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another concrete philosophical science, according to the ways one imparted a more concrete

significance to the concepts.-

It would, however, be a superfluous and thankless task to try to use such an unmanageable and

inadequate medium as spatial figures and numbers for the expression of thoughts, and to treat them

violently for this purpose. For the specific concept would always be related only externally to

them. The simple elementary figures and numbers can in any case be used as symbols, which,

however, are a subordinate and poor expression for thoughts. The first attempts of pure thought

took recourse to such aids: the Pythagorean system of numbers is the famous example of this. But

with richer concepts these means became completely unsatisfactory, since their external

juxtaposition and contingent combination are not at all appropriate to the nature of the concept,

and make it altogether ambiguous which of the many possible relationships in complex numbers

and figures should be adhered to. Besides, the fluid character of the concept is dissipated in such

an external medium, in which each determination falls into the indifferent being outside the others.

This ambiguity could only be removed by an explanation. The essential expression of the thought is

in that case this explanation, and this symbolising is an empty superfluity.

Other mathematical determinations, such as infinity and its relationships, the infinitesimal, factors,

powers, and so ' on, have their true concepts in philosophy itself. It is awkward to want to take

and derive these from mathematics, where they are employed in a nonconceptual, often

meaningless way; rather, they must await their justification and significance from philosophy. The

truly philosophical science of mathematics as theory of magnitude would be the science of

measures, but this already presupposes the real particularity of things, which is only at hand in

concrete nature.

§ 203.

(5) Space and time constitute the idea in and for itself, with space the real or immediately

objective side and time the purely subjective side. Space is in itself the contradiction of indifferent

being outside of others and undifferentiated continuity, and thereby the pure negativity of itself and

the transition into time. Space converts into the individuality of the place. Time is, equally, since its

moments held together in unity suspend themselves immediately, the immediate convergence into

indifference, into undifferentiated being apart from one another, or into space, so that its place is

precisely in that way immediate as sheer indifferent spatiality. This disappearance and regeneration

of space in time and of time in space is motion;-a becoming, which, however, is itself just as much

immediately the identically existing unity of both, or matter.

The transition from ideality to reality, from abstraction to concrete existence, in this case from

space and time to reality, which appears as matter, is incomprehensible to the understanding, and

always converts therefore externally for the understanding, and as a given entity. The usual

conception is to take space and time as empty and to be filled with matter from the outside. In this

way material things are, on the one hand, to be taken as indifferent to space and time, and on the

other hand to be taken at the same time as essentially spatial and temporal.

What is usually said of matter is: (a) that it is composite; this refers to its identity with space.

Insofar as abstractions are made from time and from all form generally, it is asserted that matter is

eternal and immutable. In fact, this follows immediately, but such a matter is also only an untrue

abstraction. (b) It is said that matter is impenetrable and offers resistance, is tangible, visible, and

so on. These predicates mean nothing else than that matter exists, partly for specific forms of

perception, in general for an other, but partly just as much for itself Both of these are

determinations which belong to matter precisely because it is the identity of space and time, of

immediate being apart from itself or of becoming.

The transition of ideality into reality is demonstrated therefore in the familiar mechanical

phenomena, namely, that ideality can take the place of reality and vice versa; and only the usual

thoughtlessness of the representation and of the understanding are to blame that, for them, their

identity does not derive from the interchangeability of both. In connection with the lever, for

example, distance can be posited in the place of mass and vice versa, and a quantum of the ideal

moment produces the same effect as the corresponding real moment.

Similarly, velocity, in the magnitude of motion, the quantitative relationship of space and time,

represents mass, and conversely, the same real effect emerges if the mass is increased and the

velocity proportionately decreased. By itself a brick does not kill a person, but produces this

effect only though the velocity it achieves, in other words, the person is killed through space and

time.

It is force, a category of reflection fixed by the understanding, which presents itself here as the

ultimate, and therefore prevents understanding and lets it seem superfluous to inquire further after

the concept. But this at least appears without thought, namely, that the effect of force is something

real and appealing to the senses, and in force there is realised that which is in its expression;

indeed, it appears that force achieves precisely this force of its expression through the relationship

of its ideal moments, of space and time.

Further, it is also in keeping with this nonconceptual reflection that "forces' are seen as implanted in

matter, and as originally external to it, so that this very identity of time-and space, which vaguely

appears in the reflective category of force, and which in truth constitutes the essence of matter, is

posited as something alien to it and contingent, something introduced into it from outside.

II

Inorganic Physics

A. Mechanics - B. Elementary Physics - C. The Physics of Individuality

§ 204.

Matter in itself holds itself apart from itself through the moment of its negativity, diversity, or

abstract separation into parts; it has repulsion. Its being apart from itself is just as essential,

however, because these differences are one and the same: the negative unity of this existence apart

from itself as being for itself, and thus continuous. Matter therefore has attraction. The unity of

these moments is gravity.

Kant has, among other things, through the attempt at a “construction” of matter in his

metaphysical elements of the natural sciences, the merit of having started towards a concept of

matter, after it had been attributed merely to the deadness of the understanding and its

determinations had been conceived as the relations of attributes. With this attempt Kant revived

the concept of the philosophy of nature, which is nothing other than the comprehension of nature

or, what is the same, the knowledge of the concept in nature. But in so doing he assumed that the

reflective categories of attraction and repulsion were readymade, and further, he presupposed that

the category of the reflection itself out of which matter should emerge, is readymade. This

confusion is a necessary consequence of Kant's procedure, because the former abstract moments

can not be conceptualised without their identity; moreover, because the observation of these

opposing determinations suspends itself immediately in their identity, there is the danger that they

will appear, like attraction, as a mere continuity. I have demonstrated in detail the confusion which

dominates Kant's exposition in my system of Logic, vol. 1, part 1, pp. 119ff.

§ 205.

Matter, as having gravity, is only: (1) matter existing in itself or general. But this concept must: (2)

specify itself; thus it is elementary matter, and the object of elementary physics. (3) Particular

matter taken together is individualised matter, and the object of physics as the actual world of the

body.

A.

Mechanics

§ 206.

Matter, as simply general, has at first only a quantitative difference, and particularises itself into

different quanta, - masses, which, in the superficial determination of a whole or one, are bodies.

§ 207.

The body is: (1) as heavy matter the solid identity of space and time, but (2) as the first negation it

has in itself their ideality, which differentiates them from each other and from the body. The body is

essentially in space and time, of which it constitutes its indifferent content in contrast to this form.

§ 208.

(3) As space, in which time is suspended, the body is enduring, and (4) as time, in which the

indifferent subsistence of space is suspended, the body is transitory. In general, it is a wholly

contingent unit. (5) But as the unity which binds together the two moments in their opposition, the

body essentially has motion, and the appearance of gravity.

Because the forces have been seen as only implanted onto matter, motion in particular is

considered to be a determination external to the body, even by that physics which is presumably

scientific. It has thus become a leading axiom of mechanics that the body is set in motion or placed

into a condition only by an external cause. On the one hand it is the understanding which holds

motion and rest apart as nonconceptual determinations, and therefore does not grasp their

transition into each other, but on the other hand only the selfless bodies of the earth,. which are the

object of ordinary mechanics, appear in this representation. The determinations, which occur in the

appearance of such bodies and are valid, are set as the foundation, and the nature of the

independent bodies is subsumed under this category. In fact, however, the latter are truly more

general and the former is that which is subsumed absolutely, and in absolute mechanics the

concept presents itself in its truth and singularity.

§ 209.

In motion, time posits itself spatially as place, but this indifferent spatiality becomes just as

immediately temporal: the place becomes another (cf § 202). This difference of time and space is,

as the difference of their absolute unity and their indifferent content, a difference of bodies, which

hold themselves apart from each other yet equally seek their unity through gravity; — general

gravitation.

§ 210.

Gravitation is the true and determinate concept of material corporeality, which is thereby just as

essentially divided into particular bodies, and which has its manifested existence, the moment of

external individuality, in movement, which is thus determined immediately as a relation of several

bodies.

General gravitation must be recognised for itself as a profound thought, which constitutes an

absolute basis for mechanics if it is conceived initially in the sphere of reflection, though it is so

bound up with it through the quantitative determinations that it has attracted attention and credit,

and its verification has been based solely on the experience analysed from the solar system down

to the phenomenon of the capillary tubes. Certainly gravitation directly contradicts the law of

inertia, for, by virtue of the former, matter strives to get out of itself to another. In the concept of

gravity, as has been shown, there are included the two moments of being for itself and of that

continuity that suspends being for itself These moments of the concept now experience the fate, as

particular forces corresponding to the power of attraction and repulsion, of being conceived more

precisely as the centripetal and the centrifugal forces, which are supposed, like gravity, to act on

bodies, and independently of each other and contingently, to meet together in a third entity, the

body. In this way whatever profundity was contained in the thought of general gravitation is

destroyed again, and the concept and reason will be unable to penetrate into the theory of

absolute motion, as long as the vaunted discoveries of forces prevail there.

if one closely considers the quantitative determinations which have been identified in the laws of

the centripetal and the centrifugal forces, one very quickly discovers the confusion which emerges

from their separation. This confusion becomes even greater if the separation is mentioned in

relation to gravitation; gravitation, also called attraction, then seems to be the same as centripetal

force, the law of this individual force is taken as the law of the whole of gravitation, and the

centrifugal force, which at another time is valued as thoroughly essential, is viewed as something

quite superfluous.-In the above proposition, which contains the immediate idea of gravitation,

gravity itself namely, as the concept, which shows itself in the particularity of the body through the

external reality of motion, the rational identity and inseparability of these two moments are

contained.-The relativity of motion also shows itself in this proposition, which only makes sense in

a system of several bodies standing in relation to each other in accordance with a varied

determination, so that a different determination will immediately result.

§ 211.

The particular bodies in which gravity is realised have, as the determinations of their different

natures, the moments of their concept. One body, therefore, is the general centre of being in itself.

Opposing this extreme stands individuality, existing outside of itself and without a centre. But the

particular bodies are others, which stand in the determination of being outside of themselves and

are at the same time, as being in themselves, also centres for themselves, and are related to the

first body as to their essential unity.

§ 212.

(1) The motion of bodies of relative centrality, in relation to bodies of abstract, general centrality,

is absolutely free motion, and the conclusion of this system is that the general central body is