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Second chapter. Essentialities or determinations of reflection

We began previous chapter with a study of essences or activities/methods of construction. We noted

that such activities or methods were more primary than the corresponding states of being that could

be regulated by their means – e.g. laws of movement are more stable than planets and recipes are

more lasting than cakes. We also noted that these secondary states of being were not completely

inessential for the methods: one could prove that these really were methods by applying them to

some given states of being. We then began the true study of essences through their actual use or

reflection. The simplest form of reflection – one that recognised itself to be a method of construction

– required no given element, but one could also apply it to other subject matters – i.e. one could

look whether these were methods of construction – and thus it could be interpreted as an external

reflection. We finally noted that we could find instances of external reflections that resulted in

essential modifications or interpretations of the given material: at least such that noted the

independency of their given material. Thus, we arrived at the notion of “determinate essences” or

reflections of determination: in effect, these are methods of construction that are aspects of some

“larger” method of reflection – e.g. a method of construction applied to some determinate situation

or object is an aspect of the same method of construction as applied to a wider field. We could also

call them abilities of situations and objects.

The aim of this chapter is to study the most general sort of abilities a situation or an object

could have. The abilities or determinations of reflection discovered in this chapter (identification,

differentiation etc.) have actually been in use in the first book, although they were not taken as

topics of investigation until this book. The truly novel method of construction of the book on essence

– a construction for finding an explanation for some situation or object – is studied in the next

chapter, and it is one task of this chapter to find an example of this method. The division of the

chapter would seem rather natural – a method of identification, a method of differentiation and a

method for making incompatible differences into aspects of a larger unity (idealisation of

contradictories) – if in Encyclopaedia Hegel hadn’t presented a different division, where it is the

construction of explaining situations and objects that takes the third place: a further reason to think

that Hegel’s classifications are rather artificial.

1./740. When we apply a method of construction in different manners, we get determinate methods of construction from

any given method of construction.

We begin by noting the result of the previous chapter. Note how Hegel does not speak of a

determining, but of a determinate reflection: Hegel emphasises how we have discovered many

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different manners of applying methods of construction. Thus, although we would have begun from

only one method of constructions, we are now in a position where we can interpret these different

applications of one method of construction as different types of method of construction: that is, the

same method, when applied to different areas, can be interpreted as many different methods, which

just happen to be aspects of the original method of construction.

2./741. Reflection is an application of some essence or method of construction. A method of construction is not

immediately known as essence, but only by going through its possible aspects: these aspects can then be interpreted as

“smaller essences” or as independent methods of construction.

The story how essence “shows itself” in its moments and thus makes them independent may sound

like a fancier way to describe the story of creation where a primordial creature bestows its own

existence to other entities. Yet, there is a rather simple way to interpret this perplexing idea.

Essence is not an immediate, but negative simplicity: that is, it is not a mere given structure, but a

method of construction which allows us to go through different aspects of some structure or process

by constructing – discovering or manufacturing – these aspects. Thus, we may e.g. discover

positions of planets through the laws of their movement and we can bake cakes with appropriate

recipes. Now, the essence shows itself in its moments. The moments or aspects are held together by

the possibility of constructing one aspect from another by using the “essence” or method of

construction: we may always apply the method of construction to one aspect in order to construct

another aspect from it and we may also use the method of construction to construct this particular

aspect from any other aspect – e.g. we may calculate when a planet has been in a particular position

of its orbit. Thus, every aspect of the essence comes with its own method of construction – we can

construct it from other aspects of the essence – and it is therefore independent in some sense.

3./742. A) The whole essence as an ability to find identical unity in different contexts is the first example of determinate

methods of construction, although at this first stage it is not yet determined or compared with anything.

The natural starting point for discovering aspects of an essence (a method of construction) is the

method itself: the aspects of the essence are such structures that can be found by using some method

implicit in the original method. Now, in one sense the essence itself is the first example of such

aspects. The essence is or involves a method, by which one can identify structures that are aspects

or modifications of the essence: for instance, through a law of the movement of a planet I am able to

pinpoint positions of the planet in its trajectory and through knowledge of right recipes I can

identify a particular cake when its ingredients are told to me. This method of identification is one

method among many, but at this particular stage we are not supposed to know certainly that there

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are other possible methods of construction: we should be in a context where there is nothing but this

one method of construction. Thus, at this first stage the method of identification is still

“indeterminate”, and it is our task to determine this method by finding other methods with which to

compare it.

4./743. B) When we truly determine methods of construction, we find differences: a differentiating method can

construct external diversities or essential oppositions.

Because the essence is a method of construction, we may by its means find instances of different

situations and objects: that is, essence involves not just a method of identification, but also a

method of differentiation – like a law of the movement of planets enables us not just to construct a

single trajectory of the movement of a planet, but also to find different positions the planet may take,

or like our capacity to recognise ourselves involves also a capacity to recognise different aspects or

stages of life of ourselves as different from one another. Now, when such a method of

differentiation has been found, we have also found an instance of “determined reflections”: that is,

we have then two related methods of construction. These methods of construction – identification

and differentiation – can then be used as examples of further structures and especially their

relationship can be used as an example of different sorts of differences: indeed, they are different

methods of construction. The movement of the different sorts of reflections is repeated now in the

level of the different types of differences or differentiations. The first method of differentiation

might be a mere differentiation of non-independent aspects: that is, what is differentiated might be

different only according to the construction – somewhat like me as the perceiver and me as the

perceived are not truly different entities. Now, the method of identification and the method of

differentiation are more truly distinct objects: they are different even before the differentiation. The

differentiation of these methods is then an example of what could be called an “external”

differentiation. Finally we note that when we are given such a differentiation of previously diverse

objects, we must also be capable of constructing an example of a “non-external” or essential

differentiation of these objects: otherwise, we wouldn’t be justified in calling them truly distinct.

5./744. C) An opposition can be presented as a contradiction [– that is, we can present this same opposition in

incompatible, but equally adequate manners –]: we can then find an essence or a method by which one could produce

one side of the contradiction from the other and then explain the whole contradiction.

The final section of the chapter is important at least for two reasons. Firstly, it introduces Hegel’s

notion of contradiction, and although its importance for Hegel’s philosophy has been exaggerated, it

is still a vital part of Hegelianism. As we should have seen by now, Hegelian contradiction has little

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resemblance with contradictions in the logical sense on the word: they are rather just examples of

one and the same thing appearing in different and even incompatible guises in different contexts – a

person changing the colour of her hair is a perfectly fine example of Hegelian contradiction. Here

Hegel is especially interested in showing an example of a “necessary” or essential contradiction. He

begins from an instance of an essential difference – such as the difference between the two methods

of identification and differentiation – and notices at once two incompatible descriptions of their

relation: in one sense they cannot both apply to same situations – because they are supposed to be

incompatible – but in another sense they must apply to same situations – because their opposition is

essential, that is, whenever we have an instance of one opposite, we can construct an instance of the

other opposite. This “contradiction” is no logical contradiction, because the adequacy of the

descriptions depends on e.g. what sort of classification of situations we are given.

Secondly, Hegel introduces the more important notion of ground or explanatory-causal

relationship that has been implicitly introduced in the transition to the second book. An instance of

such an explanatory relationship is given already in a Hegelian contradiction, which involves a

method by which to move from one side of the contradiction to the other: an existence of such a

method thus explains in some sense why such an apparent contradiction must occur – that is, it

shows why this “contradiction” or possibility of connecting incompatible situations is necessary.

This explanatory move is what Hegel in some places calls the speculative move of the flow of

reasoning.

Remark

Subject matter of the remark is the group of “universal laws of thinking” that are based on the

determinations of reflection. These laws are familiar from the Leibniz-Wolffian school of

philosophy: law of identity, non-contradiction, identity of indiscernibles etc. The determinations or

concepts of reflection, on the other hand, appeared as an independent group of characteristics in

Kant’s Critique – although Kant didn’t arrange his group in a similar manner as Hegel does. Still,

even Kant mentioned some connections which these determinations had with the laws of Leibnizian

philosophy. Particularly Kant noticed a problem in Leibniz’s and Wolff’s manner of applying these

determinations and the corresponding laws to all entities: before one could apply these

determinations and laws, one should find some group of entities to which this application was made,

and because only entities given to human beings were given through senses, so Kant insisted, the

application was hindered and conditioned by the form of human sensibility. As we have seen, Hegel

tries to avoid Kant’s results by noting that we do not need sensibility in any strong sense, because it

is possible to construct at least a virtual set of objects – pure structures – to which the

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determinations could be applied. Yet, even then the laws of Leibniz-Wolffian school wouldn’t apply

unrestrictedly: the context of the word “all” must always be predetermined to some finite context,

and one law may have different applications in different contexts, depending on what is accepted as

existing.

1./745. Determinations of reflection have been presented as universal laws of thinking applicable to all things: as laws

which cannot be proved, but which everyone will accept.

2./746. For instance, identity can be expressed as the law “A = A” or “A cannot be both B and not-B”.

It is interesting to note that the word Satz can be understood in two different manners in this remark.

Firstly, there is the ordinary meaning of the word where Satz is a proposition within some context.

In this sense, the “laws of thinking” would refer to analytical, almost meaningless truths which

anyone would truly accept, but which wouldn’t really tell us anything new. Thus, “A=A” would say

nothing but the trivial truth that anything that is accepted as existing in some context in some

manner exists in this manner in that context; or “A is not B and not-B at the same time” would just

point out the triviality that one entity cannot have incompatible predicates in the same context.

Secondly, there is the more essential meaning connected with the role of determinations of

reflection as determinate methods of construction: the laws of thinking reveal some abilities implicit

in all things, that is, abilities which tell us what sort of characteristics entities could have in some

contexts we could construct. Thus, “A=A” would not be a mere trivial statement of intracontextual

identity, but an indication of our ability to identify different aspects of the same entity appearing in

different contexts: thus, we can, for instance, identify different moments of life of the same person

as mere modifications of this person. Similarly, “A cannot be B and not-B at the same time” reveals

the corresponding ability to differentiate between different aspects of the same entity, if they

happen to have some differentiating characteristics: we may hence also differentiate between the

different moments in the life line of a person. These abilities together make it possible to identify in

one context what is differentiated in another and vice versa.

3./747. At first sight similar laws could be constructed from categories of being (“everything is”, “everything is here”,

“everything has quality and quantity” etc.). On another hand, such sentences would be true of certain entities only in a

given context, and we would have to prove that they would apply in a certain context.

In the Encyclopaedia Hegel indeed starts to speak of such “laws” even in an earlier stage: all

categories or general ontological structures could be used as possible predicates of “all objects”:

that is, given any entities in some contexts we could construct a context in which these entities

would be characterised by these structures. Now, Hegel notes that when it is the structures of the

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previous book that are so applied, then these “laws” have only a restricted applicability: they apply

in some contexts, but not necessarily in all contexts, and furthermore, these different contexts might

be equally informative or adequate. Thus, “everything is” or “everything is here”, that is, given any

entities in some situation, these entities are taken as existing. Yet, these entities or objects might not

exist in another context: although I exist now, I didn’t exist a thousand years ago and I won’t

probably exist thousand years from now. Furthermore, there are situations, although only abstract

ones, where nothing exists: an empty bottle, according to one possible interpretation or viewpoint,

is truly without any objects. Similarly, “everything has a quality” or “everything has a quantity”, but

the quality or the quantity that an object has may differ from one context to another: if the rose is

red in the summer, it might be brown in the fall. Furthermore, there are contexts, although

admittedly abstract, where there are only qualities and no quantities or only quantities and no

qualities.

4./748. Determinations of reflection are more complex than mere qualities, or they are independent and essential

abilities of objects. It is thus natural to present these determinations as mere sentences: a mere sentence is a structure

which implicitly contains connections between objects or aspects of objects, while in a judgment these connections have

been abstracted from the rest of the structure. All that the determinations of reflection need in order to become

sentences are objects to which they are applied, and they can be applied to any objects.

What difference is there between a determination of reflection and a quality, that is, what makes the

former more natural to express in a sentence of the form “All x are...”? When we construct a

situation where a given object has some wanted quality – we are assuming that such a construction

can be made with this object – we may have to modify the object somewhat: e.g. to show that a seed

can become a rose, we have to make it change its “being a seed”. On the other hand, if we want to

construct a situation where a given object explicitly has some required determination of reflection,

we may have to go through some modification – for instance, to show that a berry is poisonous, we

may have to feed it to an animal – but after this modification we may note that the object had this

determination of reflection or ability already in the original situation – the berry is now known to

have been poisonous all along. The outcome of this construction is that we have gained more

information on the original modification of the object: we now see it in a more adequate or more

informative context.

Hegel makes here a curious distinction between Satz and Urteil, which is repeated in the

third book, where the judgments are taken as an explicit subject matter: on the other hand, in some

versions of Logic Hegel designated the subject matter of this part to be propositions. As we have

seen, the Hegelian “propositions” or “sentences” are no mere descriptions of given contexts or

situations, but contain a reference to many contexts and their relationships: we might say that

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Hegelian sentence is essentially modal or contextual in nature. Satz is then a structure where this

relationship of contexts is part of the whole structure: for instance, “I walked yesterday” describes a

complex structure where my current situation is related to another context where I happened to walk.

In Urteil, on the other hand, one particular modal relationship between contexts has been isolated as

a distinct part of the structure: “I am yesterday’s walker” describes a relationship between my

present state as a unified person and my aspect of having been walking yesterday, where this aspect

has then a further structure that is not emphasised in the judgment.

5./749. It is futile to investigate these sentences, when we can study the determinations themselves: furthermore, these

laws of thinking suggest erroneously that the object having these determinations would be more essential.

In order to make Satz or Hegelian “sentence” from a structure, one still needs some given objects:

after all, Hegelian sentence is proved to be true through a construction of a context where a given

object – the subject term of the sentence – has the required structure. Now, such a construction tells

us that the object in question could have a certain characteristic. The sentence thus suggests that the

object designated by the subject term is somehow independent of the structure: the structure is only

one possible aspect or modification of the object – e.g. if I prove that rose can be red, the rose may

still have a different colour in a different situation. The form of Hegelian sentence implies that the

object is more essential than the structure. In case of determinations of reflection this implication is

misleading, because construction of a context where the object has such a determination does not

require a true modification of the object, but only some more information of the object involved: the

object has naturally the determination of reflection. Indeed, it is the object that is arbitrary in

comparison to the determination, because other objects may have the same abilities also: indeed, as

we are about to see, we need only some methods of construction in order to construct examples of

certain abstract determinations of reflection.

6./750. We can present the determinations of reflections as independent, but in another sense they are mere aspects and

related to one another: thus, when we look at independent laws of thought, we abstract from all others – when we look

at the ability to identify everything, we forget that there are many things, or when we look at the ability to separate

things, we forget that they can be identified in some sense.

The main reason why determinations of reflection shouldn’t be expressed in form of laws of

thinking is that these laws fail to reproduce all aspects of the determinations. A determination of

reflection is an ability to construct something and thus is always connected with the ability to

construct something different – after all, one needs to be able to construct “opposite” or unwanted

situations in order to show that even in such cases one can construct the required structures. When

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the determination is expressed as a sentence this connection is left implicit: we seem to abstract

from all the other possible cases. Thus, if we would have a mere ability of identification which is

expressed in the law “A = A”, we could construct a context where everything is identical – a

context with just one object – but not any other objects beyond this one “identity”. Thus, we

couldn’t make any classifications of different objects – there wouldn’t be anything to classify – and

furthermore, we couldn’t explain anything, because true explanations require an explanandum

differing from explanans. Then again, we could have an ability to differentiate objects or to

construct many objects from a given object, but we wouldn’t then have an ability to note similarities

in different object and thus we would have no ability to classify objects according to some schema,

because classification requires that the classified objects or situations are in some sense similar or

under same genus.

A. Identity

We begin the study of determinations of reflection from the most immediate of them, that is, the

ability to identify something similar in different situations as contexts: in effect, this is the ability to

interpret these differences as mere aspects of one unity – such an ability is included in all methods

of construction that work as essences of some structure, because by this method the aspects of the

structure can be identified as belonging to this structure (through the laws of movement we can

recognise one planet in different positions to be the same planet, and through a method of

recognising oneself I can identify different parts of my life as belonging to the same person etc.). In

modal terms we could identify this “identificatory ability” as a method of discovering so-called

transworld identities, that is, identities of objects from one world or context to another. Such ability

to identify different aspects of a structure as belonging to the same structure is connected with the

ability to find different aspects of the same structure (that is, an ability to find different “worlds” or

contexts) – in fact, one could even identify these abilities of identification and differentiation as

mere two sides of one method of construction – and it is this ability of differentiation that is the

issue of the next subsection. This section has a somewhat strange structure: it is divided into two

unnamed subsections, where the first subsection notes that an essence or a method of construction

can be taken as a method of identification and where the second subsection differentiates two sides

of this method: a method of differentiating different aspects and a method of “mere or abstract

identification” – a method of intraworld identification of objects, one could say. Even this division

into mere two parts is extraordinary, but even more fascinating is that both these subsections are

given their own remark: a flow of construction is interrupted suddenly.

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1./751. 1. Essence as identity. A method of construction as essence is in some sense simply given, but in another sense

it is discovered through integration of something given into a larger unity: it is essence of some structure because we

can go through seemingly independent aspects of the structure and view them as mere aspects – it is something that can

be identified in these different aspects.

We once more return to investigate the manner how we discovered something to be an essence: we

had some arbitrary group of states of being and then we noticed that we had an infallible ability to

construct one state of being from another – in effect, we saw that one state of being was only an

aspect of a larger structure held together by a method of construction keeping the different aspects

together. Thus, we could see e.g. that a planet moved regularly from one position to another in such

a manner that we could calculate its next position, or I could see that a certain arbitrary flow of

events formed a part of the life of the same person because all these events were experienced by me.

The method of construction that led us from one aspect of the structure to another was thus the

essence of this structure: this essence was simple – it was one “entity” – but also “mediated” by a

manifold of states of being – we could see it as an essence only, because we had used it to construct

different aspects of the same structure. This essence or method of construction was then an ability

to identify these different aspects as belonging to this particular structure: only because we could

apply the method of construction to a certain state of being or object, could we identify this

situation or object as a mere modification of some underlying unity.

2./752. The first stage of construction is identity: it is not a mere given state of being and not even a mere state of

nothingness, but a unity that can be naturally produced. It is not a mere identity within one situation, which presupposes

an abstractive movement from a context with differences, which is at least equally adequate as this context of abstract

identity. An essential identity is constructed naturally, because several states of being have been integrated through

application of an identifying construction,

Hegel here sets the identity proper against mere abstract identity: that is, identity across many

different contexts against identity within one context – for instance, I am an identical person

although I live through different stages and thus in a more “abstract” sense stages of my life would

form separate entities. Objects in one state of being are abstractly identical with themselves, but not

with anything else – this is the usual logical identity – but identity in a proper sense can attach

entities in apparently different states of being: cow in the evening can be same cow I saw in the

morning. It is one thing to define such different identities and another thing to provide a criterion

when a group of apparently different objects or situations are actually aspects of concretely identical

entity. In one sense Hegelian answer might be contextual: in fact we have seen that in different

contexts we may have different criteria of identity, because we may e.g. use construction of

idealisation to find a context where things different in one sense are identical – this was the idea

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behind transitions from finity to infinity and from multiplicity to unity.

Still, Hegel also provides us with one special criterion, although the application of this

criterion may also depend on the context. Hegel says that a proper identity is connected with the

production (Herstellen) of a structure, where this production should be pure and happen within this

structure: that is, if we have some method of constructing different aspects of some structure from

one another, we are allowed to assume that this structure is connected by an identity across different

contexts – e.g. because we could construct a causal chain from one stage of my life to another, I

could reasonably assume that I have been the same person during my whole life. Abstract identity,

on the other hand, is defined more by its relation to other contexts: it is not so much production, but

“reproduction” (Widerherstellen) and relative to some other context, that is, when we begin from

some entity in some situation and note that this at least should not be identified with the object we

are interested of, we abstract from this difference to a context with merely the object – outside this

abstract context the object involved still has some relation to the entity from which it differs.

3./753. Proper method of identification is then an essence of some structure.

The criterion of identity in the proper sense is not a mere method for abstract denial of everything

that does not belong to a certain structure, but a method for integrating all situations and objects that

can be constructed from one another into aspects of one common structure: we might call this a

semi-causal criterion of identity, which in some important cases, like when we are dealing with an

identity of a person, equals causal criterion of identity. The kernel of this criterion or method of

identification is some method of construction: we must be able to discover or manufacture aspects

of the structure from one another. This criterion of identity involves then an essence of this structure:

if we know how to identify different aspects of the structure as aspects of this structure, we must

know how to construct these aspects from other aspects of the structure.

Remark 1.

The analysis of the structure of proper identity is interrupted by the solitary remark, which once

more emphasises the difference between the proper and abstract identity. It is here where Hegel

might be said to launch an attack against the so-called logical atomism – if we may speak in such

anachronistic terms, because the ideology of logical atomism was introduced only at the beginning

of the twentieth century. What Hegel wants to show is the possibility of phenomena that cannot be

properly analysed in terms of “atomic” and independent objects: this does not, of course, mean that

he would want to endorse a wholesale holism where “everything depended on one another” –

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Hegel is not saying that atomism cannot describe anything, but only that it cannot describe

everything.

1./754. If one thinks that all thinking is mere external interpretation, one cannot construct any examples of proper or

essential identities: external interpretation can only abstract identities from some context of difference or it sees only

alternative contexts of identity and difference. Because it is possible to modify objects and situations, we can construct

different and even contradictory aspects from a state of identity and interpret these differences as mere aspects of a

larger state of identity: thus, there is a natural manner of constructing essential identities, while by abstraction we can at

best achieve mere states with many different and unconnected entities.

What is this thinking that knows of no other thinking but external reflection? It is thinking which

begins from a given world of many objects and then analyses this world: it abstracts from the

relations between these objects and thinks they are at most external relations, because one can so

easily abstract from them. True, this thinking can then return to the original condition of many

objects, but this return consists in nothing more than a “second abstraction” or recollection of a state

familiar from an earlier state of thinking. The result of such thinking is the conviction that the

proper and actual entities of the world are atomic objects independent of one another and only in

some external or quantitative relations to one another: in later times such an ideology was to be

known as logical atomism.

If logical atomism were truly the only possible and proper way to describe the

situations, then e.g. Hegelian identities would not be acceptable: we couldn’t have one object in

different contexts or one object having different aspects etc., but this apparent object would be only

a logical construction out of primary objects – for instance, an object with many different properties

would be a mere conglomerate of independent tropes or an object apparently existing in different

times would be a mere four-dimensional aggregate of smaller parts. Hegel’s retaliation against

logical atomism is to point out that it also is merely one possible interpretation of certain

phenomena and that we can construct in a natural manner examples of “proper identities”. Given

anything identical or any object, we can produce something differing from it: at least a different

aspect or a modification of the same object – examples of such constructions have been given

already in the previous book. And given any apparently different objects that can be in this manner

constructed from one another, we may naturally interpret them as mere aspects of one given

structure. Of course, such an argument is no proper proof: logical atomist could still hold on to her

convictions and interpret the constructed Hegelian identity as a mere “logical construct”. Yet, Hegel

has at least been able to shake the certainty of logical atomism, which is not anymore the only

possibility from which a reasonable person could choose.

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[The remark ends]

4./755. 2. Differentiation of identity proper into absolute difference and abstract identity. A proper method of

identification is the same method of construction as the respective essence. We may use this method to differentiate

different aspects of a structure, but these aspects can then be immediately identified as mere aspects: we notice that the

underlying unity could be something else, but is not at this moment and then we can instantly note that these different

aspects of the same unity cannot exist at the same context. Still, we are able to differentiate at least possible aspects

within the unified structure: we have thus found a method of constructing differences within a structure or a method of

discovering absolute differences.

Before the remark we noticed that a proper method of identification equals some method of

construction that is also an essence of a structure. Now, such an essence involves clearly not just a

method for noting that an object or situation belongs or is an aspect of a structure, but also a method

for discovering or creating arbitrary examples of such aspects of a structure, when some other

aspect of the structure was given: this is why the essence was supposed to be a method of

construction. Thus, a proper method of identification should, according to Hegel, contain at least

implicitly a method for constructing differences, that is, different aspects of the same structure. This

method of differentiation differentiates in another sense nothing: e.g. if I start from one moment of

my life and discover another moment of it, I have still not discovered a different person, but a

different part of the life of the same person. True, by such a method of differentiation we construct

that “something does not hold”: that is, we construct another possible context where the same object

or situation is looked from a different angle and has then different characteristics and we note that

this constructed context differs from the “current” or designated context – e.g. I may find that I had

different opinions of some issue when I was younger as compared to opinions I have now. Still,

because these separated contexts are never “current” or designated “at the same time”, we may

without any fear of contradiction integrate these differences once again back into the original

structure – I was still same person even when I had different opinions. Hence, in a more informative

sense, there has been no “true” differentiation or differentiation has not resulted in any independent

objects or situations.

Although the method of differentiation within any proper method of identification does not

result in any differentiation of independent objects or situations, we may still say that it is

differentiation of some sort: it does not differentiate the original structure from another structure,

but only differentiates aspects within it. Earlier we faced a peculiar kind of reflections or

constructions which required no external given, but merely e.g. noted that they themselves were

methods of constructions: such constructions or reflections Hegel called pure or absolute. Similarly,

we here have a method of differentiation that does not differentiate any given independent objects

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from one another, but merely some aspects implicit in the method itself: thus, we could call it a pure

or absolute method of differentiation.

5./756. A method of identification integrates something that has been constructed by it, and constructs apparently new

entities that can be then be integrated by it: it is then in another sense a method of constructing continuing differences –

we may use it to construct always something different beyond what has been integrated into the identity, even when no

material to differentiate is given. Because these constructed differences would not exist without the method of

construction, we may then once again integrate them into the original identity.

The previous paragraph tried to show that a proper method of identification contains in itself a

method of differentiation, although only a method for differentiating non-independent aspects

within a structure. This paragraph then tries to show that actually the method of identification itself

can be regarded both as a method of identification and as a method of differentiation. A proper

method of identification contains two constituent construction steps. Firstly, there is the step of

identifying or integrating apparently different aspects into one unity: this is what Hegel here calls

reflection-into-itself. Secondly, there is the constructive step by which these apparently different

aspects are discovered or manufactured: this is what Hegel calls “pushing away” or “repulsing”.

Now, the order of these steps is actually arbitrary. We may begin from some state of identity and

construct something apparently differing from this state and then return to the original unity: for

instance, we may begin with an arbitrary finite line, find a point outside the line and finally find out

that we can extend the original line to the point we discovered – such a process can be regarded as a

continuous maintenance of the original identity. Then again, we may begin from a state of apparent

difference, construct identity from it and then just create a new difference: for instance, we may

begin with a line and a point beyond it, extend the line to a point and then find a new point beyond

this line. This sort of process would then be a continuous maintenance of difference: furthermore,

the difference maintained would even be identical in one sense – its relata would be something

presumably identical (the line in our example) and something not identical with this reference point.

The next steps in Hegel’s construction may seem like mere puns: difference is identical with

itself when it is not identity, but absolute non-identity. Behind this pun lies something substantial.

We may have two sorts of differentiations: firstly, we may have some identity external to the

method of differentiation and we may apply this method to this given identity – for instance, when

we compare some given object to other objects we happen to find somewhere – or secondly, we

may find or manufacture some differences beyond a structure that is essentially bound with a

method of producing new differences – that is, we have a natural manner of producing differences

from some given object or situation. While in the first case we could say that it is the identity or

original unity which is more essential and that the differentiation of this unity from something else

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is arbitrary, in the second case this difference seems more essential and natural: thus, it is the

second sense of differentiation which we are looking at here. Now, Hegel concludes, we may still

interpret this “absolute differentiation” as a sort of identification. The construction of identity may

once again seem like a mere wordplay: absolute non-identity should not be non-identity in

comparison to something else, but in comparison to oneself. Yet, there is once again a sensible

meaning behind this wordplay. An absolute process of differentiation does not begin from some

external state of identity which is then arbitrarily manipulated, but it works naturally in order to

construct new objects or situations beyond a given one: thus, it is natural to assume that this new

object or situation is a mere aspect of the structure, the essence of which this method of

differentiation is – e.g. new moments of my life are not some arbitrary objects or situations

compared with my earlier life, but results of my own self-modification. Hence, the constructed

differences can then be naturally interpreted as mere aspects of the larger structure: the method of

absolute differentiation can be interpreted as a method of proper identification.

6./757. A method of proper identification is in some sense a method of absolute non-identification, but in another sense

the method of identification can be identified with the state of identity that results from the use of the identification: we

may then separate this state of underlying identity from the process of differentiating aspects within it.

In one sense a method of identification, and the resulting “identity” of an object, contains within

itself the method of differentiation and the possible aspectual and contextual differences within the

relevant structure. In another sense we could refer by a method of identification to a partial step of

the larger method of identification: namely, to the mere pointing out of the common substrate

behind the different aspects. Such a method would result only in an abstract identity, because it

could be used to completely abstract from the differences within a structure: thus, we could point

out my personality or “soul” behind the stages of my life or the subsisting “essence” of a planet

behind the variable positions the planet might take. After this isolation of one step – mere

identification – the other step and its result are still left behind – that is, the differentiation and the

differentiated aspects: for instance, the concrete stages of my life. It is the relationship of these two

steps – abstract method of identification and method of differentiation – and of their results – state

of abstract identity and a corresponding state of difference – that is dealt with in the later sections of

the chapter.

Remark 2.

Hegel begins to study the series of “laws of thought”, first of which are the so-called law of identity

and the law of non-contradiction. In this remark Hegel also expresses his famous criticism against

15

formal logic and analytical propositions. As we shall see, this criticism is usually misunderstood.

Hegel does not want to replace the usual logic with another sort of logic, but to point out that it

cannot express “the whole truth”: that is, that formal logic gives us very little information of

anything – it merely tells what holds true in all contexts, but it doesn’t tell what sort of contexts and

situations there in general might be.

1./758. In this remark I shall study the law of identity “A=A”.

2./759. This law has no content or it expresses an abstract, tautological identity as something independent of difference,

although if identity differs from difference, it is itself a natural part of difference. Mere identity expresses no or a mere

limited and formal information: more information is gained by seeing in what different contexts an identical object or

situation can exist.

The law of identity was held in great esteem by Leibniz who thought it was the basis or criterion of

all truths of reasoning, which included beyond logical and analytical truths also the whole of

mathematics. Leibniz had equated law of identity with the law of non-contradiction, and this was

common enough in the later German philosophy, although Kant was at least in his pre-critical days

of the opinion that the two should be separated and that it was the law of non-contradiction that was

the truly important proposition. In any case, Kant estimated that the principle of non-contradiction

was the criterion for all analytic truths, which didn’t include mathematics anymore. Even Russell

and Whitehead pay homage to the old idea of the importance of the law of identity and present it as

a theorem of their Principia mathematica, although they have to admit that it isn’t as important

axiom as it once was thought to be. In any case, there has been a distinct tendency to present the law

of identity as a sort of exemplary case of truths based on nothing more than meaning of the terms

and even as a case of a truth based on nothing else but the form of the proposition: “A = A“ is true

no matter what the A is supposed to mean.

The law of identity is true in every context or in every situation, but just for that reason

Hegel cannot find it very interesting: it would hold even in an empty situation, because it says

nothing at all. Hegel even goes so far as to say that the supposed law is not true: “true” here has the

obvious sense of “having an information content” – the law of identity has no content and is

therefore not “true”, although it undoubtedly is true in the usual sense of the word. The law of

identity abstracts from all but one object or situation: it restricts its attention to one context and

declares that in this context everything is as it is. What this law lacks is a differentiated content:

after all, one must investigate at least several aspects of one and the same thing in order to get some

interesting information. Such a differentiation requires a multiplicity of contexts: we must either

have many objects with their own contexts related to one another or then we must have many

different contexts from which to regard one object. What Hegel has then against the law of identity

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and the formalism it symbolises is the blindness towards the contextuality of the world it brings

with itself: in other words, Hegel rejects logic as an aggregate of formal truths, not because it would

be incorrect, but because it is in anachronistic terms restricted to relations within one “possible

world” or situation.

Formalism merely disregards the further content and thinks what could be said even if

nothing was given, while Hegel would want a proper Logic to construct its own content even when

nothing was given: that is, a proper Logic should construct models for basic structures from any

given material or even from an empty situation. Then again, Hegel notes, one could easily use the

abstract identity expressed in the law of identity to construct further content. It is easy to see how

this construction could be done with a Hegelian identity which is nothing else but a method for

constructing new aspects belonging to an identical structure as aspects, but how could such a

construction begin from an abstract identity? The abstract identity as an abstract identity is

supposed to be a result of some abstraction: it is not like a mere given situation of which we knew

only that the laws of formal logic apply there, but a situation which we have constructed from a

more concrete situation through abstraction. Thus, one would just have to note that this abstracted

situation differed from the original situation from which it was abstracted, and then one would

already have discovered an example of different situations: if we then interpreted these situations as

objects, we would have constructed examples of different objects.

3./760. Often the law of identity is justified through experience: everyone agrees that e.g. tree is a tree.

4./761. But no conclusive experiment with this abstract law has truly been made. Furthermore, one cannot even retrieve

this law through abstraction from concrete statements, because then one discards an essential part of these statements,

namely, diversity.

Even Locke criticised the idea of immanently certain propositions, because children and uneducated

people wouldn’t even understand if one would ask them whether e.g. “A is A” is true. Later Kant

noticed that necessity of a proposition can never be justified through experience: one cannot start a

vote concerning the question what propositions we should accept in formal logic. The second

interpretation of this “test of experience” is far more convincing: one does not try to justify law of

identity through experience, but tries to show that all experience presupposes this law in the sense

that the truth of this law is contained in every experience. Suppose we express our experience

through some proposition, say “the sun is shining”. Now this proposition describes a unitary

experience or a unitary situation: if sun is shining, then sun is shining, unless someone changes the

situation. This reference of the proposition – the state of the affairs or the situation that the sun is

shining – is then an object that must obey the law of identity, as one easily sees: this situation is

itself and not e.g. a situation where sun is not shining.

17

Hegel admits all of this, but points out that the analysis of the proposition and its

reference change what is analysed in an inappropriate manner. The result of the analysis is a single,

unified and apparently simple situation with no intrinsic connection to other situations. But the

original proposition and the corresponding situation are complex. We have the sun and as its one

possible aspect of shining: here we already have divided the situation into two components, both of

which could have their own viewpoints or contexts. Furthermore, if the proposition is to be

informative, it must contain at least an implicit reference to other possible propositions: something

in the shining of the sun is surprising, that is, perhaps the sun might have other possible

characteristics in other situations – maybe it doesn’t shine always – or maybe there are other

possible objects which do not shine. In any case, when we extract the law of identity from this

proposition, we have to do some violence to the original proposition: we abstract quite a lot of

explicit and implicit information from it in order to reach the contentless formality of an abstract

identity.

5./762. When identities are expressed in a conversation, everyone admits that they are not very interesting.

6./763. This boredom occasioned by identities is caused by their contradicting the meaning of propositions in general:

the beginning starts a movement to something different, but the end returns to the beginning – thus, one can construct

contradictions from an abstract identity.

At first sight Hegel’s argument in these paragraphs seems farfetched. Of course, one admits that

tautologies like “A = A” are not very interesting, and indeed, “say nothing” or convey no

information: thus, they are not “true” in the peculiar sense of truth Hegel uses here, which would be

better expressed by words like information. One just may wonder what sort of contradiction this is

supposed to be: surely an uninformative sentence is still not on that account contradictory? But we

must remember the peculiar sense of contradiction that Hegel uses: in a Hegelian contradiction we

have the same thing with different and even incompatible characteristics in different situations or

contexts. What Hegel is saying is that when we try to express that something is identical with itself

– even when this identity is merely an abstract identity or identity within a context instead of proper

identity across different contexts – when we then model this expression, we must turn the abstract

into proper identity. Thus, suppose we have an object that is, undoubtedly, self-identical in some

context. Suppose we then express this identity in a context through a sentence like “A = A”. Then

the model of this sentence would contain two different objects – the “first A” and the “second A” –

and these two As would then be properly identified, that is, identified as mere aspects of the same A

or object.

7./764. The form of proposition adds to an abstract identity a possibility to seemingly move away from the identity and

18

then to integrate the seeming difference into the identity: similarly, it adds some content differing from the abstract

identity – even the abstract identity itself as a content differs from the identity as a form. Thus, given an abstract identity,

we can always find a method of creating differences.

By modelling a sentence describing an abstract identity – modelling a model of the abstract identity,

one could say – we managed to construct an example of a proper identity, that is, an identity

connecting different aspects within itself: by modelling the sentence, we added to the original

identity, in Hegel’s terms, a movement from one aspect of the identity to another. Now, there is also

a further manner of constructing differences from the abstraction of a state of identity. Suppose we

are given something identical, say, a tree. Then we may compare this tree with its state of identity:

thus, we may say that the tree or the content of the state of identity differs from its state of identity –

this is a modification of the construction by which we could find multiplicity from any given

unified object. One could say that this differentiation already presupposes something differing from

the state of identity – namely, the given content. What if we were given only the method of identity

and we then applied this method to itself by saying “the method of identity is a method of identity?

This would be an example of a pure reflection or of a self-application of a method of construction,

and as we saw there, it would be possible even in this case to differentiate between the two aspects

of the method: the method as the object of construction and the method as used in the construction.

Thus, although in one sense a sentence “a method of identification is a method of identification” is a

result of a mere application of the method of identification to itself, in another sense we may

separate the identification as the subject matter of the sentence from the identification as the making

of that sentence. Hence, by applying identity to itself we may use it to construct something at least

contextually different from the original identity.

8./765. A second way to express identity – the law of contradiction – states negatively that nothing can be both A and

not-A at the same context. Not-A in this expression arises from the possibility to construct differences from an identity:

we change context with A into a context with something different and only then we find out that this different from A

can be interpreted as a mere modification of the original A.

The law of contradiction was held by Leibniz to be a mere modification of the law of identity –

indeed, both are logical truths – but some, like Kant, had noted that it contained a negation that was

not present in the law of identity: if one was to express the law of contradiction (“something cannot

have contradictory predicates at the same time or something cannot be both A and not-A”), one

needed then more than in expressing the law of identity. Hegel notes that because one can construct

from abstract identities examples of proper identities, which contain differences, one can thus

construct examples of the required “not-A” differing from the A, although these differences are in

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some sense only ideal or aspectual – the not-A appears just to disappear. That is, with a proper

method of identification one can construct something that apparently differs from what is originally

given – a “not-A” – and then one can instantly “return to the identity” by noting that the constructed

not-A is only a modification of the original A: here the first step is in Hegelian parlance first

negation – movement from one part of a classificatory system to another – while the second step is

second negation or “negation of negation” – movement to an underlying unity behind apparently

different classifications.

9./766. These laws are not just analytic, but also synthetic: law of contradiction is such explicitly, because it can be seen

as speaking of entities that are in some sense identical, although they are in another sense different, while the law of

identity is such implicitly, because one can interpret it as a movement of identification of different object.

10./767. (i) If one interprets these laws abstractly, they are inadequate; (ii) otherwise, they contain also a reference to

implicit differences.

Hegel ends the remark with a note on the ambiguity of the so-called laws of thinking. In their usual

sense, these laws express certain truths certain within any context, that is, logical or analytical truths.

In this sense these laws have no informational value, but they could have such value, if they just

were interpreted as synthetic propositions, that is, as propositions dealing with possible

interrelations between contexts. Thus, the law of identity in its explicit form says only that within

any context all things are what they are: a rather evident, but on that matter also uninteresting

statement. Yet, the law of identity can be interpreted in a more interesting manner, namely, as

expressing the possibility of proper identities: “A = A” expresses the possibility that we could go

forth from an object in one context, find something else in this other context and then identify this

apparently different thing with the original – this is what we do when we follow the lifeline of any

object. Similarly, the law of contradiction in its analytical interpretation says nothing, but the

obvious triviality that different things – thus, anything within different contexts – can be known to

be different and unidentifiable. Although here an explicit reference to the relationship of many

contexts can be made – an object in one situation (possible world, place in space, moment of time

etc.) can be separated from an object in another situation – this relationship is only one of fixed

separation: we abstract from other things and contexts and concentrate on this given one.

Interpreted in a synthetic manner, “nothing can be both A and not-A at the same time” can be seen

as a description of different possible aspects of the same object: one and the same object is A and

not-A, yet not in one context, but only as embodying Aness in one context and not-Aness in another.

B. Difference

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We began with a method of identification – that is, with a method by which one can identify

different aspects of the same structure (a horse yesterday and the same horse tomorrow etc.), but by

which one can also discover new aspects of the structure when one aspect is given. Thus, such a

proper method of identification contains also within itself a method for differentiating or of

discovering differences, although only differences of aspects. We further could abstract a mere

method of identification from this method of differentiation: thus we had found two methods

contained within the same method of identification. It is the task of this section to describe, firstly,

any method of differentiation found within any proper method of identification, and secondly, its

relationship to the corresponding abstract method of identification: we go through several different

structures of difference that could apply to the relationship of the identity and the difference. The

final result of the investigation is that these two are obviously different and even “opposite”

methods, but they are also somehow connected to one another, because they form sides of one

proper method of identification. Thus, the relationship of these two methods provides us with an

example of what Hegel calls contradiction: this relationship has in one sense characteristics that it

doesn’t have in another sense.

The division of the section is quite natural, and indeed, resembles the division of the

forms of reflection in the previous chapter: first we look at a “pure” or “absolute” method of

differentiation which differentiates merely aspects within some structure, then we investigate a

method of differentiation that applies some external classificatory schema to a given set of

independent objects, and finally we discover an example of such a differentiation where the

classification is natural and essential to the objects themselves. Unfortunately, the beginning and

the end of the classification are not independent: absolute difference is already known to be

contained with a proper method of identity, while a structure of opposition is already an example of

contradiction. Thus, the only properly independent structure investigated in this section is actually

the construction of applying external classifications to given objects.

1. Absolute difference

An absolute reflection was a reflection with no given material – e.g. a construction that merely

identified itself as a method of construction – and similarly an absolute difference is a method of

differentiation that differentiates merely aspects within some identical structure: a good example

would be a method for finding new positions of a planet when one position was given. Such a

method of differentiation presupposes a method of identification, of which it is a mere aspect:

otherwise, it wouldn’t be a mere method of “absolute” or “pure” differentiation or it wouldn’t

differentiate mere aspects of some unified structure. Hence, if we are justified in calling a method of

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differentiation absolute, we should be able to find a counter method which can be used to identify

what this method differentiates: we have then two different methods, and thus an example of objects

that can be differentiated and that are in some sense independent of one another – this is the

transition to the next subsection. The subsection has a tripartite division which modifies the usual

differentiation to stages of introduction, analysis and transition: here the introduction is done

before the classifications begin, while the first division analyses the method of differentiation and

the second its relationship to an abstract method of identification.

1./768. A method of differentiation that we have discovered is contained within a method of integrating different

aspects to one unified structure: it is the step of discovering something apparently new which can be differentiated from

the step of identifying what is apparently different.

Suppose we have a method of identifying different appearances of a certain object – say, a method

to identify a certain planet in different places of its orbit by counting where it should be located at

the required moment. This method of identification contains as one step a method of discovering

new positions of the same planet: we may use this method to calculate where the same planet would

be located in another moment of time. In addition to this “differentiating” step, the whole method

contains also a step by which we note that the planet in the calculated new position is the same

planet which was located in the original position earlier, just because we could use this method to

calculate it: this would be the respective abstract method of identification. Through these

submethods two different results are constructed: by method of differentiation we discover many

different positions of the planet, while by the abstract method of identification we find a common

“planethood” behind all these different positions – thus, the “identity” of the planet can be separated

from the different positions it may take.

I just described one sort of “pure differentiation” – indeed, any differentiation of aspects of a

structure would have done – but it would be interesting to know what the simplest sort of

differentiation would be. Now, every absolute differentiation is a “part” of some method of proper

identification or essence of some structure, and as we know, the simplest essence or method of

construction is a method that consists of two phases: one of making an object out of the method and

the other of identifying this object as a mere external shell or appearance of the method – e.g.

writing down the rules of the method and recognising them as rules of a method. Here, the step of

abstract identification is obviously the phase of recognising the method, while the step of

differentiation is the phase of making an object out of the method. Thus, it appears that the “purest”

form of differentiation consists of an objectification of a method: e.g. writing down rules of a

method in a sense creates something that differs from the method itself, namely, its written

expression.

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2./769. 1. Analysis of absolute difference. Such a difference of aspects of some unified structure is absolute: that is, it

is not a difference of independent objects. An absolute difference is a unified structure: different modifications of same

content are differentiated just by the possibility of modifying this content in different manners. Even difference in

general is a unified structure: things can be differentiated within one context of classification – a method of

differentiation unites different states of being within one viewpoint. Two alternative states of being here hold

independently in different situations, while aspects of an essentially unified structure can be constructed from one

another: such constructions could be made in the realm of mere being-here, but there they seemed like arbitrary

movement from one situation to another, while here we have explicitly constructed this movement as capable of

manipulation.

An absolute difference – and indeed any sort of difference, Hegel adds – is a “simple”, or better, a

unitary structure. The necessary point of comparison is a structure of states of being-here, that is, a

framework of many alternative situations or states of being which possibly characterise some

objects. In the case of such alternative situations and objects it is necessary that none of them hold

at the same time, for instance, that a ball cannot be coloured both completely red and completely

blue at the same time: otherwise, these situations wouldn’t be alternative. Now, Hegel admits that

these alternative situations can form in some sense a unity. This possibility of seeing apparently

different situations and objects as a unity is occasioned by our ability to move from one possible

situation to another or to actualise situation types that are at the moment merely possible, e.g. we

could paint a ball that is red with blue paint: I have called this possibility idealisation. Still, within

the chapter on being this construction or movement between different possibilities appeared merely

as something that happened: the constructions were not yet taken as objects, or they were used, but

not investigated. Here, on the other hand, we explicitly look at the “reflections” or methods of

construction as objects. A method of differentiating, say, As from Bs is for Hegel not just a method

for recognising whether a given object or situation is A or B, but a method by which one can, given

A, find or make B, and vice versa: it is arbitrary whether the As and Bs are supposed to be mere

aspects of a larger unity or independent objects or one in one sense and the other in another sense.

Thus, a Hegelian method of differentiation includes all different possibilities in a certain framework

as possibilities: A and not-A are differentiated by a simple “not”, or more generally, a method of

moving from one alternative state to another and vice versa unites these different alternatives into

one classificatory structure.

3./770. 2. Comparison of absolute difference with identity. An absolute or abstract difference is a differentiation of

mere aspects: thus, the method of absolute differentiation contains also a possibility of changing differences into an

identity. An absolute method of differentiation implies thus as possibility of differentiating both an abstract method of

identification and an abstract method of differentiation: here the method of differentiation is in one sense a method of

23

construction and in another sense an aspect of application of such construction. In another words, a mere differentiation

without connection to any identity wouldn’t really differentiate anything: indeed, we could naturally identify as mere

aspects what is differentiated in this manner. Both methods of differentiation and identification can be seen as whole

constructions and individual steps in these constructions: this is the nature of all methods of construction and makes it

possible to start movement without any presuppositions – methods of differentiations and identification can be applied

to themselves.

By identity one could refer, firstly, to a proper method of identification: this is a method of first

finding apparent differences – new aspects from given ones – and then noticing that these

differences are mere aspects of certain identical structure or mere modifications of the same

situation or object. Secondly, identity could refer to the second step of the proper method of

identification and especially to its result abstracted from its relation to the difference from which it

is constructed, that is, to the abstract state of identity. Thus, identity refers both to a method of

construction and to a resulting state. Furthermore, we could then apply the identity as a method to

the identity as a state: we could discover from the state of identity a state of difference which could

then be identified with the state of identity. Here we would have “related a reflection to itself”, that

is, we would have applied a method of construction to itself: this ability is the basis of all “self-

movement”, that is, an application of any method to itself is the basis for using this method without

any given material – e.g. a living thing can apply its force to itself, that is, it can move itself and

thus affect its own bodily condition without the help of any mechanism (or at least it must be able to

do so in some level if it is to have the ability to truly move itself).

This “nature of all reflections” of being “self-applicable” does not concern only the method

of identification, but also any method of absolute or pure differentiation. An absolute, pure or

abstract differentiation is not a differentiation of objects or situations from some given “identical”

reference point: we are not looking e.g. what differs from the tree outside my window. Instead, an

absolute differentiation differentiates aspects within some structure. In the purest or most

undetermined case possible we could apply the method of differentiation only to itself: that is, we

could construct something that differs from the given method of differentiation – e.g. we could

write down rules of a method that differed from a method of differentiation, for instance, of a

method of identification. Indeed, a method of identification is something that we must be able to

construct from any method of absolute differentiation, at least if we are justified in calling it

absolute differentiation: we must able to somehow see that the differentiated things are in a truer

sense mere aspects, that is, we must be able to identify them. Thus, we must always have this ability

of finding something differing from the method of differentiations: that is, the differentiation is not

just a method of differentiation, but in another sense also a possible object of differentiation.

24

4./771. We do not need anything different from a method of differentiation in order to relate it to something different,

like a method of identification: in another sense, a method of differentiation is not something foreign to a method of

identification, but can be identified with it.

Hegel concludes this division by once more summarising the interconnected roles that methods of

differentiation and identification have. A method of differentiation is something that has “in itself”

or naturally a capability of being related to another method: at least to a respective method of

identification. Thus, it is always naturally possible to “differentiate something from differentiation”,

namely identity: e.g. given a method for calculating the future and past positions of a planet, it is

just natural to assume that these positions are positions of a single planet moving through different

situations and not a mere arbitrary aggregate of different objects. On the other hand, a method of

identification can be naturally “identified” with a corresponding method of differentiation: that is,

when we have discovered the new method of identification from the method of differentiation, we

may note that both methods can be interpreted as mere aspects of a proper method of identification

or a method of discovering new aspects of a structure and of recognising them as mere aspects of

this structure. Similarly, a state of identity resulting from the use of the identification can be

naturally identified with a preceding state of difference. Thus, for instance, the common

“planethood” behind different positions can be naturally identified with the range of the different

positions it takes in its journey.

5./772. 3. Transition to diversity. We can differentiate methods of difference and identity from one another and thus

present them as aspects of a larger structure. A method of identification is given as an independent construction, but the

method of differentiation can also be interpreted in that manner: thus, we have differentiated objects that are in some

sense independent – we have constructed an example of diversity.

The previous paragraphs have pointed out that both a method of identification and the respective

method of differentiation can be interpreted as what Hegel calls “reflections in itself”. That is, we

can take either method as a natural reference point or “the designated structure” and interpret the

remaining method as a mere background or step in the “whole construction”. Thus, we could regard

the differentiation of new aspects as a mere temporary stage in the whole process of identifying

more and more aspects of a unified structure (e.g. we could regard the movement through different

positions as being a mere appearance of the common planethood); or we could regard the common

identity apparently behind the different aspects merely as one aspect that can be differentiated (e.g.

we could regard the common planethood just as one aspect of the movement through different

positions). Now, there are two options of interpreting this “set of two independent methods”. Firstly,

we may identify them and explain that they are mere different modifications of one method of

25

proper identification (the variable positions and the planetary substrate could be seen as mere

aspects of the “essential planet”): thus, we would return to the beginning of this section. Secondly,

we can differentiate these two methods as two truly independent and separate objects (e.g. we may

separate the change of the positions from the planetary substrate). It is the second route that we are

about to take here: the result of this interpretation is an example of a structure of diversity –

differentiation of independent objects instead of mere aspects.

2. Diversity

We began the section by investigating absolute differences, that is, differences of mere secondary

aspects of a larger, unified structure. We had a method of constructing such absolute differences –

and here it was more a case of manufacturing than finding these differences, because the

differences had no independent nature beyond being differentiated parts of some structure. We

noted that we could construct from an example of a method of absolute differentiation an example

of a method of identification, because the produced differences were something that could be

identified as mere aspects. Finally, we noted that both the original method of differentiation and the

discovered method of identification could be regarded as independent, but alternative methods:

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thus, we had found an example of a diversity, and hence, also a method for discovering diversities

or for differentiating between some independent individuals.

Hegelian method of differentiation is not just an ability of being capable of recognising

where in a classification some object or situation belongs to: instead, it is more of a capacity to find

a new type of instance from some classificatory scheme, when an instance of a different type in the

same classification has been given. Now, in case of the two methods of identification and

differentiation, the method of differentiating between them should be quite natural: it is natural to

be able to discover a method of identification from an absolute method of differentiation and vice

versa. Clearly, all differentiations of objects or situations are not so natural. For instance, we may

have the ability to differentiate between trees and rocks, because when seeing a rock we may

remember that there are also trees, where this remembering is a sort of construction: still, this

construction is what might be called a “mere construction for us”, and we might not have a proper

ability to construct in any current situation trees when rocks have been given.

The aim of this subsection is to find an example of such natural differentiations or

oppositions when an example of mere diversities is given. This task is actually familiar from the end

of the previous book, where we had to find an example of a natural or essential classification of

objects, when a mere external and arbitrary classification was given. The answer to the problem

here resembles the answer to the problem there: although the classification of some genus to

species or some “realm of objects” to parts would be arbitrary, the division of this division to the

genus or “realm of objects” and to the species or parts isn’t – indeed, this is once more an example

of a necessary relatedness of proper identities and differences. The division of this subsection

modifies the familiar division schema slightly. While the first part introduced the structure of

diversity, it also analyses it somewhat, and the second part then analyses the structure of similarity

and dissimilarity: final part then performs the transition to oppositions.

1./773. 1. Introduction and analysis of diversity. We may divide a proper method of identification, because it is in

another sense a method of differentiation and it is possible to regard differences constructed through it as independent:

the differences are stable, because the differentiated are self-identical.

We begin with a reminder on how the structure of diversity or differentiation of independent objects

was introduced. We were given a structure with a method of identification, that is, with a method of

finding new aspects of the structure and recognising them as mere aspects of this structure: with a

method that constructs new situations and objects and then integrates them at once into a larger

unity. Thus, this method of identification contains as one step a method of differentiation, that is, of

constructing new situations and objects. Even though the results produced by this method of

differentiation can be regarded as “mere show”, the method itself is independent and differs from

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the other step involved in the method of identification, namely, the mere recognition of identities.

Indeed, from viewpoint of either of the two submethods, the other submethod can be interpreted as

a mere aspect or background: that is, both submethods of the identification come with their own

“method of identification”, or although we would have moved from one submethod to another, it is

still possible to integrate the new to the original submethod. Thus, both submethods are more stable

than mere passing phases of the “lifeline” of some structure: they are not just secondary aspects, but

can be interpreted as independent objects. Hence, by concentrating our attention to the two

submethods – taking them as objects – we construct an example of a structure with actually

different and independent objects. The construction has succeeded just because we have been able

to transfer the stability of the larger structure to its aspects and thus to interpret them as independent:

the diversity of the objects or situations is based on their being “self-identical” or able to manifest

different aspects without destruction.

2./774. Ability to separate diverse objects and situations is the form how multiplicity of different objects appears as a

method of construction: while in a framework of many states of being different situations and objects survive only by

being actualised or taken as the designated reference point at the moment, here diverse objects and situations come with

an ability to survive being undesignated or mere background for a moment.

Hegel explicates a bit more how the differences are present, first, in the framework of alternative

situations and objects, and then, in a structure of diversity. As was mentioned in the previous

subsection, alternative states of being cannot be actualised or “designated” at the same time or in

the same situation: if we are in a certain position in some “space”, we cannot be at another position

of the same “space” – e.g. when we are looking at something green, we cannot be looking at

something red. In this sort of structure, the alternatives are upheld only be their being “designated”

or actual at some particular time: in fact, when one alternative is undesignated or “mere

background”, one could almost say that it didn’t exist. In this sort of structure, e.g. an object would

truly vanish, when we happened to lose it from our vision, although it – or something very like it –

could appear and thus “come to life” later: a more reasonable example would be the flow of time,

where one moment may be said to lose its existence, once it has become past.

Here, on the other hand, it is not just the designatedness or “being actual” that is

supposed to support the existence of the diverse situations and objects. Instead, we should now have

also a method for finding any of these diverse objects if we were given one of them: thus, “trees and

rocks are different from one another” would imply that when we were looking at rocks, we would

have the conscious ability to change our reference point to some tree. It is interesting to note that

this “self-identity” of diverse objects appears to be no novelty in Logic. In fact, in the structure of

multiplicity we saw a similar phenomenon: there we could take anyone of many objects as the

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reference point, although it had been a mere secondary background for a while. This similarity of

multiplicity and diversity seems to speak for the fact that Hegel uses some unnecessary

complications in his constructions: we have already found an example of diversity when we found

an example of multiplicity.

3./775. We can differentiate methods of identification and differentiation: if we take them as merely independent, we

abstract from their natural connection to one another. Thus, it seems external that we can apply a method of

differentiation to them: we can take them as mere diverse objects and not as determinate methods of construction.

The structure of diversity should consist of a collection or at least a pair of independent objects to

which a method of differentiation can be applied, albeit only externally: like there is no intrinsic

connection between a rock and a tree lying next to each other, but only the external connection that

we can transfer our attention from one to the other. The problem is that our supposed paradigmatic

example of diversity – the differentiation of some methods of identification and differentiation – is

not as external differentiation as is supposed to be: the two methods are essentially connected as

aspects of or steps in a “larger” method of construction. But we are here concentrating on the

independence of the two methods and we thus ignore that they are supposed to have some essential

relation to one another: we view them merely as two separate objects. Because of this abstraction,

we actually almost forget the manner how these objects are determined as two different methods:

such a determination is on this viewpoint quite external – that we call one of the objects a method of

identification and the other a method of differentiation is of no concern to the objects which in this

sense have no connection to one another – and we may thus interpret them as any two arbitrary

objects.

4./776. 2. Similarity and dissimilarity. When we abstract from the essential relation of the two methods, we are in

differentiating the resulting objects applying a method of construction to other methods, which seem like mere given

objects and to which the differentiating construction appears as a mere construction. The two methods are independent

wholes, and thus their determination as mere methods of identification and differentiation appears as a limited

viewpoint – we can move away from comparing the two methods, which in this context appears as completely

secondary interpretation. Thus, we can separate within the method two aspects: the ability to see them as independent

reference points and the secondary ability to construct them as alternatives to one another – because this classification is

known to be secondary, its construction implicitly contains the possibility to see them as independent, although this

possibility is not explicitly noted at this stage.

Although we noted at the previous paragraph that we could now choose any group of separate and

differentiable objects as an example of diversity, Hegel still chooses to use his paradigmatic

example of methods of identification and differentiation. The obvious difficulty in this choice is that

29

we now have to apply further methods of identification and differentiation to the method that are

taken as objects, making it rather difficult to determine what Hegel means when he speaks of

“identity” or “difference”. Indeed, Hegel says that here reflection has become external to itself:

what he means is nothing more than that we are now using a method of construction – say,

differentiation of given objects – to other methods of construction, which serve thus as material for

another construction – we use one method of construction to differentiate two other methods from

one another.

Hegel starts a closer investigation of his paradigmatic example of diversity by noting the

familiar fact that the two methods of construction which are the objects of differentiation can be

seen as “unities of themselves and their other”: that is, we could take either one of the methods of

identification and absolute differentiation as the reference point and then we would interpret the

other method as a mere background and a mediating step in the reference or “designated”

construction – we could say that differentiation of aspects is a mere step towards identifying them,

or we could say that identifying or integrating a structure would be a mere step in discovering some

new aspect that has not yet been integrated into the whole structure. In terms of Hegelian parlance,

we could “reflect” either one of the methods “into itself”. A similar, albeit a bit weaker construction

should be possible for all merely diverse objects. Say that we have a rock and a tree beside it: we

then have the possibility to take either of the two as the centre point of our attention, thus relegating

the other to the status of a mere background.

Because of this possibility of seeing either of the diverse objects as the essential one,

the differentiation of them appears rather external. Remember that a Hegelian differentiation means

the infallible ability to go from an arbitrary position in the differentiation to another: for example, if

we could differentiate reds and greens in the Hegelian sense, we could discover an example of

something red when a green object was given to us and vice versa. Furthermore, in a Hegelian

differentiation we have the possibility to see the differentiated situations or objects as mere aspects

of the whole “differentiation structure” or classification: the method of differentiation would be a

Hegelian essence to which the differentiated things would be related as a mere outer shell. If the

differentiation of the diverse objects would be natural or essential to them, it would be more

adequate to say that these objects are mere aspects in a larger structure – somewhat like when we

would differentiate the seasons of a year, these seasons would be natural to take as mere secondary

parts within the development of the whole year, if we could show that one season would necessarily

follow another.

Now, in a structure of diversity it is presupposed that the independence of the diverse

objects from one another is the most correct assessment of them: a method of identification, for

instance, is not a method of differentiation, because we can interpret the method of differentiation to

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be a mere partial step in the method of identification, or a rock differs from a tree, because we can

ignore the tree when we look at the rock. Thus, the ability to connect the different objects by some

method of differentiation – by putting them in some classification structure, as it were – must be

something secondary: it is a mere construction or an interpretation which fails to see the objects in

an adequate manner – like it is indifferent to the rock that we can change our attention from it to the

tree. Albeit this classification of objects is external, it in some sense is “the whole” of the structure

of diversity, Hegel says: if we know that a differentiation – or connection – of objects is arbitrary to

them, we may abstract from this differentiation and conclude that the objects just are independent –

e.g. we may note that our choice of a reference point is completely external to both the rock and the

tree, which would exist without having any connection to us or to each other. Although we can

hence always go back from our external classification of objects and see them as independent, this

possibility is not yet explicitly present in the structure of diversity: the classification of objects

appears only as a mistake and a false or at least distorted interpretation of the objects.

5./777. The identification and the differentiation as applied to some diverse objects – like to the previous pure methods

of identification and differentiation – are respectively an abstractive and an external method of construction. Here, a

method of identification is abstractive, because the method of differentiation is regarded as arbitrary in comparison: it is

the ability to take any of the diverse objects as independent and essential – we can as well suppose that this method of

identification is same for all objects, because their difference is external to this ability. The method of differentiating the

different objects is an external construction: we call the objects e.g. identity and difference, but this is a mere

unessential construct.

The paradigmatic examples of the structure of diversity are the methods of identification and

absolute differentiation: of course, we are speaking here of some particular method of identification

and a respective method of differentiation. Furthermore, any example of diversity involves also a

method of identification and a method of differentiation, namely, as methods that can be applied to

some given diverse objects: in the paradigmatic example, these applied method differ obviously

from the methods to which they are applied, although in some sense or context we may say that

“they are same methods”, that is, they have a similar structure. Hegel characterises the method

applied to diverse objects: the differentiation is an external reflection – this is a familiar expression

– but the corresponding identification should be a reflection “an sich”. What is this “Reflexion an

sich”? Foremost, it is not the same as reflection in itself. Instead, as the term “an sich” should by

now tell us, it is an “abstract reflection”: that is, when we apply this identifying construction to the

diverse objects, we ignore the fact that we can also apply a differentiating reflection to them – when

using this construction, we imagine that the diverse objects are completely segregated from one

another. How this segregation of objects is an application of a method of identification, one might

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wonder. In a sense, we are here not applying a method of identification across different contexts,

but within one context: we choose any arbitrary context with one specific object as its centre and

identify other objects as mere background of this designated object. Through use of this method of

identification we, as it were, shield this one object into a world of its own, although beyond it there

are in a wider sense other contexts with other reference points: e.g. we may concentrate on a rock

and simply forget that there is a tree next to it. Thus, we can isolate every object into its own

environment or viewpoint by applying the method of identification to that particular object alone. In

this application of the method, the object to which it is applied is arbitrary: anyone of the diverse

objects would do, and it is just a coincidence that there happens to be several objects to which this

application can be made.

The word “an sich” also implies that the application of the identification to the objects

is – or at least appears to be – more essential than the application of the differentiation. Indeed, the

differentiation or classification of the objects should be external. Hegel refers once again to the

paradigmatic example of diversity, when he says that the classification of the diverse objects as

identity and difference is arbitrary: similarly, it is indifferent to the objects that we happen to call

one of them a rock and another of them a tree. Yet, this terminology of identity and difference has

also a more general meaning, as we shall see in the following paragraph: Hegel intends to say that

any – or at least any twofold – external classification could be described in terms of identity and

difference.

6./778. We may call identity in a mere unessential classification similarity and difference in this same classification

dissimilarity: here we construct in some external manner a context with one arbitrary reference point and call anything

identical with it similar and anything different from it dissimilar – such an external classification does not touch the

classified objects, but comes from some external viewpoint.

A differentiation of any kind consists of steps of identification and differentiation proper: we first

determine some starting point as identical and then follow by differentiating something from it.

Thus, in our paradigmatic example of diversity, we might begin by “identifying” some method of

identity – we designate it as the reference point and note that it is same as it itself is – and then carry

on to differentiate the corresponding method of differentiation from it – we note that this method is

not same as the designated reference method. Now, the choice of the reference point in the case of

diversities is arbitrary: we might as well have begun from the method of differentiation, and

similarly, it is arbitrary whether we should say that a rock differs from a tree or that a tree differs

from a rock. Furthermore, there might not just be one possible differentiation of a group of objects,

but several, which differentiate and identify things in different manner, and the choice of the criteria

of differentiation seems equally arbitrary. Thus, if we are given a triplet of a rock and a tree and a

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bird flying in a sky, we might compare all objects to the tree as a living object and conclude that the

bird cannot be differentiated from the tree, but the rock can; on the other hand, we might compare

the other objects to the tree as an object on a ground and then we could differentiate the bird, but

not the rock from the tree. Here Hegel implies a curious and rather interesting definition: similarity

is an identity in some possibly arbitrary context. Hence, “red objects are similar” can be also said in

the form “if we distinguish objects according to their colour, then all red objects must be identified”:

of course, in some other context the red objects might have to be separated from one another.

7./779. 3. Transition to opposition. Only an external construction or comparison connects the states of similarity and

dissimilarity by being able to move from one to the other: because this comparison is external, we should be able to

isolate these states from one another. This sort of differentiation is a modification of absolute differentiation, because

one cannot identify the states it goes through as its dependent aspects: instead, by using a method of identification we

would destroy the classification and make the classified objects reveal their independency.

When we apply the external differentiation to a group of diverse objects, we divide, as it were, the

domain of these objects according to an arbitrary, twofold classification: that is, we speak of things

that are similar with some reference object according to some criteria and of things that can be

distinguished from that object according to the same criteria. Now, because these two divisions of

the original group consist of independent objects, the two groups are also independent of one

another: say, if we divided the objects of a landscape into rocks and trees, we could easily think that

the rocks might exist there without the trees. Of course, we have the ability to construct an example

of one group from an example of the other group, but this ability is based only on the fact that we

happen to know examples of both groups: if only one group was given to us, we wouldn’t have any

necessary ability to construct an example of the other group, because all the objects are presumably

independent in this context. As Hegel says, the construction of absolute differentiation has been, in

a sense, “negated”: our differentiating construction is dependent on the existence of a suitable set of

objects – we cannot construct or move our attention to rocks from trees, if we are not given both

rocks and trees beforehand. Thus, we cannot justifiably assume that the states of “objects similar to

some x” and of “objects dissimilar to the same x” would actually be mere aspects of a larger

structure, that is, we cannot identify these states and objects within them with one another. The only

way we can use identification is to identify the different objects with themselves, that is, to separate

them from one another: the use of identification would actually destroy all connection between the

objects.

8./780. Although we could in this context apply notions of similarity and dissimilarity to same pair or group of objects,

we would have to separate these applications into different viewpoints: different objects can be indifferently described

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as similar or dissimilar according to different external viewpoints, which have no connection to one another.

The external differentiation or classification of diverse objects constructs some viewpoint in which

the objects are characterised in a certain manner, although according to another viewpoint they

might be characterised in a completely different way: thus, although trees and rock are similar in

being located on ground, they are dissimilar in one being living and another lifeless object. How

does this construction of contexts differ from the construction of different structures in Logic?

Firstly, these viewpoints and their construction should be completely external to the objects

involved: they are merely arbitrary ways of interpreting the objects, but these interpretations are not

guaranteed to be essential to these objects. This externality of the interpretations is caused by the

second point of difference, namely, that the moments of such a classification are only contingently

connected. Thus, we can construct from a viewpoint where a tree and a rock are identified a

viewpoint where they are differentiated, but this construction is based only on the fortuitous event

that we can beforehand differentiate trees and rocks in some manner: that is, we do not have a

general and infallible method for constructing contexts where objects are differentiated from

contexts where they are identified. In Logic, on the other hand, we are interested in finding just such

infallible methods of construction – methods that work for any object or situation of the correct type

and that therefore tell something essential of the type of objects or situation involved: e.g. if we can

infallibly construct quantities from qualities, we know something essential about the dispositions of

all qualities.

9./781. By separating aspects of similarity and dissimilarity into isolated viewpoints we make it possible to move away

from them, although all this separation was done to avoid contradictoriness: similarity and dissimilarity are meaningful

structures only when they are essentially connected into one classification – by isolating them we break the possibility

to compare them.

The parts of a classification are supposed to be external to one another and to the classification

connecting them: thus, in a landscape full of trees and rocks, if we would abstract from the fact that

the trees and rocks happen to exist in the same location, we would have no infallible method of

constructing an example of rocks from an example of trees or vice versa. We might say that the

trees and rocks in the previous example form their own universes which just happen to be put

together, and generally, classes of independent objects are independent of the existence of other

classes: ultimately, the objects themselves are independent of one another and it is arbitrary that one

has collected them into such and such classes – the classification could have been done in a

completely different manner. Now, because of the independency of the classes, we can separate

these classes into different “worlds” or domains with no connection to one another and with no

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possibility to compare them.

The consequence of this isolation of classes is that it becomes meaningless to speak of

dissimilarities. We should have chosen one object as a reference point and then classify other

objects according to whether they are like or unlike it according to some criteria: rocks are like this

rock, but trees are unlike it. If we now segregate the two thus formed classes from one another, it is

meaningless to say that the class of “dissimilars” would contain any dissimilars, because there

wouldn’t be any reference object to which they could be compared. All the classes would contain

only “similars”, that is, objects that are similar to one another according to the relevant criteria: and

even this concept of similarity would lose its meaning, if there was no meaningful dissimilarity to

compare it with – in this context, all things would be similar according to the relevant criteria, thus,

the similarity of all things in it would be a mere tautology. Of course, one could classify e.g. the

class of rocks anew and thus find new similarities and dissimilarities: still, a similar separation of

the new classes could follow, when no classes are supposed to have any natural connection to one

another.

10./782. If we completely isolate the different classes, we can as well identify them as mere modifications of one unity

and thus move completely away from the differentiated classification. A similar unification of the classes is done in a

comparison, which can move from taking one class as designated to taking another as designated. The comparison is an

external unification of the classes, but we have seen that it is natural to unite these classes: when we isolate the classes

from one another, we lose the ability to distinguish them properly.

When a Hegelian differentiation of a group of objects into more than two classes is given, it is

possible, in the context of that differentiation, to assume that the different classes are mere aspects

of the differentiating structure: in such a differentiation we can construct examples of one class

when an example of another class is given, thus making it possible to move from the context of one

class to the context of another class – the method of differentiation works like a Hegelian essence.

Of course, in the case we are investigating now – the classification of objects into those similar to

some reference object according to some criteria and those not similar to it according to the same

criteria – this method of differentiation or “comparison” is supposed to be external: it is only the

comparer who connects the different classes together and it is quite possible and more natural to

separate these classes from one another.

Suppose then that we separate the two classes and abstract from the external

connection imposed on them by the comparison. Then we are faced with two independent classes,

neither of which can be described as different from other: such a description would already require

comparison and application of some external differentiating structure. Instead, we might note that

both of these classes contain objects that are similar to one another according to the relevant criteria:

35

we thus have one criterion by which to identify these classes. Thus, we could well suppose in this

case that the two classes are actually mere modifications of the same class of objects. This

reinterpretation of the group of different classes resembles the possibility of interpreting a group of

apparently independent objects as a mere group of aspects or modifications of one object, because

the objects have no differentiating characteristics: here a similar construction has been applied to

classes instead of objects.

11./783. Whether we compare or isolate the class of objects similar to a reference point and a class of objects dissimilar

to it, we can always justifiably interpret them as mere modifications of the same class. This possibility of changing the

two classes to one another can be explicitly constructed when we compare either of the classes with the reference point

abstracted from the classes: then the first class consists of objects that are identified with an object that in another sense

is not identical with them, while the second class consists of objects which are named dissimilar only according to an

external reference point. Thus, in comparison with the reference point, the two classes change their significance in some

sense: a class of similars becomes a class of dissimilars and vice versa.

In the previous paragraph we compared the construction of a unified structure from classes of

“similar” and “dissimilar” objects to a construction of unity from a group of many independent

objects, and there are further similarities to be found. Perhaps the most interesting similarity is the

fact that Hegel needs to go over both constructions in three different ways. Now, in the case of the

transition from “Many” to “One”, these three different constructions could be divided into two sorts:

firstly, there were two constructions that relied on justifications that were not specific to the nature

of the independent objects – in these constructions Hegel merely noted that the objects in question

had some similarities and could thus be interpreted as “being one” – while secondly, one

construction was based on the specific of nature of these objects, namely, on the fact that we could

take anyone of them as the reference point and regard others then as mere background aspects of

this one unity. Similarly, here the two first constructions relied on justifications that could be

applied to any sort of external classification: we can make a subjective and connecting comparison

within all classifications and we can isolate classes in such a manner that no differentiating

comparison is possible. The third construction, on the other hand, should be specific to the classes

of “similarity” and “dissimilarity”: that is, it should show us a natural method for changing what is

similar in some sense to dissimilar in another sense and vice versa.

The third construction is based on comparing both of the classes with what Hegel calls

reflection “an sich”. As we should remember, by this Hegel referred to the ability to consider

anyone of the diverse objects as independent and merely self-identical object, outside any external

classification: we are therefore supposed to compare the classes of similarity and dissimilarity with

the reference objects that determine which objects are described as similar and which as dissimilar.

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Now, the transformation of dissimilar to similar is quite easy to understand. An object is dissimilar

in comparison with some external reference point: thus, all we need to do is to choose another

reference point from the same class of objects as the object to be compared and we have naturally

changed the “dissimilar” object into “similar” object.

The transformation of similar into dissimilar seems more problematic, because the change of

the reference point from the member of one’s own class to a member of another class does not seem

as natural as the change to another direction. Here Hegel uses another strategy: the things that are

identified in one sense can be differentiated in another sense. Thus, supposing we are saying that

one rock is similar to another, we could also point out some difference that separates them: if

nothing else, at least their position in space. But what about the case of comparing an object with

itself? Here we can at least interpret different aspects of the same object as independent entities

constituting that object: the object as a reference point differs in some sense from the same object as

an object to be compared to that reference point – the same object works in two different roles, and

it is possible to distinguish these two roles, hence, making similar into dissimilar.

12./784. The classification of similar and dissimilar objects was supposedly a mere construct in comparison with the

independency of diverse objects, but it is possible to interpret their relation in an opposite manner: the objects differ

only because we can distinguish them in some classification of similar and dissimilar objects, while their independence

shows merely their abstract identity, which can be constructed as a mere aspect of a larger structure. If the difference of

the objects is merely external, we might as well interpret the objects as non-independent: by isolating the objects we

make it possible to discard the difference between similar and dissimilar objects – thus, we can interpret the different

objects as mere modifications of one underlying unity or as essentially connected in opposition.

We have seen that it is possible to make object that is in some sense dissimilar into similar – by

changing the reference point into something that is similar with the object – and that it is possible to

interpret an object that is in some sense similar as being dissimilar – by noting that the compared

object and the designated reference point are at least different aspects of one object and thus

distinguishable. We might think that this possibility of transforming aspects of this basic

classification into one another would not mean anything to the objects themselves, because the

classification is meant to be external: we do not need to describe any object in terms of an external

differentiation, because we can merely take it as an identical point within its own isolated universe.

Problem is that this possibility makes it quite possible also to identify these objects:

this is a familiar move used in constructing unity from given many objects – if there is discernible

difference between objects, we might as well say that they are mere modifications of the same

object. We have thus a possibility to interpret apparently independent objects as aspects of a larger

structure: the isolation of objects leads to their complete identification. This does not mean that we

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would have completely denied their difference from one another: Hegelian constructions are no

proofs. Instead, Hegel has merely shown that the independent objects can be naturally regarded as

mere modifications of a larger unity, but it is still true that they can be also differentiated from one

another – this is a specific characteristic of the structure of opposition.

One could note that this cannot be the final result to the problem of discovering an

example of opposition: although we might be able to interpret a group of apparently independent

objects also as a group of mere modifications of one object, this wouldn’t show that these objects or

aspects would have any “natural” or essential connection to one another. But the meaning of the

previous investigation was different: it was merely meant to show that the seemingly more essential

independence of diverse objects can be actually valued as inessential compared to the

differentiation of objects according to some classification, because on the basis of the mere

independence of the objects they cannot be distinguished. Furthermore, the isolation of an object

from other objects into a limited domain of one object reveals only a situation abstracted from

general surroundings: as we should know by now, there are natural constructions by which to

discover or manufacture connections to other situations or contexts when such an abstract context is

given – thus, even if we would try to segregate an object from its surroundings, we might construct

a new structure where the object in question would be connected to other objects.

The proper example of opposition is then provided by the “similarity” and

“dissimilarity” or methods of finding similarity and dissimilarity – more precisely, a method of

finding from a group of given object those which are similar to a given reference objects and a

method for finding from the same group those which are dissimilar to the same reference object.

These methods are known to be naturally connected to one another: both methods contain versions

of the other method as steps within them – the method of similarity identifies objects or aspects that

can first be distinguished and the method of dissimilarity differentiates objects that can be first be

described as similar to themselves. Similarly, in the case of constructing an example of essential

classification when only an arbitrary, quantitative classification was given, Hegel did not attempt to

interpret the latter classification as somehow essential, but showed that the capacity to divide the

indifferent quantitative realm into arbitrary parts and the capacity to return any such classification

into the indifferent identity were essentially connected: the current construction of an example of

opposition is a modification of this former construction.

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Remark.

The remark continues the series of “laws of thought” with a law or proposition of diversity:

actually, such a law was indeed spoken of by e.g. A. F. Hoffmann, who meant by it what is

nowadays known as Leibniz’s law of the identity of the indiscernibles, although Hegel thinks this

law is more akin to the law of opposition. Indeed, the main purpose of the remark is to point out the

relative inessentiality of all mere external diversities: such a context with mere quantitative

differences is possible only because of the interconnected abilities to identify and distinguish

objects in some manner in an otherwise undetermined domain of objects.

1./785. We can express diversity as a proposition separate from the proposition of identity.

2./786. This proposition says “everything is different” or “there are no two completely similar objects”. The law of

diversity is in a sense opposed to the law of identity: while the law of identity presents the object as undetermined, the

law of diversity presents it as determined – thus, it separates at least two aspects of the same object.

The law of diversity “all things are different” can be, like the previous “laws of thought”, read in

two distinct manners. Firstly, it could just say the tautology that if there are different things, then

there are different things. Secondly, it has the more interesting reading as confirming the existence

39

of a method by which it is possible to find an example of a structure with different objects or

situations. Clearly this statement says something more than the law of identity in its abstract sense,

which merely states that there happens to be (at least one) object that can be identified with itself:

thus, while the law of identity describes merely the conditions within one context, the law of

diversity presupposes the existence of many contexts or situations (one for each object that is

supposed to exist). But how is this difference of two sorts of structures – one with mere single

situation or object and one with several situations or objects – supposed to produce a difference

within an object? Here it is a question of an aspectual difference: we can regard object as

“undetermined”, that is, as isolated from other possible objects, and as “determined”, that is, as

related to other objects. These two different aspects can then be segregated from one another, which

was the point in the construction of dissimilarities from mere similarities.

3./787. “All things are different” is in a sense tautology, because “things” expresses already a diversity of objects.

“There are no two completely similar objects” – Leibniz’s law of the identity of indiscernibles – expresses something

more: it states that things cannot be diverse, unless they are in some sense dissimilar, or that there are no mere

numerical differences.

4./788. Leibniz’s law should be justified, because it is commonly required proof for any combination of all apparently

different things. We should show how one can construct diversities from identities and dissimilarities from diversities:

we have seen that an external diversity can always be disregarded, if there is no essential classification of objects where

the moments of the classification were naturally connected.

Hegel moves quickly from the “law of diversity” to the better known law of the identity of

indiscernibiles: “there are no two things that are completely similar or indiscernible” – the

proposition does not just state the existence of many things, but also notes that there must be some

classification in which these things can be separated. This law was made famous by Leibniz in his

correspondence with the English Newtonian Clarke. Unfortunately, Leibniz gave no proof of the

principle that would have convinced Clarke, although he did not think that the pretty anecdote of

the test of trying to find completely similar leaves made by ladies of the court would satisfy the

requirements of a proper proof. Leibniz tried to base this principle on the law of sufficient ground:

if there could be two completely similar things God couldn’t have decided in which order to create

them – Clarke noted quickly that God could have just arbitrarily chosen to create them in some

order.

Hegel’s “proof” of this law is, once again, no proof in the traditional sense of the word:

Hegel does not show that the “law” would function in all contexts, but only that we can find some

contexts in which it is clearly true, and indeed, that the existence of diverse entities as such depends

on the ability to find such contexts. Hegel’s “proof” should be familiar to us by now. Firstly, we

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must show that given any identical structure it is possible to find at least some internal differences

within it. And given any group of different objects, it must be possible to find a context with

essential differences. For instance, if we want to differentiate between two completely similar

appearing balls, we must put them in a situation where one is left and the other is right: although the

place of the balls in this “left-right”-classification can be changed either by moving the balls

themselves or by moving ourselves, the distinction between left and right itself must be essential –

otherwise, we couldn’t by itself tell which of the directions in our field of vision is left and which

right. In the case of the diverse objects – e.g. the two similar balls – this possible construction

implies an ability to separate the things themselves in some context, even if this context would be

arbitrary to the objects themselves.

5./789. The identity of indiscernibles moves us beyond mere diversity: two different objects are similar in one sense (at

least they are objects) and dissimilar in another (otherwise they wouldn’t be diverse) – thus, their contexts of similarity

and dissimilarity form an opposition.

6./790. We can undoubtedly interpret the two contexts as mere external interpretations: thus, it would be a mere external

construction that unites two seemingly different situations – the [apparent] contradictoriness would have been merely

transferred from objective to subjective.

The law of the identity of indiscernibles in its Hegelian sense tells us that any different objects can

be put in a context where they can be differentiated from one another. Furthermore, Hegel points

out, all objects can also be identified with one another in some context: at least in such an abstract

context where all things are identified, that is, where we identify things merely on basis of their

being things. Thus, we can naturally move from a state where some things are identified to a state

where they are differentiated and vice versa: these states form thus an essential classification or

opposition. Hence, if the identity of indiscernibeles is justifiably accepted – that is, if we truly have

a method for differentiating all separate things that come across us – then we have also a possibility

of constructing an instance of opposition.

One might object that these states are mere external interpretations of the relationship of the

given objects and that the constructed opposition is such that depends on the subject thinking of it.

Hegel here uses the misleading word “contradiction” of something that is no logical contradiction:

he is speaking of the fact that a class of objects can appear in many forms in different contexts –

they could be identical in one sense and different in another – and discusses whether this

aspectuality belongs to the “world” or to the class of objects or whether it is caused by the

consciousness looking at these things. He notes that moving the aspectuality to subject does not

change the fact that we can construct an instance of such aspectuality in some context – although it

would be a mere subjective context.

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3. Opposition

The simplest form of differentiation was a differentiation of non-independent aspects of a structure

that could be at once identified with and integrated back into the unity from which they were

distinguished. Yet, at least these steps or methods of differentiation and identification could be

interpreted as independent objects which were connected in a merely external manner. The next

issue to be discussed was then any group of such independent objects and their external

classification through noting which of the objects were similar to an arbitrary reference object

according to arbitrary criteria and which were, on the contrary, dissimilar. We quickly noted that

not all of these classifications or differentiations could be external, because otherwise it would be

too easy to just interpret the apparently different objects as being mere modifications of one object.

Furthermore, the methods of identifying and differentiating objects within some context according

to some criteria – that is, methods of discovering similarities and dissimilarities – contained in a

sense one another: in order to separate an object from some reference object, this object must be

identifiable with itself, and in order to identify an object with some reference object in an external

manner, these objects must be in another sense separable, at least as different aspects of the same

object. These methods formed then a paradigmatic example of an essential classification or

opposition. The next task should be to show that an opposition is an example of Hegelian

contradiction. Although this requires only a bit of analysis, Hegel has left it to the next section,

while in this section he merely goes through the primary characteristics of oppositions by analysing

the just constructed paradigmatic instance.

1./791. The most complex form of differentiation is opposition, aspects of which are in some sense identical, but in

another sense different.

The task of this section is here identified as realising perfectly the idea of a determined reflection,

that is, of an (interpretative) construction that is applied to objects distinct from the method of

construction itself. A determined reflection, as it were, characterises an object in some manner –

places it in a certain classification, perhaps – and this characterisation is supposed to be essential or

natural: this is just the meaning of Hegelian opposition. Hegel also states that the opposition is a

“unity of identity and diversity”. The “parts” or “sides” of opposition or essential classification are

independent in some sense – this is no mere absolute differentiation – but they also are part of larger

structure: one can naturally construct one side of the opposition from another. The latter

characteristic differentiates opposition from mere external diversity.

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2./792. Mere methods of identification and differentiation were aspects of a method of differentiation which could be

taken as the whole method. Methods of similarity and dissimilarity were not just separated from one another, but also

from what was supposedly essential and they thus appeared as mere secondary given states: when one applied these

methods, the corresponding states were actual, but otherwise they weren’t.

Hegel looks one again to the road travelled thus far, and especially to the previous forms of

differentiation. The absolute differentiation contained the steps or “parts” of identification and

differentiation. Both of these moments “reflected the whole”: that is, one could regard the whole

consisting of both steps either as a method of differentiation or as a method of identification,

depending on what order these steps were taken: either the whole method was one of constructing

differences on basis of some identical structure or one of identifying apparent differences as mere

aspects of one structure. In the structure of diversity, the methods of differentiation and

identification were applied to something external to them, that is, to a group of given objects. These

objects contained “reflections”, as they came with an ability to be regarded as reference point within

that group. Thus, we had not just two methods of construction, but at least three: one for identifying

different objects, one for differentiating them and one for taking the object completely apart from

their relation to one another. In comparison with this third construction, the two former and the

results of their application were thought to be external or mere secondary states: their relation to

that third was similar to a relation of states of being to an essence behind them. Thus, the states

resulting from the use of these secondary constructions were actual or designated only in some

sense or in some situation, namely, whenever one happened to construct them: e.g. a rock and a tree

should be similar only when we identify them according to some criteria and dissimilar only if we

differentiate them according to other criteria.

3./793. In opposition these in one sense merely secondary aspects are in another sense independent and essential: when

we can interpret methods of similarity and dissimilarity as essential, they are an example of opposition. These methods

are essential if they are shown to contain the other method as a step in themselves: indeed, a method of similarity

identifies objects that are in some sense dissimilar, while a method of dissimilarity differentiates objects that are in

some sense similar. Hence both methods are “wholes” or they contain the other method as an aspect in some sense:

because the other method can be used to construct states differing from those constructed by the first, states of similarity

and dissimilarity point naturally to alternative states of being.

The construction of the methods of similarity and dissimilarity as forming an essential classification

or opposition happened through discovering that these method could be “reflected into itself”, that

is, interpreted as the reference method that contains the other method as a mere step in itself. Thus,

in a method of similarity, we begin by finding some reference point that can be differentiated in

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some sense from all members of a group of objects and then note that these objects can be identified

in some context with the reference point. Similarly, in a method of dissimilarity, we begin by

finding some group of objects that can be in some sense identified and differentiate them from some

reference point. In this sense, the relationship of the methods of similarity and dissimilarity

resemble pure methods of identification and differentiation. The difference between these two pairs

of methods is that the methods of similarity and dissimilarity have more independence, because of

the relative independence of the states produced by them: if we apply the two methods into the

same group of objects comparing them with the same reference point according to the same criteria

of identification, the resulting states of similarity and dissimilarity divide the domain of objects into

two sets with no common objects. The natural connection between the two methods implies that one

type of state can be “annihilated” by changing it into a state of opposite type: if one group of objects

is in some sense an example of similarity, it can be changed into an example of dissimilarity, thus

“destroying” the similarity in viewpoint of that group of objects.

4./794. A method of similarity which explicitly contains a method of dissimilarity as its step is an example of something

positive, while a method of dissimilarity which explicitly contains a method of similarity as its step is an example of

something negative. In other words, whenever we have an essential classification of methods or of objects and states

with abilities that can be applied to the situation where they happen to be put, then anything with an ability to produce

something similar from a given situation is positive, while anything with an ability to produce something dissimilar

from a given situation is negative. When a positive method is applied to the classification of positive and negative

methods, it recreates a state of dissimilarity: when a negative method is applied to this classification, it changes the

classification into a state of similarity – thus, methods of similarity and dissimilarity can both be used to construct states

of similarity and dissimilarity.

The relationship of a method of similarity and a method of dissimilarity is an example of Hegelian

opposition or necessary classification. Indeed, it is not just an example, but a paradigmatic example:

by looking at it carefully, we should note the important characteristics of all oppositions. The most

crucial aspect of Hegelian oppositions is that its parts or aspects – the classes that are opposed or in

an essential classification – should contain entities (objects or situations or anything else) that have

some intrinsic abilities by which to affect their “environment”. These objects should be able to

“reflect in itself what has been posited”: that is, when we construct some situation where the objects

in question have been placed, then these objects come with an ability to reconstruct the situation in

a manner natural to the class to which the objects belong – this reconstruction could mean either

interpretation or real modification of the situation.

Furthermore, the nature of these classes of objects and their abilities is even further

restricted. A Hegelian opposition consists always of two sorts of classes. Firstly, there is the class of

objects that come with an ability to “reflect what is posited in similarity”: that is, objects of this

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positive class come with an ability to faithfully reproduce any situation – thus, a method of

similarity allows us to find what is similar to a given object. Secondly, there is the class of objects

that come with an ability to “reflect what is posited in dissimilarity”: that is, objects of this negative

class come with an ability to change any situation – thus, a method of dissimilarity allows us to find

what is dissimilar to a given object. In addition to the opposition of similarity and dissimilarity, we

might mention the opposition of theoretical and practical abilities of human spirit: a human being

can either theoretically reproduce its environment or practically change it. A more abstract example,

which Hegel himself shall study in a remark, is the relationship between positive and negative

numbers,

Now, if one can apply the abilities of positive or negative objects to any situation

where they happen to be posited, one could also in some sense apply these abilities to the

classification constructed of them, that is, to a situation where they are compared with one another.

If one applies an ability of a positive object to the classification, one constructs a faithful

reproduction of it, that is, a situation with many different and even opposed objects: for instance, if

we are given an opposition of states of similarity and dissimilarity and we are asked to find

something similar to this opposition, the result is a state of dissimilarity – or if we are investigating

the theoretical and practical aspects of ourselves, we may theoretically model this separation. In any

case, the result of the application is “a negative state”, while the result of applying an ability of a

negative object to the same classification is “just the opposite”: we end up by assimilating the

differences into one unity. For instance, if we must find something that is dissimilar to an

opposition, the result must be a state of similarity, while we have a practical ability to unite the

apparent distinction of our theoretical and practical aspects.

5./795. Positive and negative objects can be interpreted as being independent of their classification, because they

contain the ability to construct the whole opposition: they can be interpreted as mere aspects of the classification,

because they can be compared with one another. Because of their independency, they contain the ability to construct the

other side of the opposition from themselves. Thus, in one sense a state of the opposition contains the alternative state

of the opposition as a mere aspect: in another sense this relation holds vice versa – one side holds in one context or

situation, because the other side holds in other context or situation.

Positive and negative objects and states are determined by their ability to construct similarity or

dissimilarity, that is, to reproduce or to modify something. As we have seen, positive objects also

contain a secondary possibility of constructing dissimilarities and negative objects contain a

secondary possibility of constructing similarities. These secondary possibilities have a “positive”

and a “negative” consequence for the objects and states containing them. Firstly, because of these

possibilities, we can interpret any of opposed objects as the essential or reference point: e.g. we may

45

say that positive objects and states are the true substrate and that the supposed negative objects and

states are mere steps in the possible process of applying the abilities of positive objects and states –

a method of dissimilarity can be regarded as a mere step in the use of a method of similarity, and

our practical skills may be seen as mere mediatory links for our theoretical abilities. Secondly,

because both sides of the opposition have such abilities, it seems equally adequate to interpret both

of them as independent objects or states of being: thus, any side of an opposition contains an ability

to construct an alternative object or state of being, that is, a context where the original object or

state of being does not exist or isn’t valid. For instance, through a method of similarity we may find

a context with no method of similarity – that is, a context with a method of dissimilarity – and with

our theoretical skills we can find aspects of our being that are not theoretical.

6./796. (i) Positive and negative entities are in one sense mere aspects in the structure of opposition, which unifies them:

it is arbitrary which of them should be called positive and which negative, because both are mere alternative states. (a)

According to one viewpoint, a side of opposition is instantiated only in contexts where another side is also instantiated,

or it can be seen as a mere construct; b) according to another viewpoint, it is instantiated only in contexts where the

other side isn’t, or it can be seen as independent – in any case, all of these possibilities are contained in one structure.

Hegel continues by isolating three aspects of the opposed entities and of their relations both to one

another and to the structure of opposition: we are looking at the positive and negative entities from

three contrasting and even mutually exclusive viewpoints. The first view emphasises the role of the

whole structure of opposition: this structure contains a method of finding an example of one

opposed side, when the other is given, and can be therefore regarded as an essence of these opposed

sides. In light of this viewpoint, the opposed sides appear to be of a mere secondary importance, or

they seem like mere aspects of the general structure: true, we can regard them as independent of one

another, but we can also see them as essentially related to one another, and it is the second point

which in this context is the more informative or essential. Thus, we could say that the methods of

similarity and dissimilarity are of no importance in comparison with the whole methodology of

comparing objects with one another, or that the whole person is more essential in comparison with

its theoretical and practical abilities. This viewpoint ignores the individual characteristics of the

opposed sides: it is indifferent to the general structure which side is taken as positive and which as

negative, as long as these sides are just essentially related to one another.

7./797. (ii) In another sense we can regard the apparently positive and negative entities as independent of the opposition,

which is natural interpretation of the objects in question, but still a mere interpretation. Thus, both sides are actually

independent of one another, and it possible to interpret either one as the positive or as the negative.

46

If the first aspect of the opposition emphasised the essentiality of the structure of opposition, the

second aspect concentrates on the independence of the objects or states involved. We can regard the

opposition or the classification of objects as external, that is, we can abstract from the possibility to

construct the other side of the opposition and thus return to the stage of mere diversity. This is even

not a forced interpretation: the ability to construct the other “opposite” from one opposite is only

one potentiality within that opposite and one that need not be actualised – for instance, although we

can use a method of similarity to construct dissimilarities, we need not do so. In this sense, then, the

classification of the object as opposite is only a mere external interpretation. Thus, in this context it

is even indifferent which of the objects or states should be called positive and which negative: e.g.

because a method of similarity can be used to construct dissimilarities, why couldn’t it be also

called a method of dissimilarity?

8./798. (iii) We have seen interpretations of positive and negative entities as mere aspects of the opposition or as

independent of the whole opposition, but they can also be seen as naturally containing the ability to be classified as

opposite: opposition is an essential classification, and such a classification is actualised only when it can be interpreted

as a natural ability of opposites. Positive entities contain the natural ability to be compared to other entities as positive,

and it is not just an external comparison, but natural to call negative entities negative.

The basic lack of the previous viewpoints was that they failed to express the specific nature of the

opposition that separates it, for instance, from the structure of diversity: that is, the fact that

opposites are naturally characterised by the terms “positive” and “negative”. Thus, it is not just we

observers who decide to call a method of similarity positive and a corresponding method of

dissimilarity negative. Instead, it is the nature of this opposition that specifically the method of

similarity is positive and the other negative: this is defined by one merely reproducing what is given

and by other modifying the given in some manner. True, both sides of an opposition contain the

opposite possibility of construction – e.g. the method of similarity can be used to construct

dissimilarities and vice versa – but these possibilities are mere secondary steps in comparison with

the essential task of the abilities of the opposed entities. The purpose of the secondary step is to

provide the essential step a starting point, that is, to point out or even construct a place where it

should start. Hence, a positive method is used to identify things, either by finding a context in

which they are identical or by modifying the other in a manner that changes it to look like the

original: yet, it also contains a secondary step of discovering a context with apparently different

objects or situations. Similarly, a negative method is used to differentiate things, either by

discovering something differing from some reference object or by literally making such an object:

but even this reference point need not be something merely given, because a negative method

contains also an ability to find or make such a reference point.

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Note that the criteria of opposition Hegel gives here do not apply to all things that have

usually been stated as examples of Hegelian opposition. Magnetic poles are a good example of such

supposedly Hegelian opposition which on a closer look is revealed to be something else. The first

viewpoint fits magnetic poles: we can say that there is no positive pole without another. The second

aspect is more dubious: true, we may cut a magnet into pieces and thus separate one pole from

another, but this cutting results also in a generation of new poles. Finally, the third aspect of the

opposition appears to be completely lacking. Why is the one pole defined as north and the other as

south? At least at the time of Hegel, there was only the external definition that north poles tended to

point to the South Pole, while south poles tended to point to the North Pole: names of the poles

were not definable through their own nature, but only through their relationship to other objects, or

specifically, to other magnets.

9./799. Both sides of the opposition are independent and can be taken as a reference point. In one sense a positive entity

is a mere aspect of an opposition, but this “aspecthood” is a mere construct or a mere aspect of the whole nature of the

positive: a positive entity is determined by an ability to integrate all differences and oppositions into a unity, although it

can be itself opposed to an entity with contrasting ability. A positive entity has an aspect of being-related-to-another-

thing, but it contains the ability to move away from this alternative to itself: then again, the other thing is not a mere

aspect, but also something independent – thus, the ability of a positive entity to move away from its opposite is an

ability to construct a context where the alternative does not exist.

Hegel continues by further characterising positive and negative entities or methods. The essence of

something positive is to be “not-opposite”: that is, it is natural to view it as an aspect of some

opposition – otherwise, it wouldn’t be positive – but the positive is or has an intrinsic ability to

integrate all such oppositions within one unity. A positive entity is a “reflection in itself that negates

state of there-being-something-else”, that is, the positive thing comes with an ability to construct a

situation where some difference has turned into an identity: this construction is either a

reinterpretation of the difference – like a method of similarity can be used to find a context where

two given objects are identical – or then a true change of the differing objects – for instance, if

Kantian force of attraction would be embodied in an object, this force could be called positive,

because it would literally assimilate separate particles of matter into itself. Yet, we have also an

ability to construct a negative entity, if a positive entity is given to us: at least we have the

possibility to interpret as negative the aspect of a positive entity producing the required starting

point for the integrative ability of the positive. In addition, this negative entity is not a mere aspect

of the positive entity – that is, not just something that we could integrate to the positive entity

without a further thought. Instead, this negative is an independent object or state of being in its own

right: therefore, the construction of integrating everything in sight into a positivity is in some sense

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a mere “exclusion” of negativity or difference from one limited context, because there is always the

possibility that we might find or produce a further negative object in some context.

10./800. A negative entity is not just something that is given as negative, but it is or comes with a method of going

through many secondary aspects and revealing them as mere aspects: a negative entity has an ability to move away from

its relation with an independent positive entity, which it thus excludes from some context. A negative entity has the

ability of producing oppositions and differences from itself and is thus essentially separated from positive entities that

have abilities to integrate all oppositions and differences into unity.

If a positive entity has an ability of integrating all differences into a unity, a negative entity has the

opposite ability of producing differences and oppositions. The negativity of this entity is connected

not so much with the current status of it, but its abilities: negative entity is not just something

“immediately negative”, but the negativity that comes with integrating mere aspects, that is, with

going through many different aspects of a structure. Paradoxically the results of a negative entity

using its ability to construct differences can be quite well understood as mere secondary

modifications of this negative: these differences are something that has been constructed without

any other means, but the ability of the negative entity to produce differences. This construction can

be either discovering – like when we use a method of difference to find some new objects differing

from the method – or then true manufacturing – like when our practical efforts produce a burst of

action in our body, and still in both cases we could think that the results are something secondary. It

is only when the negative entity comes in contact with something positive when the differences

begin to take an independent form. For instance, if we return to the example of the previous

paragraph, but add an embodied force of repulsion into the picture, we have a situation where one

object continuously produces new copies of itself, while another object makes these “balls of

repulsion” attach to one another and thus gain an independence from the original repulsion.

11./801. Opposite entities are characterised as positive and negative not just in some abstract context, but also in their

concrete individuality: they are abstractly characterised in this manner, if they are characterised as such when abstracted

from their relationship – then their opposition belongs to the nature of their species. But when abstracted from one

another, positive and negative entities are mere objects or states of being: because they are essentially aspects of their

opposition, this abstraction views only their independent aspect. When we characterise something as positive or

negative in itself or without any relation to other entities, we study only such abstract context: still, this characterisation

tells also that the opposition is no mere interpretation, but belongs to the nature of this entity – the possibility to relate

an opposite to an entity of the opposite side belongs to it intrinsically.

Hegel raises here a distinction between an opposition “in itself” and an opposition “in and for itself”

only to note that this distinction is no true distinction. The distinguishing characteristic between

49

these two “forms of opposition” should be clear by now. Something is positive or negative “in itself”

if it is positive or negative also when we abstract from any contexts where it is opposed to

something else: an entity like this would be positive or negative because it belonged to a certain

species of entities, like a method of similarity is positive just because it is a method of similarity.

This entity would be positive or negative “in and for itself” if also one would have an infallible

ability to construct an actual case of opposition when this entity was given. But this ability is

implied in the entity being “in itself” positive or negative: e.g. if something is positive in some

abstract context, it is always possible to construct an example of a corresponding negative object

from it. Thus, what is “in itself” opposite is or can be seen also as “in and for itself” opposite.

Remark.

Hegel has described what sort of structure an opposition should be, and now he gives a concrete

example of opposition. Interestingly, Hegel does not exemplify opposition through any physical

example, although Hegelians have often used e.g. magnetic poles as an instance of Hegelian

opposition – I have already remarked that magnetism is actually quite bad example of opposition.

Instead, Hegel provides a mathematical example, namely, the relation of positive and negative

numbers. Here it is not so much whole numbers as an additive group that exemplifies opposition,

because it is their role in multiplication which makes them “truly opposite”: because the positive

and negative numbers behave in different manner in multiplication, we can call one group positive

and other negative.

1./802. We shall apply both aspects of opposition to arithmetic: opposites are in one sense independent of one another

and opposition, but on the other hand opposed by their nature.

Hegel summarises the three aspects of opposition mentioned in the previous section. The first

section is only briefly mentioned: opposites are in one sense “mere opposites” or they are non-

independent aspects of the structure of opposition. This aspect is ignored because it doesn’t really

tell us anything specific of the opposed entities: they can be seen as mere secondary entities, but this

doesn’t yet prove that they couldn’t be seen as independent also. Indeed, the second aspect of the

opposition emphasises this independence of the opposed entities: we can abstract the supposedly

positive and negative entities from the opposition and after this abstraction they bear no apparent

connection to one another or to their opposition – it seems inadequate to call one positive and other

negative. Yet, the third aspect reveals that these characterisations are actually quite apt and belong

to the opposed entities even in their state of independency: an object is e.g. positive, because it has a

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certain integrating ability differing from the differentiating abilities of negative objects.

2./803. Positive and negative numbers are opposed numbers with a common basis (a for + a and – a): it is arbitrary to

the a that it can be modified in a positive or negative manner.

3./804. Indeed, the opposition is in some sense external even to the opposed numbers, because either of them could be

seen as positive or as negative.

Number systems or variables in an inverse ratio could be interpreted as the same system or variable

modified differently, at least when it comes to multiplication: if x and y are variables in an inverse

ratio, we can map the values of one variable to the values of the other by using the formula ax = y/a.

A similar interpretation can be made of positive and negative numbers in the context of addition:

the system of negative numbers is in a sense nothing but the mirror image of the system of positive

numbers. From this viewpoint it seems arbitrary why one of the systems is called positive and other

negative. For instance, we could flip a thermometer upside down and start to call the cold

temperatures positive: it is only the relatively contingent fact that human beings survive better in

warm than in cold temperatures that makes us want to relate warmness to positivity.

4./805. According to this viewpoint adding positive and negative numbers cancels both of them: if you walk to one

direction and then into opposite direction, you end up in the same place, and debts and credits cancel each other. It is

arbitrary which direction is called positive, and debts are credits for someone else.

5./806. In another sense the numbers are connected by their similarity, and adding positive and negative numbers to one

another merely reproduces the original number that is their basis: debts of one person are the same amount of money as

the credits of another person, and opposite directions form one road.

The connection of positive and negative numbers or their “addition” can have different outcomes

depending on which aspect of the opposition we concentrate our attention. Firstly, if we regard the

numbers as merely opposed, the connection of positive and negative numbers cancels both: + 2 – 2

= 0, or if I travel from Paris to Marseille and then from Marseille to Paris I will end up in Paris,

where I would have been if I had travelled nowhere – furthermore, if I receive salary and then go

and spend it, I am left with no money. All these are examples of a “proper” addition, that is, they

give the result that a teacher would expect you to give for an exercise in arithmetic. Then again, we

can emphasise the fact that positive and negative numbers can be seen as mere modifications of one

number system: “adding” positive to negative results then in a mere repetition of their common

basis. This “addition” is no mere sophistry, but points out a crucial characteristic of some opposed

quantities. A road from Paris to Marseille and a road from Marseille to Paris go to opposite

directions; yet, they are not two different roads, but aspects of one and the same road. Similarly, if I

give shopkeeper two euros and he receives from me two euros, the total amount of money that has

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moved is not zero, but two euros.

6./807. We can also interpret the opposite numbers as two independent entities.

7./808. A calculation –a + b has a + b absolute units: when travelling from East to West and back you travel two times

the journey from East to West, and a sum of money that is lent provides subsistence for both the lender and the person

receiving the money.

We have seen that positive and negative numbers can be seen as aspects of an opposition and as

mere modifications of an underlying substrate: these two aspects are implicit in the first

characteristic of opposites that they are parts of an opposition. A third manner of regarding the

positive and negative numbers derives from the second characteristic of opposites, that is, the

possibility of interpreting them as independent: we can ignore the fact that positive and negative

numbers are supposed to be opposite and concentrate on their absolute values. In this sense, “adding”

+ a to – a produces as a result 2a. This sort of “addition” is once again no mere sophistry, as

Hegel’s examples show: it is sometimes convenient to forget that two quantities have “opposite

directions”. For instance, if I travel from Paris to Marseille and back, my travels to opposite

directions have not cancelled the amount of energy used in travelling: on the contrary, I have

consumed twice as much energy as I would in a single trip from Paris to Marseille. Similarly, when

I buy something – say, a house of my own – I am not simply giving up money, but also gaining

something, that is, the house which has its own monetary value. Thus, in this transaction has

occurred a movement of value that is a double of the value of the money I gave to the person selling

the house.

8./809. Numbers are also positive and negative by their nature: if we abstract from oppositions of positive and negative

numbers, we must assume given x to be positive, because positivity is inherent to entities which are independent of any

opposition.

9./810. Furthermore, we can differentiate between extrinsic and intrinsic opposition of numbers: in a – (–b), the first

minus expresses the external act of taking a quantity away from another, while the second minus refers to the natural

negativity of the quantity itself.

The two first aspects of opposite entities do not really reveal their basic essence, because on their

account only it would be completely arbitrary which side to call positive and which negative. The

third aspect is then that one of the sides of opposition is naturally characterised as positive and the

other as negative. Hegel aims now to point out why it is natural to call positive number positive

instead of calling it negative and vice versa. The positive numbers have the advantage that even

when only the addition is involved, it is in the nature of positive numbers to call them positive,

because the system of positive numbers can be identified with the system of absolute values of all

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numbers: that is, we can map the group of natural numbers to the group of non-negative numbers

and thus identify the two groups. The negative numbers have as yet no such independent status, or

they can still be too easily interpreted as mere modifications of positive numbers: –2 means in one

sense nothing more than a task to subtract two units from a given number. True, Hegel makes a

half-hearted attempt to separate a “natural” negativity from such external negativity: for instance, in

a calculation of the form a – (– b) only the first minus should refer to a “negativity in comparison”,

while the – b is supposed to be “truly negative”. Still, this differentiation of two levels of negativity

does not really justify the existence of naturally negative numbers: – b can still be interpreted as a

mere task to subtract b from some number, and two minuses in front of a number merely cancel one

another.

10./811. It is in multiplication where the essential opposition of numbers is revealed: when we calculate – a x + a, the

negative number turns the positive number into negative, while when we calculate + a x – a, the positive number

reproduces the negativity of the second number.

The essential nature of opposites was revealed in the nature of the abilities they had: a positive

entity had an ability to do something similar, while a negative entity had an ability to do something

dissimilar. This aspect of the opposition of positive and negative numbers is better expressed in

their role in multiplication. Hegel’s “expected rules of multiplication” may seem rather unintuitive

to a person who is well-acquainted with the correct rules of multiplication – surely – a x + a must

have the same result as + a x – a. Hegel’s point is that we can interpret such multiplications as

functions or left operations: + a x – a would then be an application of the function + a () to a value

– a. Now, one could suppose that an aspect of such a function would be the change of the sign of

the value to the value that the function has. Indeed, this would be a possible sort of function, but it

wouldn’t be naturally opposite. A function + a () is instead a “function of similarity” in the sense

that it reproduces the sign that the value has: such a function maps positive numbers to positive

numbers and negative numbers to negative numbers.

11./812. This is inevitable, because the positive numbers are negative only in the sense of differing from another group

of numbers and they thus have no power to turn something into what it isn’t: only negative numbers have this ability.

12./813. Hence, multiplying a negative number with a negative number turns it into positive.

If a multiplication by a positive number can be interpreted as applying to a value a function which

reproduces the sign of the value, the multiplication by a negative number should be interpreted as

the opposite action: that is, when we multiply a number with a negative number we change its sign.

In the case of multiplying two negative numbers we “apply” the one negative number as a function

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or left operator to the other and change the sign of the product so that it differs from the sign of the

original value: the sign of the result becomes positive.

C. Contradiction

We began the chapter by studying a method of identity of some structure, which could as well be

interpreted as a method of difference – it was a method by which one could find different aspects of

a structure and then identify them as mere aspects of this structure. We could then differentiate the

two steps involved in this method and take them as different objects: these methods served as an

example of a diversity of independent objects. Such a group of diverse objects could then be set in

an external differentiation by using a method of similarity and a method of dissimilarity to find

which objects of this group were identical to a given reference point according to some criteria and

which were different from the same reference point according to same criteria. These two methods

served then as an example of opposition: an essential differentiation of objects that in some sense

are independent of one another and of their opposition, but in another sense have a natural ability

which justifies their opposite characteristics and which also enables one to construct an example of

other opposite, when an example of one opposite is given.

The task of this section is, firstly, to show that an example of opposition is also an

example of contradiction, that is, of a structure consisting of many situations that have equally

adequate characteristics, but cannot be valid at the same time: e.g. in an opposition the opposite

entities in one sense cannot exist in the same context, but in another sense they come with an

intrinsic ability of constructing one from the other. This task is fulfilled in the first subsection, while

the second subsection analyses a contradiction and notes that one cannot “combine” contradictory

situations or contexts into a “larger” context: that is, one cannot say that if x has characteristic A

in this context, but it has the opposite characteristic not-A in another context, then it is

characterised by both A and not-A in some context. In the third subsection we then note that

contradictory situations or contexts can be “united” in another sense: one can say that they are

“possible aspects” of a larger structure: e.g. that an x can be A in one situation or context and not-

A in another situation or context. Such a larger structure explains in a sense the smaller structures,

which completes the second task of this section: namely, that of finding an example of explanatory

or grounding relation.

1./814. 1. Introduction of contradictions. A structure of [absolute] difference has merely secondary aspects, while in a

structure of diversity these aspects has become independent entities: in a structure of opposition, opposed entities are in

some sense mere aspects, but in another sense independent of one another and of their opposition.

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Hegel begins with a short summary of different levels of difference: difference meant for Hegel a

method of constructing separate situations or objects, which were thus, at least in a sense, mere

aspects of a larger structure of which the method of difference was the essence. A difference “in

general” – that is, a mere or “absolute” difference – is a difference within a structure, that is, a

difference of mere moments or secondary aspects: for instance, we could differentiate states of my

life, but all of them would still be mere aspects of me. The next sort of difference we met was

diversity, where the objects differentiated were actually independent of one another and connecting

them into a unitary structure was a mere external interpretation or classification of the objects: for

instance, we could classify different rocks in the field in a variety of manners, but all of them would

be indifferent to the rocks themselves. The final mode of difference or opposition was then, in a

sense, a combination of the characteristics of previous modes: opposite entities were in one sense

mere moments of the opposition, but in another sense they were independent of one another. The

unique characteristic of opposition was that the classification of opposites was natural in the sense

that even in separation from their counterpart they had the ability of constructing it: opposites were

“independent determinations of reflection”, that is, they came with the ability of constructing the

whole classification or opposition from themselves.

2./815. One of the sides of opposition is naturally positive and other is naturally negative: they are independent of one

another, because they contain the other side as an aspect. Because of this containment both demand the other as an

aspect: in another sense, both exclude the other side from a situation in which they exist.

The opposite entities are classified by their intrinsic abilities: something was positive because it had

the ability to “reproduce” what was given to it, while something was negative because it had the

ability to “produce something different” from what was given to it. Now, these entities also

contained in a sense the ability of the other entity as a moment, because they came with the ability

to find a starting point for their characteristic methods: e.g. a method of similarity begins by

differentiating a reference point from another object or from another aspect of the same object and

ends by declaring this new object or aspect as in some sense identical with the original object, while

a method of dissimilarity begins by identifying some reference point which is then differentiated

from some object. Thus, in one sense a positive entity contains as an aspect or step a negative entity

and vice versa. Yet, in another sense, positive and negative entities exclude one another: if

something is a positive entity, it cannot be negative and vice versa.

3./816. Opposite entity is independent, because (i) it contains implicitly the whole opposition in itself and (ii) it

excludes the other opposite: these two aspects of this entity are contradictory.

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The contradiction involved in opposition is no “true” or formal contradiction, but only involves a

necessary connection between two aspects of the same situation or object which happen to contain

mutually exclusive characteristics: this is the essence of what Hegel means by contradiction. Thus,

the opposites exclude one another or what is positive is not negative and vice versa: in this sentence

we are looking at context where positive and negative entities of the same level or the applications

of their abilities are compared with one another – a situation with a positive entity is not a situation

with a negative entity, when these entities are understood as unanalysed. On the other hand, the

opposites contain one another or an application of positive ability or method contains an application

of negative ability: in this sentence we are looking at context where the application of the positive

and negative abilities are analysed and compared with applications of a lower level – a situation

with a positive entity may well be a situation with a negative entity, if the positive entity has been

analysed into “smaller” steps.

4./817. Even in an absolute difference we can analyse a contradiction: it is a method that unites apparently different

aspects and differentiates aspects that are in another sense identical. In constructing positive and negative entities we

make this contradiction apparent, because these entities contain the ability to construct also examples of opposite

entities: thus positive and negative entities can be used to discover contexts in which no entity of their kind exists.

The opposition is undoubtedly not the first structure that has exemplified a Hegelian contradiction.

Hegel mentions the structure or method of absolute difference – a method of absolute difference can

be used to differentiate situations or objects that in another sense are mere aspects of a larger

structure – but such “contradictions” have appeared even in the book on being. The particular

example of absolute difference is a case where the contradiction does not involve the structure itself,

but its aspects, which can be characterised as both different and identical. An opposite entity, on the

other hand, is a more explicit example of contradiction, Hegel says, because it comes with an ability

to construct a context where it doesn’t exist: e.g. if we are given something positive – say, a method

of similarity – we may analyse its application – revealing steps of finding something dissimilar and

then identifying it with a given reference point – and then separate the analysed parts into opposites

of their own and concentrate our attention to the negative part: as a result we find a context with

only a method of dissimilarity and no method of similarity. Similarly, all opposites contain an

ability to “destroy” themselves.

5./818. Let us look at both opposites separately. A positive entity has an ability to construct similarities from

constructed classifications, that is, it has the ability to make what is apparently a mere aspect into something

independent: thus, it is in some sense a construction for making something different from what is given. When we use

an ability of a positive entity to produce a context of identity, we find something differing from difference and so we

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can interpret the positive entity as negative: on the other hand, the excluded difference is in its own context taken as

independent – when we apply a positive ability, we in a sense also apply a negative ability.

Hegel continues by showing in detail how one can construct “contradictions” from both positive

and negative entities, that is, how one can begin from one sort of entity and construct an example of

other sort: this paragraph investigates positive entities, while the next concentrates on negative

entities. A positive entity is characterised by “a reflection from being-posited to self-similarity”,

that is, by an ability to move away from a context of differentiation to a context of mere identity:

e.g. by a method of similarity one finds a context in which given objects or aspects are identical and

by our theoretical abilities we modify our representations in such a manner that they correspond to

some state of affairs –we might say that one constructs from a group of related and dependent

aspects their common substrate. Now, this movement presupposes a previous state of difference

from which it starts: e.g. we must presuppose that our representations and states of affairs differ in

some sense, if we are to make one correspond with the other. If a positive ability is to be

independent, it must then contain an ability to construct or discover such a starting point: e.g. our

theoretical abilities contain in addition to representation an ability to sense something that differs

from our representations.

This analysis of positive ability implies two consequences. Firstly, the second step of

identification relates to the result of the first step as a negative ability, or the second step produces

something that differs from the result of the first step: if I make my representations correspond to a

state of affairs, I must change my representations or at least interpret them differently. Hence, we

can interpret the original positive entity as being negative in some sense. Secondly, we can interpret

the two steps as independent and mutually exclusive and hence interpret them as an opposition: thus,

a positive ability contains as a component a negative ability, or we can construct from a positive

ability an example of a negative ability and thus “cancel” the original positive ability.

6./819. Negative entities are in same sense contradictions as positive entities, because in constructing an example of one

sort one also implicitly constructs an example of the other sort. Negative entities are characterised by their ability to

construct dissimilarities or alternative aspects that are known as mere aspects: because its results are known to be mere

aspects, the negative ability can be used to construct structures of which they are essences. Negative entity is not

negative in the sense of a qualitative state of being that is given in one sense, but related to alternatives from a

viewpoint of an external observer, because negative entity has a natural ability to produce its own alternatives:

otherwise, the negative entity would not be naturally negative. Because its alternative is its own construction, we may

identify a negative entity and its alternative.

While a positive entity comes with an ability to construct similarities, a negative entity comes with

an ability to construct dissimilarities: e.g. by our practical abilities we are able to change our

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surroundings into different shape. Hegel emphasises the fact that the resulting dissimilarity is not a

dissimilarity given to us, for instance, it is not a difference between two differently coloured flowers.

In the latter case, the difference seems external to the differentiated objects: a flower doesn’t care if

its colour differs from the colour of the flower next to it. In the case of naturally negative entities,

on the contrary, the alternative object or situation is constructed through the abilities of the entity

itself. Because it is constructed through the negative entity, the alternative may be naturally

interpreted as a mere aspect in a structure of which the negative ability is an essence: for instance,

we can interpret the results of our practical ability – our actions and in some sense even the artefacts

we manufacture – as mere aspects within the structure of our practical behaviour. In this

interpretation, the result of an application of negative ability has actually been a state of identity: the

negative ability can therefore be characterised as being positive.

7./820. Both opposites consist of same contradictory aspects: they in some sense construct classifications of alternative

aspects, in other sense they construct independent structures. A positive entity is revealed contradictory only after an

analysis, while a negative entity comes explicitly with an ability to construct contradictions: when compared to itself, a

negative entity seems independent, but it is natural to relate it to an alternative state of identity with which it is

incompatible.

The “contradictions” that are constructed from positive and negative entities have similar structures:

in one sense, these entities have abilities for constructing states of identity, but in another sense the

result of applying these abilities are more like states of difference. Hegel notes that in positive

entities this contradiction is only “an sich”, while in negative entities it is “gesetzt”: that is, only an

external observer would note the contradiction in positive entities, while the negative entities

represent more explicit examples of this contradiction. Indeed, in case of positive entities the

contradiction is discovered only through an analysis of an application of its abilities: the result of

the whole process is a state of identity, but it goes through or has as its precondition a state of

difference – the state of difference is here less informative than the resulting state of identity. In the

case of negative entities, on the contrary, the unwanted state of identity is more informative than the

state of difference resulting from the use of the negative ability: we use a negative ability to

construct differences, but because the difference is constructed by the negative ability we may

interpret them as mere aspects of the negative ability itself – for instance, if I manufacture

something differing from me, I can interpret this new object, so far as it is product of my actions, as

a mere aspect of practical abilities. Because of this possible interpretation we may move away from

the state of difference resulting from a use of negative ability to a new state of identity which

contains this state of difference as a constituent.

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8./821. A negative entity comes with an ability of constructing oppositions without anything given or with a method of

absolute differentiation: in one sense it excludes a method of identity, in another sense it is itself a method of identity.

A negative entity comes with a method of finding something that is dissimilar to a given reference

point and thus it also contains an ability to find something dissimilar to itself, that is, a negative

entity comes with what was earlier called an absolute method of differentiation: we can use this

method to differentiate something, but the differentiated objects or situations can be naturally

interpreted as mere aspects of the method itself. One may wonder why Hegel then in the beginning

of the section noted that in a structure of absolute difference contradiction was merely “an sich”,

while he now admits that it is also “gesetzt”. The answer is that previously Hegel was speaking of

the contradiction involved in the aspects of the absolute difference – they are in one sense

independent, but in another sense mere aspects – while here he speaks of the contradictory

characteristics that the method itself may have: it is a method of identity in one sense and a method

of identification in another.

9./822. 2. The collapse of contradictions. Contradictions have a natural tendency to vanish.

Hegel begins a new subsection with a paragraph that works almost like a title that summarises the

whole content of the subsection: contradiction solves/dissolves (Auflösung) itself. The ambiguity is

clearly intended, although it is more of a succinct way to express the result of the study of Hegelian

contradictions than a proper justification of anything. Contradictions of the Hegelian variety

dissolve themselves. If we are given two situations describing different aspects of the same object,

we can usually connect them into a simple larger situation – like if according one situation this rose

is red and according to another it is thorny, then there is a situation in which the same rose is both

red and thorny. In case of contradictions the two situations cannot be combined similarly: one

cannot say e.g. that an entity is both a unified object called book and a collection of independent

atoms. Still, contradictions also solve themselves. This solution occurs just at the same time as the

dissolution, that is, when we reject the attempt of combining the contradictory situations: we can

say that an object is in some sense a book and in another sense a collection of atoms and no proper

or formal contradiction ensues.

10./823. Positive and negative entities come with a natural ability to change into one another: thus, both of them seem to

vanish.

Given a positive entity, we can interpret it also as negative, because it in one sense has the ability to

construct differences; similarly, given a negative entity, we can interpret it also as positive, because

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it in one sense has the ability to construct identities. Because the classes of positive and negative

entities are mutually exclusive and because the entities in question are supposed to be naturally

positive and negative, this reinterpretation seems more like a vanishing of the original entity and a

replacement with a completely opposite entity. Both sides of the opposition come then with a

natural construction by which to destroy this side, similarly as finite entities pointed towards a

context in which they didn’t exist. This “seed of death” in every opposite is their ultimate

contradiction in the Hegelian sense: they exist or subsist in one situation, but do not in another.

These considerations imply that nothing can come out of contradiction: one is just forced to move

from one fleeing moment of an opposition to another.

11./824. But we do not merely have an ability to change an opposite into something different or exclude it, but also an

ability to make it independent of the opposition or construct it. When we construct an opposition of positive and

negative, we reconstruct something independent as divided into secondary aspects: the contradiction merely shows that

one can move away from this secondary reconstruction.

When Hegel says that the example of contradiction we have investigated does not contain just

negative, but also positive, this is no mere rhetorical way of saying that the contradiction leads to

something. Something was negative if it had the ability to construct something different from what

was given to it: thus, the negativity contained in a contradiction referred to the fact that one can

change one side of a Hegelian contradiction into something incompatible with it. Then again,

something was positive if it had the ability to construct identities from given differences: hence,

when Hegel speaks of the positivity involved in a contradiction, he means the fact that we can find

some identity behind the opposition – if what is positive can be changed into something negative

and vice versa, we may suppose that both are in a wider sense mere aspects of some underlying

unity. The collapsing aspect in the contradiction is the “being-posited of independency”, that is, the

fact that we separate some opposite aspects within the opposition. Thus, when one sees that a

natural opposition leads to a Hegelian contradiction – that is, makes it indeterminate how to

characterise the opposites – one is justified in assuming that there is something independent of the

opposition: that is, we can suppose that the opposites are mere aspects of a larger unity.

12./825. When we first make the opposite entities independent, we separate them as different aspects of the opposition,

and thus in a wider sense still interpret them as secondary entities: when we apply the construction of excluding the

other side, we make the opposites independent according to their own viewpoint. Yet, such an independent object still

comes with a natural tendency to construct the opposition anew: we can construct a classification of mere secondary

entities from the supposedly independent unity.

Although the previous paragraph suggested that a Hegelian contradiction leads only to the

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realisation that one may construct something independent from an opposition, this seems not to be

any final solution, because the “contradiction” still follows in another level. At first, we may have

entities that are independent only according to some external observer – like us who can abstract

from the opposition – but which still in a more informative context are shown to be aspects of an

opposition. Now, we may use the ability to change one side of the opposition into an entity of the

other side and vice versa: we can then suppose that there is some unity behind the opposition, of

which the original opposites are mere aspects – this is the familiar construction of idealisation. Yet,

this independent entity is something that is merely constructed from the opposition: it is an

alternative to the original opposition, and thus we still have an ability to move from this newly

found unity to the contradiction – it seems that we are merely interpreting the opposition in a

different, but not better way when we regard the opposites as mere aspects of some unified entity.

13./826. There is more to exclusion than this movement through different stages. We have an entity that is by its nature

independent and then constructs itself as independent by moving away from its state of being-a-mere-aspect: in some

sense we have then merely created a new classification of alternative situations, but the alternative from which we have

moved away is not of an equal level, but is only a secondary interpretation or modification of the independent object. In

one sense the object has an ability to make itself a mere aspect, but in another sense it has the ability to interpret this

being aspect as its mere aspect: we may first move the object away from some classification and then construct a new

classification for it – all of these steps can be interpreted as mere phases in a possible “lifeline” of the object, which then

comes with an essence or a method of constructing different aspects which can be seen as mere aspects.

Although the previous paragraph appeared to destroy our hope of avoiding the contradiction, a new

hope blossoms in this paragraph. The problem was how we are justified in our statement that the

result of the idealisation of opposites was more “true” or essential than the opposites. This is a

question that we could ask of any example of idealisation: we may ask whether it is more correct to

say that a line is a collection of points or a “movement” of one point through many places. In some

cases the original interpretation seems more natural, in other cases it is difficult to decide. What

makes this instance different is that the idealised entities are already supposed to mere secondary

aspects of their opposition: one is an infallible method or activity of turning positive entities

negative and vice versa. A similar justification for idealisation occurs when we ponder whether we

should interpret our life as a collection of separate segments or as a continuum of a single person:

here it is a causal chain connecting the different segments that makes the idealisation more

convincing option. Likewise, it seems natural to interpret methods of dissimilarity and similarity as

aspects of one method, because they appear to be mere interchangeable roles depending on the

context where the method is applied.

The idealised unity is then more essential than the opposition: still, one cannot just discard

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the opposition, because it is something that we truly may construct from the discovered unity. This

opposition of exclusive sorts of entities that can be transformed into one another is what shows the

unity to be essential in comparison to something. This unity is no mere substrate behind the

opposition, because this opposition is the only manner in which the unity can be found. In fact, the

unity is what Hegel would call the essence of the opposition: in effect, it is the method of

construction by which one can transform positive activities into negative activities and vice versa.

14./827. 3. Transition to ground. When we first construct an opposition of mere aspects from something independent

and then integrate this secondary level into the original independent, we construct the ground of this opposition. At first

we have apparently independent and opposite entities which we then construct as mere secondary constructs, and thus

we have a constructed a common unity or essence behind these oppositions, which also grounds or explains these

opposites: we return to the essence from which we began the construction, but now we know it contains the ability to

construct entities of secondary level.

The construction of an example of a ground has paralleled the construction of an example of an

essence: in both cases we noticed the natural ability of constructing identities from given

differences and differences from given identities and then concluded that we could suppose there

was some method of construction which unified these two states into a single structure. Indeed,

Hegel admits that the method of construction behind the example of an opposition is an essence of

the opposites: it is ability to make positives into negatives and vice versa. What progress has then

happened from the beginning of the section where we already investigated an essence? Here we

have an essence that is explicitly “an exclusive unity of reflection”. That is, the essence from which

we started could have been an instance of a “pure reflection”, i.e. a mere capacity to express the

method of construction in some manner and then to recognise it as a method of construction. Here,

on the other hand, the essence is known to be an essence of more states than its mere expression: it

is an essence of some positive and negative activities, which can be differentiated at least in some

level of investigation.

15./828. At first it seems that we would have begun from an opposition of independent entities and only later

constructed a ground for them in order to explain the possibility to change them into one another: thus, the essence or

ground seems like something secondary in comparison. In a more adequate sense we have seen that it is natural to

regard the opposition as a mere construct: it is natural to explain the opposition as a mere application or construct of the

essence from which we can naturally return to the essence when we note the connectedness of the opposites. An essence

or a method of construction has been used to ground an aspect of itself, which can be known to be a mere aspect of a

larger structure, thus, we can immediately return from it to the original ground.

An essence or a method of construction is a ground, when it has some concrete aspects that it has

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been used to construct: thus, “pure reflections” are yet no grounds. In the next chapter we shall see

that not all grounds are necessarily essences, because some grounds still need some external

material in order to ground something. Why an essence is then called ground of something? The

word “ground” indicates some sort of explanatory or even causal relationship: “something happened

on ground of...” says almost same as “something happened because of...”. In case of essences this

grounding means a very strong relation: what is grounded or constructed through the essence or the

method of construction is something secondary in comparison with this essence. Thus, although it

seems like we would have begun from an independent pair of opposites and then constructed or

merely supposed the existence of an essence behind them, which would indicate that the essence is

something dependent on the opposition and on our arbitrary construction, we have in fact only

revealed something that was already there in a more primary sense than the opposites, because this

essence was found by noticing that the opposites were mere aspects of a larger structure. For

instance, we may at first think that our theoretical and practical abilities form independent parts of

our consciousness, but their necessary interconnection would reveal that they are actually mere

aspects of my whole essence or the whole structure of my abilities and capacities.

16./829. The solution of the apparent contradiction was the discovery of an essence that is both a positive and negative

method and which thus grounds the opposites: in opposition we have made aspects of some classification independent

in some sense, but a ground is something truly independent of the opposition. A ground can then be compared with the

structure of opposition as a mere positive entity, but because the opposition can be seen as a mere secondary viewpoint,

the ground is also actually primary: we can thus integrate opposition within the viewpoint of ground, but we can also

construct a new opposition between the ground and the previous opposition. A ground or a method of construction is in

a state of identity, but it can also be used to construct a classification and still we can return from this classification to

the unity of the ground. A structure of opposition contains in some sense everything that the ground does, but it still is a

mere collection of states instead of a single method of construction: this unity was found by noting that one can change

the sides of the opposition into one another and thus interpret them as mere modifications of one essence.

An essence as a ground is the “solution” of the contradiction, that is, it contains the movement

between positive and negative entities as a mere potential in itself: it is the capacity to move from

positive to negative and vice versa. It is also the unity of positive and negative: that is, while

positive was a method for finding similarities and negative was a method for finding differences,

the respective essence is a method for constructing both. In opposition the determinations of

reflection became independent, that is, the different steps of differentiating and identifying

contained in any essence were taken as independent methods: still, these methods have been

revealed as secondary in comparison with the method that is their essence. This more essential

method is in one sense merely “positive”, that is, we can still compare it with the opposition of

secondary methods and thus regard it as a mere aspect in another opposition. Still, in a more

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informative sense it is “identical with itself in its negativity”, that is, the opposed methods are

known to be mere secondary aspects of their essence. The structure of contradictory opposites

already was a ground in some sense, that is, the opposite methods contained both an ability to be

regarded as independent of the opposition and to be integrated in the opposition: the only difference

is that in opposition there was still two such methods, while at this level we have interpreted them

as mere aspects or modifications of one method, on basis of our seeing how one opposed method

could be changed into another.

Remark 1.

The purpose of this remark is to explain how positive and negative entities can be “translated” into

one another. This translation is based on the fact that positive and negative entities are not just

qualitatively different, but also “opposite forces or abilities”. Thus, supposed counterexamples of

this “necessary translation” are usually examples of things that would not be opposite in the sense

Hegel means. Hegel also provides the reader with a collection of examples of opposition: we might

disagree whether all of Hegel’s examples are truly oppositions in the required sense, but this is still

no argument against the “interconnectedness” of positives and negatives.

1./830. One can say from an external viewpoint that positive and negative entities are similar, but this does not tell what

they are from their own viewpoint: the previous investigation has shown that one can change positive into negative and

vice versa according to their own point of view.

Hegel begins by comparing external comparison of opposites with an investigation of their “own

reflection”. The first sort of investigation is easy to understand: here we are given two entities – or

merely a description of them – and we are supposed to determine which one of them should be

called positive and which negative: criteria of the choice if left for the examiner to decide. The

result of such an investigation is clearly arbitrary: a different examiner might make a different

choice. How can one then investigate the “own reflection” of opposites? This is possible, because

the opposite entities are supposed to be “reflections” or they are supposed to have abilities by which

one can construct a new state of affairs: positive activities are used to construct similarities, while

negative activities are used to construct dissimilarities. Now, if it is shown that one could use

positive activities also to construct dissimilarities and negative activities to construct similarities –

as we have seen to be possible in the previous section – we have shown that opposites can be turned

to one another even according to their own viewpoint.

2./831. Even an external comparison shows that positive and negative are only relative determinations, but it is

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uncomfortable of this seeming contradiction and ascribes it to some subjective failure. One should see the necessity of

the possibility to translate opposites to one another in order to understand it: positive entities 1) have a necessary

relation to negative entities and 2) have the ability to change states and methods of dissimilarity into states and methods

of similarity; negative entities 1) have a necessary relation to positive entities and 2) come with an ability to see its

constructed dissimilarities as mere aspects of an identical structure.

The alleged difficulty in understanding how positive and negative entities could be transformed into

one another is mainly caused by a belief that such a transformation would lead to a formal

contradiction, although this need not be so. Indeed, a possibility of this transformation would

merely imply that what is positive in one context or situation could be negative in another context.

This is evidenced even by the external comparison described in the previous paragraph: if one

changes the criteria, one is bound to find the extension of the classes of positive and negative

entities changed. Still, one could object that such a change would be merely subjective and that

there is some “absolute context” in which we could once and for all decide what to call positive and

what negative. On the contrary, Hegel tries to show that even in such a supposed “absolute context”

it would be necessarily possible to construct another equally absolute context in which the positive

and negative entities would be changed.

Hegel’s first point is to note the interconnectedness of the terms “positive” and

“negative”: even if we had a context with mere positive entities, we could find a context with mere

negative entities and vice versa. Although this “interconnectedness” or “necessary relatedness” of

opposite concepts is sometimes seen as the primary insight of Hegelian logic, it does not

characterise even this case completely. One must still show that one can literally take e.g. a positive

entity and change it into negative either through an actual modification or through a natural

reinterpretation of the entity: this is done by noting that a use of positive entity to states of

differences produces something differing from these states, that is, works like an ability of a

negative entity. Similarly, when one applies negative entity to itself and produces something

different from the original negative, the result of this construction can be interpreted as being a

mere aspect of the original entity: thus, one could interpret the negative as having the ability to

construct similarities or as positive. These reinterpretations change the context in question and

hence lead to no real contradiction: still, they are natural changes and therefore show that the

“possibility to become opposite” belongs essentially to the opposites themselves.

3./832. Sometimes only positive entities are interpreted as objective, while negative entities are interpreted as mere

subjective objectifications of a lack of something: in this case the supposed positive entities wouldn’t be truly positive.

Light is called positive, but it has the power to produce life and thus make things different: darkness is called negative,

but it has the power to cover all differences in featureless blackness – furthermore, darkness is no mere lack of light,

because it has a power of making light into greyness and colours. Virtue is not just positive, because it has the power of

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struggling against evil: vice is not just negative or a mere lack of virtue, because it has the power to assimilate all

actions to self-will – even innocence is no mere lack, because it has the capacity to become good or evil. Truth is not

just positive, because it presupposes a differentiation of object and cognition: mistake is not just negative, because it is

an independent belief – even ignorance is no mere lack, because it has the capacity to become either truth or mistake.

Hegel returns to an issue that he has dealt already in the first book of Logic, namely, the question

whether negative entities are truly entities or merely lack of something. Earlier Hegel interpreted

the question as concerning negative situations and concluded that such situations truly are real

situations: if I am in a situation where a cow is not in a field, surely the cow then truly is not in a

field – the lack of a cow makes a difference. Hegel thus interpreted the word “reality” in a different

manner than it had been usually done: he ascribed reality to situations instead of objects within

situations. Here it is case of positives and negatives, that is, of situations or objects with certain

abilities, or more precisely, of activities. Hegel’s point is, firstly, that the terms “positive” and

“negative” are relative to their possible effects, and secondly, that even if a situation would be “a

lack of objects of certain kind”, it could still have possible effects.

Even in previous book Hegel used the example of light and dark and the same example

occurs here, which has led some critics to complain Hegel of following the nowadays outdated

theory of colours invented by Goethe. Earlier we saw that Hegel’s ascribing of reality to darkness

could be interpreted in quite a harmless manner: state of darkness is undoubtedly a real and not

fictional situation. Here Hegel first emphasises that it is arbitrary which of the light and dark is

called positive and which negative. One might feel tempted to call light positive, but in light of

Hegel’s definitions, light should be called negative: light has the power to differentiate, that is, a

state of lightness lets us see different things, and furthermore, light has the power to concretely

enliven things. State of darkness, on the other hand, has a power to cover all differences into a state

of apparently unitary blackness and should thus be called positive or a power to construct states of

similarity. Secondly, Hegel tries to show that darkness has some powers e.g. in producing greyness

and colours from a mere white. Here Goethe’s theory has affected Hegel’s reasoning, but one can

still accept some of his points without assumption of darkness as some existing object. Instead of an

object called darkness we could speak of a power or ability of darkening, that is, of an ability of

making things darker than they are: the ontological framework behind this ability could be ignored.

Then this ability would indeed be something “positive” in the Hegelian sense of being a method of

producing states of darkness.

Hegel’s examples of virtue or vice and truth or mistake are clearly parallel in nature. Firstly,

there is the apparently positive ability, which on a closer look could be called negative: virtue is a

power to combat against and change states of badness, while truth – understood here clearly as a

conscious process of finding and asserting truth and not as a property of a proposition – is a process

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of changing the state of consciousness-and-object-being-in-discrepancy. Secondly, there is the

apparently negative ability, which on a closer look could be called positive: vice is a power of

maintaining one’s own will against the will for goodness, while mistake – or more properly, holding

on to a known mistake – is a process where one maintains her own beliefs against the evidence for

the contrary. Thirdly, there is a state of a lack of positive or negative abilities – innocence in case of

virtue and vice, and ignorance in a case of truth and mistake – which on another sense still contains

an ability to move to the positive or negative side of the opposition: understood in this “positive”

manner this state of innocence or ignorance seems like the Hegelian ground.

Remark 2.

Surprisingly Hegel deals with the so-called law of excluded third after the section on contradiction,

although he connects this law with the structure of opposition. This quirk shows most likely that the

sections on opposition and contradiction are closely related: both deal with the relationship of

positive and negative entities – indeed, in the so-called Encyclopaedia Logic Hegel ignores the

whole contradiction and moves straight from opposition to ground. As was the case with all

previous laws of thought, the law of excluded middle admits two different interpretations: firstly, it

can be seen as a formal statement that a thing must have one of two opposite predicates, and

secondly, it can be regarded as a statement of an infallible method for producing oppositions.

1./833. The possibility to construct opposition from everything is expressed in so-called law of excluded third.

2./834. “A thing is either A or not-A”.

The law of the excluded third was known already to Aristotle who was also aware that it differed

from the law of non-contradiction: a fact that philosophers have not always appreciated enough.

Although this principle seems innocent enough, it is much stronger than the law of non-

contradiction. Indeed, the intuitionist school of logic among others denies that the principle would

be valid for all truths. The intuitionists’ rejection is based on their understanding of truth: one

cannot call a proposition true unless one has a way of proving it true and one cannot call it false

unless one has a way of proving it false – clearly, if one can neither prove a proposition true or

prove it false, one cannot say anything of it. Because of a similar reasoning Hegel denies the

universal validity of the law of excluded middle.

3./835. This law tells that everything can be determined as positive or negative, although usually it is understood in the

trivial sense that every predicate should belong or not belong to a thing: here an essential determination is replaced by a

mere indeterminate non-being.

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The formal sense of the law of the excluded third is familiar from such sentences as “I either have

grey hair or I don’t have”: Hegel has nothing against such sentences, except that they happen to be

trivial – they are undoubtedly correct, but tell us nothing. Hegel’s own modification of this law

concerns a different issue. Firstly, the contrasted pair of determinations in Hegelian opposition is

not a mere pair of predicates like A and not-A, but a positive and a negative in Hegelian sense of

the terms, that is, two forces, abilities, actions or such like that, as it were, work in opposite

directions: e.g. one has a unifying and other separating tendency. Secondly, the copula of the law

does not mean that such tendencies would exist in any situation, but merely that one has the ability

to construct such opposite tendencies from any given situation. For instance, if we are given an

object, we can find a tendency or ability to construct more objects from it and a tendency or ability

to integrate all these new objects into a unity.

4./836. The law of the excluded third differs from the law of contradiction: while the latter denies that anything could

have opposite attributes in the same context, the latter denies that anything could have neither of the opposite attributes

in some context. In fact, the law itself points to a context where the object in question does not yet have either of the

opposite tendencies, although it could have either of them: this possibility is the ground uniting the opposites.

Hegel has a habit of using ordinary sentences to express a possible process, although they

seemingly talk of an actual state of affairs: this habit often confuses the reader and Hegel’s

discussion of the law of excluded third produces such confusion easily. At first Hegel states that it is

a law that any A must have either a positive or negative predicate and then he adds at once that this

A actually does not have either predicate. We saw in the previous paragraph that this law in the

Hegelian sense said only that we have a possibility of constructing oppositions from anything given:

that is, that we can develop the situation with something given to two different directions – for

instance, if we have a belief we may either test it with experiments or we can ignore all experiments

and hold on to the belief no matter what other evidence we shall have. In this sense it is obvious that

we have something that isn’t opposed, namely, the state before we have constructed opposition: or

then we could say that this state is both of the opposites, that is, potentially – our belief cannot be

called truth unless we compare it with how things stand. Similarly, an intuitionist says that a

proposition cannot be called either true or false unless we have shown it to be either true or false.

The difference between the intuitionist understanding of truth and Hegel’s discussion of “truth” is

that for Hegel any belief could become true through the necessary comparison with experience:

what Hegel calls truth in this context means merely the state of cognition that it is willing to

surrender its beliefs to a comparison with reality. Thus, the “third state” of cognition is a ground of

the opposed states: we have theoretically the ability to decide whether we want to compare our

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beliefs with what we experience or not.

Remark 3.

Hegel is famous for being the philosopher who rejected the law of non-contradiction: because of

this, those who value the so-called classical logic have thought Hegel as a bungler while those who

endorsed so-called paraconsistent logic have sometimes made Hegel into their philosophical hero.

Hegel-scholars have felt embarrassed for Hegel, rejected classical logic or then tried to show that

Hegel’s dismissal has nothing to do with logic as the science of proper deductions. As we have seen

time and time again and as this remark will also show, the third manner of behaving is the correct:

Hegelian contradiction has almost nothing to do with logical contradictions.

1./837. In addition to laws of identity, difference and opposition we must have also the law of contradiction –

“everything is contradictory”. This law tells us more than the other laws and it merely states explicitly the necessary

connection of different and mutually exclusive aspects which is implicitly contained in the law of identity.

2./838. Usually identity has been taken as more essential than contradiction, but actually converse is truer: identity by

itself expresses only one state or aspect of a thing, while a contradiction guarantees that the thing has more aspects in it.

While people familiar with modern logic usually have a rigorous understanding of what

contradiction means – a proposition which implies two contradictory propositions, and thus,

according to classical logic, any proposition – this clear and well-defined meaning of contradiction

is relatively new. Firstly, in the times of Aristotelian logic contradiction was usually defined as one

thing having two contradictory predicates. Secondly, with almost no proper tools it was hard to

discern when a given situation was a true case of contradiction and when only an apparent one.

Thus, when Hegel talks of contradiction, he is usually speaking of a case where one object has

contradictory predicates in different contexts: in modern terms this would be no contradiction.

Hence, when Hegel contrasts his “law of contradiction” with the law of identity, he is not speaking

against formal logic and for formal contradictions. Instead, he merely points out that if we

investigate a mere abstract identity of an object, we see only a static picture of it: at worst, a mere

entity with no information what it is – that is, when we look at an object in one situation or context

only, we see only a portion of the aspects it contains in itself. In contrast, when we move on to

looking at different contexts and situations we learn more details of the object, and indeed, we may

even find out that the object in question has different and even contradictory properties in different

contexts. This “contradictoriness” is a necessary condition of living, because an object cannot

change, if it cannot have different properties in different contexts.

A usual logic provides only a static picture of one context – it speaks of truths in

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certain context and investigates what can be deduced from those truths. Even paraconsistent logic is

static in the sense of being restricted to one context. A modal logic, on the other hand, deals with

relationships of truths in different context – e.g. something may be possible according to one

context – and although modal logic wouldn’t cover everything in Hegelian Logic, it would be a

more natural starting point for Hegelian studies than paraconsistent logic.

3./839. It is usually said that objects cannot be contradictory and that contradictions belong to subjective reflection: on

the other hand, it is said that one cannot even think of anything contradictory – contradiction is understood as a state of

sickness.

4./840. But because contradiction is an essential determination, we should be able to find it in all situations: and indeed,

there are several contradictions. Contradiction is no sickness, but a condition for anything to move itself: even spatial

movement is contradiction – a moving object is in two different places during same period of time.

We cannot think contradictions – we cannot imagine what it would be like if a book in front of us

would be both completely green and also not completely green – and even less can contradictions

occur objectively – a book cannot be both completely green and not completely green. Such

contradictions are not even “abnormal”, but impossible states. When Hegel then states that

contradictions must occur, he is clearly talking of something else: indeed, the German word

Widerspruch refers also to antagonisms and conflicts and such do occur – an object can be in

“conflict with itself”, when it shows in one context characteristics that it couldn’t have in another.

As Hegel says, a self-induced movement or change wouldn’t be even possible without such a

conflict: one couldn’t change one’s condition if one couldn’t have different characteristics at

different moments of time. A similar precondition contradiction is for motion of objects: a moving

object is at one time here and another time there. Hegel perplexingly states that a moving motion

would actually be in two different places at the same time. One must here remember that a Hegelian

time does not consist of dimensionless points, but of smaller and smaller stretches of time: similarly,

for Hegel space consists of smaller and smaller areas. Hence, given a moving object, we can find

for any stretch of time or “now” a division of space such that the object exists in two different areas

or “heres” during the “now” in question: of course, by dividing the “now” in question into further

parts we could find two “nows” corresponding to the two “heres”.

5./841. In drive one feels both oneself and also a lack of something: such a contradiction creates life – if a creature has

not the power to sustain this contradiction it dies. Speculative thinking is such thinking of contradictions, which does

not let contradictions lead to a mere negative conclusion.

6./842. While movement, drive and such contain implicit contradictions, relative terms are explicit contradictions: left

demands necessarily right like son demands father – while a son has an independent personality, as a son he needs a

father.

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Hegel continues to find examples of “contradictions”. When a living entity is driven towards some

action it in one sense feels itself to exist – in the current situation and also in the context of what

should be – and in another sense feels itself not to exist – in the possible future on in some further

level of perfection. Both of these feelings should occur in the same context, Hegel says. In the

previous paragraph a similar remark meant only that in any stretch of time where one was at one

place one could also find a part of this stretch in which the moving object was in a different place:

thus, here Hegel undoubtedly means only that in both contexts there is an infallible method for

finding a context of the other sort. If a living entity exists or is at some level of perfection, we can

find a further point of time in which it might not exist or a further level of perfection at which it

isn’t. Similarly, if a living entity has such a lack – if it is in danger of dying or fails to uphold some

criteria – then it can modify itself and so produce a new context in which it is “as it should be”: that

is, if it has the necessary means by which to do this – otherwise it dies or stops developing.

Hegel’s next example is speculative thinking: or it is not so much an example of

contradiction, but of an investigation of contradictions. If understanding meant for Hegel a study of

objects in single situations and contexts and dialectical thinking meant discovery of ways to change

these situations and contexts, speculative thinking means apprehension of these changes as natural

to the object in question: one at first describes a seed, then investigates in what conditions such seed

will change into something else and finally comprehends the results of the study into a complete

description of the potentialities of the species in question. The speculative thinking investigates

contradictions, that is, it investigates objects that have different characteristics in different contexts.

Yet, it is not “moved by contradictions”, that is, it does not merely move on to describe new

contexts, but produces a full model of all the possible changes of the objects in question.

The final example of contradictions is the strangest: Hegel says that terms dependent on

relations should contain contradictions. Those acquainted with modern logic are bound to feel

perplexed: what contradictory is there in a person being a father? One must here remember the

meaning of Hegelian contradiction, that is, that same object has different characteristics in different

situations. If I am a father, then there must be someone who is a son or daughter: thus, my existence

in the context of being a father is dependent on the existence of another person. Then again, my

existence as a mere human being is not conceptually dependent on any other human being. Thus,

relational words point out a context in which things are dependent on one another, although in

another sense they would be independent.

7./843. We thus see contradictions everywhere, although we are not conscious of them: we try to see opposites

separately, although one can move from one to the other. It is more civilised to let contradictions appear and in its

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highest state reason knows how to construct such contradictions.

8./844. We have seen that when God is defined as the sum of all realities, He is either an empty and unrelated state of

being or a possibility of actualising contradictory predicates.

After describing some examples of contradictions, Hegel returns to a more general discussion. At

first, Hegel describes three different viewpoints on contradictions. These viewpoints share some

remarkable similarities with the threefold division of “phases” of thinking, that is, understanding,

dialectical reason and speculative reason. Still, the three viewpoints are not identical with the three

phases, because two of the viewpoints occur “before” thinking, that is, they belong to the level of

representation. First of the viewpoints is indeed representation itself, that is, describing and

modifying of material given by intuition: like understanding, representation ignores the fact that one

can change one structure into another and concentrates on one structure – for representation, this

structure is given by senses, and for understanding, this structure might be its own construction.

Understanding is “awakened” by dialectical reason which is a method of changing structures

investigated by understanding. On a level of representation one cannot yet do such changes

independently, but one can still observe these changes happening. This is the work of “spiritual

reflection”: in effect, this reflection notices that one object has different characteristics in different

contexts and tries to make this “contradiction” known. The final phase Hegel mentions is not

anymore a part of representation, but of thinking: it is the viewpoint combining understanding,

dialectical reason and speculative reason, that is, the viewpoint which does not just observe

contradictions, but knows an infallible method for producing them.

Hegel also returns to the definition of God as the sum of all realities, which he mentioned in

a remark in the chapter on qualities. There he already noted that so-called “negative” properties

should also be understood as realities: they described situations which were as real as so-called

“positive” properties. He also pointed out then that God should then be understood as a

contradiction: that is, He would not be a conglomeration of all properties, but a method of

producing examples of all properties – by the way, one should note that the “all” here should be

restricted to a definite, even if implicit context. God would then be “absolute ground”, i.e. a name

for any grounding method, as long as one does not compare it to other grounding methods.

9./845. We have seen that contradictions occur naturally and that they point to a more essential principle or to the

common ground of contradictory aspects: this ground can then be interpreted as a mere aspect of more essential ground

etc. The movement from a state of being to its ground does not make ground dependent on the state of being: on the

contrary, ground is constructed by interpreting this state of being as a mere secondary aspect.

The final paragraph returns to the main theme that contradictions are possible, but also serves as an

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introduction to the structure of ground: when one experiences contradictions – that is, necessary

connections between apparently incompatible situations – one is allowed to assume that these

situations share something common or a ground. For instance, if I see now a seed and tomorrow a

flower in the same spot, I can make the assumption that the seed and the flower are stages of the

same entity. Hegel makes two interesting remarks. Firstly, he points out that the first ground that we

have constructed may not be the “ultimate” ground: behind a ground of seed and flower one can

possibly find a more comprehensive ground, like a ground of seed and flower and fruit. Indeed, one

could ask whether the expression “ultimate ground” would make any sense for Hegel: if the

discovery of ever new grounds is always possible, one would imagine that such a “non-grounded

ground” would be impossibility, similarly as there could be no “largest quantity in every context”

according to Hegel. Secondly, Hegel notes again that the movement from a state of being or

situation to its ground is not a movement from a primary entity to secondary: although we find

grounds through states of being, the states of being wouldn’t even exist if there wouldn’t be grounds

for it in some context. This is a point that Hegel also makes of the so-called cosmological proof of

God, which is actually nothing but a general formula for all constructions of grounds from states of

being.

Glossary:

Reflexions-Bestimmung = ability or latent activity for some particular process of construction that

can be discovered through a process for discovering such abilities

Wesenheit = ”essentiality” or ”small essence”; a determined ability or latent activity for some

particular construction, when compared to some more extensive activity or construction or essence

Identität = method or process of identification; activity of producing ever new aspects that are

instantly seen as mere aspects of this same activity

Abstracte Identität = a passive state of identity resulting from a process of identification

Unterschied = 1) method or activity of differentiation (i.e. finding or making differences); 2) state

of differentiation

Absolute Unterschied = 1) method or activity for differentiating aspects within structure or process;

2) result of such a method or activity

Verschiedenheit = state of many (at least apparently) independent things that can be distinguished

through some external process of comparison

Reflexion an sich / an sich seyende Reflexion = process (or the result) of isolating group of

externally related things from one another

Gleicheit = process of finding things similar to some given reference point (or its result)

Ungleichheit = process of finding thing different to some given reference point (or its result)

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Gegensatz = ”opposition”; relation of two processes or activities that work in opposite directions

Positive = activity producing similarities, when it is compared with an opposite activity

Negative = activity producing differences; applied to itself will produce an opposite activity

Widerspruch = 1) (generally) structure of some entity having different and even contradictory

features in different situations or contexts; 2) (especially in this context) event of activity acting in

such a manner that it cancels itself