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Second chapter. Idea of cognition

We began the study of embodied self-maintaining processes or ideas from an “immediate idea” or

a self-maintaining organism. We could modify such an organism and construct a whole “world of

organisms”: in that world we could separate one organism interacting with its environment,

controlling it and finally assimilating the environment. But the organism could also relate to other

organisms as organisms, although it could not by itself step into their shoes. The organisms could

then unite and form a new organism: perhaps concretely, through some sort of copulation, but at

least through our modelling a model of a general living being on basis of many individual

organisms. It was thus possible to construct a cycle of organisms begetting ever new organisms.

This cycle could be seen as a new sort of self-maintaining process or idea, but this one used the

“ideas of first level” as its means: this kind of structure is also exemplified by consciousness or

cognition.

The aim of this chapter is then to study a structure of a Hegelian idea using other ideas as

objects: the final goal is to show how to perfect such a structure, so that the idea is to have

complete control over its objects. The chapter is intriguingly divided into two and not three sections:

firstly, the second-order idea is taken as passively copying the first-order idea, and secondly, the

second-order idea is taken as actively changing the first-order idea.

1./1479. The undeveloped shape of self-maintaining process is life: when this process divides into two aspects, it

becomes cognition.

The divisions of the subjective logic share a similar structure that could be expressed in the terms of

the first division as “concept”, “judgement” and “syllogism”. The stage of “concept” is

characterised either by unity or by unrelatedness: in the concept as such, we had an unrelated and

unified self-modification, while in the chapter on mechanism, we had only externally related objects,

and in the chapter on life, we had an embodied and unified self-modification which was unrelated to

other self-modifications. The stage of “judgement”, then, continues by either separating this unity or

by relating the unrelated things: the judgement proper divided the aspects of self-modification, a

chemical system consisted of interrelated forces and the cognition is an embodied self-modification

having another self-modification as its object. The state of syllogism has then been one where these

related and differentiated entities have been unified in some manner: the syllogism proper is a

method for uniting different aspects of self-modification, while external purposiveness was a

method for uniting real world with the desired goal. We can thus expect that the final result of the

Logic shall consist of a method for uniting or harmonising cognition with its object.

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2./1480. Self-modification becomes an independent entity, when it exists as a universal capacity to govern other entities

and organisms: such a self-modification produces something different from itself, but this apparently different is just

another self-modification. Self-modification is determined by its relation to other objects (whether it is subjective or

embodied): a merely embodied or living self-modification cannot be separated from the system of objects that embodies

it. Self-modification becomes free of organism, when it is characterised as a universal capacity: then self-modification

is divided into a mere self-modification and a living organism. Such structure characterised by the division of self-

modification from something similar to itself is exemplified in human self-consciousness.

We have already seen one example of “concept freeing itself”: this happened at the end of chemism,

when we constructed an example of a self-sustaining cycle of chemical processes and then

interpreted this cycle as an “entity” using these processes as an externally purposive agent.

Previously, we had a mere “subjective” self-modification with no external environment to apply

itself to and then an “objectivity” or a system of objects that could be used by self-modification,

although there was no self-modification: only in the teleology did we see independent “subjectivity”

and “objectivity” interacting with one another. In the structure of life these two elements had

harmonised with one another: although “subjectivity” or self-modification was the controlling

aspect, it was still immediately embodied or identified with some system of objects. When we

moved from life to cognition, we once more made “concept free” in the sense that we constructed

an example of a second-order process using the first-order process of life as means: a “higher

subjectivity” (e.g. a consciousness) has been separated from subjectivity of mere life.

3./1481. The rational psychology tried to determine in the manner of physics from the experience of personality,

whether personality had such and such characteristics, but the problem was that personality had even opposite

tendencies: the rational psychology also abstracted from all empirical notions and thus became completely empty. Kant

also noted that rational psychology couldn’t use any empirical notions without losing its purity. The only notion to use

would then be the empty idea of an indeterminate awareness: furthermore, Kant noted that such awareness couldn’t

really be differentiated from other experiences, because it accompanies all experiences. Rational psychology tried

paralogistically to use determinations of such awareness as characteristics of a determinate object.

One part of the pre-Kantian metaphysics consisted of what was called a rational psychology that

studied the structure of human consciousness or soul, as it was then called. Everyone was expected

to know from experience what a soul was: indeed, one’s own self was supposedly what one was

most familiar with. Yet, rational psychology did not mean making experiments with one’s

consciousness, somewhat one might do in physics: any mere empirical confirmations would have

been part of empirical psychology. Instead, rational psychology tried to base its results on mere

deductions starting from the notion of consciousness. Hegel notes that the problem with the rational

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psychology from his perspective was the same as with the pre-Kantian metaphysics in general: the

Wolffian philosophers tried to find clear-cut answers to questions about consciousness (whether it is

a unity or a multiplicity etc.), when the answers depended from the viewpoint from which the

consciousness was investigated (the consciousness is a unity connecting different states, but it does

have many aspects etc.).

Kant had also his own reasons to distrust rational psychology, differing from Hegel’s. Kant

started by thinking what could the rational psychologist assume, if he could use no empirical

notions: Kant suggested that nothing else but the empty idea of “having an awareness” that

accompanied all experience. Kant noted that this generality of the idea of consciousness was in

itself a hindrance to rational psychology: because we always had this awareness, we could not really

tell how to differentiate it from any “state of unawareness”. But the major failure of rational

psychology was to assume that it could deduce from the notion of this awareness what the person or

thing having this awareness was like: thus, Wolffians had tried to deduce 1) that awareness was

connected to an aware entity, 2) that because awareness could not be split into smaller pieces, the

conscious entity was also indivisible, 3) that because awareness appeared to last from one moment

to another, the thinking entity was equally stable and 4) because self-consciousness could be

separated from the consciousness of even the body, this thinking entity was immaterial. These four

apparent deductions were for Kant mere paralogisms that failed to reveal the truth.

4./1482. I have explicated these views in detail, because they reveal something of the pre-Kantian and Kantian notions

of consciousness. Pre-Kantian metaphysics tried to show what capacities consciousness had from the empirical notion

of consciousness. Kant studied only Wolffian metaphysics, but not Plato’s or Aristotle’s notion of soul: his criticism

was limited to Humean scepticism, according to which we cannot know anything of the entity that thinks. But Kant had

not even tried to explicate what thinking means, but only named it. It is a strange criticism that it would be hard to use

consciousness to become conscious of itself: indeed, consciousness does not use itself as an external means, but it does

have the capacity of taking itself as its own object, which can be verified even empirically. A stone cannot think of itself

and requires thus the assistance of an external thinker.

The pre-Kantian or more precisely modern and especially Wolffian metaphysics wanted to know

what was that thing that had thoughts: whether it was material or immaterial etc. Hegel points out

that the whole question is actually unimportant for determining the essence of thinking, which is

especially a process and not a thing – similarly, it would be a mistake in semantics to ask whether

an explosion as a process is gaseous, liquid or solid. Indeed, Hegel was convinced that Plato and

Aristotle had already had this insight: Plato had said that soul was characterised by self-movement,

that is, by a certain process, and Aristotle had expressly defined soul in general as the form or

structure of a living entity and human soul in particular as the form or structure of thinking entity.

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The question what thinks is thus inessential – and there actually might be a number of entities that

might think – while the essential problem is what thinking itself involves.

Hegel’s criticism against Kant’s criticism of rational psychology is then not meant insinuate

that rational psychology would have been somehow correct: instead, even its questions are so

wrong that the whole discipline hardly requires any refutation. Kant assumed that study of a soul or

consciousness could not be anything else but what Wolffians tried to do and so failed to see what

study of thinking might be (paradoxically, some of what Kant actually says in his three Critiques

might well have been called psychology in the Hegelian sense).

Hegel especially criticises Kant’s assumption that we cannot really discern thinking subject

or the state of “being aware” from other states, because we are always aware of something – or at

least we cannot be aware of any state of non-awareness. Kant’s point was targeted only against the

possibility of discerning the thinking subject from other possible objects, but some of his successors

developed this idea a bit forward: we could not even be aware of the subject as a subject of thought,

because we already made it an object of thought in thinking it. For Hegel, this whole problematic

involved the common problem of trying to find some entity behind thinking: a pointless exercise on

his opinion. Indeed, Kantian criticism had not really even tried to say what thinking was: it had

merely named it as thinking and then immediately moved its attention to the supposed person

behind this mask of thinking. But it is the mask or the structure of thinking that is the essential point,

Hegel says, and one of the most essential properties of this activity is that in addition to other

objects, it can also take the activity of thinking as its object: this is in fact what had been done even

in the formal methodological investigations of Kant himself.

5./1483. Conscious entity cannot remove itself as the subject of awareness, and it also cannot reduce itself to a mere

intuited object. Here Kant is identifying sensuous reality with objectivity: indeed, Kant is regarding consciousness

either as subjectivity without objectivity or as a demanded objectivity without subjectivity. But it is equally impossible

to think of a mere conscious subject, because such a subject is always conscious of something: it is the very nature of

consciousness that in it subject and object are interconnected. Kant’s hazy idea of consciousness is as abstract as the

characterisations of rational psychologist, but fails to touch Aristotelian notion of a thought thinking itself: Kant should

have seen that psychology should not deal with mere consciousness without any relation to its interaction with objects.

Kant thought that the possibility of rational psychology would demand a capacity to intuit thinking:

that is, a possibility to look from a third-person perspective the process of thinking, as we study the

process of movement in physics – only through intuition could we be sure that there really existed

some thinking entity (Kant did admit that we could intuit ourselves internally, but that intuition

apparently could only discern our internal states and not any subject behind them). Hegel’s point is

that such a thinking from a third-person perspective would actually not be thinking anymore, but at

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most thinking from the perspective of mere passivity (one aspect of thinking). Furthermore, such

third-person perspective on thinking is impossible, but equally impossible it is to think of a pure

activity of thinking subject, because thinking is always connected to some determinate object: if

nothing else, then it is thinking of thinking. Indeed, it is also to this phenomenon of “thinking of

thinking” to which Hegel refers in his remark on Aristotle’s “highly speculative notions on thinking”

– thinking is not just a passive viewing of objects, because it can construct its own object, at least

by taking itself as an object (note that thinking is here meant to include also practical determination

of objects). Mere thinking entity in abstraction from any actual process of thinking is “untrue”: not

in the sense that it would be completely impossible that a thing that happens to think might stop

thinking, but in the sense that the process of thinking is much more important issue than the

question what sort of a person one is, when one is not thinking of anything (at least not a conscious

or thinking person).

6./1484. Kant criticises specifically only Mendehlssonian proof of the immortality of soul: Mendehlsson supposes that

soul is qualitatively simple and thus cannot change into anything else. We have seen that qualitative characterisations

change from one situation to another: self-modifying structures, on the other hand, merely modify themselves, but these

modifications are still modifications of the original structure. Kant tries to counter Mendehlssonian proof by applying

quantitative notions to consciousness: although consciousness cannot be divided into parts, it has a grade of awareness

that can be diminished. But quantitative notions do not concern self-modifications.

Hegel returns to Kantian criticism of Mendehlsson’s proof of the immortality of soul that he has

already investigated in the first book of Logic (or more precisely, that he will investigate in the

second edition of that book). Hegel’s answer to both Mendehlsson and Kant is actually same: they

both try to categorise thinking through notions that are irrelevant to thinking understood as a self-

modification/determination. Thus, Mendehlsson tries to say that because consciousness cannot be

divided like a piece of matter, it cannot be destroyed. Hegel correctly points out that qualitativeness

itself is no guarantee for changelessness: what is something from one viewpoint or in one situation

can well be something else from another viewpoint or from another situation. Indeed, if we uphold

that consciousness cannot be identified with something unaware, we cannot be conscious from the

perspective of any other thinker looking at us from external viewpoint and not being aware of our

consciousness.

Kant’s own criticism that the soul could still lose its own “grade of awareness” is

rejected by Hegel for just the same reasons as Mendehlssons’s original proof: thinking as self-

modification is not restricted to any quality of consciousness or to any grade of awareness. This

implies the radical notion that even in the state of death consciousness exists in the sense that this

state of death is just modification of the original state of consciousness: it is just the final stage in

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the process of self-nullification, but still a stage of that process. One could say that Hegel thus

upholds accepting one’s immortality through redefinition of the original question: one should not

fear the state of death with possibly no consciousness at all, because this state is still just a

consequence of one’s life.

7./1485. Even Wolffian metaphysics tried to separate the inessential from the essential: Kant’s criticism ignored such

questions. It shows lack of philosophical mind, when one buries oneself in the phenomena of everyday life and believes

all else to be beyond human reason: actually, the capacity of self-modification is something higher, and the phenomena

and abstractions themselves can be shown to be inessential.

At this point we can finally start to discern what the true point of contention between Kant and

Hegel is, at least as Hegel saw it. The traditional metaphysics had tried to determine which aspects

of their environment were just fleeting, inessential and without any value and which were stable,

essential and valuable: this is what the difference between substance and phenomenon amounts to,

when we read them as Hegel does. Thus, it was not so much a question of truth in the sense of

propositional truth, but the question of goodness that Hegel is concerned about. When Kant then

had said that the “unconditional” cannot be known, Hegel at once interpreted this as a sort of value

judgment: we are locked in a world of worthless items and we cannot ever find anything truly

valuable. Indeed, Hegel even thought that Kant had forgotten this question: for instance, Kant had

failed to ponder whether it was the supposed thinking entity or the very act of thinking and

engaging with the objects that was more important. Hegel’s own answer was that the very power of

self-modification that our thinking has could show what is truly worthy of study: “thing in itself” or

objects and their aspects that lie beyond our possible experience and “I that cannot be an object of

itself” or power of thinking in its latent stage are clearly not worth of a serious study – indeed, they

cannot be studied at all.

8./1486. We have shown how to construct the structure of personality from the structure of life: this construction makes

the structure of personality something with which we have to measure the worth of the phenomena. Living organism

was already an embodied self-modification, but not the highest possible: organism is an individual object governed by a

possible new process of self-modification, which is actualised by human personality that assimilates life in order to

have power over itself. In this book we study only the abstract structure of personality: in more concrete sciences we

would look at how personality exists in nature.

Hegel’s manner of demonstrating the “truth” of consciousness is to show that one can construct it

from more abstract and “less true” structure of life. The structure of life was indeed already “an idea”

or a cycle of self-modification embodied in some system of objects (body). Yet, life appeared only

in the shape of individual organisms that did not have the capacity to “become one another”, while

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the general power of creating life out of life was something external to the organisms (this power or

genus is only something “inner” or not an entity in its own right). The “truth” or the next stage of

progression from life was then this general capacity controlling individual living organisms (at least

in the sense that it could model all of them), taken as something existing. This “universal capacity

over life” or “idea of an idea” was then the logical shape of personality, that is, an ideal model of

personality/consciousness. A concrete human consciousness, of course, has other traits beyond this

general capacity of self-determination: a human being is, for instance, a spatio-temporal creature.

These more concrete characteristics of humanity are not the subject matter of logic, but of other

sciences that can assume the results of the philosophy of nature.

9./1487. Human personality is often called a soul: soul is seen as a thing that could exist in some definite place and that

might be immortal – especially in monadology soul is like any piece of matter, just more aware of its surroundings.

Self-modification exists also as united with its given life, as it is studied in anthropology: but even in anthropology soul

is no thing. Anthropology studies the influence of nature to a personality and the capacity to instinctively be aware of

the changes of nature: furthermore, it studies all the various idiosyncrasies of a person.

Hegelian “idealism” differs from what is usually understood as idealism. In particular, Hegelianism

does not imply immaterialism of everything, if by immaterial we mean something that is not part of

the realm of natural. Indeed, Hegel here consistently denies that soul or consciousness would be an

immaterial entity: consciousness is not even an entity in the same sense as e.g. stones are entities

(collections of certain molecules), but a systematic process. It would be completely impossible to

determine e.g. where in the human body the process of life or where in the human brain the process

of consciousness is situated: such processes occur in the whole system of objects. Even more

ridiculous is to ask whether consciousness could exist without any substrate: equally ridiculous it is

to ask whether fire could exist without anything that burns. Somewhat misleadingly Hegel calls

materialistic all theories of consciousness that try to present it as any sort of entity. In this sense,

even Leibniz’s monadology would be materialism, because it takes consciousness to be an

indivisible substance just like any piece of dust – it has merely become conscious by arising to the

level of a central monad of a certain group of monads.

Although Hegel denies that human consciousness could be described as some entity – it is a

process of self-modification – he does admit that consciousness does not create itself out of thin air,

but has a certain starting point from which the process of consciousness begins. This starting point

is something that cannot be determined through an ideal model of consciousness, but must be

accepted as given by experience: and because experience can reach only contingencies,

consciousness might have different starting points. The starting point is determined, firstly, by the

natural environment in which the process of consciousness begins: a child born in jungle has

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different experiences than a child born in Arctic zone. Furthermore, the human being itself can have

various personal characteristics that are not shared by all human beings: these characteristics are in

practice just given, although they might have e.g. genetic or environmental causes. The point is that

human being need and should not stay in this level of immediacy. Instead, the science of

anthropology does not just study human beings in this “state of nature” (original or caused by

regression), but also shows how human beings should not let their idiosyncrasies and especially the

effects of natural world determine their action completely: human being should try to subjugate the

various impulses she receives without and within herself under the guidance of her own personality.

Paradoxically, only this struggle against impulses creates the conscious subject separate from mere

natural impulses.

10./1488. The next level from natural human being is consciousness: self-modifying process of human personality frees

itself from its environment, but is still on equal standing with it. The environment as an object of human personality is

independent of consciousness, although consciousness is hostile to it: the human consciousness has here opposite

tendencies of both modelling object as it is and assimilating it into the control of consciousness.

While anthropology studied the natural basis of human consciousness or soul, the phenomenology

of spirit is a science studying consciousness after its separation from its environment: consciousness

is already aware of itself as something different from the objects around it. This science was studied

by Hegel in a renowned book of a same name, but this book investigated much more than what the

phenomenology in Hegel’s philosophy of spirit does: in the book, Hegel studied also the historical

determination of modern times, but in the later phenomenology, he concentrates on the question of

how to lead a single human consciousness from the state of “appearance” to the “truth” of humanity.

The problem in the mere consciousness is that despite its becoming free of the nature it still doesn’t

manage to harmonise nature with itself. The consciousness has actually two strategies for this

harmonisation. Firstly, it might try to become passive and just theoretically model the objects

around it: this strategy ends up by consciousness noticing that what it really should model – laws

and forces controlling the natural objects – are actually in an important sense structurally similar to

the consciousness itself (that is, consciousness can use these laws and forces for its own control of

natural objects). Secondly, the consciousness might take an active stance and try to subjugate all

objects: this strategy ends up by consciousness noticing that all objects should not be subjugated,

that is, that other conscious entities should instead be recognised as equals to interact with.

11./1489. Perfected consciousness has idealised objects and deals with its own representations: this is the issue of an

empirical psychology made scientific. The perfected consciousness is still imperfect, because its content is given, but it

should aim to find the ability to construct its own content and thus to become completely perfect.

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The phenomenology of spirit ends with harmonisation of the consciousness and its environment:

consciousness learns that the environment is not something foreign, but a realm of possible actions,

and furthermore, not merely something inessential, but contains also other essential or conscious

entities. After this lesson for changing one’s viewpoint, consciousness has become “spirit” or

human personality that is at least instinctually sure of its own freedom and worth. Human being

need not then anymore struggle with the world around it. Instead, it should internalise what is given

to it – produce mental representations out of external sensations and internal feelings. The

capacities for manipulating such representations had been traditionally handled by psychology, but

Hegel does not regard these capacities as inessential and arbitrary tools: instead, they are like

modifications of the very process of self-determination. The goal of psychology is to show how one

can completely determine the content of these representations: this is possible, because human

beings are active and can produce at least linguistic signs. At the highest point of this progress lies

the Logic, whereby one constructs models of structures that all conscious entities would be capable

of constructing. After this, the conscious entity should turn its newly gained abilities to world

around her: just like her own representations, she should be able of controlling the unconscious

world around her, together with her fellow conscious entities.

12./1490. The pure structure of consciousness does not deal with the natural or given side of human consciousness,

because it is a) at stage where there is no given anymore and b) because it has not constructed a model of nature: we

should thus merely study self-modifying process that uses another self-modifying process as its means – yet, even this is

not the highest level of progression.

Hegel once again emphasises the difference between the logical structure of cognition and the

concrete human consciousness: when we are constructing an ideal structure of cognition, we are not

taking into account the possible starting point of the process of cognition. The cognition could have

various starting points, just as long as the process itself confirms to the structure of cognition, that is,

the process is self-modifying and uses some other self-modifying processes as means for its own

maintenance. In Logic we need not deal with the question of the starting point, because in Logic we

could construct any possible starting point: the time of given natural determinations is long gone,

when human beings reach the level of Logic. Then again, we have yet not constructed any model of

the nature around us: in this sense, the nature (or its model) awaits us and our construction, which

will happen in philosophy of nature.

13./1491. In its given stage, the self-modification acting on self-modification has not yet harmonised itself: it must still

perfect itself. The self-modification tries to fill itself with appropriate reality: the object of self-modifying process

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becomes some modification of this process, and the process thus achieves its goal.

In the current stage, we are looking at a structure of imperfect cognition: the cognition involved is

merely “subjective” or it is not yet completely harmonised with the system of objects that is

supposed to maintain it. The goal of this imperfect cognition is then to perfect itself or find “truth”.

Truth here does not mean any correct proposition or even collection of all such propositions. Instead,

the truth is here, as elsewhere in Hegel’s philosophy, “unity of concept and reality”: that is,

“concept” or self-modification should “realise itself” or construct all the possible modifications it

can. This means that self-modification should change the object that is given to it – e.g.

representations – into “determinations of concept”, that is, to its own modifications: that is, it must

either find ways to reconstruct what is given to it or then change what is given to it to something

that it can construct.

14./1492. Cognition is a process uniting self-modification trying to realise itself with external environment restricting it:

both extremes are embodied self-maintaining processes, although self-modification is an active and conscious, but

undetermined process, and the environment is a passive and latent, but rich process. The process of cognition constructs

the unity of these extremes and is first a mere means for this unification. The conscious self-modification separates

itself from its environment, but also tries to fulfil itself by assimilating the environment: the self-modification has the

intrinsic capacity to control the environment, and it both changes the environment to correspond to itself and changes

itself to correspond to the environment.

The Phenomenology begins with a supposedly misguided definition of cognition as means by which

the subject reaches out to the “absolute” or some object: the very same definition is here applied to

the imperfect cognition, in which “concept” or self-modifying process tries to unite itself with an

external world or environment restricting it by means of the cognition, which is then interpreted as

something different from both subject and object. Actually, both the extremes are from an abstract

viewpoint just modifications of the same structure: they are both supposed to be “ideas” or self-

maintaining systems of bodies (the environment is a living totality and the subject is a self-

modifying consciousness). Different extremes just emphasise different aspects of the idea:

consciousness is “for itself” or actively separates itself from its environment, but “abstract” or in

need of some content to fill itself with, while the environment is “in itself” or the passive unity from

which consciousness separates itself, but “concrete” or full of different aspects and modifications.

Now, in one sense the self-modifying subject just separates itself from the environment and acts in a

hostile manner towards it, but in another sense the consciousness requires the environment in order

to find “real truth” for its “formal truth” or “certainty” – that is, something to fulfil it. Thus, the self-

modifying subject has actually two different strategies. Firstly, it may try to fulfil itself through the

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content given by the environment: that is, it may try to theoretically model the environment and its

various aspects. Secondly, it may try to practically change the environment so that this environment

will correspond to its wishes. We shall see that the subject has to actually use both these strategies

in order to perfect itself.

15./1493. In its first stage the imperfect cognition is theoretical: external world is given and the self-modifying subject

is a mere form that has the formative operation of moving from latent to active modification, but requires a given

structure as its object.

Although the self-modifying cognition must ultimately use both strategies, Hegel begins from the

more passive or theoretical strategy. Indeed, the external environment appears first as something

given to cognition. The cognition is the more active part of the relation: it is “form” or an operation

moving some “content” or passive, but not featureless structure through different modifications.

The modifications that the self-modifying subject applies to this content are the familiar aspects of

self-modification, that is, the latent capacity of being modified and the activated state of having

been modified: the cognition interprets the content as having certain general capacities for

characterisation, one of which happens to be activated (e.g. this is a cup [general] that has been

filled with coffee [particular activation of one possibility]). The self-modification does not see at

this stage that it could take also itself as its own object: thus, it requires some given content to

which it can apply its cognitive capacities.

A. The idea of truth

The first state of the imperfect cognition is the theoretical attempt to passively fill itself with

whatever the environment gives to it. Yet, the cognition does not stop here in its striving for truth: it

also tries to model the various aspects and characteristics of the environment, and this modelling

requires some active effort. Thus, the theoretical cognition divides naturally into two parts:

analytical, which merely divides the given object into its element, and synthetical, which tries to

reconstruct the various interconnections between these elements. The outcome of the theoretical

cognition should then be a possibility for using the knowledge of these interconnections in practical

activity.

1./1494. Cognition has a goal: it can use itself as an object, but it cannot yet interpret its modifications as independent

objects – thus, it must make its differentiations truly independent by filling them with details of a discovered

environment. From another perspective cognition holds itself to be essential and the environment inessential and it tries

to assimilate the inessential into itself: the product of this assimilation would actually be the original passive

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environment as an object constructed by the cognition and a structure that could be indifferently moved from one

modification to another.

Hegel gives two different descriptions of the relations of the theoretical cognition and its

environment: note that both descriptions are meant to apply to theoretical cognition, although one

might be at first tempted to read the second as a description of a practical cognition. The

descriptions both characterise the relation in terms of a “contradiction”: the cognition should be

something, but it fails to do this and thus has an urge to fulfil that what it should be. Interestingly,

the descriptions characterise the terms of the relation in somewhat opposite manners: in first

cognition has qualities that the environment has in the second and vice versa.

The first description starts by characterising the cognitive subject as something that has itself

as its object: cognition can then think of itself. Yet, this self-thinking is too abstract, because the

cognition does not yet have the ability to interpret this “self as an object” as something different

from itself: in other words, the cognition can modify itself and thus apparently construct many

virtual models, but it has not the required imagination for regarding these virtual models as

independent of the subject and one another. Here, the simple and unified cognition requires then

multiplicity and variety that can be given only by the external environment that is independent of

the subject and that the subject merely discovers without creating it. This model of cognition

resembles Kantian idea of an understanding requiring the sensuous manifold in order to produce

true cognition.

In the second description, it is the cognitive subject that is characterised by the multiplicity

and the cognised environment that is characterised by the unity. Here the subject is something that

actively separates itself from the world around it, and because of its activity, it regards the passive

world that it discovers outside it as something inessential in comparison. Yet, just because this

supposedly inessential environment is independent of the subject, the subject tries to show that it

can “find itself within the environment”. That is, the subject tries to see the object as something that

it can understand and hence harmonise itself with – paradoxically this harmonisation leads then to a

return to the original unity from which the cognitive subject separated itself. If the previous story of

cognition reminded us of Kant, this description has clearly Schellingian overtones: understanding

has fallen from the unity of life and through the process cognition it strives to reunite itself with the

unity.

2./1495. This is the urge to truth in the theoretical sense. An object can be suitable for some self-modification and thus

be true, but a proper truth can be found only in cognition: this higher sense of truth is expressed in value judgements,

where an object is related not just to independent characteristics, but to an evaluative comparison between model and

reality. The self-modifying subject is theoretical, because its activities have yet no internal object: the cognition can

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only change environment without truly controlling it, and therefore it can just change the environment into its own

modifications, but not find the true essence controlling it – the unification of subject with object is then like a

unification of opposed forces, instead of a unification of elements that can be constructed from one another. Cognition

can externally assimilate an object into its system of knowledge, but this is a mere external assimilation of a given

material: it fails to perfect itself while it seeming perfects itself – the passive environment remains independent of the

subject. Peculiarly modern philosophy takes this imperfectness of cognition as its perfect condition: it assumes there is

some abstract and unreachable thing behind cognised thing – the value of thought structures is here determined by their

relation to the environment, instead of being determined by their own worth.

Hegel's crusade against Kant's notion of a thing-in-itself continues: this time Hegel's criticism need

not be restricted to some structures that Kant fails to analyse correctly, but to the very cognition

Kant's theory was meant to describe. Hegel is not saying that cognition could not assume such a

shape. On the contrary, he is just insisting that we should not call such a cognition the highest

possible – not even highest humanely possible. True, one should try to discover truth also in the

theoretical sense. Generally, an object that is as it should be is “true” or valuable”, but the highest

truth is not to be find in objects, no matter how valuable they are, but especially in the relation of

objects to some self-modification (objects satisfy their ultimate purpose by helping to maintain

some self-modifying process).

One possible manner of finding this “truth in cognition” is theoretical cognition of objects: a

person should be able to understand and model things around her in order to find perfection. The

problem with the cognition of the Kantian sort is that it cannot find this ultimate (and possible) goal.

It can “unite” itself with the object in the sense that it finds a view of some object, but this

unification is artificial: the object and the subject are “originally separated” or have no tendency to

unite with one another. Indeed, the subject has no capacity to provide an object for itself, and hence,

it requires a given object to satisfy itself. In a sense, this given object independent of the subject

appears more essential than the cognition received from it. Even if Kant himself would have

admitted that the goal of cognition is to know the object as it is known, it is no wonder that

Kantians would have desired something more, namely, the object itself before it interacted with

cognition: instead of understanding, they would have wanted a unification of subject with the object.

Hegel is here attacking those Kantians for desiring something that is actually inessential in

comparison with the cognition, which is the true goal of theoretical subject.

3./1496. The imperfect cognition should in one sense be in contact with what fulfils it, although in another sense it is

not in contact with it: this duality of viewpoints vanishes, if we don't take the mere subjectivity or the mere objectivity

as essential – this is an external change, but the cognition itself solves the problem by realising its goal and filling itself

with knowledge. We have to now consider the activity of cognition: the self-maintaining process of cognition tries to

modify the object so that it can be assimilated to the subject. Object cannot resist the modification by subject: in the

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imperfect cognition object is not yet a pure self-modification, but is modified in a particular manner – still, the object is

potentially inessential in comparison to subject, which just has to activate this certainty of itself and to realise its powers.

Hegel's simple solution for the dilemma of cognition not being able to reach things in themselves is

just to ignore these things: it is not things as they are beyond all possible cognition or the subjects of

cognition before any actual cognition that are the essential thing – instead, the very act of cognition

should be the ultimate goal we should study. Furthermore, cognition itself shows its own possibility:

we do have knowledge – even Kant admitted this. Indeed, the very activity of cognition consists in

the subject of cognition going over the discovered object and changing it into a propositional form

the cognition can handle. The subject of cognition is already sure that it can have cognition, because

it does have the abilities to do so, and the only thing it need to do is to use these abilities and to

realise its goals.

4./1497. The process of assimilating the environment begins similarly as purposive action by self-modification just

appropriating an object: objects cannot resist the force of self-modification. Self-modification remains in a state of

identity, but its own modification corresponds now to some state of being: self-modification modifies itself not to

modify the object, but to take it as it is.

Hegel describes the beginning of the process of cognition in terms of purposive action: the goal is to

fulfil the supposedly empty subject with material received from the object, and the first “premiss”

or step towards this is the immediate appropriation of the object by the subject. Hegel describes this

appropriation in terms of subject transmitting itself towards the object: a similar language was used

of a spreading of some characteristic in a mechanical system. Hegel also uses the terminology of

subject sending light towards the object, which is very appropriate here: subject of cognition is

actively seeking some objects to discover. These “light rays” then return or “reflect back” towards

the subject, and the result of this information gathering is thus a continuation of the self-feeling of

cognition: the process of cognition does not change anything within the world, but only causes

something to happen within cognition. The new state of cognition is still in a sense new: it

resembles some state of being or situation. The subject of cognition has in a sense sent “rays of

cognition” towards objects and from the rays returning it constructs a picture of what is out there:

an inner representation has been created of an external object. The act of cognition is now not

directed towards the object or its representation, but towards the cognition itself: cognition restrains

itself and tries not to do anything to that representation.

5:/1498.In the first step, cognition does not apply structures, but finds them and merely removes hindrances of seeing

them: this is analysis.

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Interestingly Hegel says that in this first analytic step cognition does not apply logical

determinations, but merely accepts them as given. Hegel does not then think that the environment

around cognition would be completely structureless. Instead, it already has some structure – in the

limiting case, a structure of there not being anything. The cognition then need not externally apply

some structure to its environment – indeed, it even should not do this, because its goal is just to take

the structure of the environment as it is.

a. Analytical cognition

The first step in the process of a cognition seeking truth or fulfilment through an appropriation of

its object is analytical: the cognitive subject is aware of some situation and then it just takes this

situation as it is. A pure analysis would leave the matters at this point, but Hegel appears to accept

some more concrete operations as still analytic: dividing a situation into its constituent elements

and arithmetically reorganising it seem also to belong to the analytic step of cognition. The aim of

the analysis is, of course, not a mere taking of situation as it is: the analysis must leave itself open

to a further synthesis, where separate situations are connected to form a framework of situations.

1./1499. Analytical cognition is sometimes defined as a process from known to unknown and synthetic cognition as the

reverse process: this is an unclear thought. Cognition in general must begin from a state of ignorance, because otherwise

it would not start, but already exist: then again, one always proceeds from familiar to unfamiliar facts – that is, when the

cognition in general has started.

Traditionally analytic method was defined as starting from a given theorem or problem and then

proceeding from this concrete statement towards the axioms and principles underlying this

statement: the synthetic method started from the opposite place of axioms and principles and from

these deduced the theorem or showed how the problem was to be solved. The concrete theorems

and problems could be thought as familiar from everyday life – one could know from experience

that e.g. angles of a triangle always summed up to two right angles. Similarly, the axioms as far

removed from concrete experience could be seen as unfamiliar to readers – for instance, it takes

quite a lot of abstraction to even understand what the parallel axiom says. Yet, in a sense these

descriptions are misleading. If we already know something, we already start to gather new

information through the information we are already familiar with and proceed to gain information

we are unfamiliar with: even in synthetic proof of a theorem already known from experience we

know the axioms (otherwise, the whole proof is only hypothetical) and we gain the formerly

unfamiliar information that the familiar theorem could be based on something more than mere

experience. Then again, the whole process of cognition must begin from a general state of

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ignorance, because otherwise the cognition would never had really started: thus, even before we can

analyse some phenomenon into its constituents, we must familiarise ourselves with it.

2./1500. Analytical step of cognition is defined as a given connection to an object: this connection involves the

application of self-modification to the object, but the cognition must inhibit this application. Only the cognition is

affected by this process and all differentiation of objects is just supposed to be given by the environment: the cognition

abstracts such an object or element from the whole environment – it cannot connect such abstract elements to one

another.

Hegel himself defines analytical cognition through the idea of a “mediation cancelling itself”: the

self-modifying subject interacts with the object, but at once restrains itself and merely takes the

object as it is. As we saw before, the object itself should have various aspects by which the subject

can fulfil itself: if nothing else, the cognition can take as its object its own interaction with the

object, and this interaction undoubtedly consists of several elements (the subject and the object).

The cognition does not then construct this diversity, but merely discovers and copies it. The

cognition thus uses only the capacity for “abstract identity”: it isolates certain elements from the

variety of its environment and presents them faithfully, without changing them or connecting them

to anything.

3./1501. Analytical step begins from a discovered object with various properties, although the discovery of the object

might still be a task left to do: the analysis does not just break this object into various smaller objects. The products of

analysis should be structures that can be constructed through a self-modifying process: these structures are also

something that can be developed out of the object in question. Thus, Kantian theory that cognition constructs all the

structures apparently discovered in featureless object is equally one-sided as empiricist theory that cognition merely

discovers structures within the object. Cognition is from one perspective construction and from another perspective

discovery: the abstracted structures do not exist in this form without the analysis of cognition, but they exist in latent

form in the object.

Hegel loosens up somewhat his definition of analytical cognition: analysis does not need to start

from a discovered ready object, but it can also begin from a task to find or make that object, as long

as all the necessary ingredients and instructions for finding or making this object are given. Thus,

Hegel can include also most of the simple arithmetic into analytic cognition: after all, an

arithmetical problem often begins with a proposal to do a certain task (e.g. summing two numbers)

and then the result is just apprehended as a single number. Furthermore, Hegel comments that the

results of the analysis are not just mere representations, but “conceptual determinations”. Now, the

difference between representations and concepts in Hegel lies in that the representations require

something given for being actualised, while concepts come with some recipes for actualising them.

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Thus, Hegel tries to say that analysis does not merely cut an object into pieces, but that it cuts them

to pieces it can itself construct (that is, at least model).

Hegel also comments on the clash between two different ways of interpreting the work of

cognition: one side or the empiricists, whom Hegel here calls realists, suppose that cognition just

discovers the various structures within the experienced objects, while the other side or extreme

Kantians like Fichte, whom Hegel here calls subjective idealists, suppose that there is actually no

structure to be found in the external objects and that the cognition itself latches these structures onto

the reality. Hegel’s position could be said to be a sort of synthesis of the two positions. Clearly,

even the results of an analysis do not exist in the original object in the same form as they do in the

cognition after the analysis: for instance, if I analyse a triangle by separating the sides and the

angles, the sides and the angles do not clearly exist as isolated in the triangle. Still, the possibility of

finding such and such elements in the analysis is clearly dependent on what is being analysed: we

wouldn’t find angles in a circle.

4./1502. Analytical cognition requires no mediating links, but just finds determinations given in the object. A true

cognition should also connect diverse aspects and situations to one another: the imperfect cognition cannot construct

diverse situations and thus must just satisfy itself with given diversity. The analysis could undoubtedly continue by

making further abstractions from its results and finally end up with a collection of isolated situations: this is no true

development, but a repetition based on the possibility of seeing one situation in one sense as abstract and in another

sense as concrete. Some structures do involve the possibility to move to other structures: e.g. we can move from cause

to its effect. Yet, such structures are just intrinsically bound up with one another and even their connection is just given:

cause is connected to an effect, because it is essentially just an aspect of a larger structure. From the perspective of

analytical cognition, this connection is merely given: it is thus indifferent whether it is called a priori or a posteriori –

even Kant failed to construct examples of such determinate connections through the capacity of self-modification.

The main problematic of analytic step in the imperfect cognition is its sterility: it can merely discern

what is already there in the object, but it does not have the ability to construct completely new

structures and thus predict what there might be. The richness of the analysis depends then on the

richness of the object involved: the results of the analysis might be abstract in comparison with the

original object, but if they are as isolated still complex, the analysis can still continue. The final

stage of the analysis is taken by an “abstract identity” – situation isolated from everything – and a

mere “diversity” – collection of other situations and objects with no intrinsic connection to one

another. Although analysis does not then by itself lead to any intrinsic connections, it might still

accept and perhaps even use them, that is, if they are given in the original structure. In such a case,

the original object has actually been an intrinsic aspect of a larger structure: if we know A to be a

cause, we can assume that it has some effect, with which it forms a structure of causality. A perfect

cognition could even produce such connections by using its own capacity of self-modification for

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constructing them – this is what Hegel himself has been doing all along in the subjective logic, what

Fichte before him attempted to do and what Kant failed to do in his Critique.

5./1503. Arithmetic is often described as analytic and it truly is so. Analytical cognition begins usually from a given

complex with diverse elements involved: arithmetic and algebra deal only with abstractions that are connected just

externally. Arithmetic and algebra are based on unconnected, independent unities: such unities can be indefinitely

multiplied and connected into further sets. Only the cognitive subject decides how to collect such unities: units in

numbers do not have any intrinsic connections. When cognition has produced several numbers, it can connect these also

through various methods: it might seem that these methods are merely given to analysis. Yet, they consist merely of an

ever growing similarisation of numbers: in addition, numbers can be unequal, multiplication is an addition of a certain

number of equal numbers, while exponentiation involves equality of the factors of multiplication.

Hegel returns to the issue of constructing number system that we have already dealt with in the first

book of Logic: this time Hegel concentrates on the analytical nature of the “theorems” within this

system. The construction itself involves something more than mere analytical method, but even this

more is not very much above analytical method, and furthermore, it is usually ignored. The

peculiarity of the number system, in comparison to other objects of analysis, is that the number

system is not given, but is indeed nothing but a human construction: this is a place where Hegel

most clearly accepts the fictionality of arithmetic. Indeed, it is not so much that the mathematics is a

work of imagination like literature, but it is more like a work of abstraction: only connections and

characterisations left are external and dependent on the arbitrary choice of a unit or reference point.

The unit itself can be anything that can be arbitrarily multiplied and collected in sets: one possible

candidate for the indefinite set of units is the series of situations starting from an empty situation.

But it is completely arbitrary what this unit it, as long as it has the required structure: thus, the

mathematician does not need to wonder where her units are coming from. Numbers then arise by

forming collections of units, and the simplest calculation or addition is nothing but an application of

this general formation of numbers: add these units and then these other units together. The series of

arithmetical operations proceed now towards more similarity of elements. By restricting the

addition to collections of similar size, we multiply: and by determining that the multiplied

collection and the multiplying amount should be similar, we raise numbers to higher powers.

6./1504. The product of an arithmetical operation is completely characterised by the operation, and therefore there can

be only arithmetical problems and not theorems: an arithmetical theorem would be just a solution of a problem and thus

a triviality. Kant has thought that “5 + 7 = 12” is a synthetical truth, because five and seven differ from twelve: but an

analysis need not be a mere tautology, just as long the difference between the starting point and the goal is completely

arbitrary. The starting point “5 + 7” expresses a task: this task is completely mechanical and its result is 12 – no true

change happens in this operation.

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7./1505. Arithmetical theorems would require a proof, but only possible proof is the actual operation of combining five

units with seven units and recognition of the result as twelve units: but this would be a problem. Problem determines

what should be done and is not restricted by given objects, which are assumed as capable of being operated in certain

manner: the result is just an actualisation of what is asked in the problem.

We have already seen that the supposed disagreement between Kant and Hegel on the question of

analyticity of arithmetic is actually more of a difference of degree and emphasis. Kant emphasises

the fact that the structures of five units and seven units do not of itself lead to the structures of

twelve units: we still have to combine the two collections either with some concrete tools or in our

heads. Hegel admits that we undoubtedly have to add the two collections, but he also points out that

this task has already been described in the statement “5 + 7”. This statement is a problem instead of

a theorem: in Euclidean geometry one differentiated between theorems (all triangles have angles

adding up to two right angles) and problems (draw an equiangular triangle), where theorems

required a proof and problems some concrete construction. In fact, all supposed theorems of

arithmetic would be mere solutions of some problems. Furthermore, the geometric problems were

not as simple as arithmetic problems, which can usually be solved through a very mechanical

operation told in the very statement of the problem: on the contrary, a geometric problem requires

some thought even to decide how to solve the problem – and even after that, we have to show that

the problem is truly solved. A purely arithmetical problem, on the other hand, requires nothing else

but the actualisation of the operation stated in the problem: add these units to those units and count

the whole collection.

8./1506. We should not try to express arithmetic in terms of synthetic geometry: we could just show that solution is

correct because the required operation has been effected. A proof of the solution of addition is to show that we have

added: more complex problems, like multiplication of decimals, might require some justification for the used procedure

– yet, separating this justification from the solution would ruin the immediacy of the analysis. Higher analysis might

require use of a more synthetical method, because the problem does not express the full solution: even the further

method used should be at least implicit in the problem. Finding sum of powers of roots of an equation can be solved by

adding the functions representing the coefficients of the equation: in addition to this method, everything else is purely

analytic – Gaussian solution of an equation through residuum is even more unanalytical.

Although Hegel makes a rather clear division between analytic and synthetic methods of cognition,

he is also aware that the two methods form more like a continuum and that e.g. individual proofs of

mathematics can be partially analytic and partially synthetic. A sum of two numbers requires

nothing else but following a mechanical operation, but even a multiplication of decimal numbers

requires at least a more careful analysis in order that we see how the multiplication is to be

performed (for instance, we have to determine where the decimal point of the result is to be placed).

20

More complex problems of number theory might then require use of operations that are not implied

in the original problem: it requires a change of a perspective and thus a Hegelian synthesis to see

that these operations could be used. Then again, the solution of the problem might also have

significant portions where no synthesis is required and the proof proceeds through mere analysis or

use of given operations.

9./1507. We have studied the infinitesimal calculus more closely in the first book: we saw that a relation of qualitatively

different number systems can be handled only through structural considerations. The construction of qualitatively

different number systems is not analytic: thus, Leibniz and others could only assume the methods of calculus, although

they can then be applied mechanically.

One particular place in mathematics where Hegel thought that mere analytics did not suffice was

differential and integral calculus. In the first book of Logic, Hegel suggested that the infinitesimal

calculus investigated “qualitative determinations of magnitudes”: in other words, the calculus

looked at relations of different number systems (e.g. different powers) and especially the “rate of

change” of one system compared to the other. The operations of differentiation and integration

involved then a move from one number system or dimension to another (e.g. from space and time to

velocity or from lines to areas): thus, they require synthesis in the sense of a movement between

different viewpoints, perspectives or situations. Then again, the actual operations are quite

mechanical or “analytical” and can be learned even by the dumbest of students, who then happily

differentiate even in contexts where they should not.

10./1508. Analysis becomes synthetic, when it has to use characteristics that cannot be constructed through the methods

given in the problem: generally move to synthesis involves a construction of differences from abstract identity.

Analytical method isolates situations, but as determined they can be inserted into relations with other situations: even

structures constructible through self-modification are handled as given in analysis – still, analysis presupposes a

complex from which it begins, and the cognition must be able to reconstruct this complex.

Analysis by itself cannot construct anything truly new, but only dissect what is given to it into ever

smaller pieces: indeed, one could analyse even structures constructed by oneself, but even then

these structures would be interpreted as something given. Analytical method can be made a bit more

complicated by allowing the use of some mechanical operations inherent in the problematic itself:

this is what happens in arithmetic. Yet, even here analysis cannot use any operations not implied in

the original problem – then it is already in its way to becoming synthetic. Still, we can move beyond

mere analysis. The analysis has as its object a situation with various aspects and elements that it

then isolates from one another: the starting point of the analysis thus already assumes that there can

be connections between such apparently isolated things and situations. Because the aim of cognition

21

is here to model its object perfectly, it must, in addition to analysis, also combine these various

elements into something resembling the original structure – this is a task for synthesis.

b. Synthetic cognition

Cognition tried to fill itself with an object with various aspects or it tried to unite itself with the

object by making a model of it. The cognition started this task by analysing the given manifold

object into its elements: or at least the object was taken as given, although from a wider perspective

it might be something completely constructed by cognition, like number system. The original object

was then a collection of various elements, aspects, situations and perspectives: even the seemingly

simple case of a number system could be embedded into a framework of mutually related and still

qualitatively different number systems. The results of the analysis should then be synthesised or

connected to one another in order to produce a complete model of the original object.

Although the model is now made for the sake of “truth”, we shall see that it can be used for

other purposes: after all, the model shows how different situations can be constructed from one

another (it is a picture of a framework of different possibilities) and thus can be used for practical

purposes (picture becomes a map). The construction of this map is divided in the Hegelian manner

into three parts: the object is defined, it is embedded into a wider division of objects and more

concrete theorems of it are constructed.

1./1509. Analytical method merely takes the object as it is: synthetic method tries to combine the various analysed

elements into a unity. Synthetic method is the second step of cognition and it aims in constructing a framework of

situations connected by the relation of necessary constructability. Different elements can be combined in a structure

where they are in a sense mere aspects and in a sense independent of one another, or they can be combined through a

self-modification capable of constructing them: the imperfect synthetic method results only in the first and thus shows

merely that one can connect such elements to one another – synthetic cognition constructs a system, but the elements of

the system are merely given as united.

Hegel begins by distinguishing two different manners, in which the aim of the synthetic method or

combination of elements separated by analysis can be achieved. Firstly, the structure resulting from

synthesis might be only a Verhältnis: that is, the elements might be united in one sense, but from

another perspective they might still be as independent and separate as before. Secondly, the

structures might be united by “concept”: that is, we could have some self-modifying process uniting

all the elements to one another. While the second possibility is clearly the ideal that the cognition

should strive for, in Hegel’s opinion, the first is the one studied in the current section. Here, the

elements are unified only in some more or less external manner, or the connection is merely “inner”

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or “mere necessity”: the elements are not in any actual process of unifying with one another, but

there is a mere latent possibility of uniting them and some external force unites them arbitrarily.

2./1510. Because the cognition is imperfect and has not actualised any connecting process within the elements, these

elements remain independent of one another, and because cognition is not an active object, it can only determine

various states, but cannot be itself an object and requires something given: cognition changes its environment into the

shape of aspects of self-modification, but still cannot construct its own objects – similarly, the cognition can construct

connections between various elements, but only from its own standpoint and not through self-modifications inherent in

the elements.

3./1511. We shall investigate various aspects of the synthetic process.

The imperfection of cognition has various results. Because the analysed elements are not unified by

any process inherent in the elements themselves, they are, from their own perspective, not even

unified, but still separate from one another. Thus, cognition might go on establishing various

connections between these elements: in effect, these connections would be laws expressed through

theorems given by cognition. Yet, these laws would be valid only from the standpoint of cognition,

while they would not have been established by constructing one element of the supposed connection

from the other element of the supposed connection with the methods and processes inherent in that

element itself (“concept”).

Furthermore, because the connections between the elements are not established in this

manner, the “subject” or the underlying element of and the force driving the cognition is not any

self-modifying activity or “concept”. In other words, the only self-modifying process involved in

the process of cognition occurs only externally in relation to the elements: that is, the cognition

comes with its own processes, which can be used to construct various examples of classification,

but these classifications are then merely latched on the elements. If the self-modifying processes

would be something occurring within the elements themselves, the whole system could be seen as

mere modification of this one process. Then the process itself would be the true individual object or

issue studied by cognition: now, instead, the cognition investigates merely some object discovered

by it.

1. Definition

The first step in the synthetic method or the combination of the analysed elements is to connect such

elements of certain object that correspond to the aspects of self-modification: in other words, we

must view the object as a certain modification of a structure with the latent capacity for that

modification. If the method used would be perfect, the defined object would actually be constructed

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while making the definition: we would truly actualise the latent capacity and see what comes out of

it. Now, the definition is just externally connected to some given object. The next step of the method

is then to embed the defined object into a system of differently modified objects.

1./1512. The cognition begins by changing the object into forms corresponding to the aspects of self-modification. The

object itself as given corresponds to the self-modification as object; the latent state of self-modification corresponds to

the genus controlling the object and having a capacity for being modified in different manners – one of these possible

modifications is then activated by the difference of the objects from other objects in the same genus.

Hegel begins by explaining what a perfect definition should be like. The synthesis of the analysed

elements should follow the example of self-modification, that is, the connected elements should

correspond to various aspects of the self-modification (this is the beginning, because cognition as

self-modification must begin from mere “concept” or self-modification and not yet move on to

judgements and syllogisms). The investigated object itself is, of course, the individual, but what are

the corresponding “universal” and “particular” elements? Hegel notes that the element

corresponding to the latent capacity of self-modification should be the “genus” of object: remember

that by genus Hegel did not mean a mere class the object belongs to, but the combination of all

methods for controlling this very object. The genus in question should also be “nearest”, not just in

the quantitative sense, but in the sense that this structure should contain the method for constructing

the various subdivisions or modifications of genus, one of which is the object itself. The particular

modification that the object should be, which Hegel calls with the traditional name “specific

difference”, corresponds then to the activated state of self-modification. The definition is then no

mere description of the object, but a recipe for constructing it: use this method in this particular

manner to make this sort of object.

2./1513. A definition abstracts from the external characteristics of the object: these are described by the representation.

Definition reduces the richness of characteristics into a few elements determined by self-modification: the object has in

one sense a general capacity, which it has activated in another sense in certain manner – the object itself is seen as

beyond these perspectives.

Definition should not be a description, because description leaves objects into the mere level of

representations: that is, description does not reveal how this certain combination of characteristics is

to be constructed. A definition, on the other hand, tells precisely this and nothing else: the rest of

the characteristics could be discovered by constructing an actual example of the object of the

definition. A definition should correspond to the aspects of self-modification, because these aspects

are nothing more than stages in a construction process of certain individual object: a true definition

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should also describe such a process. Then again, at this imperfect level of cognition, this process of

construction might seem external to the object itself: it is indifferent to the object itself whether we

happen to construct it or not.

3./1514. Self-modification finds something corresponding to itself in the aspects of definition: yet, the individual object

is not itself self-determining and the cognition of the correspondence is merely external. Structure defined by self-

modification is external to the process: it is arbitrary what object is defined and even which characteristics are used in

the definition.

The cognition tries, firstly, to fulfil itself, and secondly, to see the object as corresponding with

itself. Both desires are apparently achieved in the definition: the defined object is something

differing from the cognitive subject and therefore something that can fulfil cognition, but at the

same time, the definition describes a similar process that the self-modification itself is. Yet, at this

level the object is something that is not really “subjective” or self-modification: the object might

perhaps be externally manufactured or modelled with the instructions in the definition, but the

object itself has no power to produce such results. Thus, the relation between the object and the

cognition is from a wider perspective still external. The object is external to the step of definition:

we could choose a number of objects and all of them could be defined using the same method.

Similarly, the definition is external to the object: because we cannot find any “objective definition”

or any process within the object realising it, we could choose a number of characteristics as the

defining elements of the object.

4./1515. We shall explain this in more detail: if the individual object is completely external to the cognition, there is no

criteria for determining what characteristics correspond to the modifications of self-modification. This makes it difficult

to construct proper definitions: yet, some cases are more difficult than others. (i) Product of purposeful activity can be

defined easily, because it is completely determined by the chosen purpose: some of the required materials and the other

characteristics of the object might be determined by definition, others are arbitrary.

Hegel has already mentioned the difficulty of choosing in an external cognition of a given object

what elements of latter should we take for the definition: we only know that these elements should

correspond to stages of self-modification, but if there is no known self-modifying process within the

object investigated, we have really no clue how the choice should be made. Of course, the difficulty

level is not stable, but varies according to the object investigated. Thus, objects that are meant to

serve some purpose – vehicles, bookshelves etc. – are relatively easy to define, because the essences

of these tools, as tools, is to satisfy some need: vehicles are tools for getting people from one place

to another. Because the Hegelian definitions should also be instructions for constructing the object

or situation in question, we should already be in a position where we can construct such tools: thus,

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we couldn’t yet have a proper definition of a matter transmitter, because we cannot build such

things. Hence, a proper definition of a tool should imply e.g. what materials are required for making

such a tool.

5./1516. (ii) Geometrical objects are abstract figures constructed freely in abstract space and just like tools and

arithmetical objects depend on prior construction. True, space has its own characteristics, like three-dimensionality: still,

these characteristics are merely assumed and in connection with free constructions produce synthetical relations.

Numbers are mere constructions, but the externality of space can be used in proving further theorems.

It is fascinating that Hegel once again emphasises the complete dependence of numbers on previous

production: in this they resemble objects of purposive action. Similarly in geometry, most of the

figures do depend at least partially from the geometrician constructing such and such objects: we

can know triangle perfectly, because we know how to produce triangles. Then again, (Euclidian)

geometry has also characteristics not dependent on our production: the space studied in geometry of

Hegel’s time has three dimensions, is continuous, Euclidian etc. Hegel is quite aware that in

contemporary geometry such characteristics had to be assumed (the other possibility would have

been to treat the space of geometry as one possible model that happened to coincide with the

physical space, at least as far as then could be known). Still, these characteristics of space do not

hinder the capacities of geometrician in constructing her objects, although they make it possible to

form more substantial theorems than in mere arithmetic.

6./1517. (iii) Concrete natural and human phenomena cannot be defined so easily: such objects combine a variety of

characteristics. Cognition should separate the genus controlling the object and then its specific modification: it should

determine what characteristics belong to genus and what to this modification, what characteristics are essential etc. – yet,

there is no other criterion for this choice, but to follow the object or situation itself. An essential characteristic should

correspond to a latent state of self-modification: in case of mere situations and objects this can mean only durability or

commonality (existence over many situations). The cognition should find the whole nature of an object in a simple form:

to do this, one should construct this simple structure from the concrete object – this requires a higher analysis that does

not just dissect objects, but shows how the various aspects of the object can be united in one structure governing them.

While mathematical objects and tools can be defined easily, the independent objects belonging to

nature or to human life are far from it. In case of such objects, the definition should at least show

how to model such objects – and to do this, we should see what general forces govern this object

(its “genus”) and what modification of these forces the object is (“the specific difference”). Yet,

when it comes to such concrete objects, we have literally no other choice, but to try to determine

these things by looking at the objects in question: they are not made by us, so we cannot a priori

know what to expect of them. The problem in the case of imperfect cognition is that we cannot see

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the object as a self-modifying process, where one general structure modifies itself and thus assumes

some particular form: to do this, we should have used “a higher analysis” – apparently some form of

Goethean intuition of nature, where concrete objects are seen as modification of some Ur-form.

After an imperfect analysis, we witness a mere combination of externally related situations and

objects. The only generality we can find in such a static combination is the existence of certain

characteristics across different situations and objects: these characteristics endure through different

temporal situations or are common to differently qualified situations – a far cry from a force

controlling these situations.

7./1518. The possibility to connect various characteristics of a situation to a simple method should be demonstrated:

definition, on the other hand, should be something given as isolated characteristic of an object, which is common to

several aspects of this object. Often cognition has to satisfy itself with mere characteristic marks, which subjectively

describe an object for cognition. Such a mark could be chosen arbitrarily, just as long as it serves its purpose. Thus, an

earlobe could serve to distinguish human beings from other animals: yet, earlobe is nothing essential to a human being.

It is indifferent, how well these marks have been chosen: indeed, true cognition does not begin from such marks, but

from inexpressible feelings. We cannot choose one characteristic to represent all the richness of an opened up force of

self-modification: indeed, the various characteristics of an object might be seen as arbitrarily combined – from that

standpoint, none of these characteristics literally controls the others.

The only way to truly justify the choice of a characteristic as the defining property would be to

show that the whole structure of the object defined can be “developed” out of the supposed

definition: that is, the definition should be based on the object defined. Yet, this method would be

against the demand that definition should be the first stage, from which the rest of the object should

then be constructed: in other words, the structure of the object should be in a sense based on its

definition. As we saw in the previous paragraph, the imperfect cognition tries to handle the

problematic by choosing the second horn of the dilemma: it merely takes some characteristic that is

common to all the aspects of the object to be defined or that endures in all the stages of the object.

In other words, it replaces the demand for a central force controlling the object with demand for a

generality.

An even more radical move away from the perfect method of definition is to choose a

characteristic that is not essential for the object even in a weaker sense of generality, but only a

characteristic serving the cognition in the recognition of an object and separation of it from other

objects: in the logic of Hegel’s time, concepts were usually defined through such characteristic

marks. Of course, such marks might be completely external to the object in question: a human being

could be differentiated from other animals by the fact that humans have earlobes, but if we

genetically engineered an opossum with earlobes, it still would not be a human being. Indeed, the

choice of a characteristic mark cannot even be the starting point of the process of defining, because

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we must already be aware, at least hazily, of an object that is unified and distinguishable from other

objects, before we can say what its characteristic marks are: we do not go on looking for animals

with earlobes and find humans, but we feel that humans differ from other animals and go on looking

for some distinguishing characteristics of them.

The problem why a mere characteristic mark does not suffice to define a concrete object is

that the object is at this level a conglomeration of a number of characteristics. Even an object that is

not a mere arbitrary combination, but has a defining force controlling all its aspects appears as such

a conglomeration, because such a force produces several modifications through its activity. Yet,

such an interpretation of characteristics as independent of one another – properties as tropes and

human activities as independent forces – makes it impossible to define them in the Hegelian sense

of the word.

8./1519. The difference between the defining characteristic in abstract and its realisation causes also problems: these

problems appear, because natural and mental/social objects are also dependent on their surroundings. Thus, an object

can also fail to correspond to what it should be: we could therefore argue against all definitions, because some instances

of the genus to be defined do not correspond to the given definition. Bad plants, people and states do not perfectly

correspond to their essence, yet, they still are plants, people and states – brains fail to be characteristic mark of

humanity, because some human foetuses have no heads, and the drive to protect citizens fails to be a characteristic mark

of states, because some states kill their citizens. If definition is justified by ignoring bad instances, the definition is not

based on what has been seen: definition should still be justified by what is given. Method of definition cannot be based

on the value of the objects and thus faces the dilemma of less than perfect instances.

Hegel makes the interesting point that the current method of definition, which is based merely on

what is given, cannot solve the problem of bad or imperfect specimens. We might want to define

certain structures according to ideal examples: e.g. a state according to what states should be and an

animal species according to an individual in hospitable surroundings. Then again, such objects exist

in an environment where they are in constant contact with a number of influences, and some of

these influences might hinder their ideal development: a genetic malfunction or pollution could

cause non-ideal animals, and corrupt leaders or aggressive neighbours could suppress an ideal

development of a state. Now, the current method of definition tries to follow what is given: any

example of some genus should correspond perfectly to the proposed definition, or else the definition

is not valid. Hegel hints that in these cases we should, on the contrary, hold on to the definition as

an ideal to be followed. Furthermore, the correspondence between object and a definition need not

be black and white: an object might correspond to the definition in some sense and thus belong to

the species defined, but still fail to be an ideal specimen.

9./1520. When definition is just assumed as given, it is not justified that we can even construct it: definition merely

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dresses a given structure in shape of self-modification without considering the self-modification itself.

Hegel summarises the problems of the imperfect method of definition by contrasting immediacy of

these definitions with the “necessity of concepts”. Definitions are merely assumed: we take some

given structure, analyse it and through this analysis try to determine how it might be defined. In

case of ideal definitions, on the other hand, the object to be defined is first constructed through

some self-modifying process and the definition is provided by this very process of construction. In

the latter case, we can be sure of the “necessity” of the objects and their definitions: that is, we

know that we have an infallible method for constructing objects corresponding to that definition.

10./1521. A given state is reached only through some possible construction, thus, we must also consider this

construction: in other words, the defined object differs from other objects and should thus be differentiated from them.

“Immediacy appears only out of mediation”, that is, every given state or object can be regarded as a

result of some possible or actual construction. Thus, we now have an object that can be defined like

this, but this object is only part of a larger framework of possible situations and objects connected

by the relation of possible constructability: it makes no sense to define an object, if we cannot find

or make objects that do not correspond to the given definition. Hence, if we are given an object we

want to define, we obviously suppose that the object can be embedded in some classification of

objects with different definitions.

2. Division

We began the study of synthetic cognition from definitions, in which from an object analysed into its

elements some elements were chosen as corresponding to the latent and the active states of self-

modification: in other words, the object in question was represented as a particular modification of

some general force. Then again, because the cognition is here in an imperfect stage and merely had

some given object, it had no proper criteria for choosing the correct elements. Still, even such a

poor definition places the object into a framework of possible objects: some objects correspond to

this definition, others do not. The current section then investigates such divisions and especially

notes how the imperfect cognition fails to make proper divisions.

1./1522. A self-modification modifies itself in various manners and thus explains divisions: on the other hand, definition

is already a particular modification and the division shows its connection to other modifications. In a state of many

particular modifications, all these modifications have been actually separated from one another, and the self-

modification is found as their common element: an individual object is embedded into such framework of particular

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modifications and thus revealed as modification of a general structure which has the power to modify itself in various

manners.

We have seen that the “self-division” or process of self-modification is for Hegel the ideal type of

classification: a latent state with the capacity to modify itself produces a modification of itself,

which thus differentiates itself from the first latent state. In this ideal case, the division begins then

from “universal” or from the capacity of self-modification. The synthetic cognition, on the other

hand, begins from definition, which is already a particular modification of such a capacity. The

move from definition to division then proceeds by noting how in addition to one modification there

must be other modifications of the same genus. Of course, the ideal method of division should still

be reached, so the perfect process of division in synthetic cognition would go like this: we begin by

defining one individual object, note that it is one of many particular modifications, proceed to find

the capacity it is a modification of and then finally show how all the various modifications can be

constructed from this one capacity.

2./1523. Ideal division as a movement from general capacity to its particular modifications is determined by the

structure of self-modification: a single definition concerns an individual object, while several definitions are required

for several objects – the ideal division makes it possible to systematise knowledge.

It is somewhat unclear what the “transition” is that Hegel says to be determined by the “form of

concept”. The first candidate would be the transition from a definition to a division – indeed, that

was what the previous paragraph was mostly about. Yet, it seems that the more correct candidate is

the ideal division that truly starts from “universal” and proceeds to “particular” and thus

corresponds to the process of self-modification. The last two sentences of the paragraph then

contrast the two different methods for constructing divisions. The first method begins from a

definition that describes an individual object and then finds out that there are also other possible

modifications that have different definitions. The second or ideal method, on the other hand, is what

makes systematic science possible: that is, the ideal science is essentially based on the possibility to

construct examples or at least models of particular modifications of the structure investigated from

the given structure (e.g. we should be able to model, for instance, physical objects through space,

time and matter).

3./1524. Systematic science should start from a latent state of some structure: in actuality we meet only individual

modifications, but in cognition we should follow self-modification and begin from a potential capacity – still, someone

might protest that it would be easier and therefore more natural to begin from intuitions than from cognitions. Yet, in

cognition we are not anymore just passively intuiting, and we need to decide what is most proper for cognition. Indeed,

it is easier to cognise simple capacities than their complex realisations: latent capacity is simpler and its actualised

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modifications are more complex and need to be constructed from the simpler. This remark is valid in case of all

cognition. Indeed, we first learn to read alphabets and only later words: in geometry, we investigate first points and

lines, then triangles and circles and only later more complex figures. In physics, we should study phenomena and

objects in separation from all external connections: for instance, magnetism or electricity must be studied in separation

from their concrete surroundings – we have to experiment with them by only accepting their necessary conditions and

by varying the other conditions. Goethean manner of investigating first subjective or physiological colours arising from

the way our eyes work, then non-subjective and non-objective physical colours arising from reflections etc. and finally

objective or chemical colours residing in the objects seems natural: yet, we should actually begin from the most abstract

sort of colours, that is, from non-subjective and non-objective colours – other colours are dependent either on the

affections of seeing subject or on the characteristics of the coloured object. The same priority of abstract is valid also in

the realm of organic or human phenomena.

Hegel makes here the important remark that cognition should properly begin from more abstract or

simple matters and then proceed to more complex and concrete issues. True, this is not where

human beings naturally start: the human being in its first state intuits or perceives and an object of

such perception is usually a complex of properties. Then again, such a first state is not yet cognition,

which involves active modelling of objects instead of mere passive receptivity.

Hegel’s statement that cognition should begin from simplest and move on to more complex

refers undoubtedly to the formal ordering of systematic knowledge: one begins with simple

definitions describing a structure as a modification of some capacity and only afterwards proceeds

to demonstrate what other characteristics such a modification has. Yet, Hegel has a more general

point: even the structures first investigated in cognition should be as simple as possible, and only

later on should we discuss more complex structures. Thus, even in the simple case of learning to

read, child is not asked to decipher a word with a given meaning: instead, she must learn what

sounds the individual letters correspond to. Similarly, the Euclidian Elements does not begin from

geometry of solids, but from triangles and circles and other figures and only later proceeds to three

dimensions.

Hegel’s description of physics is interesting, because it is one of the rare cases where Hegel

tries to actually describe what natural scientists should be doing. He notices that scientist uses

experiments as a method, and also points out that the aim of a scientist ought to be the isolation of

phenomena and elements in their purity. Now, the scientist does not make mere random

experiments, but engages in controlled experiments. The aim of the scientist is to minimise the role

of other conditions in determining the phenomena. Thus, she tries to vary the conditions related to

the phenomena. If some conditions cannot be varied, then they are clearly necessary for the

phenomenon in case. In this manner, the scientist sees what characteristics the phenomenon

necessarily has and how it is connected to other phenomena.

Hegel also interestingly criticises Goethe’s theory of colours, although he is usually credited

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as a defender of this theory. Yet, Hegel is not so much arguing against any theses of Goethe, but

only against his method of presenting his case. Goethe begins from the colour images caused by

human manner of seeing: e.g. when we move our gaze from a coloured object to a bright white wall,

an image of an opposite colour seems to appear on the wall. Goethe’s point is to start from the way

how eyes see things, because it is involved in all cases of seeing some colour. Hegel, on the other

hand, says that this method starts from a complex structure of a colour interacting with our organs

and is therefore not a proper beginning. Neither is the colour of a concrete object a proper beginning,

because this is affected by the constitution of the object. The proper starting point, then, is coloured

light appearing e.g. in prismatic effects, because it is neither merely subjective nor dependent on

any object.

Hegel just mentions that in organic and human structures we should also begin from what is

simple, although he gives no concrete examples. Still, we could fathom on basis of Hegel’s

philosophy of nature that he means the investigation of organisms to begin from individual

organisms and only later introduce its environment and other organisms. Similarly, the study of

human beings should begin from individuals and only later move on to societies.

4./1525. A division separates particular modification from the latent capacity, but this latency is also in a sense a mere

modification of a more general capacity: we could thus build an indefinite number of generalities. Indeed, imperfect

cognition has no natural starting point: it could take any isolated characteristic as a beginning of a science, just as long

as it would be familiar with it – thus, definition begun from a given structure.

A peculiar characteristic of Hegelian ideal of divisions through self-modifying is that the genus of

the division is also one of its own “species” (all modifications are generated from the latent state,

which is also a modification in addition to others).Thus, the general capacity is also in a sense

particular, and this characteristic should be reflected in all sorts of divisions, in so far as they are

truly divisions. When it comes to imperfect divisions, this characteristic can be modelled only by an

indefinite process in which the current genus can always be seen as a particular species under a

more general genus. Because of this indefiniteness, the system of genera in an imperfect cognition

has no natural starting point from which the division of classes could begin. Indeed, the only

manner in which we can begin in imperfect cognition is just to take some object that we have

discovered and start to investigate it: any object is as good as any other, because no most abstract

object can be found. Indeed, even in definition the imperfect cognition began by taking some given

object, instead of constructing it, as in perfect cognition.

5./1526. From definitions cognition moves to divisions: a proper construction of divisions from definitions would

require use of a self-modifying process, but this is lacking from a cognition that has to find its structures from given

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objects. Nothing determines then the method of division or the relation of the divided species to one another: cognition

can only order the given differences and discover their common elements. The common elements are then the only

method of division and there are arbitrarily many of these: thus, the relation of differences is determined only by their

being modifications of some contingent ground of division.

We have seen that a proper division should on Hegel’s account be based on the use of self-

modification: the first latent state would “divide itself” by modifying or replicating itself, because

the earlier state could then be differentiated from the new state. In case of imperfect cognition, on

the other hand, the cognition is not looking at “self-division of concept”, but merely using such self-

divisions to model divisions with a given object. The problem is then to decide how the division is

to be made. Firstly, this problem concerns the “ground of division” or the common element which is

then to be defined. Secondly, the problem concerns the relation of the divided species: if they are

not modifications of the same process, what should they be? The only answer is to assume that the

issue investigated has some different aspects and situations. Then one is to search for any

similarities between these different situations and objects: such common elements can then be used

as a ground for the division. Problematic is that there is usually a number of equally possible

common elements to choose from: one must then just choose one common element and base the

division on it. In such a division, the divided species are not modifications of the same process:

instead, they are just particular and different instances of the same general structure.

6./1527. Because there is no proper principle of division, the cognition can follow only formal rules. Some say that

division should use up all of the concept, but actually individual divisions should correspond to the whole of the general

concept: in fact, they want to say that all the modifications of the concept should be used up, but even this is impossible

to follow in an empirical case, where we can always find more species – at most we could tautologically say that we

should find all the divisions we can. Empirical findings can lead us to find specimens that do not follow the given

definition of genus. Then we can add new species to the genus: or we can exclude these new species from genus – this

is a completely arbitrary decision. Physical nature can be divided in various manners, and in some case one principle

works better, in other cases another, and there still remains the possibility of specimens belonging to many divisions:

what is essential in one division is pointless in another.

Diatribes against the imperfections of mere empiricism are rather common in the annals of

philosophy, and Hegel here adds himself to the list of such criticisers: if we cannot find any self-

modifying method of construction for the principle of division, the whole method of division

becomes unreliable, because we cannot foresee whether empirical research might discover instances

against our current division. Indeed, Hegel even says that we have no method of empirical division,

because there is no criterion by which to truly decide how the division should work: it is completely

irrelevant whether we find a hundred or a thousand species of fruit flies. Despite the aggressive tone,

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we must note that Hegel admits that sometimes this lack of proper method is in some cases almost

inevitable. Especially the realm of physical nature, which in Hegel contains all the inorganic, but

material objects of nature, is a place with no good way to divide things, or better, too many ways to

divide things: things could be divided according to their density, colour etc.

7./1528. Empirical species merely differ from one another without having any opposed activities: if division follows no

self-division of a self-modifying process, the divided species are indifferent to one another – this happens especially in

nature, where divisions often follow mere numbers.

If the empirical divisions do not correspond to the self-division of a self-modifying process, what

structure do they follow? Hegel suggests that this is the structure of mere diversity from the book on

essence: diverse things are indifferent to one another, although they could be divided in a number of

ways according to a variety of external standpoints. Such a diversity is especially prominent in

nature, where things exists side by side without any intrinsic connection to one another: one rock

does not care whether another one lies next to it. Hegel points out that often things of nature can be

classified only according to numbers. The primary example he must be thinking is the classification

of metals according to their density: clearly metals with different densities differ also according to

other characteristics, but no apparent connection between these characteristics can be immediately

seen.

8,/1529. Although divisions of natural object seem arbitrary, in some a more correct division has been instinctually

discovered: for instance, animals have been divided according to their teeth and claws – with these organs, individual

animals separate themselves from their surroundings. Plants have been divided according to their sexual organs: indeed,

this is the highest stage of individuality plants can reach.

Still, Hegel does not think that all empirical divisions have been just a futile waste of time: in some

cases the taxonomists have hit upon some natural manner of distinguishing one object from another.

Hegel appreciates the idea of classifying animals according to the organs they use for eating: indeed,

these organs embody how animals try to survive or “separate themselves from their environment”,

and without them, the individuals would quickly waste away. Now, animals are for Hegel already

individual organisms, but plants are usually more like a process of growing without any

individuality combining the grown parts: thus, we could separate a leaf from a plant and a new plant

would arise. This lack of unity is amended in the case of sexual reproduction of plants, where the

whole plant uses its energy to create first a flower and then a fruit containing a seed: thus, Hegel

endorses the Linnean idea of classifying plants according to their different sexual organs.

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3. Theorem

The synthetic method begins by constructing a definition of an object: that is, by representing this

object as a modification of some general capacity and thus as corresponding to self-modifying

processes. A definition as a modification can then be related to other modifications, which then, in

an ideal classification, reveal a process by which all these modifications can be constructed. Yet, in

imperfect cognition the methods of definition and division often fail to correspond to their ideals:

for instance, objects are classified according to some external standpoints.

The final step in the synthetic method is the establishment of a theorem, by which

Hegel means a fulfilment of the definition: while definition introduces a capacity for constructing

an object, theorem shows what other characteristics are connected to this capacity. The final goal

of the synthetic cognition is then a framework of characteristics – what is connected to what –

which could also be used for practical change of the environment (change this characteristics to

remove that other characteristic). The investigation of theorems is divided into two subsections:

first, Hegel considers theorems as such, second, constructions of such theorems.

1./1530. 1. Theorems as fulfilment of definitions. The third step in a cognition following the hints of self-modification

leads to individual in theorem: theorems show how the different aspects of an object are connected to one another.

Definition showed one modification and division a relation of different modifications, but theorem presents an internal

diversity of a modification: if definition was a mere latent capacity, theorem realises it. Definition and theorem together

form then an embodied process of self-maintenance: yet, the imperfect cognition cannot see how the further

characteristics of an object follow from its definition.

If the definition corresponded in a sense to the latent state of self-modification – it showed what an

object is, when taken abstractly – and the division corresponded to the activated state of self-

modification – it differentiated an object from other objects – the final stage of the synthetic

cognition should then correspond to self-modification as a concrete individual. In other words, the

final stage or theorem should show that the individual is not as simple as it appeared in definition,

but unites many different aspects, modifications and characteristics. In this sense, the theorem

realises definition or fills it with some content. If the definition in question is a true definition, that

is, a method for constructing an object having that definition, then “theorem” or the concrete object

with many aspects forms in a sense the embodiment of the definition: i.e. the definition and the

theorem combine into what Hegel has called an idea. Of course, in the current imperfect cognition,

the definition was not proper, thus, as we shall see, the realisation of this definition becomes

problematic.

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2./1531. Theorem is particularly synthetic, because it unites different characteristics through an infallible construction:

on the contrary, in definition and division, self-modification is just externally applied to given objects. One might think

that because cognition does not justify its divisions or its definitions, it has no need to deduce theorems: yet, the

characteristic mark of cognition is the use of self-modification, which is applied to a given structure in definition and

division, but in case of theorem cognition reaches the concrete individuality where it must deal with independent

situations – theorem as a connection between independent entities requires more justification than mere use of self-

modification.

Definition and division did not need any justification. Hegel justifies this lack by noting that both

definition and division are meant to be mere application of the form of self-modification to a given

content: definition interprets an object as a particular modification of a general capacity, while

division presents a system of objects and situations as constructed through a self-modification of

some general capacity. Thus, in definition and division one just needs to look what aspects of the

object correspond to the aspects of self-modification. In case of a theorem, on the other hand, we

are dealing with something more properly synthetic: in theorem we should connect seemingly

independent aspects and characteristics of an issue and show that this connection is necessary, that

is, that we have an infallible capacity of constructing one characteristic, when the other is given.

Because the aspects to be connected are at the beginning of the construction apparently independent

of one another, establishing the connection requires the use of mediating positions: mere

observation must be replaced by a demonstration.

3./1532. It is difficult to determine what aspects of an issue should belong to definitions and what to theorems: one

might suggest the method of including all immediately given aspects in definition and others in theorems. Yet,

definition is already one modification in a classification of many other possibilities and is thus given only from the

contingent standpoint of cognition: furthermore, the supposedly given object might itself consist of further aspects, from

which it could be constructed. Even Euclid assumed a parallel axiom, which some have tried to prove: furthermore,

other theorems of his have been shown to be in need of further assumptions. Yet, Euclid did right when he just assumed

the parallel axiom, because its justification would involve a consideration of the structure of parallel lines, which must

be assumed in geometry.

To someone well versed with modern axiomatic systems of logic and mathematics, it might appear

incomprehensible why Hegel makes so much of the supposed difference between

definitions/axioms and theorems: it is indifferent what propositions are taken as axioms and what as

theorems to be proved, and often the choice of basic axioms is guided by such extrinsic matters as

the wish to have as few and as simple axioms as possible. But we have seen that a Hegelian

definition – we will speak of axioms later – should not be a mere arbitrary proposition chosen as the

beginning of a system, but the central capacity of construction from which all the rest of the

capacities for connecting objects and situations are to be derived. Note how Hegelian “theory of

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theorems” follows closely Euclidian Elements: “definitions” are the constructions of primary

figures (circle and straight line), while “theorems” are mainly constructions of further figures

(equiangular triangles etc.) in addition to demonstration of characteristics of these figures. True,

Hegel sees that his ideal of definitions as primary capacities of construction is rarely achieved and

then just some object is picked as the primary to be defined. The only possible guideline to take into

definition what is immediately given is of no use, because “the content of definition is already

determined and thus mediated”: that is, definition presents an object as a modification of some

general capacity, and we could just as well show how to construct this object with capacities for

constructing other objects.

Hegel’s reference to Euclid’s parallel axiom makes the reader wonder whether he is truly

suggesting that this axiom could be deduced. Clearly, he is of the opinion that Euclid himself could

well just assume this axiom without proving it: it is not up to mathematics to decide whether the

axiom is true, but merely to use it. Yet, Hegel suggests that one still could justify the axiom from

the “concept” of parallel lines, which appears to say that there should be a purely a priori proof of

the parallel axiom. Now, we must remember that concept means for Hegel a method of self-

modification/replicating, and in the case of a concrete structure, a method for realising some

possible structure (replicating the structure in the reality). Thus, a concept of parallel lines means

for Hegel some concrete method for constructing parallel lines. Even then, Hegel’s terse remark

makes one suspect that he is not aware of all the complexities involved in the matter. True,

constructing parallel lines in the space we know follows some rules, but there could be different,

non-Euclidian spaces where the construction follows different rules or is even completely

impossible. Still, Hegel might answer that he is merely modelling the properties of space he knows

and can construct: if non-Euclidian spaces are beyond the capacities of construction, they are

beyond all reasonable discussion.

4./1533. Axioms are similar: they are often just assumed as not requiring any justification. But then they would be mere

tautologies and could not move us from one viewpoint to a different viewpoint: if they allow this, they must be based on

some other science. Thus, many of the so-called axioms can be constructed in Logic: for instance, many axioms of

geometry that deal with mere quantities, like the quantitative method of deduction, are of this sort. Axioms, definitions

and divisions all need a justification, although usually they are just assumed as presuppositions of one standpoint.

We have seen that Hegelian syllogisms or deductions are actually movements from one situation or

viewpoint to another through a third: thus, the so-called “quantitative syllogism” meant for Hegel a

movement from thing having a characteristic identical with the characteristic of another thing to a

third thing that also had the same characteristic. Thus, even axioms as judgements are not for Hegel

mere propositions, but possibilities to construct one situation from another. Furthermore, even such

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capacities of construction cannot just be accepted, but their validity must be demonstrated. This

does not mean that we have to somehow prove them from more general axioms – this would just

land us back where we were, although on a higher level – but to construct a situation where it is

possible to apply such axioms: in more modern terms, we have to construct a model for those

axioms. Similarly, definitions and divisions can be justified by showing how to construct something

corresponding to a definition or division: this is, of course, no straightforward deduction of them,

but resembles more the Hilbertian manner of justifying axioms by having some possible place to

apply them.

5./1534. Some theorems might describe only the connection of partially interesting aspects of an issue, while others

might reveal the essence of all the aspects: theorem expounding such an essence is realised form of the definition –

together they form an idea.

Hegel returns in more detail to the notion that definition and theorem together form a Hegelian idea

or embodiment of some self-modification. This is, undoubtedly, not true of all definitions and

theorems, but only of ideal definitions and theorems. We have seen that an ideal definition is for

Hegel a self-modification or a capacity for constructing an individual belonging to some general

structure. Now, theorems in general are realisations of the definition in the sense that they expound

the object defined in more detail: they show how some aspects of the defined object are connected

to one another. But some of these theorems might only deal with some insignificant details of the

object in question, while others reveal connections between central aspects of the object. It is the

latter that in a more prominent sense realises the definition: the definition is the capacity for

constructing some object, while such a central theorem then shows how the various aspects and

parts of the object are connected to one another.

6./1535. For instance, in geometry some theorems are more important than others: theorems are not equally valuable,

although they all might be correct and had a place in some deduction. The importance of theorems is very closely

connected to the order of deduction: we have to look at Euclid, who has been lauded as never using theorems he hasn’t

yet established – note that this point is important only from the standpoint of some external purpose. Euclidian

definitions take figures as they are given to sense and describe them as actualisations of some capacities of construction:

the first theorems do not merely describe figures, but point out that determining one aspect of them determines also

other aspects. Thus, the first theorems on triangles show that determining some elements of a triangle determines also

other elements: Euclid uses the help of senses to prove this point and compares two triangles to one another. These

theorems have a side behaving like a central capacity and another side behaving like its realisation: three elements of a

triangle determine the triangle for abstract thinking, although in intuition we see six elements – the theorem describes

necessary conditions for constructing a certain sort of triangle. While the congruence theorems compared the

determinacy of the elements of a triangle, the Pythagorean Theorem provides a way to count sides of a triangle, when

others are known: this theorem is thus more complex and perfect. The Pythagorean Theorem closes the first book of

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Euclid, while the second book reduces first other triangles to straight-angled and then rectangles to squares: this

reduction is based on the definition of a circle which is based on Pythagorean Theorem.

It is clear that Hegel held Euclid’s geometry to be a high point of synthetic cognition: we have

already seen how Hegel said geometry to be one place where definitions could be easily provided.

Now Hegel is anxious to explicate his statement that definition and theorem together form an idea

through concrete examples, and his chosen exemplary science is once again geometry, especially as

it was presented in Euclid’s Elements. Thus, after the definitions Hegel moves on to the so-called

congruence theorems, first of which occurs as the fourth theorem of the first book of elements.

These theorems already realise the definition of triangle or make it more complex: if definition of a

triangle tells what it means to construct a triangle, these theorems tell what it takes to construct a

triangle of particular sort. Hegel even points out that the theorems themselves divide into two

aspects corresponding to “concept” or determining method and “reality” or determined elements. In

other words, when a congruence theorem tells that when determining some elements of a triangle

(such as three sides), the other elements (i.e. the three angles) are necessarily also determined: the

determination of the primary elements corresponds to the “concept” or determining method,

through which the remaining elements or “sensible reality” of the triangle is determined.

The congruence theorems can so be understood as methods of construction: determine these

elements of a triangle according to some model and you determine those other elements in the same

fashion also. Yet, these theorems do not tell anything of the respective sizes of the elements. This

lack is corrected in the Pythagorean Theorem, which is essentially “an equation”: when you

determine the size of the two catheti in a straight-angled triangle, you also determine the size of the

hypotenuse. Hegel also points out how this theorem is essential for determining other methods.

Thus, in the second book of elements, Euclid shows how one can use a similar method for

determining the sizes of the sides of other triangles, once you know Pythagorean method.

Furthermore, the end of the second book of Elements, which shows how to construct a square equal

to a given rectangle, is based essentially on the possibility of applying Pythagorean Theorem in a

circle – the trick is to notice that coordinates of all points in circle and the radius of the circle follow

Pythagorean Theorem, and in a circle having as its radius half of the sum of the sides of the

rectangle, the point with one coordinate half of the difference of the sides of the rectangle has as its

other coordinate a line, square of which equals the rectangle.

7./1536. Ideal synthetic method moves from general capacity of construction to connection of the various aspects of the

issue investigated: in other sciences, concreteness usually comes from empirically given individuals.

Euclid’s Elements shows the development of synthetic cognition in its perfection: the book begins

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from a general manner of constructing certain geometric figures and moves on then to construct

figures with more determinate properties (e.g. having sides of certain size), where these properties

are determined by the original definitions (e.g. triangles have a certain number of sides and angles).

But the other sciences, by which Hegel probably means physics presented in mathematical sciences,

do not have so natural progression: when it comes to applying laws of physics to actual movements

of the planets, we have to accept e.g. the number and size of planets as given by experience.

8./1537. Whatever the essentiality of the theorem is, it must be proved, because it combines seemingly independent

structures. Even in realised definitions the realisation makes the aspects of the definition in some sense independent of

one another: in a starting definition they merely correspond to aspects of self-modification.

Hegel has already stated that all theorems should be justified, because they connect seemingly

separate situations and objects: we have to show that these situations and objects can truly be

constructed from one another and thus can be regarded as mere aspects of a larger unity. Then again,

one might object that in the so-called “second” or realised definitions such justification would not

be needed, because the combined aspects can be corresponded with aspects of self-modification:

thus, in the congruence theorems, one might say that the three determining elements are the general

capacity and the three determined elements their modification. Yet, because this “second definition”

is realised, that is, the aspects to be combined are at least in some sense independent of one another,

the justification is needed: sides of a triangle seem at first sight to be completely irrelevant to the

angles of the triangles.

9./1538. 2. Construction of theorems. We can move from an aspect to others in one or in several moves: because the

cognition has here no capacity for modifying itself to various and even opposed directions, it must receive such a

capacity from somewhere else – this search for capacities happens in an imperfect construction.

The previous subsection dealt with theorems themselves and concluded by noting the need to justify

these theorems: we have to show that we can move from a situation characterised by one quality to

a situation characterised by another quality. Now, in the Logic we have proceeded through several

such contradictions and they have often involved a change of the given context into a completely

different form and in many times also a creative use of given constructions for purposes almost

opposite they were meant to. The imperfect cognition, on the other hand, has no such capacity of

itself modifying the situation at hand, and furthermore, it particularly finds it impossible to move

from one end of spectrum to another. Therefore it cannot use its own tools for justifying the

connection and it must then find and use some other tools that are given for this task. While Hegel

has usually called constructing a positing of something, he now uses the term ”construction” for a

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sort of external construction, in which the methods of construction are not given in the situation in

hand nor are they inherent capacities of the constructor.

10./1539. Construction uses any means capable of helping the justification of theorem: the construction seems pointless

without its purpose – afterwards, it is easy to see, why such constructions had been made. It is irrelevant, whether the

construction is made for a theorem or for a problem, because it always is something external to the task given.

The main problem in the imperfect construction is its apparent purposelessness. Indeed, the

constructions do help the proof at the end, but when the person is following a proof, she might well

wonder why such seemingly irrelevant constructions have been made – for instance, why certain

lines have been added to the figure. In this, the imperfect construction follows the structure of

external purposiveness: construction works for a purpose, but for this particular purpose a number

of constructions might suffice. Note the difference with constructions of Logic, where doing just a

certain sort of construction is the point: one e.g. observes a situation as an object and thus adds

entities to her environment.

11./1540. Proof shows the purpose: it shows how the seemingly separate aspects can be connected to one another. The

construction was not self-modifying and the proof is a movement not embodied in any system of objects: the cognition

acts externally towards independent entities. Proof does not generate the connection, but merely discovers it: cognition

is thus a mere external operation moving from external surroundings to the inherent nature of a structure. The external

surroundings or the construction is actually a consequence of the capacities of the object, but cognition reverses the

relation: the mediating link is then also a mere external method – the order of nature is opposed to the order of cognition.

Presumably in perfect cognition construction and proof would happen simultaneously: the aim of

the whole enterprise is to see what given constructions do and by using these constructions we

immediately see where it leads to. In imperfect cognition, on the other hand, the two processes are

separated and thus one-sided. We already saw that construction by itself was a pointless task.

Construction emphasises objectivity, that is, it uses some mechanics inherent in the area

investigated (e.g. the possibility to draw lines in geometry). Yet, the construction fails in

“subjectivity”, in other words, it has no intrinsic purpose, but only serves the external goal of

proving some theorem. The proof, on the contrary, is a mere subjective action without any

objectivity. That is, in proving we do mere formal deductions or move from one viewpoint to

another without causing any true change in the object itself: it is only the cognition that changes in

the proving, when its information level rises. In other words, proof does not generate the connection

of aspects, but only discovers it, while it has actually been already there in the object.

12./1541. We can now see the limits of synthetic cognition: it is best applied in geometry. Geometry investigates only

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magnitudes and thus can satisfy itself with mere formal deduction: figures in space are mere abstractions. Geometry is

to be honoured, because it leads us away from subjective interests: yet, it is still connected to mere sensibility as the

abstract structure for organising all sensations. Often the intuitiveness of geometry has been seen as the cause of its

greatness: yet, only self-modifying conceptual systems are the true sign of systematic science. Intuition gives to

geometry only sensuous verification: intuitiveness is thus merely holding geometry down – the true greatness of

geometry lies in its abstractness, which separates it from so-called empirical sciences.

We have already seen that Hegel has applauded (Euclidian) geometry as the high point of synthetic

cognition. Furthermore, he has earlier also criticised the Kantian notion that geometry has the so-

called pure intuition to thank for its success. Kant thought that pure intuition guaranteed a) that the

geometrical truths were necessary for all human beings (because all humans had the same

geometrical intuition) and b) that the geometry had at least a possible area of application (in our

imaginations, at least, and also in our sense world, if we just had any sensations). Now, Hegel is not

so interested of the question of finding any area of application for geometry and even less

enthusiastic is he to find out that the world of sensations provides this area. This is not to say that he

would in this case disagree with Kant: even for Hegel, geometrical notions truly describe the way

how our external sensations are ordered (this ordering or space is “insensible”, that is, not an

individual sensation, but still in another sense “sensible”, that is, in close connection with

sensations). What Hegel is not willing to admit is that this connection to sensation would make

geometry scientific or systematic. Instead, it is the form of synthetic science that does the trick – in

other words, the ordering of geometrical truths into definitions, axioms and theorems following

from these axioms. Now, what makes it possible to apply this form to space so well, according to

Hegel, is actually the abstractness of space: when considering mere space, we have isolated so

poorly determined object that no complications or ambiguity is left to hinder the investigation.

13./1542. The abstractness of space makes it possible to draw in it restful figures that do not change into something

completely different: geometry thus describes only one limited situation and especially quantities. When geometry tries

to compare figures with completely different construction principles, it finds incommensurabilities: it tries to move past

its limits and compare magnitudes of different qualities. At this point geometry cannot anymore rely on rules working in

limited situations: it must use the help of functions combining different situations and structures.

Regular geometry investigates only a fixed situation in which we move at most from the standpoint

of taking one figure as our reference point to a standpoint with a figure of same size as our

reference point: thus, we see that certain figures, lines, angles etc. are of the same size. Then again,

in some geometrical problems we have to connect sizes of quantities belonging to different qualities

– having different dimensions etc. – to one another. In this case the methods used by Euclid do not

suffice anymore and we have to apply infinitesimal calculus: we have to e.g. determine the tangent

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of a curve or size of an area with a known circumference. In such cases the synthetic method does

not work, according to Hegel, as well as in elementary geometry. The reason is that the move from

one standpoint to another that is essential to the proofs of geometry cannot be as purely subjective:

while in geometry we stayed well within the range of one static situation, which was merely

regarded from different viewpoints, in infinitesimal calculus we move from one qualitative system

to another and almost literally turn straight lines into curves and lines into areas.

14./1543. For other sciences synthetic method is even more insufficient: especially the relation of definitions to

theorems is unsatisfactory. The ordering is especially insufficient in such empirical sciences as physics, in which certain

forces analysed from experience are defined as the ground which is applied to individual cases. The supposed grounds

are not based on anything else, but their consequences: the deduction of the individual cases is in one sense tautology,

in another sense opposite of the true development and often merely hides the incompleteness of the theory. Only the

perceptions corresponding to theory are considered: the true grounding relation starts from the experience. The most

difficult thing in physics is thus to learn the supposed definitions, which cannot be constructed and not even properly

described, but only symbolised through images: the learning is stopped by a desire to understand why these definitions

have been chosen.

Even in geometry the synthetic method failed in more complex issues, and in other sciences it fares

even worse. Hegel returns to his criticism of the manner of presenting empirical sciences in

axiomatic guise. His point is not that the axiomatic method is completely worthless, but that it hides

the true hierarchy of importance in the science. In geometry, the definitions and axioms were

clearly something more primary – they concerned simple objects and the manner of their

construction – and the theorems then proceeded to characterise these objects and to construct more

complex objects. In case of axiomatic physics, the structures discussed at the beginning are actually

the least familiar, because they are most removed from the common experience: one does not run

into basic forces in a regular day. Although the axiomatic method might reflect the supposed order

of nature – that is, how basic forces and entities construct the phenomenal world – they certainly

don’t follow the order of cognition. Indeed, the cognition begins from complex phenomena and

introduces the basic forces and entities as results of analysis or as explanations required by

phenomena. Furthermore, without the connection to phenomena, these basic entities and forces are

completely meaningless: we cannot construct them, but we even cannot understand what they are

supposed to be, unless we say something like “it is the force that makes the apples fall” etc. Without

the connection to everyday experience, the student of physics has then no choice but to imagine

these basic entities in the best way she can – often such visual representations then misguide the

student to introduce characteristics that these entities actually don’t have (e.g. electrons might be

thought as small balls, although they are nothing like ordinary balls).

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15./1544. We have seen that synthetic method should not be used in analytic sciences: Christian Wolff tried this and

even applied synthetic method to mere empirical information, like architecture and military matters. Wolff’s attempt has

ridiculed even the method itself: still, the synthetic method has been hailed as the true method of philosophy by such

names as Spinoza. Actually Kant and Jacobi have shown that metaphysics using such method must fail: Kant showed

that metaphysics necessarily stumbles upon antinomies – yet, he still also tried to apply the synthetic method in his own

philosophy. Jacobi showed that the very method of metaphysics prevented it from conceiving freedom and other truly

worthy matters. Kant argues that metaphysics failed, because it tried to overreach the limits of cognition, while Jacobi

insisted that it failed, because its method could only categorise causal sequences: indeed, method used for limited

contexts cannot be used in case of self-modification constructing these contexts. The metaphysical method can at most

build a framework of situations connected to one another, where it is only infallibly possible to move from one situation

to another, while the situations still remain independent of one another: the connecting construction is only latent and

external to the situations, while we are looking for the self-modification generating this framework.

A synthetic method used in analytic problems appears to be a bit of overkill: when all you need to

do is to follow some instructions mechanically and see what you get, there is really no need to

change any viewpoints at all. A similar overkill is to use the synthetic method in craftsmanship,

where you should merely learn to apply some skill. The Wolffian “proofs” of building windows big

enough for two people to stand by and of constructing fortifications all around one’s encampment

could well have been expressed in a less rigorous manner as simple explanations why certain

manoeuvres are usually chosen: at least one need not put it in axiomatic form.

In case of applying synthetic method in philosophy, it is not so much a case of overkill:

instead, synthetic method bluntly fails to be philosophically useful. True, Spinoza and later

Schelling used the “geometric method”, but it clearly had its faults: e.g. Spinoza just defines

substances, accidences and modes without first establishing that there truly is some structure where

such concepts can be meaningfully applied. Hegel gives to Kant and Jacobi the credit for

dismantling the use of synthetic method in metaphysics. In case of Kant, the justification for the

praise is not so straightforward. Kant does not actually attack the axiomatic method and even uses it

in some of his writings. Yet, especially in his antinomies Kant showed how metaphysics had to run

in dilemmas, where it had to choose between two equally plausible, but mutually contradictory

characterisations of an issue. Hegel has tried to argue that the generation of antinomies lies not so

much in cognition somehow overstepping its limits, but is caused by there truly being several

equally plausible ways to characterise some issues – and that these optional standpoints contain

constructions by which we can move to another possible standpoint (e.g. a seemingly final division

of matter still contains a capacity for dividing the matter into even smaller pieces). The synthetic

method cannot capture this move to other standpoints, because it can make only “subjective moves”,

that is, moves from one state of information to another, which do not essentially affect the issue in

case.

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Jacobi criticised directly the synthetic method for its incapacity to handle certain ontological

structures. The proofs of synthetic method move merely from one given situation to another that is

not generated by the proof: the cognition does not construct – or the construction is a separate step

in the process – but only moves in an already established framework of possible standpoints,

situations and contexts. The various contexts are then actually independent of one another, and the

capacity to move from one context or situation to another is “merely internal” – a mere latent

capacity – or “merely external” – subjective moving that does not arise from the contexts

themselves. Such a method is then useful only in cases where the “roads are already given”: that is,

where there issue is already at least implicitly full of connections between characteristics etc. and

the cognition is forced to use these connections to move from one aspect of the object to another,

because nothing else has been given. In other words, in a synthetic method the object forces the

cognition to follow certain route, or at least it restricts the possibilities of what the cognition can do

– the world is like this, so you cannot do this or that etc. Thus, the world as described by synthetic

method seems to leave no room for freedom: one cannot go on making one’s own roads and

connections, but one is forced to use the existing network. Hence, one cannot also show any true

connection between the various contexts, because one cannot literally construct one context from

another context.

16./1545. In synthetic method self-modifying cognition sees merely the process of latent self-modification activating

and dividing itself represented in its object: yet, this object fails to be itself a self-modification. Self-modification has

thus not truly mastered the object: the cognition has not found its perfect state, because of the failure of the

correspondence between itself and its object. Still, a framework of situations related through a relation of infallible

constructability can be interpreted as produced by a self-modifying process: we have seen how this happens at the end

of the second book on Logic. Here we are not merely constructing self-modification from this framework, but self-

modification as object of self-modification from the framework as an object of self-modification: yet, the construction is

essentially same. The construction is also effected by an external observer and not by the cognition itself, which only

discovers the result of the construction: cognition aware of its own powers of construction is active or practical.

The aim of the cognition has been to view the object investigated as corresponding to itself, but its

success in its theoretical task has been only partial. True, it has been able to view the object as a

combination of aspects corresponding to the aspects of self-modification: that is, in the division the

whole area of investigation is seen as a modification of a central structure, and even in an individual

object the cognition can discern one central definition or core pointing out to theorems or more

concrete aspects of the object. Yet, the cognition is still seen as external to the object in question: it

does not have the capacity to itself construct such an object from its own materials – not even a

model of such an object – but it is forced merely to mimic the object and modify its own state of

mind according to the aspects of the object. The result of theoretical cognition seems then to be

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nothing else than mere framework of various aspects connected externally to one another, in which

the self-modification is forced to move without any capacity of changing it (if I take triangle with

sides this long, the angles must be that large etc.).

Yet, we have already seen that from a structure of “necessity” or framework of situations

connected through a relation of infallible constructability it is possible to construct a “free concept”

or self-modification that apparently creates such a framework. The trick was to change one’s

viewpoint. The framework should not be seen as an environment restricting one’s actions, but as a

set of possible choices open to oneself in a particular situation: furthermore, the aim of the choices

should not be seen in changing the environment, but in changing one’s own possibilities of action.

The set of choices available for a person undoubtedly varies from one situation to another, but at

least everyone can choose how to view the choices in question: even in the extremely restricted

situation where one can only change subjective states of mind, this possibility of change can be seen

as a sort of freedom. Now, we are here not dealing straightforwardly with such a framework, but

with a cognition examining such a framework: still, the basic construction is similar. The cognition

itself cannot yet do this construction by itself, but it can follow our example and thus note that

beyond mere theoretical powers it has capacities for at least some free action.

B. Idea of good

We began the study of cognition from a state where it tried to find truth, that is, where it tried to fill

itself with the fullness of its environment and at the same time find something corresponding with

itself in this environment. The cognition started by analysing its environment into smaller

constituents. Then it chose suitable aspects to make a definition of the investigated environment or

its elements: in the definition, cognition regarded its object as a modification of some general

structure. This one modification was then embedded into a system of modifications of the same

general structure in a division. Finally, the cognition tried to establish theorems of connections

between the central definition of an object and its further characteristics. Its method was to use the

mechanisms of the object for constructing sufficient material to be used in the proof, in which

cognition moved from one way of looking at the object to another, thus, establishing the wanted

connection between the aspects.

The result of the theoretical task of cognition was then a sort of map of its environment:

from here you can get to there, but not to anywhere else. Although this map appeared to restrict the

cognition, from another angle it served the cognition by showing how it could change things. Thus,

we could construct practical cognition on basis of theoretical cognition. The aim of this section is

then to show how practical cognition is able to truly make its environment what it wants that to be:

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the problem is, like in the theoretical cognition, the independence of the environment.

1./1546. When self-modification has the capacity to determine its own condition, it is an individual object separate from

its environment: it strives to realise itself in its environment. Theoretical cognition required the environment for filling

itself with some object: practical cognition is itself an object among other objects, but it values itself more than its

environment – the cognition has the capacity to determine itself and is thus perfect, but the environment is only

determined by external constructions.

Cognition in its theoretical task was not taken as an object in its own right, but merely modelled

itself on basis of some given object. When the cognition has “itself as its object” and is “in and for

itself determined” – that is, when it strives to further its own existence and knows its own capacities

of construction – it can be seen as an object in its own right. Indeed, the cognition is here acting and

can thus produce for itself a system of objects that it can control. Even though cognition is now an

individual object or embodied in a system of objects, it also is separable from other objects and

generally from its immediate environment: cognition discovers something independent of itself. Yet,

the cognition also now places value judgements on to its environment. As a self-modifying process,

the cognition should value itself over mere objects. Thus, it should think that it is (in addition to

other self-modifications of the same level) the only truly worthy object, while the environment at

large is “nullity”, that is, worthless and unable to resist the self-modifying processes: its own

determinations can be “posited” by some external agent, and furthermore, it lacks any central force

of its own that would organise and determine it.

2./1547. When self-modification is modified to exemplify itself, it strives for goodness: goodness has an absolute worth

as a system of objects governed by free self-modification – this striving for goodness is more valuable than striving for

truth, because it is not merely passive, but acts. The cognition strives to see goodness realised as something that it can

discover, but it already controls a system of objects. Cognition does not then try to appropriate aspects of its

environment, but to implant its own determinations to environment and in this manner show its superiority. Because

cognition or will can determine itself, it can choose some particular structure it tries to implant on objects around it: this

is only one possible and hence limited structure that the environment might not contain. Yet, this structure also

maintains the will and is thus perfect: the imperfection of the chosen structure means only that it has not yet been

realised in the environment – the structure or goal in its unrealised form already is immeasurably worthy, because it

conforms to the general structure of self-determination.

Hegel begins the new paragraph by identifying what good is: “this determination which is contained

in the concept and which is same as concept and which concludes the demand for individual

external actuality”. Beginning with the word “this”, we can at once see that the structure designated

as good has actually already been mentioned in the previous paragraph: this must be the

“determination of the concept within itself as a universality that as such determines itself”. Thus, we

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are speaking of some modification within a self-modifying process known as cognition – or as

Hegel shall soon name it, will. Yet, it is not just any old modification, but a modification that

corresponds with the self-modification itself: that is, it is cognition looking at itself or its awareness

of its own capacities and processes that should be called good.

Furthermore, the good “concludes” the demand for realisation of cognition. This

“conclusion” must be understood in two different senses. In one sense, the goodness is already this

realisation: a person capable of many things and aware of her own capacities is already an object or

even a system of objects, and furthermore, she also constantly maintains a self-modifying process of

her own consciousness. Still, the “conclusion” suggests, in another sense, a decision to realise itself.

Although the person is already an actual entity, the object of herself – the good – is only one

possible structure among many others. Indeed, the person can construct – in this case, discover –

situations where other structures hold: that is, the environment around the person contains places

that no person or self-modifying cognition controls. Now, the cognition of good strives to realise

itself by taking over these given situations. One might ask what right the person has to take control

of the external environment. Hegel would answer that the very object called “good” or the

realisation of a self-modifying process is the ultimate source of value: it is already “true”, although

it has not yet been realised, or it is “absolute”. The task is then only to spread the goodness of the

person to all regions that are not yet under the rule of any self-modifying process of consciousness.

2./1548. The process of realising good resembles the process of realising any goal: the difference is that the good is a

valuable goal. A further difference arises in the realised state: a limited goal can only provide means for new actions,

because they are not truly valuable. Because good is also in a sense limited, its realisation will not stop the need for new

actions: although a good goal is inherently valuable, its realisation is a mere situation that can change. As limited, a

good goal may have to combat with other good goals: furthermore, the independent environment can hinder and even

prevent the realisation of a good goal. Good remains a mere unrealised task in comparison with the actual situation in

hand: the realisation of good is postulated, but a postulate is a mere wish. We can thus separate the realm of goodness or

human consciousness from the realm of evil or mere reality: the battle of these realms has been described in

Phenomenology. The cognition is here aware of another self-modification, which is also a system of objects, or it is

conscious of itself.

We have seen that the good is a goal, and like all goals or purposes, it follows the structure of

purposive action and is to be realised. Still, good goal is not just any goal whatsoever: although the

good goal is one among many possible, it is still “absolute” or valuable in itself. Thus, while a mere

goal cannot satisfy self-modifying subject and remains thus a mere mediating link towards other

goals, a realisation of good goal is a truly worthy achievement: it is an end in itself.

Despite the worth of a good goal, an action striving for such a goal is still open for various

imperfections. Firstly, although the good person as such has the capacity to achieve her goals, the

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goal itself is not a self-modifying process, but a simple situation, although a good one. Thus, further

events might ruin even a worthy goal: even if I would try to be good and give money to charity, all

the cash I gave might disappear into the pockets of a corrupt charity collector. Furthermore, even

though a good goal conforms to the well-being of some self-modifying process, the very same

process might also have other good goals and other self-modifying persons still others and some of

these might even contradict one another: I may want to help my sick aunt by stealing some

medicine for her, but at the same time my wish contradicts the rights of the person owning the

medicine.

Hegel summarises the problems the good-seeking will or cognition encounters by noting

that the cognitive and volitional subject still faces an independent environment: this environment

consists both of physical nature and of the multiplicity and possible strife of persons. Thus,

although in subjectivity all thoughts would be tuned towards the good of any self-modifying subject

and these goals would be “transparent” or in complete control of the subject, the reality might still

be full of “darkness” or thing not under the definite control of any subject. Hegel refers here to his

Phenomenology and especially to his criticism against Kantian theory of postulates, which just

assumes that we must believe in the possibility of overcoming this opposition, although no real

progress towards this goal is ever made.

3./1549. Will as self-consciousness fails to change itself into consciousness. That is, practical cognition is in need of

theoretical: theoretical cognition is a mere passive capacity that requires some fulfilment, which it gets from its

environment, which is thus the truly valuable element. Practical cognition regards its environment as in itself worthless:

it cannot perfect itself before becoming theoretical.

At the end of the previous paragraph Hegel noted that the practical cognition studied here

corresponds to the self-consciousness in phenomenology: both self-consciousness and practical

cognition hold that the self or subject is the most important object there is and strive therefore to

extend the control of subjectivity over its environment. Here Hegel then notes that practical

cognition lacks consciousness, which similarly corresponds to theoretical cognition. That is,

practical cognition sees worth only in conscious self-modifying processes, but no worth in any mere

situations. Thus, its attempt to translate its own process of good action into a form of stable

situation is bound to fail, because the result achieved is not worthy at all: for instance, embodying

democratic process into a constitution would fail to produce any really good effects, because

constitutions by themselves are mere dead words and not democratic processes. A solution to the

dilemmas of moral action would then be simply to accept that even such static situations and objects

have some worth in themselves and not just as playing field for good action.

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4./1550. The move to consciousness from self-consciousness happens without any effort: action begins by will

immediately appropriating some object and continues by will using this object as means for furthering its efforts. Good

activity is the truly worthy embodiment of self-modifying consciousness, while the environment opposes the will only

by being determined against this activity or by being undetermined: yet, good action has already shown its power over

the environment in the first step. We must thus merely unite the two steps: the second step adds only the capacity to

control the environment through mediating links. Just like in purposive activity in general, the first appropriation of the

object is already an achievement of a goal, and the second step merely shows how to extend this achievement to regions

not immediately under the control of will: in the first step, will attaches itself into an object among others, but in the

second step it shows that it can discard any object it has happened to take. If the activity still seems unable to achieve

what it aims to, then we are forgetting the power of activity over mere situations and objects: here we do not recognise

the general capacity of controlling the environment. The good activity can achieve its goal and the will just needs to

change its own attitude.

In the last paragraph Hegel defined the solution for the problem of moral activity: one should be

able to see the external environment also as worthy of something. Here Hegel then tries to show that

this in some sense happens automatically during good activity. Firstly, it is not all of the

environment that we should worry about, but only that part in which goodness has not prevailed:

this part consists of evil – self-modifying process turned rampant or against itself or other self-

modifying processes – and of indifferent that is not good, but also not bad – the world without any

control. Now, Hegel points out that self-modifying processes have already shown their power over

mere situations and objects: will has the capacity to take the environment appearing to it and use it

to further its own purposes and the purposes of all wills (of course, in those ways that it is simply

possible to act on the environment: all impossible activities are ruled out from consideration as

completely meaningless). In this first appropriation of its environment, the will attaches itself to a

particular situation or object: this is what I will use. Still, the will is not inherently glued to the

situation in question, which it then shows in the second step: it uses the given situation in order to

construct another one.

Through its own action, the will has shown itself to be in control of its environment,

while the environment is not in control of it. Still, the will might refrain from admitting its own

power: after all, when the action has ended, there still is some environment independent of it. What

the will has apparently forgotten is that it itself has caused the new situation and that it still has the

ability to make a better situation, if this one does not satisfy it. Thus, Hegel concludes, the will has

nothing else but itself to blame for not being happy with the way the situation is: the will should not

try to change merely its own environment, but also its own attitude.

5./1551. Although the second step of action appears to result in a mere repetition of the opposition between subjectivity

and its environment, in another sense it shows the control of will or embodied self-modification over the given

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environment: the environment is at first seen as a mere unimportant field for activity realising its own goals. The action

raises the worth of the environment: thus, the opposition between the environment and the good activity is cancelled

and there is then no need to repeat the same action. The result is a situation not dependent on action anymore: thus,

good activity has implanted its goodness to the reality surrounding it. Subject is not just separate from the environment,

but can harmonise itself with it: here the cognition theoretically perceives its environment as something practically

controlled by cognition – this is the final goal of Logic.

Hegel’s strategy in showing the will its hold over its environment is to change the viewpoint from

individual actions to universal capacities: essentially the same strategy that Hegel uses against all

cases of infinite progression. Indeed, even at the beginning of the action, the environment is

supposed to be something that the will can and should control. What the good action of the will

does is actually raise the worth of the environment from the level of mere world to the level of

world controlled by conscious beings. Thus, at least this part of the environment of the willing

cognition is already good in some measure and there is no need to do any good actions to improve it

to this level – and if need be, other parts of the environment could also be raised to this level or this

part could be improved to another level of goodness. Shortly, the willing consciousness has the

ability to raise the value of its environment. Now, the result of the good action – the environment in

so far as it is controlled by the willing cognition – can be taken as a new object of the cognition, but

unlike the original object of the cognition, this object is immediately in harmony with the cognition.

The cognition has then the opportunity to see its own capacities embodied in its environment: it can

know what it can do. This process resulting in self-knowledge of one’s own capacities of

construction is the final “absolute idea” that ends the Logic.

Glossary

Erkennen = 1) “cognition”, an “idea” or self-maintaining process using another self-maintaining

process (its environment as an object) as a means for some goal; 2) “cognition proper”, cognition

attempting to model its environment (this goal is called Wahrheit)

Analytische Erkennen = operation of cognition proper, in which the object is merely divided into its

constituents

Syntetische Erkennen = operation of cognition proper, in which objects or constituents of an object

are connected through operations, by which one object or constituent can be infallibly constructed

from another

Definition = “definition”; operation of representing a given object as a particular modification of

some general structure

Einteilung = “division”; operation of relating several objects as modifications of same general

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structure

Lehrsatz = “theorem”; operation of representing a given object, with a known definition, as having

certain characteristics

Zweite Definition = “second definition”; theorem containing essential principles, from which to

determine or construct the whole object

Beweis = “proof”; finding a link from definition to a theorem

Construction = operation of modifying object, required for the proof to work

Willen = “will”; cognition attempting to accommodate its environment by making it suitable for

self-modifying processes (this goal is called Gut)