confronted by the world of essence.
§ 1087. Appearance becomes correlation or essential relation.
§ 1088. 1. Appearance is the existent mediated by its negation, which constitutes its subsistence.
§ 1089. Appearance has two sides: one which is contingent, unessential and subject to transition; the other exempt from this flux, the enduring element.
§ 1090. This contradiction sublates itself; and its unity is the law of Appearance
§ 1091. 2. The law is therefore the positive side of the mediation of what appears.
§ 1092. Appearance and law have one and the same content. Law is the reflection of Appearance into identity-with-self.
§ 1093. Law is the substrate of Appearance; Appearance is the same content, but has the unessential content of its immediate being.
§ 1094. Law is not beyond Appearance but is immediately present in it; the realm of laws is the stable image of the world of Existence or Appearance.
§ 1095. 3. Law is therefore essential Appearance.
§ 1096. That which Appearance contains distinct from law, determined itself as a positive or as another content.
§ 1097. This defect is present in law in this way, that the content of law is at first only diverse and so indifferent to itself.
§ 1098. 1. The existent world tranquilly raises itself to a realm of laws.
§ 1099. Law is, in fact, also the other of Appearance as such and its negative reflection as into its other.
§ 1100. Since the different sides of law are different in their negative unity, the identity of law is now a posited and real identity.
§ 1101. Law has obtained the moment of the negative form of its sides which was lacking, which previously belonged still to Appearance.
§ 1102. The realm of laws contains only the simple, changeless but varied content of the existent world.
§ 1103. This world in and for itself is also called the supersensuous world.
§ 1104. 2. The world in and for itself is the totality of Existence; outside it there is nothing.
§ 1105. Existence becomes Appearance; ground is sublated in Existence; it reinstates itself as the return of Appearance into itself.
§ 1106. The world in and for itself is the inversion of the manifested world.
§ 1107. The two worlds are such that what is positive in the world of Appearance is negative in the world in and for-itself.
§ 1108. It is just in this opposition of the two worlds that their difference has vanished.
§ 1109. The world of Appearance and the essential world are each in themselves self-subsistent wholes of Existence.
§ 1110. Law is realised; its inner identity is also determinately present, and conversely the content of law is raised into ideality.
§ 1111. Law is essential relation. There have arisen two totalities of the content in the world of Appearance.
§ 1112. The truth of Appearance is the essential relation.
§ 1113. The essential relation is not yet the true third to essence and Existence, though it already contains the determinate union of both.
§ 1114. The identity it contains is not yet complete.
§ 1115. The essential relation is therefore immediately the relation of whole and parts.
§ 1116. Secondly, the relation passes over into the relationship in which one side is moment of the other and in it as in its ground.
§ 1117. Thirdly, the inequality still present in this relation now sublates itself and the final relation is that of inner and outer.
§ 1118. The essential relation contains first, the self-subsistence of immediacy, reflected into itself.
§ 1119. 2. This relation contains the self-subsistence of the sides, and equally their sublatedness, and both simply in one relation.
§ 1120. The whole is the reflected unity which has an independent subsistence of its own; but is equally repelled from it.
§ 1121. The parts likewise are the whole relation. They are immediate, as against reflected, self-subsistence.
§ 1122. The whole and the parts therefore condition each other, but the relation here is realised.
§ 1123. Since each has its self-subsistence not in itself but in its other, what is present is only a single identity of both sides.
§ 1124. There is nothing in the whole which is not in the parts, and nothing in the parts which is not in the whole.
§ 1125. Although the whole is equal to the parts it is not equal to them as parts.
§ 1126. The parts are equal to the whole; but because they are in themselves otherness, they are not equal to it as the unity.
§ 1127. The whole and the parts fall indifferently apart. But as thus held apart they destroy themselves.
§ 1128. The truth of the relation consists therefore in the mediation;.
§ 1129. The relation of whole and parts has passed over into the relation of force and its expression..
Remark: Infinite Divisibility
§ 1130. The antinomy of Infinite Divisibility consists in the contradiction in the relation of whole and parts and has been resolved.
§ 1131. Matter as whole consists of parts, and in these the whole vanishes. But the part taken by itself is also not part but the whole.
§ 1132. Force is the negative unity into which the contradiction of whole and parts has resolved itself.
§ 1133. In the essential relation , the immediate and the reflected self-subsistence are posited as sublated or as moments.
§ 1134. Force appears as externally connected with a thing and impressed on the thing by an alien power.
§ 1135. Instead of magnetic, electrical &c forces, magnetic, electrical &c matters are assumed and an ether holding everything together.
§ 1136. Force contains immediate Existence as moment, a moment which, though it is condition, passes over and sublates itself.
§ 1137. Force is the unity of reflected and immediate subsistence, or of the form-unity and external self-subsistence.
§ 1138. Force is at first only an activity in principle, an immediate activity.
§ 1139. The activity of force is conditioned by itself as by the other to itself, by a force.
§ 1140. Force is a relation in which each side is the same as the other.
§ 1141. The externality which is present for force is its own presupposing activity, which at first is posited as another force.
§ 1142. This presupposing is reciprocal.
§ 1143. The other force against which it is active is not passive, which would involve the entry of something alien; the impulse solicits it.
§ 1144. The Notion of force is simply the identity of positing and presupposing reflection, or of reflected and immediate unity.
§ 1145. One force is determined as soliciting and the other as being solicited.
§ 1146. A force exerts an impulse on another passively receiving the impulse but then passing into activity, so the force expresses itself .
§ 1147. What force expresses is this, that its externality is identical with its inwardness..
§ 1148. 1. The relation of whole and parts is the immediate relation.
§ 1149. The inner is determined as the form of reflected immediacy or of essence over against the outer as the form of being.
§ 1150. 2. They are in this way the different form-determinations which have an identical substrate, not in themselves but in an other.
§ 1151. Something which in the first instance is only an inner, is for that very reason only an outer.
Remark: Immediate Identity of Inner and Outer
§ 1152. The movement of essence is the becoming of the Notion. In the relation of inner and outer, the essential moment of this emerges.
§ 1153. The seed is at first only inner plant. Thus God in his immediate Notion is not spirit. Immediately, God is only nature.
§ 1154. 3. The content is the form itself in so far as this determines itself as difference.
§ 1155. Each of the differences of form, the inner and outer, is posited within itself as the totality of itself and its other.
§ 1156. What something is, it is wholly in its externality. Its Appearance is the expression or utterance of what it is in itself.
§ 1157. The essential relation, in this identity of Appearance with the inner or with essence, has determined itself into actuality.
§ 1158. Actuality is the unity of essence and Existence.
§ 1159. This unity of inner and outer is absolute actuality, in the first instance, the absolute as such.
§ 1160. Secondly, actuality proper; Actuality, possibility and necessity constitute the formal moments of the absolute.
§ 1161. Thirdly, the unity of the absolute and its reflection is the absolute relation - substance.
§ 1162. We have to exhibit what the absolute is; but this 'exhibiting' is the self-exposition of the absolute and only a display of what it is.
§ 1163. The absolute itself is the absolute unity of both Being and Essence.
§ 1164. The absolute is to be the absolute form. But conversely, the absolute is the absolute content.
§ 1165. The content has not been raked together from outside, or submerged in the abyss by a reflection alien to that content, but through its inner necessity.
§ 1166. This positive exposition thus arrests the finite before it vanishes and contemplates it as an expression and image of the absolute.
§ 1167. This expository process though it is an absolute act through its relation to the absolute into which it withdraws.
§ 1168. The exposition of the absolute is, in fact, its own act, which begins from itself and arrives at itself.
§ 1169. The absolute is not merely attribute because it is the subject matter of an external reflection and something determined by it.
§ 1170. The absolute absolute, denotes the absolute that in its form has returned into itself.
§ 1171. The absolute is attribute because as simple absolute identity it is in the determination of identity.
§ 1172. It is as inner form that reflection determines the absolute into attribute, something still distinct from the externality.
§ 1173. The attribute is first, the absolute as in simple identity with itself; secondly, it is negation.
§ 1174. Mode, the externality of the absolute, is not merely this, but externality posited as externality.
§ 1175. The absolute as first indifferent identity is only the determinate absolute or attribute, because it is the unreflected absolute.
§ 1176. The true meaning of mode is that it is the absolute's own reflective movement, a determining.
§ 1177. The distinction between form and content is simply dissolved in the absolute.
§ 1178. The Absolute is only as the absolute manifestation of itself for itself. As such it is actuality.
Remark: The Philosophy of Spinoza and Leibniz
§ 1179. Corresponding to the Notion of the absolute and to the relation of reflection to it, is the notion of substance in Spinozism.
§ 1180. The notions of substance given by Spinoza are the notions of 'cause of itself', and that substance is that whose essence includes existence.
§ 1181. Spinoza's definition definition of the attribute: the manner in which intellect comprehends the essence of substance.
§ 1182. Spinoza further determines attribute as infinite, and infinite, too, in the sense of an infinite plurality.
§ 1183. There is lacking the becoming both of identity and of its determinations.
§ 1184. In the oriental conception of emanation the absolute is the light which illumines itself; only it also emanates.
§ 1185. The relation of the monads to one another, falls outside them and is likewise pre-established by another being.
§ 1186. The distinctions do not originate out of this being itself, but are the product of ratiocinative, dogmatic reflection and have not achieved an inner coherence.
§ 1187. The absolute is the unity of inner and outer as initial, implicit unity.
§ 1188. This unity in which Existence or immediacy, and the in-itself, the ground or the reflected are simply moments, is actuality.
§ 1189. Difference thus belongs at first to external reflection and is not determined as content.
§ 1190. The relation of actuality as against a possibility is necessity.
§ 1191. The reflection of relative necessity into itself yields absolute necessity, which is absolute possibility and actuality.
§ 1192. 1. Actuality is formal in so far as it is only immediate, unreflected actuality, not the totality of form.
§ 1193. 2. This possibility is actuality reflected into itself.
§ 1194. Because the determination is here the totality of form, this in-itself is determined as sublated.
§ 1195. Indifferent diversity passes over into opposition; but opposition is contradiction; everything is contradictory and therefore impossible.
§ 1196. This merely formal predication of something - it is possible - is therefore superficial and empty.
§ 1197. The possible, however, contains more than the bare law of identity.
§ 1198. Possibility as form determination posited as sublated possesses a content in general.
§ 1199. This relation is the contradiction that sublates itself; it is also the immediate and thus becomes actuality..
§ 1200. 3. This actuality is not the primary but the reflected actuality, posited as unity of itself and possibility.
§ 1201. Everything possible has therefore in general a being or an Existence..
§ 1202. The unity of possibility and actuality is contingency.
§ 1203. The contingent therefore presents two sides: immediate actuality and likewise as groundless.
§ 1204. Secondly, the contingent is the actual as a merely possible or as a positedness.
§ 1205. Actuality in its immediate unity with possibility is only Existence and is determined as something groundless.
§ 1206. The absolute unrest of the becoming of these two determinations is contingency.
§ 1207. The necessary is an actual; as such it is something immediate, groundless.
§ 1208. 1. The necessity which has resulted is formal because its moments are formal.
§ 1209. Real actuality as such is in the first instance the thing of many properties, the existent world.
§ 1210. Now real actuality likewise has possibility immediately present within it.
§ 1211. 2. Possibility as the in-itself of real actuality is itself real Possibility, and the in-itself as pregnant with content.
§ 1212. The real possibility of something is therefore the existing multiplicity of circumstances which are connected with it.
§ 1213. This existing multiplicity is both possibility and actuality, yet their identity is, at first, only the content.
§ 1214. When all the conditions of something are completely present, it enters into actuality.
§ 1215. In self-sublating real possibility, what is sublated is a duality, for it is itself the duality of actuality and possibility.
§ 1216. 3. The negation of real possibility is thus its identity-with self.
§ 1217. What is necessary cannot be otherwise; but what is simply possible can.
§ 1218. Real possibility and necessity are therefore only seemingly different.
§ 1219. Necessity is at the same time relative, For it has its presupposition in the contingent.
§ 1220. The really necessary is therefore any limited actuality.
§ 1221. The unity of necessity and contingency is present in principle; this unity is to be called absolute actuality.
§ 1222. Real necessity is determinate necessity; formal necessity does not as yet possess any content and determinateness.
§ 1223. This determinateness in its first simplicity is actuality.
§ 1224. Because this actuality is posited as being itself the unity of itself and possibility, it is only an empty determination.
§ 1225. Thus real necessity notionally implicitly contains contingency, but contingency also becomes in it.
§ 1226. It is in this very act that this actuality is determined as a negative.
§ 1227. Form in its realisation has penetrated all its differences and made itself transparent.
§ 1228. Absolute necessity is the truth into which actuality possibility as such, and formal and real necessity withdraw.
§ 1229. Absolute necessity is thus the reflection or form of the absolute: the unity of being and essence.
§ 1230. Absolute necessity is the essence of those free, inherently necessary actualities; light-shy, because there is no reflective movement.
§ 1231. The blind transition of necessity is the absolute's own exposition in which, in its alienation, it reveals itself.
§ 1232. Absolute necessity is not so much the necessary, but necessity - being, simply and solely as reflection.
§ 1233. The sides of the absolute relation are therefore not attributes but totalities.
§ 1234. This is the relation of substance and accidents, the immediate vanishing and becoming of illusory being within itself.
§ 1235. Absolute necessity is absolute relation because it is not being as such, but being as absolute self-mediation.
§ 1236. This reflective movement is identity as identity of form - the unity of possibility and actuality.
§ 1237. This movement of accidentality is the actuosity of substance as a tranquil coming forth of itself.
§ 1238. Substance is the totality of the whole and embraces accidentality within it, and accidentality is the whole substance itself.
§ 1239. The flux of accidents, is the absolute form-unity of accidentality, substance as absolute power.
§ 1240. The accidents as such have no power over one another. They are the simply affirmative something.
§ 1241. On account of this immediate identity and presence of substance in the accidents, no real difference is as yet present.
§ 1242. Thus the relation of substantiality passes over into the relation of causality.
§ 1243. Substance is power reflected into itself that posits determinations and distinguishes them from itself.
§ 1244. This relation of causality is, in the first instance, merely this relation of cause and effect.
§ 1245. 1. Cause is primary in relation to effect.
§ 1246. 2. Over against this positedness reflected into itself, stands substance as the non-posited original.
§ 1247. Effect contains nothing whatever that cause does not contain. Conversely, cause contains nothing which is not in its effect.
§ 1248. 3. In this identity of cause and effect, the form through which they are distinguished is sublated.
§ 1249. 1. Content is, only implicitly related to form, here, to causality.
§ 1250. Cause is determinate in respect of its content and so, therefore, equally is effect.
§ 1251. As finite causality, it has a given content and exhausts itself in an external difference in this identical content.
§ 1252. It is the same fact which presents itself once as cause and again as effect.
§ 1253. It is tautology to determine a phenomenon as effect and then ascend to its cause; it is a repetition of one and the same content.
§ 1254. The cause has of course a further content. Only this further content is a contingent accessory which does not concern the cause.
§ 1255. The change of form suffered by the basic fact in the passage through intermediate terms conceals the identity which it retains.
§ 1256. In physico-organic and spiritual life, what is called cause certainly reveals itself as having a different content from the effect.
§ 1257. 2. This determinateness of the relationship of causality, that content and form are distinct and indifferent, extends further.
§ 1258. This external content is therefore devoid of any relationship, an immediate existence.
§ 1259. This thing is not only substrate but also substance, for it is identical subsistence only as subsistence of the relation.
§ 1260. Rain is the cause of wetness, which is the same water as the rain.
§ 1261. Finite reflection makes it in one respect cause and in another respect effect, unable to hold fast the unity.
§ 1262. The infinite progress from effect to effect is entirely the same as the regress from cause to cause.
§ 1263. 3. We have now to see what has developed through the movement of the determinate causal relation.
§ 1264. Causality therefore presupposes its own self or conditions itself.
§ 1265. Causality is a presupposing act. Cause is conditioned.
§ 1266. This cause acts; for it is the negative power over itself; at the same time, it is its own presupposition.
§ 1267. Violence is the manifestation of power, or power as external.
§ 1268. Passive substance therefore only receives its due through the action on it of another power.
§ 1269. since passive substance is itself converted into cause, the outcome is first, that in it the effect is sublated.
§ 1270. The effect which the previously passive substance sublates within itself is, in fact, precisely this effect of the first cause.
§ 1271. That first cause reappears as cause, whereby the action is bent round, returning into itself, an infinite reciprocal action.
§ 1272. Reciprocity contains the vanishing of the immediate substantiality, and the coming-to-be of the cause.
§ 1273. Reciprocity displays itself as a reciprocal causality of presupposed, self-conditioned substances.
§ 1274. Causality has returned to its absolute Notion, and attained to the Notion itself.
§ 1275. In reciprocity, therefore, necessity and causality have vanished.
§ 1276. This is the Notion, the realm of subjectivity or of freedom.
§ 1277. Building a new city is attended with difficulties, yet there is no shortage of materials; but the abundance of materials presents all the more obstacles when the task is to remodel an ancient city.
§ 1278. Truth is, as everyone knows, something given up and long since set aside, but philosophy strives to rise again to that aim.
§ 1279. What the nature of the Notion is, can no more be stated offhand than can the Notion of any other object.
§ 1280. Being and essence are so far the moments of its becoming.
§ 1281. Objective logic which treats of being and essence constitutes the genetic exposition of the Notion.
§ 1282. The chief moments of this exposition have been given in detail in the Second Book of the Objective Logic.
§ 1283. Substance is the absolute, actuality as the simple identity of possibility and actuality.
§ 1284. 1. The movement of substance is, in the first instance, the in-itself.
§ 1285. 2. The other moment is being-for-self, which means that the power posits itself as self-related negativity.
§ 1286. 3. The Notion is the truth of substance, and freedom is the truth of necessity.
§ 1287. On the contrary, the true system as the higher, must contain the subordinate system within itself.
§ 1288. Further, the refutation must not come from outside, from assumptions lying outside the system.
§ 1289. With the Notion, therefore, we have entered the realm of freedom.
§ 1290. Each of them, the universal and the individual, is the totality.
§ 1291. Neither Individual nor Universal can be comprehended unless the two are grasped at the same time in their abstraction and unity.
§ 1292. When one speaks in the ordinary way of the understanding possessed by the I, one understands thereby a faculty.
§ 1293. Kant demanded that we go beyond the mere representation and advance to the thought.
§ 1294. But it is only as it is in thought that the object is truly in and for itself; in intuition or ordinary conception it is only an Appearance.
§ 1295. The Kantian philosophy referr us to the nature of the I in order to learn what the Notion is.
§ 1296. But the Notion is taken as something merely subjective from which we cannot extract reality.
§ 1297. The relation of the Notion to the stages presupposed by it, is determined by the particular science under consideration.
§ 1298. Intuition, ideation and the like belong to the self-conscious spirit not the science of logic.
§ 1299. The Notion is not as the act of subjective understanding, but constitutes a stage of nature, spirit, Life.
§ 1300. In Kant intuition and representation, first exists on its own account, and then the understanding approaches it.
§ 1301. Abstract thinking, is not mere setting aside of sensuous material, but as the sublating of that material to the essential.
§ 1302. If what is taken up is to serve only as a sign, it certainly may be any mere random sensuous particular determination.
§ 1303. Philosophy is not a narration of happenings but a cognition of that which, in the narrative, appears as a mere happening.
§ 1304. Kant has introduced this consideration by the extremely important thought that there are synthetic judgements a priori.
§ 1305. Kant defines the relation of reason to the categories as merely dialectical and takes the result to be the infinite nothing .
§ 1306. Reason becomes the formal, merely regulative unity of the systematic employment of the understanding.
§ 1307. According to Kant, the manifold of intuition is unified in the object solely through the unity of self-consciousness.
§ 1308. But it is equally maintained that we cannot after all, know things as they truly are in themselves.
§ 1309. Kant denounced as an unjustified extravagance and a figment of thought what he recognised as truth .
§ 1310. Kant defined truth as agreement of cognition with its object, but denied truth to the Idea.
§ 1311. A content without the Notion, is something notionless, and we cannot ask for the criterion of the truth of such a content.
§ 1312. Kant did not subject to criticism the forms of the Notion which are the content of ordinary logic.
§ 1313. Being and essence no longer have the same determination that they had and the Notion does not differentiate itself into them.
§ 1314. This reality through which the Notion has come to be is not yet the Notion's own.
§ 1315. At first, therefore, the Notion is only in itself or implicitly the truth.
§ 1316. the Notion in its objectivity is the subject matter in and for itself.
§ 1317. The Notion is free, inasmuch as it cognises this its objective world in its subjectivity and its subjectivity in its objective world.
§ 1318. The Notion is, in the first instance, formal, the Notion in its beginning or the immediate Notion.
§ 1319. As such connection of its moments, which are posited as self-subsistent and indifferent, it is Judgment.
§ 1320. The unity of the Notion is posited through the dialectical movement of the judgment, through which it has become the Syllogism.
§ 1321. The completeness of the Notion passes over into the totality, the subjectivity into its Objectivity.
§ 1322. The understanding is distinguished from reason in the sense that the former is merely the faculty of the notion in general.
§ 1323. This universal Notion contains the three moments: universality, particularity and individuality.
§ 1324. The pure Notion determines itself as a particular, distinct from others, to individuality, and becomes the judgment.
§ 1325. Essence is the outcome of being, and the Notion, the outcome of essence, therefore also of being.
§ 1326. The Notion is, in the first instance, the absolute self-identity.
§ 1327. The universal is that simplicity which, because it is the Notion, possesses within itself the richest content.
§ 1328. Even the abstract universal involves that we are required to leave out other determinations of the concrete.
§ 1329. The universal, even when it posits itself in a determination, remains what it is, the soul of the concrete.
§ 1330. The Notion is not the abyss of formless substance, but, as absolute negativity, it is the shaper and creator.
§ 1331. The universal is free power; it takes its other within its embrace, but without doing violence to it, in peaceful communion with itself.
§ 1332. We can, indeed, abstract from the content: but in that case we obtain only the abstract universal.
§ 1333. The universal possesses a particularity which has its resolution in a higher universal.
§ 1334. A lower genus, has its resolution in a higher universal.
§ 1335. The process is not a transition, for this occurs only in the sphere of being; it is creative power.
§ 1336. The particular has Universality within it as its essential being; but, Universality is a form assumed by the difference.
§ 1337. Determinations of reflection are essentially limited;hence the necessity of transition and passing away.
§ 1338. The abstract determinate is posited as one with the universality, not for itself — but only as unity of itself and the universal.
§ 1339. 1. Individuality appears as the reflection of the Notion out of its determinateness into itself.
§ 1340. The universal is in and for itself because it is in its own self absolute mediation.
§ 1341. The pure notion itself is beyond the grasp of abstraction, because it deprives its products of individuality and personality.
§ 1342. Abstraction raises the concrete into universality in which the universal is grasped as a determinate universality.
§ 1343. 2. But Individuality is not only the return of the Notion into itself; but immediately its loss.
§ 1344. The individual is immediate identity of the negative with itself, the abstraction that determines the Notion as an immediate.
§ 1345. The lowest possible conception of the universal in its connection with the individual is as a common element.
§ 1346. The judgment is the determinateness of the Notion posited in the Notion itself.
§ 1347. The judgment can therefore be called the proximate realisation of the Notion.
§ 1348. When one asks what predicate belongs to a subject, the act of judgment necessarily implies an underlying Notion.
§ 1349. The Notion is present in the judgment as Appearance, and ordinary thinking tends to fasten on this external side.
§ 1350. To be a judgment requires that the predicate be related to the subject as one Notion determination to another.
§ 1351. In the usual idea of the judgment it is not notions that are meant, but only determinations of representational thought.
§ 1352. The predicate appears as a reflection on the object, or rather as the object's reflection into itself.
§ 1353. Individuality is posited in its reflection-into-self, and the universal as determinate.
§ 1354. The subject without predicate is what the thing-in-itself is in the sphere of Appearance - an empty, indeterminate ground.
§ 1355. The predicate does not possess a self-subsistence of its own, but has its subsistence only in the subject.
§ 1356. But on the other hand the predicate, too, is a self-subsistent universality and the subject only a determination of it.
§ 1357. In the judgment, the self-subsistence of the extremes is the reality which the Notion has within it.
§ 1358. To restore this identity of the Notion, or rather to posit it, is the goal of the movement of the judgment.
§ 1359. 1. The judgment of existence, 2. the judgment of reflection,3. the judgment of necessity 4. the judgment of the Notion.
§ 1360. At first the judgment is immediate, since as yet no reflection and movement of the determinations has appeared in it.
§ 1361. The judgment of existence is also the judgment of inherence; because it is in the form of immediacy.
§ 1362. 1. The subject and predicate are names, which only receive their actual determination through the course of the judgment.
§ 1363. 2. The immediate pure enunciation of the positive judgment is the proposition: the individual is universal.
§ 1364. That the individual is universal connotes the perishableness of individual things, and their positive subsistence in the Notion.
§ 1365. First the subject is, indeed simply an individual. Secondly, the predicate is determined in the subject.
§ 1366. The individual is individual. The universal is universal.
§ 1367. 3. The individual is universal. The universal is individual.
§ 1368. First, the judgment in form asserts that the individual is universal. But an immediate individual is not universal.
§ 1369. Secondly, in respect of its content, the judgment is the proposition: the universal is individual.
§ 1370. 1. By virtue of this purely logical content the positive judgment is not true but has its truth in the negative judgment.
§ 1371. The positive judgment has its proximate truth in the negative: the individual is not abstractly universal.
§ 1372. (a) the predicate proves to be in the determination of particularity, (b) This determination results only for the predicate.
§ 1373. The individual is a particular, is the positive expression of the negative judgment.
§ 1374. The positive judgment is the relation of things, one of which at the same time is not what the other is.
§ 1375. The transition from relation to determination means that the not must be attached to the predicate.
§ 1376. 2. What is negated is not the universality as such in the predicate, but the abstraction or determinateness of the latter.
§ 1377. The individual is a particular - the positive form of the negative judgment.
§ 1378. 3. Particularity is the mediating term between individuality and universality.
§ 1379. The individual is particular, but the individual is also not a particular.
§ 1380. The negative judgment is already in and for itself the second negation or the negation of the negation.
§ 1381. The negation of the negative judgment must itself appear in the form of a negative judgment.
§ 1382. The negative judgment is as little a true judgment as the positive.
§ 1383. The positive moment of the infinite judgment, of the negation of the negation, is the reflection of individuality into itself.
§ 1384. The individual is hereby posited as continuing itself into its predicate, which is identical with it.
§ 1385. Through this reflection of the terms of the judgment into themselves the judgment has sublated itself.
§ 1386. It is the judgment of existence that has sublated itself and has passed over into the judgment of reflection..
§ 1387. The judgment of reflection expresses an essential determination in a unifying universality.
§ 1388. This universality is still distinct from the universality of the Notion.
§ 1389. We could define the judgment of reflection as a judgment of quantity, but quantity is the most external determination of mediation.
§ 1390. In the judgment of reflection, the onward movement of determining runs its course in the subject
§ 1391. The predicate no longer inheres in the subject; it is rather the implicit being which subsumes the individual.
§ 1392. The immediate judgment of reflection is again, the individual is universal.
§ 1393. This judgment which, as regards its general form, is simply positive, must be taken negatively.
§ 1394. Individuality is determined in the judgment of reflection as essential individuality.
§ 1395. The judgment that some individuals are a universal of reflection appears as a positive judgment, but it is negative as well.
§ 1396. This universality is the universal nature, that universality which is the result of the judgment of reflection, anticipated.
§ 1397. The universality which the subject has attained is allness, and the particular judgment has passed over into the universal.
§ 1398. Universality, as it appears in the subject of the universal judgment, is the external universality of reflection, allness.
§ 1399. Allness is in general the empirical universality.
§ 1400. A closer examination of the universal judgment reveals that the subject contains the true universality as presupposed.
§ 1401. However, we should not anticipate what is presupposed, but should consider the result on its own.
§ 1402. The universality which has come into being is the genus - the universality which is in its own self a concrete.
§ 1403. The relationship of subject and predicate has become inverted and the judgment has sublated itself.
§ 1404. This intrinsic and explicit connection constitutes the basis of a new judgment, the judgment of necessity..
§ 1405. The judgment of necessity is not merely the inner but also the posited necessity of its determinations.
§ 1406. Universality is now determined as genus and species.
§ 1407. The genus essentially sunders itself, or repels itself into species.
§ 1408. The determinateness of the subject, which makes it a particular, is in the first instance something contingent.
§ 1409. What is posited in this judgment is a necessary connection which is not yet posited in the categorical judgment.
§ 1410. The hypothetical judgment can be characterised as a relationship of ground and consequent, condition and conditioned, etc.
§ 1411. The disjunctive judgment is objective universality posited at the same time in union with the form.
§ 1412. The genus constitutes the substantial universality of the species.
§ 1413. When the genus is a concrete universality, then it is, as a simple determinateness, the unity of the moments of the Notion.
§ 1414. This separation of subject and predicate is the difference of the Notion; and thus the totality of the species in the predicate cannot be any other difference.
§ 1415. The disjunctive judgment has the disjunction in its predicate; but its subject and predicate are disjoined.
§ 1416. This judgment into which the extremes have coalesced through their identity, is therefore the Notion itself.
§ 1417. In this judgment the Notion is laid down as the basis, it is an ought-to-be to which the reality may or may not be adequate.
§ 1418. The judgment of the Notion has been called the judgment of modality.
§ 1419. The problematical judgment is where it is taken as optional; the assertoric where it is taken as true and the apodeictic where it is taken as necessary.
§ 1420. The concretion of universality and particularisation has to develop itself further into totality.
§ 1421. The proximate diremption of this unity is the judgment in which it is posited first as subject, and then as predicate.
§ 1422. The judgment of the Notion is at first immediate; as such it is the assertoric judgment.
§ 1423. The subjective element in this judgment consists in the fact that the implicit connection is not yet posited.
§ 1424. Accordingly, the assurance of the assertoric judgment is confronted with equal right by its contradictory.
§ 1425. The problematic judgment is the assertoric in so far as the latter must be taken both positively and negatively.
§ 1426. It appears only problematic whether the predicate is to be coupled with a certain subject or not.
§ 1427. The subject is differentiated into what it ought to be, and the particular constitution of its existence.
§ 1428. Each of the two sides of the subject, its Notion and its constitution, could be called its subjectivity.
§ 1429. When the problematic element is posited as that of the thing the judgment is no longer problematic, but apodeictic.
§ 1430. The subject of the apodeictic judgment has within it, first, the universal, what it ought to be, and secondly, its constitution.
§ 1431. This judgment, then, is truly objective. Subject and predicate correspond to each other and have the same content.
§ 1432. The subject likewise contains these two moments in immediate unity as the fact.
§ 1433. The genus is the universal in and for itself, which as such appears as the unrelated.
§ 1434. The concrete identity of the Notion is now restored in the whole.
§ 1435. The unity of the Notion has re-emerged from the judgment in which it was lost in the extremes.
§ 1436. The syllogism is the restoration of the Notion in the judgment.
§ 1437. The syllogism is the completely posited Notion; it is therefore the rational.
§ 1438. The syllogism is in the first instance immediate; hence its determinations are simple, abstract determinatenesses.
§ 1439. First, the syllogism of existence in which the terms are thus immediately and abstractly determined, demonstrates in itself.
§ 1440. Through its dialectic it is converted into the syllogism of reflection, whose terms each essentially shows in the other.
§ 1441. Thirdly, this mediatedness of the extremes is reflected into itself, and the syllogism is determined as the syllogism of necessity.
§ 1442. The first syllogism is strictly the formal syllogism.
§ 1443. 1. I-P-U is the general schema of the determinate syllogism. Individuality unites with universality through particularity.
§ 1444. the individual emerges by means of particularity into existence as into universality.
§ 1445. The individual is subsumed under the particular and the latter under the universal; so the individual too is subsumed under the universal.
§ 1446. It is a merely subjective reflection that splits the relation into separate premises and a conclusion distinct from them.
§ 1447. At the approach of this kind of syllogism we are at once seized with a feeling of boredom.
§ 1448. Everything is a syllogism, a Universal that through particularity is united with individuality.
§ 1449. 2. In the immediate syllogism the terms have the form of immediate determinations; but they are a content.
§ 1450. These syllogisms that concern the same subject must also pass over into contradiction.
§ 1451. The formal syllogism is wholly contingent as regards its content.
§ 1452. 3. The determinations of the syllogism are determinations of content in so far as they are immediate, abstract, and self-reflected.
§ 1453. It is commonly demanded of the premises that they shall be proved, that is, that they likewise shall be presented as conclusions.
§ 1454. The unending process of proving the premises does not resolve this contradiction but only perpetually renews it.
§ 1455. For the mediation of P-U, we have I (P-I-U). To mediate I-P, we have U (I-U-P).
§ 1456. 1. The truth of the first qualitative syllogism is that something is united with a qualitative determinateness as a universal.
§ 1457. The mediation is now determined as possessing within itself a negative moment.
§ 1458. In this second syllogism the premises are: P-I and I-U.
§ 1459. The universal is not in and for itself a determinate particular, but is of its species through the medium of individuality.
§ 1460. 2. But in the first instance the terms are still immediate determinatenesses.
§ 1461. The particular judgment, is both positive and negative, a conclusion to which no great value can be attached.
§ 1462. 3. The conclusion, being positive as well as negative, is a universal relation.
§ 1463. With the positing of the middle term in this determination, which is its truth, we have another form of the syllogism.
§ 1464. 1. This third syllogism no longer has any immediate premise.
§ 1465. The syllogism I-U-P, regarded in itself, is the truth of the formal syllogism.
§ 1466. 2. The middle term is the unity of the extremes, but a unity in which abstraction is made from their determinateness.
§ 1467. It is now also indifferent which of the two determinations of this proposition is taken as predicate and which as subject.
§ 1468. 3. The significance of the syllogism with the universal as the middle term, is that the mediating element is essentially a universal.
§ 1470. 1. The mathematical syllogism runs: if two things or determinations are equal to a third, they are equal to each other.
§ 1471. The mediating factor is a third in general, but it has absolutely no determination whatever as against its extremes.
§ 1472. 2. The mathematical syllogism is an axiom, an absolutely self-evident, primitive proposition, that neither allows nor needs proof.
§ 1473. 3. But the result of the syllogism of existence is not merely this abstraction from all Notional determinateness.
§ 1474. What we truly have before us is not mediation based on a given immediacy, but mediation based on mediation.
§ 1475. The immediate syllogism of existence has thereby passed over into the syllogism of reflection.
Remark: The Common View of the Syllogism
§ 1476. It is thought a great matter to discover 60 species of parrot, but is not a syllogism infinitely superior to a species of parrot?
§ 1477. Syllogistic wisdom by its own worthlessness has brought upon itself the contempt which has been its lot.
§ 1478. The dialectical movement of the formal syllogism exhibits each of the moments of the Notion.
§ 1479. The defect of the formal syllogism does not lie in the form of the syllogism, but in that the form appears only as an abstract.
§ 1480. The extreme example of irrational treatment of the syllogism is surely Leibniz's reckoning that 2,048 combinations are possible.
§ 1481. That the calculus can bring the whole of logic within reach of the uneducated, is surely the worst thing that can be said.
§ 1482. Each determinateness is in truth posited not as an individual, separate one, but as a relation to the other.
§ 1483. The middle term was abstract particularity, only externally to the self-subsistent extremes. Now it is posited as the totality.
§ 1484. The individual subject also contains determinateness as universality absolutely reflected into itself.
§ 1485. The middle term in the syllogism unites within itself individuality and abstract universality - that is, the genus.
§ 1486. 1. The syllogism of allness is the syllogism of understanding in its perfection, but is as yet no more than that.
§ 1487. The syllogism of existence was contingent because its middle term admits an indeterminable number of such middle terms.
§ 1488. 2. This very perfection of the syllogism of reflection makes it a mere delusion.
§ 1489. 3. The major premise presupposes its conclusion, in that the former contains that connection of the individual with a predicate.
§ 1490. This is the syllogism of induction.
§ 1491. 1. The syllogism of allness comes under the schema of the first figure, I-P-U.
§ 1492. 2. The second figure of the formal syllogism U-I-P did not correspond to the schema, because I was not the subsuming term.
§ 1493. Induction is not the syllogism of mere perception , but the syllogism of experience.
§ 1494. 3. Induction is still essentially a subjective syllogism.
§ 1495. The truth of the syllogism of induction is a syllogism whose middle term is individuality, immediately in its own self universality.
§ 1496. 1. This syllogism has for its abstract schema the third figure of the immediate syllogism I-U-P.
§ 1497. 2. Analogy is the more superficial, the more the universal in which the two individuals are one.
§ 1498. The syllogism of analogy is that if two objects agree in one or more properties, then a property of one also belongs to the other.
§ 1499. Analogy is a syllogism of reflection inasmuch as individuality and universality are immediately united in its middle term.
§ 1500. 3. I-P (the moon is inhabited) is the conclusion; but one premise (the earth is inhabited) is likewise I-P.
§ 1501. In the syllogisms of reflection, the mediation is in general the posited or concrete unity of the form determinations of the extremes.
§ 1502. The mediating element has determined itself (1) as simple determinate universality, but (2) as objective universality.
§ 1503. This syllogism is pregnant with content, because the abstract middle term posited itself as determinate difference.
§ 1504. That which differentiates the terms appears as an external and unessential form.
§ 1505. The realisation of this syllogism has so to determine it that the extremes also shall be posited as the totality.
§ 1506. 1. The categorical syllogism has the categorical judgment for one or both of its premises.
§ 1507. The categorical syllogism is the first syllogism of necessity in which a subject is united with a predicate through its substance.
§ 1508. 2. This syllogism, as the immediate syllogism of necessity, comes under the schema of the first formal syllogism I-P-U.
§ 1509. This syllogism does not, as does a syllogism of reflection, presuppose its conclusion for its premises.
§ 1510. The categorical syllogism is no longer subjective; in the above identity, objectivity begins.
§ 1511. 3. This syllogism still continues to be subjective. Consequently, the identity of the Notion is still an inner bond of union.
§ 1512. What is immediate in the syllogism is the individual, but there are an indefinite number of other individuals.
§ 1513. The syllogism of necessity has hereby determined itself to the hypothetical syllogism.
§ 1514. 1. The hypothetical judgment contains only the necessary relation without the immediacy of the related terms.
§ 1515. The syllogism contains the relation of subject and predicate, as the pregnant mediating unity.
§ 1516. 2. The hypothetical judgment is necessity or mutual indifference of being in the sphere of Appearance.
§ 1517. The relation of condition corresponds closely to the relation that obtains in the hypothetical judgment and syllogism.
§ 1518. The conditions are a scattered material that waits and demands to be used; this negativity is the mediating element, the free unity of the Notion.
§ 1519. We have here the identity of the mediating and the mediated.
§ 1520. 3. In the conclusion the immediate being or indifferent determinateness appears specifically as mediated.
§ 1521. The mediation of the syllogism has hereby determined itself as individuality, immediacy, and as self-related negativity.
§ 1522. The disjunctive syllogism comes under the schema of the third figure, I-U-P.
§ 1523. Particularisation is differentiation and as such is just as much the negative unity, the reciprocal exclusion of the terms.
§ 1524. The truth of the hypothetical syllogism, the unity of the mediating and the mediated, is posited in the disjunctive syllogism.
§ 1525. In the hypothetical syllogism we have a substantial identity as the inner bond of necessity.
§ 1526. That which is mediated is itself a moment of what mediates it, and each moment appears as the totality of what is mediated.
§ 1527. The different genera of the syllogism exhibit the stages of impregnation or concretion of the middle term.
§ 1528. Thus the Notion as such has been realised; more exactly, it has obtained a reality that is objectivity.
§ 1529. The syllogism is mediation. Its movement is the sublating of this mediation - each term is only by means of an other. The result is therefore an immediacy.
§ 1530. The Notion determines itself into objectivity. This transition is identical with the ontological proof of the existence of God.
§ 1531. Being as the abstract, immediate relation to self, is nothing else than the abstract moment of the Notion.
§ 1532. The difficulty of finding being in the Notion becomes insuperable when being is taken as sensuous perception.
§ 1533. The pure Notion is richer and higher than that metaphysical void of the sum total of all reality.
§ 1534. Common life has no Notions, only pictorial thoughts and general ideas; to recognise the Notion in a mere general idea is philosophy.
§ 1535. Philosophy shall be free to utilise the empty superfluity of language for its distinctions.
§ 1536. Objectivity denotes an object in general for any interest or activity of the subject.
§ 1537. Although theoretical or ethical principles belong only to subjectivity, yet that element that is in and for itself is called objective.
§ 1538. Objectivity signifies, in the first instance, the absolute being of the Notion
§ 1539. First, objectivity is an immediacy whose moments are objects outside one another. This is Mechanism.
§ 1540. Secondly, this reveals itself as the immanent law of the objects themselves. This is Chemism.
§ 1541. Thirdly, this essential unity of the objects is posited as distinct from their self-subsistence, as end. This is Teleology.
§ 1542. The purposiveness which is at first external becomes, through the realisation of the end, internal and the Idea.
§ 1543. In mechanism, the relation between the things combined, is extraneous to them and does not concern their nature at all.
§ 1544. The object is the syllogism whose mediation has been sublated and has become an immediate identity.
§ 1545. 1. The parts of a whole have a self-subsistence, but are not determined in contrast to the whole.
§ 1546. The object is a plurality, a composite, but not atoms for atoms are not totalities.
§ 1547. 2. Whether it be a mixture or a certain arrangement of parts, the combinations are indifferent to what is so related.
§ 1548. Thus the object has the determinateness of its totality outside it in other objects.
§ 1549. This explanation of an object is only an empty word, since in the object to which it advances there is no self-determination.
§ 1550. 3. The determinateness is merely doubled, once in one object and again in the other, so that the explanation is tautological.
§ 1551. If objects are regarded merely as self-enclosed totalities, they cannot act on one another.
§ 1552. In mechanism the causality of the object is immediately a non-originality; its being cause is for it something contingent.
§ 1553. The mechanical process is the positing of what is contained in the Notion of mechanism, and therefore a contradiction.
§ 1554. In the spiritual sphere there is an infinitely manifold content that is communicable.
§ 1555. Objects demonstrate also their self-subsistence, maintain themselves as mutually external and establish an individuality.
§ 1556. Reaction is equal to action.
§ 1557. This return constitutes the product of the mechanical process.
§ 1558. It is only as a product that the mechanical object is an object.
§ 1559. As regards its Notion, this product is the same thing as the object already is from the beginning.
§ 1560. The mechanical process passes over into rest. That is to say the process is only an external one.
§ 1561. In the mechanical process the objects and the process itself have a more precisely determined relationship.
§ 1562. The first moment of this real process is, as before, communication.
§ 1563. Resistance is the precise moment of the overpowering of the one object by the other.
§ 1564. Power, as objective universality and as violence directed against the object, is what is called fate.
§ 1565. The product of formal mechanism is the object in general, an indifferent totality in which determinateness appears as posited.
§ 1566. This reflection into self is the objective oneness of the objects, a oneness which is an individual self-subsistence - the centre.
§ 1567. Universality exhibited itself in communication; but objective universality is the essence of the objects.
§ 1568. It is an empty abstraction to assume that a body would continue to move in a straight line to infinity if external resistance did not rob it of its motion.
§ 1569. The central body no longer possesses the objective totality only implicitly but also explicitly.
§ 1570. this central individual is thus at first only a middle term which as yet has no true extremes.
§ 1571. The government, the individual citizens and the needs of the individuals are three terms, each of which is the middle of the other two.
§ 1572. This totality, whose moments are themselves the complete relationships of the Notion, syllogisms, constitutes free mechanism.
§ 1573. Individuality is the concrete principle of negative unity, a unity that sunders itself into the specific differences of the Notion.
§ 1574. The Notion is the ideal reality that is distinct from the reality that was merely a striving.
§ 1575. This self-determining unity that absolutely reduces external objectivity to ideality is law.
§ 1576. It is solely in the ideal centrality and its laws that the object possesses its essential self-subsistence.
§ 1577. Thus free mechanism determines itself into chemism.
§ 1578. Chemism constitutes in objectivity, the moment of judgment, of the difference that has become objective, and of the process.
§ 1579. In the chemical object the determinateness, and manner of the relation to other belong to its nature.
§ 1580. The expression Chemism must not be understood as though this relation only exhibited itself in Chemistry.
§ 1581. A chemical object is not comprehensible from itself alone, and the being of one is the being of the other.
§ 1582. 1. In Affinity there is immediately posited the striving to sublate the one-sidedness of the other object.
§ 1583. In the material world water fulfils the function of medium; in the spiritual world, language.
§ 1584. The relationship of the objects is on the one hand a quiescent coming-together, but on the other, a negative bearing.
§ 1585. The negative unity of the neutral product proceeds from a presupposed difference.
§ 1586. 2. In the neutral product, the tension of the opposition and the negative unity, as activity of the process, are indeed extinct.
§ 1587. The immediate relation of the extreme of negative unity to the object is that the latter is disrupted.
§ 1588. The same objective whole is first self-subsistent negative unity, then real unity, and finally resolved into its abstract moments.
§ 1589. 3. Chemism by the return into its Notion, sublates itself and has passed over into a higher sphere.
§ 1590. The object does not relate itself to another in accordance with an immediate, one-sided determinateness, but unites its Notion with its reality.
§ 1591. Chemism itself is the first negation of indifferent objectivity and of the externality of determinateness.
§ 1592. These processes, which have proved themselves necessary, are so many stages by which externality and conditionedness are sublated.
§ 1593. Where purposiveness is discerned, an intelligence [Verstand] is assumed as its author.
§ 1594. Just as subjective understanding exhibits errors, so the objective world exhibits stages of truth that by themselves are still one-sided.
§ 1595. It seems strange that the cognition of objects from their Notion appears as an unjustified trespass into a heterogeneous element.
§ 1596. The formal disadvantage from which this teleology immediately suffers is that it only goes as far as external purposiveness.
§ 1597. Kant has exhibited the opposition of freedom and necessity among the antinomies of reason.
§ 1598. The Kantian solution of this antinomy is the same as of the others; that reason can prove neither one proposition nor the other.
§ 1599. The end relation is not, as though an intelligence had given this unity for the convenience of our cognitive faculty.
§ 1600. End has shown itself to be the third to mechanism and chemism it is their truth.
§ 1601. End therefore is the subjective Notion as an essential effort and urge to posit itself externally.
§ 1602. If force and cause are to be predicated of the End as it truly is, they can be predicated only in a way that sublates their Notion.
§ 1603. In general, end is to be taken as the rational in its concrete existence.
§ 1604. End still has a genuinely extramundane existence to the extent that it is confronted by this objectivity.
§ 1605. The end aims to sublate its presupposition, the immediacy of the object, and posit the object as determined by the Notion.
§ 1606. The first immediate positing in end is at one and the same time the positing of an internality.
§ 1607. The end unites itself through a means with objectivity, and in objectivity with itself.
§ 1608. The Means is external as against the subjective end, and therefore also to the objective end.
§ 1609. The end being only an external determinateness in the means, it is itself, as a negative unity, outside it.
§ 1610. The middle term is the totality of the syllogism, in which the abstract activity and the external means constitute the extremes.
§ 1611. The means has also a side from which it still has self-subsistence as against the end.
§ 1612. 1. The former external activity of the end through its means must determine itself as mediation and sublate its own self.
§ 1613. As the means stands on the side of the end and has within it the activity of the end, objectivity returns into itself, into the Notion.
§ 1614. That the end posits itself in a mediate relation with the object may be regarded as the cunning of reason.
§ 1615. In his tools man possesses power over external nature, even though in respect of his ends he is, on the contrary, subject to it.
§ 1616. But the end does not merely keep outside the mechanical process; rather it maintains itself in it and is its determination.
§ 1617. The teleological process is the translation of the Notion that has a distinct concrete existence as Notion into objectivity.
§ 1618. In every transition the Notion maintains itself.
§ 1619. All the determinations of relationship belonging to the sphere of reflection or of immediate being have lost their distinctions.
§ 1620. 2. The teleological activity, we see that it contains the end only externally.
§ 1621. The product of the purposive act is determined by an end external to it; consequently it is the same thing as the means.
§ 1622. All objects in which an external end is realised, are equally only a means of the end.
§ 1623. The limited content makes these ends inadequate to the infinity of the Notion and reduces them to an untruth.
§ 1624. 3. The realisation of the end is a prior requirement before that realisation could be brought about through a means.
§ 1625. The result is not only an external end relation, but the truth of it, an internal end relation and an objective end.
§ 1626. In the realised end objectivity is present as the return of the end into itself.
§ 1627. The realised end is also means, and conversely the truth of the means is to be itself a real end.
§ 1628. Each of the single moments through which this mediation runs its course is itself the entire syllogism of those moments.
§ 1629. The original inner externality of the Notion is the immediate positing or presupposition of an external object.
§ 1630. The Notion is essentially this: to be distinct as an explicit identity from its implicit objectivity, and thereby possess externality.
§ 1631. The Idea is the adequate Notion, that which is objectively true.
§ 1632. The Idea is the rational; it is the unconditioned.
§ 1633. We reject that estimate of the Idea according to which it is not anything actual, and true thoughts are said to be only ideas.
§ 1634. Everything actual is only in so far as it possesses the Idea and expresses it.
§ 1635. Wholes like the state and the church cease to exist when the unity of their Notion and their reality is dissolved.
§ 1636. The Idea itself has a restricted content, though it is essentially the unity of Notion and reality, it is no less essentially their difference.
§ 1637. The worst state, whose reality least corresponds to the Notion, in so far as it still exists, is still Idea.
§ 1638. The Idea has not merely the more general meaning of the true being, but of the unity of subjective Notion and objectivity.
§ 1639. The Idea is, therefore, in spite of this objectivity utterly simple and immaterial.
§ 1640. The Idea is first simple truth; secondly, it is the relation of the subjectivity of the simple Notion and its objectivity.
§ 1641. In the first instance, however, the Idea is once again only immediate.
§ 1642. At this first stage the Idea is Life.
§ 1643. In this second stage, the Idea is the Idea of the true and the good as cognition and volition.
§ 1644. Thirdly, spirit cognises the Idea as its absolute truth, as the truth that is in and for itself.
§ 1645. The Idea of Life is so real, that we may seem to have overstepped the domain of logic as it is commonly conceived.
§ 1646. That which is true in and for itself, is essentially the subject matter of logic.
§ 1647. Life is to be considered here neither as instrument of a spirit, nor as a moment of the ideal and of beauty.
§ 1648. Life is in and for itself absolute universality; the objectivity has the Notion alone for substance.
§ 1649. Life is therefore first to be considered as a living individual.
§ 1650. Secondly, it is the life process.
§ 1651. Life is thirdly the genus process, sublating its individualisation and relating itself to its objective existence.
§ 1652. 1. The Notion of life, or universal life, is the immediate Idea, the Notion whose objectivity corresponds to it.
§ 1653. Objectivity has proceeded only from the Notion, so that its essence is positedness, and it exists as a negative.
§ 1654. This subject is the Idea as individuality, as simple but negative self-identity - the living individual.
§ 1655. This is life as soul, as the Notion of itself that is completely determined within itself, the self-moving principle.
§ 1656. Because this objectivity is predicate of the individual , the earlier mechanical or chemical relationship does not attach to it.
§ 1657. 2. This process of the living individuality is restricted to that individuality itself and still falls entirely within it.
§ 1658. 3. Now the Idea just considered is the Notion of the living subject and its process.
§ 1659. Sensibility may therefore be regarded as the determinate being of the inwardly existent soul.
§ 1660. As a particular living being it is on one side a species alongside other species of living beings.
§ 1661. The first two moments, sensibility and irritability, are abstract; in reproduction, life is concrete and is vitality.
§ 1662. With reproduction as the moment of individuality, the living being posits itself as an actual individuality, a self-related being-for-self.
§ 1663. The living individual opposes itself as an absolute subject to the presupposed objective world.
§ 1664. This process begins with need, that is, with a moment that is twofold.
§ 1665. The indifference of the objective world to the end, constitutes its external capability of being conformable to the subject.
§ 1666. the subject, as specifically related in its need to the externality, uses violence on the object.
§ 1667. The mechanical process passes over into the inner process by which the individual appropriates the object as a means for itself.
§ 1668. Through the external life process it has thus posited itself as real universal life, that is, as genus.
§ 1669. The living individual is a presupposition that is not as yet authenticated by the living individual itself.
§ 1670. This Idea of the individual, since it is this essential identity, is essentially the particularisation of itself.
§ 1671. This universal is the third stage, the truth of life in so far as this is still confined within its sphere.
§ 1672. Because the genus is the identity of individual self-feeling in what is another self-subsistent individual, it is contradiction.
§ 1673. The identity with the other individual, the individual's universality, is thus as yet only internal or subjective.
§ 1674. It is thus the individuality of life itself, generated no longer from its Notion, but from the actual Idea.
§ 1675. The reflection of the genus into itself is from this side the means whereby it obtains actuality, the propagation of the living species.
§ 1676. In the genus process, the separated individualities of individual life perish.
§ 1677. Life is the immediate Idea, or the Idea as its Notion not yet realised in its own self.
§ 1678. The Idea is duplicated into the subjective Notion whose reality is the Notion itself, and the objective Notion in the form of life.
§ 1679. Physics reduces the world of phenomena to general laws since it too is based on spirit merely in its phenomenal aspect.
§ 1680. Spirit is not only infinitely richer than nature, its essence is the absolute unity of opposites in the Notion.
§ 1681. The 'I' has the inconvenience that we must already make use of it whenever we want make any judgement about it.
§ 1682. In Kant's criticism of metaphysics of the soul, he followed quite simply Hume's style of scepticism.
§ 1683. Self-consciousness is just the existent pure Notion, and therefore empirically perceptible.
§ 1684. A stone does not have this inconvenience; when it is to be thought or judged it does not stand in its own way.
§ 1685. These barbarous conceptions place the defect in the fact that in thinking of the 'I', the 'I' as subject cannot be omitted.
§ 1686. The Notion has persistence, indestructibility, imperishableness, just because it is not abstract, but concrete simplicity.
§ 1687. Metaphysics had for its aim the cognition of truth and whether they were true things or not, substances or phenomena.
§ 1688. The victory of Kantian criticism over metaphysics consists in doing away with the investigation that has truth for its aim.
§ 1689. The Idea of spirit has proved itself to be the truth of the Idea of life.
§ 1690. “Soul” evokes a mental picture as a thing like other things; one enquires as to the position in space from which it operates.
§ 1691. Even anthropology must regard as alien to it the metaphysics that makes this form of immediacy into a psychical thing.
§ 1692. This is the subject matter of the phenomenology of spirit - midway between the science of the natural spirit and spirit as such.
§ 1693. The doctrine of spirit proper, would embrace what is the subject matter of ordinary empirical psychology.
§ 1694. The Idea of spirit as the subject matter of logic already stands within the pure science.
§ 1695. It is the Notion that is active in the object, and by giving itself its reality in the object finds truth.
§ 1696. The Idea is one of the extremes of a syllogism, as the Notion for subjective reality; the other extreme is the objective world.
§ 1697. The Idea as manifested Idea is the theoretical Idea, cognition as such.
§ 1698. The subjective Idea is in the first instance an urge.
§ 1699. The Notion is the absolute certainty of itself, but is confronted by its presupposition.
§ 1700. This urge isthe urge to truth in so far as truth is in cognition, accordingly theoretical Idea.
§ 1701. The fallacy of taking this finitude of cognition as the true relation has become the universal opinion of modern times.
§ 1702. But cognition must, in the course of its own movement, resolve its finitude and with it its contradiction.
§ 1703. The Idea is the Notion that exists for itself.
§ 1704. The determining activity of the Notion upon the object is an immediate communication of itself to the object.
§ 1705. This cognition does not appear as an application of logic, but as the removal of a subjective obstacle from the subject-matter.
§ 1706. The difference between analytic and synthetic cognition is, it is said, that one proceeds from the known to the unknown, the other from the unknown to the known.
§ 1707. But it must be said that cognition, once it has begun, always proceeds from the known to the unknown.
§ 1708. Analytic cognition has simple identity for its principle; and transition into an other is excluded from itself and from its activity.
§ 1709. Analytic cognition starts from a presupposed, and therefore individual, concrete subject matter.
§ 1710. It is just as one-sided to represent analysis as though there were nothing in the subject matter that was not imported into it, as it is to suppose that the resulting determinations are merely extracted from it.
§ 1711. Analytic cognition has an immanent progress only in so far as the derived thought determinations can be analysed afresh.
§ 1712. This progress is, however, nothing but the mere repetition of the one original act of analysis.
§ 1713. Arithmetic and the more general sciences of discrete magnitude especially, are called analytical science.
§ 1714. The material of arithmetic and algebra has already been made wholly abstract and purged of all peculiarity of relationship.
§ 1715. Because the subject matter is a posited one, the science of analysis possesses not so much theorems as problems.
§ 1716. The proof of a theorem of this kind would consist merely in the operation of counting.
§ 1717. The proof can express nothing but the tautology that the solution is correct because the operation has been performed.
§ 1718. Mathematics has never justified by its own means, mathematically, the operations of differential calculus, because the transition is not of a mathematical nature.
§ 1719. The transition from analytic to synthetic cognition lies in the transition from immediacy to mediation, from identity to difference.
§ 1720. Analytic cognition is the first premise of the whole syllogism — the immediate relation of the Notion to the object.
§ 1721. Although this cognition transforms the objective world into Notions, it gives it Notion-determinations only in respect of form.
§ 1722. First, the still given objectivity is transformed into the simple and first form, hence into the form of the Notion.
§ 1723. In reducing the subject matter to its Notion, Definition abstracts from what accrues to the Notion in its realisation.
§ 1724. First it is contingent in respect of its content as such; secondly it is contingent which determinations are to be selected.
§ 1725. There is no principle for determining which sides of the subject matter are to be regarded as belonging to its Notion.
§ 1726. Geometrical objects are abstract determinations of space.
§ 1727. The concrete objects of Nature as well as of spirit,are, for representation, things of many properties.
§ 1728. In existence the Notion has entered into externality and cannot be attached simply to a single one of the properties.
§ 1729. Formal truth, the agreement between the definition and an actual object, cannot be established because the individual object may be a bad specimen.
§ 1730. In enunciating the Notion as a mere immediate, a definition refrains from comprehending the Notion itself.
§ 1731. But immediacy in general proceeds only from mediation, and must therefore pass over into mediation.
§ 1732. The individual content of cognition ascends through particularity to the extreme of universality.
§ 1733. The progress, proper to the Notion, from universal to particular, is the basis of a system and of systematic cognition.
§ 1734. The beginning be made with the subject matter in the form of a universal.
§ 1735. It might be objected that, because intuition is easier than cognition, concrete actuality should be made the beginning of science.
§ 1736. In physics the natural properties have to be freed from their complications in which they are found in concrete actuality.
§ 1737. Everywhere the abstract must constitute the starting point from which spread the rich formations of the concrete.
§ 1738. Any subject matter whatever that seems to possess an elementary universality is made the subject matter of a specific science.
§ 1739. The business of cognition can only consist, partly, in setting in order the particular elements discovered in the empirical material.
§ 1740. Because a principle of self-determination is lacking, the laws for division can only consist of formal rules that lead to nothing.
§ 1741. The determinateness of empirical species can only consist in their being different from one another without being opposed.
§ 1742. It may be attributed to an instinct of reason when we find divisions that show themselves to be more adequate to the Notion.
§ 1743. 1. The stage of this cognition that is based on the Notion-determinations is the transition of particularity into individuality.
§ 1744. The theorem is the synthetic aspect of an object in so far as its relationships are founded in the inner identity of the Notion.
§ 1745. It is difficult to distinguish which of the subject matter may be admitted into definitions and which theorems.
§ 1746. Axioms are commonly but incorrectly taken as absolute firsts, as though in and for themselves they required no proof.
§ 1747. The content of theorems may be more or less incomplete and single relationships.
§ 1748. The difference in respect of the content of theorems is most intimately connected with this progress itself.
§ 1749. Theorems contain two parts, one of which may be regarded as the Notion, and the other as the reality.
§ 1750. This genuine synthetic advance is a transition from universality to individuality, to the unity of the subject matter.
§ 1751. However complete or incomplete the content of the theorem may be, it must be proved.
§ 1752. 2. The mediation may be simple or may pass through several mediations.
§ 1753. Material only comes to have meaning in the proof; in itself it appears blind and unmeaning.
§ 1754. The meaning of the construction which at first is still concealed comes to light in the proof.
§ 1755. It is solely to the abstraction of its sensuous subject matter that it owes its capability of attaining a higher scientific character.
§ 1756. The synthetic method is no longer grounded merely in positive but in negative identity.
§ 1757. If geometry with its abstract subject matter soon encounters its limit, it is evident that the synthetic method is still more inadequate for other sciences.
§ 1758. The so-called explanation and the proof of the concrete brought into theorem turns out to be partly a tautology.
§ 1759. Wolf extended the inappropriate application of the synthetic method to analytic science.
§ 1760. Wolf's First Principles of Fortification.
§ 1761. The whole style of previous metaphysics, its method included, has been exploded by Kant and Jacobi.
§ 1762. The Notion, with which alone we are concerned, and which is the infinite in and for itself, is excluded from this cognition.
§ 1763. The sphere of necessity is the apex of being and reflection.
§ 1764. The Idea, in so far as the Notion is now explicitly determined in and for itself, is the practical Idea, or action.
§ 1765. The Notion, being determined in and for itself, the subject is determined for itself as an individual.
§ 1766. The activity of the end is to sublate the determinateness of the external world to give itself reality as external actuality.
§ 1767. In its concrete existence the Good is subject to destruction by the collision and conflict of the good itself.
§ 1768. In this way, the good remains an ought-to-be; it is in and for itself.
§ 1769. There are still two worlds in opposition, one in the pure regions of transparent thought, the other an undisclosed realm of darkness.
§ 1770. The Idea enter here into the shape of self-consciousness.
§ 1771. What is still lacking in the practical Idea is the moment of consciousness proper itself.
§ 1772. The practical Idea still lacks the moment of the theoretical Idea.
§ 1773. In the syllogism of action, one premise is the immediate relation of the good end to actuality, the second an external means against the external actuality.
§ 1774. The realisation of the good in the face of another actuality confronting it is the mediation necessary for the actualisation of the good.
§ 1775. The second negation is the sublating of this otherness.
§ 1776. If the end of the good is not realised through this mediation, this signifies a relapse of the Notion.
§ 1777. It is only standing in its own way, and thus what it has to do is to turn, not against an outer actuality, but against itself.
§ 1778. When external actuality is altered by the objective Notion and its determination therewith sublated, the merely phenomenal reality is removed.
§ 1779. The determination of the good as a merely subjective end is sublated.
§ 1780. In this result cognition is restored and united with the practical Idea.
§ 1781. The absolute Idea has turned out to be the identity of the theoretical and the practical Idea.
§ 1782. It is the sole subject matter and content of philosophy. Since it contains all determinations within it.
§ 1783. Therefore what remains to be considered here is not a content as such, but the universal aspect of its form - that is, the method.
§ 1784. Method may appear at first as the mere manner peculiar to the process of cognition, but all otherwise determined content has its truth in the form alone.
§ 1785. In true cognition, the method is not merely an aggregate of certain determinations, but the Notion that is determined in and for itself.
§ 1786. 1. Since the content of the beginning is supposed true by its being pointed out in inner or outer perception, it is the determinateness of universality that is meant.
§ 1787. It may be said that every beginning must be made with the absolute, just as all advance is merely the exposition of it.
§ 1788. The non-spiritual and inanimate, on the contrary, are the Notion only as real possibility.
§ 1789. 2. The absolute method does not behave like external reflection but takes the determinate element from its own subject matter.
§ 1790. The method of absolute cognition is analytic but no less synthetic.
§ 1791. Dialectic is one of those ancient sciences that have been most misunderstood in the metaphysics of the moderns.
§ 1792. It is shown that some determination belongs to some subject matter, but further, that with equal necessity the opposite determination also belongs.
§ 1793. The common view of so-called sound common sense takes its stand on the evidence of the senses and on customary conceptions and judgements.
§ 1794. The subject matter kept apart from the Notion is an image; it is in the determinations of thought and the Notion that it is what it is.
§ 1795. The other is not the empty negative that is taken to be the usual result of dialectic; rather is it the other of the first.
§ 1796. The positive judgement is incapable of holding truth. The negative judgement, would at least have to be added as well.
§ 1797. Because the first is implicitly the Notion, the dialectical moment with it consists in positing what it implicitly contains.
§ 1798. Formal thinking makes identity its law, and allows the contradictory content before it to sink into the sphere of ordinary conception.
§ 1799. Negativity constitutes the turning point of the movement of the Notion.
§ 1800. The first premise is the moment of universality and communication: the second is individuality.
§ 1801. Instead of a triplicity, the abstract form may be taken as a quadruplicity.
§ 1802. The syllogism has always been recognised as the universal form of reason; but it lacks the dialectical moment of negativity.
§ 1803. That with which we began was the universal, so the result is the individual, the concrete, the subject.
§ 1804. On the new foundation constituted by the result as fresh subject matter, the method remains the same as with the previous subject matter.
§ 1805. The method itself by means of this moment expands itself into a system.
§ 1806. The beginning, since it is itself a determinate, shall be taken not as an immediate but as something mediated and deduced.
§ 1807. Since it is the absolute form, the Notion that knows itself and everything as Notion, there is no content that could stand against it.
§ 1808. The restoration of the first immediacy is accomplished as a system of totality.
§ 1809. By its dialectical advance it not only does not lose anything or leave anything behind, but carries along with it all it has gained.
§ 1810. Each new stage of forthgoing, that is, of further determination, is also a withdrawal inwards.
§ 1811. The richest is therefore the most concrete and most subjective.
§ 1812. Each step in the process of determination, while getting further away from the indeterminate beginning is also getting back nearer to it.
§ 1813. The truth itself resides only in the extended course of the process and in the conclusion.
§ 1814. The science exhibits itself as a circle returning upon itself, the end being wound back into the beginning.
§ 1815. In conclusion, there remains only this to be said about this Idea, that in it, first, the science of logic has grasped its own Notion.
§ 1816. The pure Idea of cognition is so far confined within subjectivity, the last result becomes also the beginning of another sphere and science.
§ 1817. The Idea, in positing itself as absolute unity of the pure Notion and its reality and thus contracting itself into the immediacy of being, is the totality in this form - nature.
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