Hegel’s Logic – A Brief Synopsis
Part One – The Doctrine of Being
Hegel’s dialectical logic, interpreted materialistically, will in the future unfold into the basis for all scientific work, including social, economic and political science. Every practical task has its own very particular corresponding theory without which its accomplishment is not possible. Materialist dialectics is the absolutely necessary theory through which alone mankind can penetrate to the inner truth of the contradictions which are tearing present society apart and to find the solutions necessary to them.
What follows is a study of Hegel’s most important book, Science of Logic, published by Humanity Books, ISBN 1-57392-280-3. All references are to this work unless otherwise stated. A study of Hegel’s work presents certain difficulties. He wrote profusely, long ago in archaic German, and although the core and essence of his work are of crucial importance today, a good deal of it is of questionable value. The reason for this is explained by Trotsky in one of his most important books, In Defence of Marxism:-
"Hegel wrote before Darwin and before Marx. Thanks to the powerful impulse given to thought by the French Revolution, Hegel anticipated the general movement of science. But because it was only an anticipation, although by a genius, it received from Hegel an idealistic character. Hegel operated with ideological shadows as the ultimate reality. Marx demonstrated that the movement of these ideological shadows reflected nothing but the movement of material bodies."
Hegel's logic, then, deals entirely with the laws of movement of thought, and not the laws of motion which govern the material world of which thought is the reflection. A critical analysis of Hegel's logic is therefore necessary from the standpoint of materialism, but before attempting this in any comprehensive way it is necessary to grasp Hegel's logic as a whole.
Like other philosophers before him, Hegel began by posing the question “With what should science begin?” He was not, of course, referring to science in the narrow sense, but to scientific, correct thought, and he approaches the question thus:-
“The principle of philosophy does, of course, also express a beginning, but not so much a subjective as an objective one, the beginning of everything. The principle is a particular determinate content – water, the one, nous, idea, substance, monad, etc. Or, if it refers to the nature of cognition and consequently is supposed to be only a criterion rather than an objective determination – thought, intuition, sensation, ego, subjectivity itself.” (P. 67)
Clearly the content of these considerations is the fundamental question of all philosophy – should the starting point of logical deduction be the external world of matter considered as existing independently of human consciousness, or should consciousness itself be taken as the starting point, and the external world be considered as dependant upon, relative to, consciousness and thought? On the following page Hegel provides his answer.
“The beginning is logical in that it is to be made in the element of thought that is free and for itself, in pure knowing.” (P.68) Hegel then refers to another of his great works, Phenomenology of Spirit, in which he expounds his theory of knowledge, epistemology.
“In this science of manifested spirit the beginning is made from empirical, sensuous consciousness and this is immediate knowledge in the strict sense of the word … but in logic, the presupposition is that which has proved itself to be the result of phenomenological consideration – the idea as pure knowledge. Logic is pure science, that is, pure knowledge in the entire range of its development.” (P.69)
Hegel uses the term “manifested spirit” to refer to the external world of nature which we perceive through our senses. Why he should use this name need not be explained here, it will become apparent at the very end of the logic under the doctrine of the Notion. According to Hegel, then, while consciousness begins with sensuous perception of the external world, logic begins from this consciousness, “the idea as pure knowledge”, and thenceforth proceeds quite independently of further sensuous perception of the external world. Hegel’s “pure knowledge” is here analogous to the “pure reason” of previous philosophy which would have been a powerful influence on him. He begins his logic from the simple fact of consciousness itself as an immediate presence devoid of any content:-
“This simple immediacy, [consciousness], therefore, in its true expression is pure being. Just as pure knowing is to mean knowing as such, quite abstractly, so pure being is to mean nothing but being in general: being and nothing else, without any further specification and filling.” (P.69). From this abstract beginning Hegel’s brilliant logic unfolds, starting with the category of Being, which falls into three parts, Quality, Quantity, and Measure.
(Being, Nothing, Becoming)
We must begin with some lengthy quotes from Hegel, since the text is so packed with meaning that little can be left out. The category of Being is at first qualitative:-
“It is easily seen from a comparison of quality and quantity that the former by its nature is first. For quantity is quality which has already become negative; magnitude is a determinateness which is no longer one with being but is already differentiated from it, sublated quality which has already become indifferent.” (P.79)
Clearly we cannot have a quantity of something without that something has its own quality. We must first have the thing or substance present as a quality, before we can conceive of a greater or lesser quantity if it. Hegel goes on:-
“Being, pure being, without any further determination. In its indeterminate immediacy it is equal only to itself. It is also not unequal relative to another; it has no diversity within itself nor any with a reference outwards. It would not be held fast in its purity if it contained any determination or content which could be distinguished in it or by which it could be distinguished from an other. It is pure indeterminateness and emptiness. There is nothing to be intuited in it, if one can speak here of intuiting; or, it is only this pure intuiting itself. Just as little is anything to be thought in it, or it is equally only this empty thinking. Being, the indeterminate immediate, is in fact nothing, and neither more nor less than nothing” (P.82)
This contains a cardinal lesson for the student of Hegel, introducing, as it does, the law of identity of opposites. Being and nothing are of course opposites, but we see above how they are also identical. Being is both itself and its own opposite, Nothing. Hegel continues by giving us the equation in reverse:-
“Nothing, pure nothing: It is simply equality with itself, complete emptiness, absence of all determination and content - undifferentiatedness in itself. In so far as intuiting or thinking can be mentioned here, it counts as a distinction whether something or nothing is intuited or thought. To intuit or think nothing has, therefore, a meaning; both are distinguished and thus nothing is (exists) in our intuiting or thinking; or rather it is empty intuiting and thought itself, and the same empty intuition or thought as pure being. Nothing is, therefore, the same determination, or rather absence of determination, and thus altogether the same as pure being.”
At this point it is necessary to remind ourselves that we are here dealing with a logical sequence, a movement or passage from thought to thought, and not a movement in time. When Hegel uses the term “movement” it is always in this meaning, never a physical movement of things in the world external to thought in time and space, but always the movement of thought. He goes on:-
“Pure being and pure nothing are, therefore, the same. What is the truth is neither Being nor Nothing, but that Being – does not pass over but has passed over- into Nothing, and Nothing into Being. But it is equally true that they are not undistinguished from each other, that, on the contrary, they are not the same, that they are absolutely distinct, and yet are unseparated and inseparable and that each immediately vanishes in its opposite. Their truth is, therefore, this movement of immediate vanishing of the one in the other: Becoming, a movement in which both are distinguished, but by a difference which has equally immediately resolved itself.” (P.82) And further, “The unity, whose moments, Being and Nothing, are inseparable, is at the same time different from them and is thus a third to them; this third in its own characteristic form is Becoming.” (P.93)
So now we have three categories, Being, Nothing, and Becoming, and from the unity of these three Hegel deduces a fourth, Determinacy, or Determinate Being. Before proceeding with this it will be useful to pause, step back and get a broader overview of Hegel’s method.
The three categories, Being-Nothing-Becoming, take the form of what became known as Hegel’s triad. The first moment, Being, is a simple affirmative statement or thesis, (something is …). The second moment, Nothing, contradicts the first, is anti-thesis, (something is not, negation of the first). The third moment, Becoming, is the unity of the first two, synthesis, which contains the contradiction between thesis and anti-thesis and at the same time continually resolves it, because Becoming is motion, which is the truth of all Being. By way of this triple rhythm, thesis, anti-thesis, synthesis, Hegel deduced his whole system of categories and their logical interconnections, starting from the universal, abstract, most general, and proceeding to the more particular, determinate, concrete. The whole of Hegel’s philosophy consists of one giant triad, The Logic, (thesis), The Doctrine of Nature, (anti-thesis), and the Doctrine of Spirit, (synthesis). Each of these itself forms a triad, for example The Logic consists of the Doctrine of Being, (thesis), the Doctrine of Essence, (anti-thesis) and the Doctrine of the Notion, (synthesis). The method is truly “dialectical”, since the final term of the triad is the result of the two sided process of the unity and conflict of the first two. Each part of the Logic, and every category, can be broken down in this way, so the whole system consists of triads within triads within triads.
The third term of every triad is a new positive affirmation or thesis which forms the first term of a new triad. This may seem difficult but in fact it makes things very easy, since it is easier to grasp a logical sequence than a homogenous mass of content. This first section, under the heading Quality, falls into Being, Determinate Being, and Being-for-Self. We have dealt with being, so we now move on to the second stage, (or “moment” as Hegel calls them), Determinate Being.
(Determinate Being as Such, Finitude, Infinity)
Determinate Being is the unity, (synthesis), of Being and Nothing, but it is not the same unity of Pure Being and Nothing we started with when we spoke of indeterminate Being, because whereas indeterminate Being is the same as Nothing, the Determinate Being which we now have is not. Determinate being is definitely something, has become now that the process of becoming has ceased, or “settled into a moment of stability”, as Hegel puts it. To put in another way, indeterminate being was simple self-identity, equal only to itself, whereas determinate being, having a logical history, is the concrete unity and identity of Being and Nothing which have separate existence. Hegel puts it thus:
“Determinate being as the result of its becoming is, in general, being with a non-being such that this non-being is taken up into simple unity with being. Non-being thus taken up into being in such a way that the concrete whole is in the form of being, of immediacy, constitutes determinateness as such.” (P.110).
It is important to grasp that so far we have only the general idea of determinacy. We know this Being is now determinate, but we do not know what kind of determinacy it is, just as we can know a thing has quality without knowing what quality is has. The passage of Nothing into Being is the thing coming into existence, coming to Be, and the passage of Being into Nothing is its passing away, ceasing to Be. In these Categories, Being, Nothing, Becoming, we have the whole Hegelian system in microcosm, like a seed from which it unfolds, like the DNA which carries the code for the development of the whole organism. Each concept and category is derived in logical sequence in the same way as Nothing was derived from Being according to the relations of genus, differentia, species. Being was the genus, nothing was the differentia, and Becoming was the species. Taking an example from the animal world, we see that the genus (animal) is differentiated into many different species, (kinds of animals). All donkeys are animals, but not all animals are donkeys. All particular cases of determinate being are Being, but not all Being is determinate in any particular way.
Hegel’s next step is to deduce the category of Quality from the category of Determinate Being. Determinate Being is a kind of Being – take away its determinateness and that kind of being would not exist. That aspect of a thing which is, in this way, essential to its very being, is Quality. Quality is that aspect of a thing which makes it what it is, determines its identity. For example, it is the quality of hardness which determines that a certain quantity of carbon is a diamond, hence in this sense determinateness and quality are identical, and the category Quality is thus deduced from the category determinateness.
“Determinateness thus isolated by itself in the form of being is quality – which is wholly simple and immediate. Determinateness as such is the more universal term which can equally be further determined as quantity and so on.” (P.111)
Further analysis of Quality is necessary before we can we can approach the question of determinateness in connection with Quantity, so we shall leave that aside for the moment. Hegel next refers us to Spinoza’s famous affirmation, “all determination is negation”, and proceeds to deduce the categories of Positive and Negative. To say that a thing is “this”, is to say that it is not “that”, or indeed any other thing. A thing, a something, taken as determined by its quality and within its limits, is to be considered in its positive aspect, while the thing taken as not being some other thing is to be considered in its negative aspect. An island is an island because it has the quality land and not that of sea. In Hegel’s conception, the land “negates” the sea, and vice versa. Every thing is determined by its quality and is qualitatively demarcated from all that is of different quality. The degree to which a quality can change while remaining itself is its Limit, hence we have the moment of identity between the categories of Quality and Limit.
Determinate Being is the synthesis of Being and Nothing, opposites which have vanished into each other, negated each other. But it is apparent that in determinate being this process of vanishing, (negation), has completed itself, so that the negation has itself been negated. Hegel refers to “the vanishing of the vanishing”. Later, this idea of the negation of the negation will be expanded into the most universal and important law of dialectics. Hegel makes identity between determinate being and a Something.
“Something is the first negation of negation, as simple self relation in the form of being.” (P.115)
It will be remembered from above that the result of the movement of thesis, anti-thesis, and synthesis is a positive affirmation which forms the first term of the next triad, a simple self-identity in the form of being. A something is such a being, is a quality and therefore limited. If something is limited then some other thing lies beyond its limits. To be limited is to be limited by something else. The island is limited by the sea. Hegel uses these terms, something and other, repeatedly, and in describing the relation between these two abstractions shows the relation between all things that exist. If two things are in connection, each limiting the other, then it is immaterial which we call something and which other. Each is both something and other simultaneously. Hence they become identical and transformed into each other.
“Something and other are at first indifferent to one another; an other is also immediately a determinate being, a something; the negation thus falls outside both. Something is in itself as against its being-for-other. But the determinateness also belongs to its in-itself and is its determination.” (P. 116)
Hegel frequently describes two things as being “indifferent to one another”. He simply means to draw attention to these two things initially without for the moment considering the way they relate to each other or affect each other, but just to consider each separately. We must note the difference in this context between “determinateness” and “determination”. Determinateness may be thought of as the essential quality of the something while determination refers to the something as an identity. It is true, as said above when considering a previous moment, that essential quality and determinate being are identical, but they are also still distinct, just as being and nothing are the same but distinct in determinate being. In saying that “the negation falls outside both”, Hegel means to draw attention to the distinction between something and other and their relation. Each negates the other like the island and the sea. But equally each contains its own internal negation, like Being and Nothing. The thing considered in its internal aspect is the thing-in-itself, and the thing considered as relating to the other is being-for-other.
“The in-itself into which something is reflected into itself out of its being-for-other is no longer an abstract in-itself, but as negation of its being-for-other is mediated by the latter, which is thus its moment”. (P.122)
Through its connection and relation with its other, its Being-for-other, the something reflects this other in itself it its own particular way. As a result it is no longer abstract but concrete, because it is a unity of itself and its reflected being-for-other. The concept of mediation is most important. Mediation is always between two things, and it implies that each one supplies the truth of the other. For example, positive can only be what it is in relation to negative. As soon as Hegel starts talking about moments we know that we are dealing with anti-thesis, two sides, "moments", of contradiction.
“Something fulfils its determination in so far as the further determinateness which at once develops in various directions through somethings relation to other, is congruous with the in-itself of the something”. (P.123)
In addition to the quality necessary to the determination of something it inevitably contains other qualities which are contingent, (accidental), qualities which are reflections of the other things with which it is connected. The relation of these things to the determination of the something is its constitution. As something changes, alters, it is its constitution which changes while its determination remains the same. To say that a thing changes is to say that it remains what it is, remains identical with itself as a thing-in-itself, regardless of its altering state. A leaf that changes from green to brown remains a leaf.
The determination and constitution are the two sides or moments of something, and these two sides mutually limit each other. The determination limits the constitution since it persists due to its own immanent quality and controls how far the constitution can go. But the determination reflects the constitution according to its own nature, and is thus limited by it. The limit must not be thought of as a sort of full stop that occurs at the end of the process of alteration. Rather it is the immanent moving limit controlling alteration, like the banks of a river which control its flow and which eventually bring about the transformation.
“Something with its immanent limit, posited as the contradiction of itself, through which it is directed and forced out of and beyond itself, is the finite. (P.129)
The limit is its “immanent determination”, and anything which is limited, (finite), by its very nature must come to an end, since limitation is negation. It must transcend its limit and be transformed into some other. This tendency for something to pass beyond its limits Hegel calls the ought. In Hegel’s conception, the ought has being as a tendency, but a tendency that has not been fulfilled.
“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.” (P. 132). “For the ought implies that one [something] is superior to the limitation.” (P.133)
This inherent tendency for something to pass beyond itself, to negate itself and become other is the transition from the finite to the infinite. Hegel describes this most important movement on page 136.
“The ought as such contains limitation, and limitation contains the ought. Their relation to each other is the finite itself which contains them both in its being-within-self. These moments of its determination are qualitatively opposed; limitation is determined as the negative of the ought and the ought likewise as the negative of limitation. The finite is thus self-contradictory; it sublates itself, ceases to be. Thus, in ceasing to be, the finite has not ceased to be; it has become in the first instance only another finite which, however, is equally a ceasing-to-be as transition to another finite, and so on to infinity.”
We must pause to consider the term “to sublate”. It means to negate and at the same time to preserve, and it is best explained in relation to the law of the negation of the negation and with an example. Pure Being, as immediate, abstract and one-sided, equal only to itself, was first negated by vanishing into its opposite, Nothing. But when this negation was itself negated, when “the vanishing vanished”, Being re-emerged in a new and developed form – determinate being; was sublated into determinate being. This is a case of sublation within the limits of logical deduction, but for better understanding we can take an empirical example as well, the life cycle of a plant. The seed is negated into the plant when in germinates. By the time the plant has matured the seed no longer exists, is negated, but the plant then produces the seed again, but many seeds, not just one. The negation of the seed into the plant is itself negated into this new affirmation and the original seed is sublated into it in the form of the many seeds in the seed head. Here we see the whole point of the law of the negation of the negation. It reproduces the original being on a higher, developed level.
Returning to the transition of the finite into the infinite, we note that Hegel says the finite sublates itself. The first negation is the mutual negation of the ought by the limitation and vice versa. With the negation of this negation, (the vanishing of the vanishing), the finite ceases to be, passes beyond its limit and becomes other, but in so doing becomes only another finite. The finite is negated only to re-appear, to be sublated into, another finite and so on to infinity. However, this endless series of finite things does not constitute infinity, because however far it goes it ends in a finite something. The actual transition to infinity is explained as follows:-
“This identity with itself, the negation of negation, is affirmative being and thus the other of the finite, of the finite which is supposed to have the first negation for its determinateness; this other is the infinite.” (P.137)
So as to be clear about this let us remind ourselves about something said above. The result of negation of the negation is affirmative being. When we spoke of the Hegalian triad, we said that the first term is thesis, a statement that something is – the second term was anti-thesis, something is not, and the third term is synthesis, the sublated unity of the two, which is the first term, thesis, (something is), of a new triad. This corresponds to Hegel’s terminology, affirmation, negation, and negation of negation. This explains why, in the above quote, Hegel says that “this identity with itself, the negation of the negation, is a new affirmative being.” The negation of the first finite something into an other is the first negation, but this negation is itself negated because the difference between the two dissolves into nothing, they are both finite, identical. This new affirmative being is the infinite.
Hegel begins his discussion of the infinite by setting out its moments as follows:-
“The infinite is:
a). in its simple determination, affirmative as negation of the finite.
b). But thus it is in alternating determination with the finite, and is the abstract, one-sided infinite.
c). the self-sublation of this infinite and of the finite, as a single process – this is the true or
Explaining point a) Hegel says:-
“The infinite is the negation of the negation, affirmation, Being which has restored itself out of limitedness. The infinite is, and more intensely so than the first immediate Being; it is the true Being, the elevation above limitation.”
The logic began with Being as such, the immediate, absolute, infinite. This became determinate being which is determinated as limited. But “the infinite is”, and this is what was said about Being in the first place. It is nothing but “is-ness”. Now that Being is elevated above its limitation its infinite nature is explicit rather than implicit.
Point b) is explained on page 138.
“The infinite is; in this immediacy it is at the same time the negation of an other, of the finite. As thus in the form of simple being and at the same time as the non-being of an other, it has fallen back into the category of something as a determinate being in general – more precisely, into the category of something with a limit … In keeping with this determinateness, the finite stands opposed to the infinite as a real determinate being; They are thus in a qualitative relation, each remaining external to the other; the immediate being of the infinite resuscitates the being of its negation, of the finite again which at first seemed to have vanished in its opposite.”
Hegel is speaking here of what he often refers to as “ordinary understanding”, or sometimes just “the understanding”. Such thought is based on the formal, non-dialectical kind of logic as epitomised by Kant and which dominates the thinking of society today. The understanding knows that every determinate being is complex, has sides and aspects, but cannot grasp the contradictory nature of the connection of these sides within the whole. It holds the sides apart in absolute separation, regards contradiction as objectively impossible and nothing but erroneous thought.
It cannot proceed to the negation of the negation and the sublation of the contradiction into new affirmation. This latter phase of thought, which is dialectical, Hegel calls “reason”. Nevertheless, the understanding is a necessary phase of logic, the phase of first negation or anti-thesis, but is sterile unless it proceeds to the stage of reason, (synthesis), by negating the negation. Hegel calls this completed, dialectical process “understanding which reasons and reason which understands.”
By thus mechanically separating the finite and the infinite, allowing both the exist side by side, formal thought allows them to limit each other as something and other, like the island and the sea. The finite is “resuscitated” and we have not the infinite and the finite but only two finites, because the infinite is merely the other of the finite and is thus limited. Formal logic, the understanding, supposes that the finite is not infinite and the infinite is not finite. This endless oscillation between the one and the other Hegel calls the spurious infinite. Under point c) Hegel shows how reason understands:-
“Taken according to their first, only immediate determination, the infinite is only the beyond of the finite; according to its determination it is the negation of the finite; thus the finite is only that which must be transcended, the negation of itself in its own self, which is infinity. In each, therefore, there lies the determinateness of the other … neither can be posited and grasped without the other.” (P.143). Hegel continues:-
“ … each contains the other in its own determination, just as much as each, taken on its own account, considered in its own self, has its other present in it as its own moment.” (P.144)
The infinite contains the finite and vice versa, the two are identical and collapse into one. The true infinite is the unity, (synthesis), of the finite and the infinite. A simple empirical example may help. If we look at a long wall through a knothole in a fence we shall see little of it. The little we can see is the finite, but nonetheless it is the whole wall, the infinite, that we are looking at.
The finite as such is being-for-other, that is, it is related to an other, is limited and negated by it. The other of the infinite is the finite, but as explained, the finite does not stand outside the infinite but is absorbed within it. Thus the infinite, in being related to the finite as its other, is related only to itself, and is therefore not being-for-other, but Being-for-Self.
(The One, The One and the Many, Repulsion and Attraction)
“ …we say that something is for itself in so far as it transcends otherness, its connexion and community with other, has repelled them and made abstraction from them. For it, the other has being only as sublated, as its moment; being-for-self consists in having transcended limitation.” (P.158)
As having transcended otherness being-for-self stands alone, is self-subsistent, is a One. But it is not a simple undifferentiated one because it contains its other within it as its moment. In being related to itself it is turned in on itself or as Hegel says it is “reflected-into-self”. This relation to self Hegel calls “negative self-relation”. Where a thing is related to itself there is distinction between the one which is related and the one to which it is related, and each limits, negates, the other. If this seems fanciful we may remind ourselves that whenever we talk about ourselves we base ourselves on the distinction between the “I” that talks and the “me” that is talked about.
The negative self-relation results in the negation of the one into the Many. The other which is contained in the being is not other in general, but only the other of this particular, (determinate), being, and consequently contains this particular being reflected in itself. Likewise, the being which contains the other does not contain other in general but only this particular, (determinate), other, and consequently reflects it and contains it. Being is both itself and other, and other is both itself and being. The negativity of the relation repels being and other from each other so that each becomes a one. But as explained, each of these ones is both being and other negatively self-related, so that the repulsion is repeated on both sides. This process continues to infinity resulting in the Many. Once again we may illustrate this empirically. If we cut a bar magnet in half we do not find a north pole in one hand and a south pole in the other – each half will have a north and a south pole. However many times we cut the magnet we get the same result, and the one magnet becomes many. The replication of organic cells is another example.
To summarise, the one was first affirmation, negative self relation was first negation, and this was in turn negated into new affirmation, the concept of the many. The one was sublated into the new affirmation since the many is the many of ones. There next arises the question of how these many ones relate to each other.
The process of the one becoming many Hegel calls repulsion.
“The many ones have affirmative being; their determinate being or relation to one another is a non-relation, is external to them – the abstract void. But they themselves are now this negative relation to themselves as to affirmatively present others – the demonstrated contradiction, infinity posited in the immediacy of being. Thus repulsion now simply finds immediately before it that which is repelled by it. In this determination repulsion is an exclusion;” (P.170)
The void to which Hegel refers is the void of Greek philosophy, particularly that of Leucippus and Democritus who were responsible for the first atomic theory. They postulated materialistically that the universe consisted of material particles too small to perceive and infinite empty space, the void, in which they moved. But, as said at the beginning, Hegel was concerned only with the movement of thought, and his deduced conception of the void is merely the total lack of any direct connection or relation between the many ones. But they are related in so far as they are all in the void, a relation which is “external to them”, so they have this common relation, just as a number of entirely disparate things lying on a table have this in common, that they are all lying on the table. The many ones have come into being, but they do not relate to each other directly. The in-itself of each one is not a reflection of the others, their relation is a “non-relation”, they are not being-for-other, but being-for-self.
But as explained above, since each is being-for-self, it is related to itself as something would be to an affirmatively present other, a relation that “demonstrates” the contradiction. We have already explained that being-for-self is the infinite, and here Hegel says the same thing the opposite way round, “infinity is posited in the immediacy of being”, [being-for-self, that is.] What is immediately before repulsion is of course the many ones, and since we are speaking of immediacy we are speaking of simple affirmation, one sided simple self-identity. So conceived, repulsion goes no further than exclusion. Hegel continues:-
“The plurality is, in the first place, non-posited otherness, the limit is only the void, only that in which the ones are not. But in the limit they also are; they are in the void, or their plurality is their common relation.” (P.170)
The plurality of the ones does not depend on their mutual negation and limitation of each other directly. The other of each one is the void, otherness which is at the same time not present, “not posited”.
“This is not a relating of them by us, an external bringing together; on the contrary, repulsion is itself a relating; the one which excludes relates itself to them, to the ones, that is, to its own self.” (P.171)
All the ones are united in repulsion, are “doing the same thing” as it were. Since the ones are identical, each relates to itself in the same way as it is related to the others, hence they are all identical, a relation which negates repulsion and tends to re-unite the ones into one whole. This positing of themselves by the many ones into one single one is attraction.
“The relation of attraction to repulsion is such that the former has the latter for presupposition. Repulsion provides the material for attraction.” (P.173)
Repulsion passes over into attraction, and the many ones pass into “the one One of attraction”. The single one was affirmation, (thesis), the negation of the single one into the one One is first negation, (anti-thesis).
Hegel then proceeds to negate this negation into new positive affirmation, (synthesis).
“Repulsion is, although negative, still essentially relation; the mutual repulsion and flight is not a liberation from what is repelled and fled from, the one as excluding still remains related to what it excludes. But this moment of relation is attraction and thus is in repulsion itself; it is the negating of that abstract repulsion according to which the ones would be only self-related affirmative beings not excluding one another … This being, in the determination it has now reached, is Quantity.” (P.175-177)
Quantity is the unity of attraction and repulsion, the one and the many. This is easily deduced from the language of every day usage. If we speak of “a” quantity, it is always one quantity of many ones. A heap of stones is one heap but many stones.
Now that we have negated quality into quantity we have completed the first part of the Doctrine of Being, which falls into Determinateness (Quality), Magnitude (Quantity), and Measure.
Plan of the Doctrine of Being
Determinate Being as such
Being for self
Being-for-self as such
The One and the Many
Repulsion and attraction
Continuous and Discrete Magnitude
Limitation of Quantity
Extensive and Intensive Quantum
The Quantitative Relation or Quantitative Ratio
The Ratio of Powers
The Specific Quantum
Being-for-self in Measure
The Relation of Self-subsistent Measures
Nodal Line of Measure Relations
The Becoming of Essence
Indifference as an Inverse Ratio of its Factors
Transition to Essence