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same time a transformation into a higher concept.

§ 195.

Nature is, in itself a living whole. The movement of its idea through its sequence of stages is more

precisely this: the idea posits itself as that which it is in itself; or, what is the same thing, it goes into

itself out of that immediacy and externality which is death in order to go into itself; yet further, it

suspends this determinacy of the idea, in which it is only life, and becomes spirit, which is its truth.

§ 196.

The idea as nature is: (1) as universal, ideal being outside of itself space and time; (2) as real and

mutual being apart from itself particular or material existence, - inorganic nature; (3) as living

actuality, organic nature. The three sciences can thus be named mathematics, physics, and

physiology.

I

Mathematics

§ 197.

(1) The first or immediate determination of nature is the abstract generality of its

self-externality,-its unmediated indifference, space. It is the wholly ideal juxtaposition, because it is

being outside of itself and absolutely continuous, because this being apart from itself is still entirely

abstract, and has no specific difference within itself.

Much has been said, from different theoretical positions, about the nature of space. I will mention

only the Kantian determination that space is, like time, a form of sensory intuition. It has also

become customary to establish fundamentally that space must be regarded only as something

subjective in representation. Disregarding what, in the Kantian conception, belongs to subjective

idealism and its determinations (cf § 5), the correct determination remains that space is a mere

form, i.e., an abstraction, that of immediate externality.-To speak of points of space, as if they

constituted the positive element of space, is inadmissible, since space, on account of its lack of

differentiation, is only the possibility and not the positing of that which is negative and therefore

absolutely continuous. The point is therefore rather the negation of space.-This also settles the

question of the infinitude of space. Space is in general pure quantity (§ 53f), though no longer as a

logical determination, but rather as existing immediately and externally. Nature, consequently, does

not begin with quality but with quantity, because its determination is not, like logical being, the

absolute first and immediate, but essentially a mediated being, a being external to and other than

itself

§ 198.

Space has, as the concept in general (and more determinate than an indifferent self-externality) its

differences within it: (a) in its indifference these are immediately the three dimensions, which are

merely diverse and quite indeterminate.

But geometry is not required to deduce that space necessarily has precisely three dimensions, for it

is not a philosophical science, and may therefore presuppose space as its object. Moreover, even

apart from this, no thought is given to the demonstration of such a necessity. The necessity rests on

the nature of the concept, whose determinations, however, because they depict themselves in

these first elements of being apart from themselves, in abstract quantity, are only entirely superficial

and a completely empty difference. One can also, therefore, not say how height, length, and width

differ from each other, because they only ought to be different, but are not yet differences.-Height

has its more precise determination as direction according to the center of the earth, but this does

not at all concern the nature of space for itself Following from this point it is equally as indifferent

whether this direction is called height or depth, or length or breadth, which is also often called

depth.

§ 199.

(b) But the difference of space is essentially a determinate, qualitative difference. As such it is (a)

first, the negation of space itself because this is immediate and undifferentiated self-externality, the

point. (b) The negation as negation, however, is itself spatial, and the relation of the point to space

is the line, the first otherness of the point. (c) The truth of the otherness is, however, the negation

of the negation. The line, therefore, passes over into the plane, which on the one hand is a

determinacy opposed to line and point, and thus is plane in general, but on the other hand is the

suspended negation of space, and thus the re-establishment of spatial totality, which, however,

now contains the negative moment within itself an enclosing surface, which splits off an individual,

whole space.

That the line does not consist of points, nor the plane of lines, follows from their concepts, for the

line is the point existing outside of itself relating itself to space, and suspending itself and the plane

is just as much the suspended line existing outside of itself.-Here the point is represented as the

first and positive entity, and taken as the starting point. The converse, though, is also true: in as far

as space is positive, the plane is the first negation and the line is the second, which, however, is in

its truth the negation relating self to self the point. The necessity of the transition is the same.-

The other configurations of space considered by geometry are further qualitative limitations of a

spatial abstraction, of the plane, or of a limited spatial whole. Here there occur a few necessary

moments, for example, that the triangle is the first rectilinear figure, that all other figures must, to be

determined, be reduced to it or to the square, and so on.-The principle of these figures is the

identity of the understanding, which determines the figurations as regular, and in this way grounds

the relationships and sets them in place, which it now becomes the purpose of science to know.

It may be noted in passing that it was an extraordinary notion of Kant's to claim that the definition

of the straight line as the shortest distance between two points is a synthetic proposition, for my

concept of straightness contains nothing of size, but only a quality. In this sense every definition is a

synthetic proposition. What is defined, the straight line, is in the first place the intuition or

representation, and the determination that it is the shortest distance between two points constitutes

in the first place the concept (namely, as it appears in such definitions, cf. § 110). That the

concept is not already given by the intuition constitutes precisely the difference between the two,

and is what calls for a definition. That something seems to the representation to be a quality,

though its specificity rests on a quantitative determination, is something very simple, and also the

case for example with the right angle, the straight line, and so on.

§ 200.

(2) Negativity, which as point relates itself to space and in space develops its determinations as

line and plane, is, however, in the sphere of self-externality equally for itself and appearing

indifferent to the motionless coexistence of space. Negativity, thus posited for itself is time.

§ 201.

Time, as the negative unity of being outside of itself, is just as thoroughly abstract, ideal being:

being which, since it is, is not, and since it is not, is.

Tune, like space, is a pure form of sensuousness, or intuition; but, as with space, the difference

between objectivity and a contrastingly subjective consciousness does not matter to time. If these

determinations are applied to space and time, then space is abstract objectivity, whereas time is

abstract subjectivity. Time is the same principle as the I = I of pure self-consciousness; but the

same principle or the simple concept still in its entire externality, intuited mere becoming, pure

being in itself as sheer coming out of itself. Time is just as continuous as space, for it is abstract

negativity relating itself to itself and in this abstraction there is as yet no real difference.

In time, it is said, everything arises and passes away, or rather, there appears precisely the

abstraction of arising and falling away. If abstractions are made from everything, namely, from the

fullness of time just as much as from the fullness of space, then there remains both empty time and

empty space left over; that is, there are then posited these abstractions of exteriority.-But time

itself is this becoming, this existing abstraction, the Chronos who gives birth to everything and

destroys his offspring.-That which is real, however, is just as identical to as distinct from time.

Everything is transitory that is temporal, that is, exists only in time or, like the concept, is not in

itself pure negativity. To be sure, this negativity is in everything as its immanent, universal essence,

but the temporal is not adequate to this essence, and therefore relates to this negativity in terms of

its power. Time itself is eternal, for it is neither just any time, nor the moment now, but time as time

is its concept. The concept, however, in its identity with itself I= 1, is in and for itself absolute

negativity and freedom. Time, is not, therefore, the power of the concept, nor is the concept in

time and temporal; on the contrary, the concept is the power of time, which is only this negativity

as externality.-The natural is therefore subordinate to time, insofar as it is finite; that which is true,

by contrast, the idea, the spirit, is eternal. Thus the concept of eternity must not be grasped as if it

were suspended time, or in any case not in the sense that eternity would come after time, for this

would turn eternity into the future, in other words into a moment of time. And the concept of

eternity must also not be understood in the sense of a negation of time, so that it would be merely

an abstraction of time. For time in its concept is, like the concept itself generally, eternal, and

therefore also absolute presence.

§ 202.

The dimensions of time, the present, future, and past, are only that which is becoming and its

dissolution into the differences of being as the transition into nothingness, and of Nothingness as

the transition into being. The immediate disappearance of these differences into individuality is the

present as now, which is itself only this disappearance of being into nothingness, and of

nothingness into being.

(1) The finite present is differentiated from the infinite in that the finite is the moment now and

hence as its abstract moments, as past and future, which is different from the infinite as from the

concrete unity. Eternity as concept, h r, contains these moments in itself and its concrete unity is

therefore not the moment now, because it is motionless identity, concrete being as universal, and

not that which is disappearing into nothingness, as becoming.-Furthermore in nature, where time is

now, there does not occur the subsisting difference of these dimensions; they are necessarily only

in subjective representation, in memory, fear, or hope. The abstract past, however, and future of

time is space, as the suspended space is at first the point and time.

(2) There is no science of time in opposition to the finite science of space, geometry, because the

differences of time do not have the indifference of being outside of itself which constitutes the

immediate determinacy of space, and therefore they can not be expressed as spatial

configurations. The principle of time only reaches this ability when the understanding has paralysed

it and reduced its negativity to the unit. This motionless unit, as the sheer carnality of thought, can

be used to form external combinations, and these, the numbers of arithmetic, can themselves be

brought under the categories of the truth as intuition or as understanding merely for itself because

the latter is only abstract, whereas the former is concrete. This dead unit, now the highest

externality of thought, can be used to form external combinations, and these combinations, the

figures of arithmetic, can in turn be organised by the determination of the understanding in terms of

equality and inequality, identity and difference. The science which has unity as its principle is

therefore constituted in opposition to geometry.

(3) The name of mathematics has moreover been used for the philosophical observation of space

and time, because it lies close to this observation, despite the fact that mathematics, as noted,

considers strictly the determinations of magnitude of its objects and not time itself but only the unit

in its configurations and connections. To be sure, time becomes in the theory of movement an

object of science, but applied mathematics is generally not an immanent science, precisely because

it involves the application of pure mathematics to a given material and its determinations as derived

from experience.

(4) One could still, however, conceive the thought of a philosophical mathematics, namely, as a

science which would recognise those concepts which constitute what the conventional

mathematical science of the understanding derives from its presupposed determinations, and

according to the method of the understanding, without concepts. However, since mathematics is

the science of the finite determinations of magnitude, which remain fixed in their finitude and valid,

and should not change in transit, thus it is essentially a science of the understanding. And since it

has the ability to express spatial figures and numbers, which gives it an advantage over other

sciences of this kind, it ought to retain this ability for itself and to avoid contamination by either

concepts, like time, which are heterogeneous to it, or empirical purposes. It therefore remains

open for the concept to establish a more fundamental consciousness than has hitherto been shown,

both in terms of the leading principles of the understanding and in terms of order and its necessity

in arithmetical operations, as well as in the theses of geometry.-If one wanted to treat the forms of

space and the unit philosophically, they would lose on these grounds their particular significance, a

philosophy of them would become a matter of logic, or would even assume the character of