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Basic Features of the Inorganic World as the natural context of Organisms and Organic Evolution. (Sequel-1)

Part XVb (of Sixth Part of Website)

Also here, in what follows, knowledge of the Aristotelian-Thomistic Metaphysics is presupposed. It can be found all over in  First Part of Website (Back to Homepage),  especially as to the notion of  Substance (in the metaphysical sense). And also presupposed is knowledge of the theory of the subdivision of Reality into the Explicate and Implicate Orders, a theory so far developed in our noëtic theory of organic evolution, especially as it has been expounded in the two-document  Theoretic Intermezzo  after Part VIII of present Part of Website.

In the present document we continue our exposition (still largely following HOENEN, 1947) of the organic world's inorganic context as seen by the Aristotelian-Thomistic metaphysics as the latter is integrated into our Explicate / Implicate Order ontology. Begun in the previous document, we will continue the discussion of  Place and Space, now including the nature of motion.

The principle of inertia, Aristotle and the impetus-theory of the Middle Ages.

For the impetus-theory and the mechanics of motion, see also  Fourth Part of Website :  part XXIX Sequel-5,  The Impetus as a Variable QualityIn that part (XXIX Sequel-5) we presented an argument leading from the ens extensum to the impetus as variable quality. Here we reproduce an overview of this argument, in order to make clear to the reader how things like "place", "motion", "the aether of Lorentz", "simultaneity" and "impetus as a quality of a moving body" are related to one another and in what broader context they belong :

The argument, leading to the demonstration of the existence of at least one variable quality is structured as follows :

( End of Overview )

Certain subjects, discussed in XXIX Sequel-5 Fourth Part of Website, have returned in the present and previous documents, but now, in these documents, they figure in the complete exposition of the "philosophy of inorganic nature" as masterly set up by HOENEN, already in 1947, and fully worth the trouble for us to translate and reproduce a substantial part of it (with changes and additions) and to comment on it [all] on the Internet, because this work is little known, and has been written only (as far as I know) in the Dutch language [which language is, I'm afraid, not too well-known]. Moreover, of all basic entities of the inorganic world (such as space, time, dimension, qualities, quantity, motion, etc.) -- already discussed in some earlier Part of Website, and now again being discussed in the previous, present and next documents -- it will be determined in what degree the Implicate and Explicate Orders are involved in constituting these basic entities.

Let us now, then, continue with following HOENEN, concerning

The principle of inertia, Aristotle and the impetus-theory of the Middle Ages.

The principle.

Among the principles of  Newtonian mechanics, classical mechanics, there is one that, already since several centuries, is seen as one of the most solid fundaments of mechanics, and of which the value and truth cannot, it seems, reasonably be doubted : The principle of inertia. In fact it is a dual principle. Let us present the formulation as Lorentz gives it in his  Principles of Physics,  1921 :  " If an object is free from any external influence, then it will, if it is at rest, remain in that state."  This first part does not cause trouble for us. But the more so does the second [part] :  "Once a body, not undergoing external influences, has a speed, then it keeps on having it with the same direction and magnitude. It is in regular rectilinear motion."
[ meaning that magnitude and direction of the velocity  v  remain constant, and when also the mass  m  remains constant, the amount of motion (= here linear impuls) also remains constant. If, on the other hand, there is such an influence, then the amount of motion (mv) changes, and its change is proportional to the force representing this influence. This is the second law of Newton,  F = d/dt mv,  where  d/dt v  is the acceleration  a  in the alternative formulation  F = ma.]
So convinced of the truth of this principle one is, that it was taken as  a priori  clear or at least  a priori  provable. Even the brilliant  L. Euler considered it as self-evident, in no need of proof. Though he gave one -- to generate more conviction -- departing from the principle of sufficient ground (which proof, as to the second part of the principle of inertia, is not correct).

Meaning and value of the principle of inertia.

Yet, the principle of inertia is by many (including Euler) understood in a sense in which it was since centuries denied, even by geniuses like Aristotle and St Thomas, being convinced of the principle of sufficient ground (the  ens  is intelligible) as well as of the causal principle. Then one would naturally be inclined to think :  If the principle of inertia (speaking about the second part only) is true, then it must be or contain a truth that only became clear from experience, that is, from sophisticated experience [otherwise ancient thinkers would have discovered it long since]. Whereby we must realize that such a principle-obtained-from-experience, once it is known, can be so "appealing" to us that we take it as to be self-evident. We spoke about the sense the principle had in Euler and others. These words [relating about the sense] also point to a preliminary difficulty. The  meaning  is not so simple as it looks at first sight. We here have an example of what has been said by us earlier :  In the first principles of mechanics there are propositions that might be held to be  a priori  clear or derivable, but which are in fact judgements of experience.
So, first then :  What does it mean when one says of a body (or of a material point for that matter) that it has motion [that it moves] along a straight line and with constant speed? As to constant speed we will speak later when we come to deal with Time. Let us now be satisfied with the unanalysed notion. So now especially about the question :  What does it mean to say that the body traces out a straight line? It seems simple but is rather complicated. We know :  "motion" essentially means :  motion with respect to another extensional reality [i.e. to some other body]. So rectilinear motion then is :  Motion tracing out a straight line  inside  [i.e. through] that other reality. But this same motion may not be rectilinear with respect to another real extensum. For example :  In a railway car ruuning down the track on throws up an object. It ascends to its maximum height and then descends (the first movement is decelerated, the second accelerated). In both cases, up and down, it moves while tracing out a straight line  with respect to the railway car,  that is, in a coordinate system fixed with the car. But  with respect to the railway track, and thus to the Earth, that is, in a coordinate system fixed to the Earth, the object traces out a parabole. If the object would have had a regular motion with respect to the train [more generally, when the vertical velocity-component would have been constant], then also its motion with respect to the rail-track would have remained rectilinear [it would have traced out the two sides of an isosceles triangle] if the train itselves moves with constant speed with respect to the track. When the speed of the train itself varies, then a regular motion with respect to the railway car would be an accelerated or decelerated motion with respect to the track.
So when, in the principle of inertia, it is spoken of  "rectilinear regular motion"  one must specify with respect to precisely what other reality (real coordinate system), the motion must be rectilinear and regular, if the principle is to hold. And we see that things are not so nicely well established if they concern the immediate evidence of this principle [because  "rectilinear"  in  "rectilinear motion"  seems not to be an absolute determination (of some given motion)]. Newton took as coordinate system  "cosmic space", as also did Euler. But unfortunately space is not something real, in itself it is nothing, and, as we already saw, motion with respect to nothing is absurd (in what way Newton tries to deal with that, anyway without success, we will see in due course). This point undoubtedly remained a weak stone in that fier edifice of Newtonian mechanics. In the 19th century C. Neumann assumed a mysterious "body alpha", and with respect to this body the principle of inertia would hold. One should note :  We are still discussing the very  meaning  of the expression "rectilinear motion", figuring in the principle, because this  meaning  is not fixed as long as the real medium with respect to which the motion is rectilinear is not indicated. So also the meaning of the principle is still not yet established. And of course it should be established before one can legitimately speak about its validity. Mach finally came with the, at least partial, solution :  The motion [as expressed in the principle of inertia] must be rectilinear with respect to the cosmos as a whole. And indeed, the conviction of the correctness of the principle of inertia is mainly based on the wonderful results of Newton's theory in its application to the celestial bodies. And there motions are determined with respect to the cosmos as a whole. And then the principle of inertia (with limitations to be discussed in due course) turns out to be correct. But then it is an experimental principle.
We said that this is only partially the solution. First, Mach wants to attribute regular motion to the  influence  of the mass of the celestial bodies. But then, undoubtedly, this influence should have to change with the [change of] distribution of these masses and their distance. Another distribution or a different distance would render the principle of inertia invalid. So the principle would be contingent, and thus not a principle at all. [This is entirely correct, because the principle of inertia says, "if no forces were acting on the body . . ., then : . . ."  When we then see a body, far away from all the stars, moving rectilinearly, then we assume that a mutual cancellation of all forces has taken place (so this assumption is based on the principle of inertia). But we do not know whether indeed all those forces have been cancelled out mutually, i.e. that their net value has become zero. So if the motion of a given body is rectilinear, without mutual cancellation of all forces, then the principle of inertia does not hold. Suppose that one observes a given celestial body which is far away from all other celestial bodies. Then one says :  because the influence of those other celestial bodies taken together practically is zero, or has been mutually cancelled out alltogether, then, according to the principle of inertia, the motion of that given celestial body must be rectilinear. But then the principle of inertia is not really discovered with respect to the motion of this celestial body but simply applied.]. So one must look for a correction of Mach's opinion. And this correction is clearly at hand :  The extensional reality, with respect to which the principle is valid, must be the aether, the universal medium of localization already discussed. [The aether here is viewed as an object of reference, not as a cause]. Now in this aether a coordinate system must be defined (by us), first of all by using the world of stars, because we cannot directly observe the aether itself. For this then, following Mach's thought, the [individual] stars do serve. In this established and observable coordinate system the principle of inertia, as has been  experimentally  verified, is valid. The world of celestial bodies does not, as in Mach, exert a  physical  influence, of which [influence] we must expect that it depends upon the distribution and distance of masses in the cosmos. It [i.e. the world of celestial bodies] now has merely a geometric influence [as establishing a system of coordinates] if we may so express ourselves [instead of "influence" we might say "significance" or "relevance"]. It only serves to determining the origin of the coordinate system and its axes. And -- this is  a priori  evident -- this  very determination in Nature is independent of the magnitude of the masses and their distance :  Drawing a small tetrahedron [in the cosmos] is already sufficient. In this way being corrected, Mach's idea is undoubtedly correct, and this, we believe, always has been in the physicists' minds afterall, although they did not manage to analyze and formulate it. That is Mach's merit.
Mach's word was only a partial solution also by a second reason. He assumes a  physical influence  of masses of celestial bodies  [and this cannot be done, because inertia must completely originate from the body itself.  ( The first reason of the incompletenes of Mach's solution was the principle of inertia becoming contingent.)]  and in this way actually denies the principle of inertia. This [principle], afterall, speaks of a body "upon which no external influence is exerted". And by Mach this influence is demanded, demanded as something essential. [But in this, one means of course that that influence (established experimentally, namely by observation) is merely a resultant (of existing forces) equalling zero. So this turns out to be the case in the present Universe, but being established by applying the principle of inertia.]. And also for that reason one would perhaps prefer to accept the  a e t h e r  as medium of localization, as it was described earlier, because thereby one would, at least in the initial stage of the consideration, not have to assume that physical influence. The eather then carries only the meaning of coordinate system, i.e. has only geometrical meaning [insofar as it concerns the principle of inertia].

Critique of the  ( just given )  classical view.

This solution we cannot accept. We think that, in order to understand the experimental truth that one wants to formulate in the principle of inertia, we need a physical influence, a  continuous and active cause.  We know very well that we will then come into conflict with the position that is held by many of this experimental truth. But our view does not have any modifying influence upon the formulas of mechanics [because this supposed active cause is not a force]. It does, however, has an influence on the understanding of mechanics [and that means it completeness].

Active cause demanded.
Suppose there is a [moving] body, which is [situated] so far away from other (ponderable) bodies that the gravitational forces emanating from these bodies can well be neglected. Also the pressure of light and other forces (emanating from these bodies) may legitimately be neglected. Now, then, this body, freed from the physical influence of all ponderable bodies, will, as long as these conditions are satisfied, with its constant speed trace out a straight line [trajectory] in a coordinate system determined by the cosmos as a whole.  This is the genuine sense of the principle of inertia.  And its correctness is experimentally established, because this we have learned from the exact observations, lying at the foundation planetary theory. And "classically" one interprets this such that in that case there is no physical, active, external influence anymore whatsoever. And one sees it as evident that no such active cause is necessary, just like the fact that a body, being at rest, and those same external conditions remaining the same, remains at rest (as says the first part of the principle of inertia), does not need further explanation, i.e. is self-evident. We think we must oppose this view. We mean that the case of the moving body is in itself not entirely intelligible, and in order to become so intelligible demands an active cause. We deliberately do not say that a  force  is demanded. Afterall, in mechanics "force" precisely means, if used in the technically proper sense, "cause of change of movement, cause of acceleration (or of deceleration)", and it is measured by this acceleration. And then it becomes a contradition in terms when one asserts that a regular motion [i.e. a motion with constant speed] supposes a "force". Therefore, our assertion does not oppose the  formulas  of mechanics [these only describe the play of forces], in which "force" only figures as cause of acceleration. It does oppose, however, the usual  interpretations  of [the results of] mechanics, which, where no "force" is present, exclude also all other active causes, i.e. interpretations in which all activity is identified with "force". We, namely, think that the intelligibility, and thus the very being, also of regular rectilinear motion [motion with constant speed] demands the presence of a continually active cause [while to explain accelerated motion one has already brought-in the continuous presence of, in this case, a force]. [This thinking is in fact the ontological interpretation and completion of mechanics]. There are two reasons making us think like that.

First reason.
The first reason we may formulate as follows :  Every change demands an active cause (this is nothing else than applying the principle of causality, the metaphysical principle of active causality). A real movement (also a rectilinear, regular) is a real change (namely of place), and, specifically, a continuous change :  So it demands an active cause, and, specifically, one which continually works. It then only remains to find out what this cause is, as we do this in every application of the principle of causality.
But in the present consideration we may also work our way differently. In the case of motion we can obtain a direct insight into the principle of causality, i.e. we can discover it. We, namely, ask the question -- afterall, this is our problem -- as to the intelligibility of that [sort of] "becoming" that is [called] motion :  Is a body that is in a state of motion, i.e. that is subjected to this special "becoming",  in itself, without inclusion of something else that is not contained in the notion of  "this is now in a state of motion", intelligible, yes or no? If not, then that something else that has additionally to be supposed to make things intelligible, is an active cause. This cause must supplement the missing part of intelligibility. Well, this real entity :  "a body that is in a state of motion"  is in itself, without something else, surely partially, but only partially, intelligible. This is almost directly evident. First, we have two extensa [spatial beings], namely the body and its "place", and we immediately have insight that motion of the first with respect to the second extensum is perfectly possible. Then there is something more :  If the [moving] body passes by the point A, then it necessarily must pass by a point, say the point B, lying nearby, before it is able to reach the point C lying farther away. This remark might look trivial, yet it is good to make it. It pays attention to an aspect which is, as it is in the "being moved", in and by itself intelligible and clear. We can say :  Because  the situation is such, as described, before [reaching] C, another, nearer, point is passed by. But the fact that the body is at point A (or even passes it by) does not [necessarily] imply that it will actually reach B or C. We  cannot  say that  because  it is at A it will later be at this or that other point. And this not only because we cannot recognize it, no, we see that it is  not  so [because an active cause having the body placed at that other point is not yet assumed]. Would it become apprehensible when we add :  "it was already moving with constant speed up to the point A, so we may expect that it will remain so moving"?
But this previous motion again contains the whole problem of intelligibility of  "motion in itself, without something else" [i.e. to understand that B or C will be reached, we must understand "motion as such" all over again (motion that made the body reaching the point A )]. We might obtain a result in this way :  "motion in itself, without something else", is only then intelligible when beforehand the preliminary condition has been satisfied, that it is intelligible, and so into infinity, which is absurd. From this we can learn [i.e. from this follows] that  "motion, all by itself [as it is in itself], without something else",  is  not  intelligible. It is, as we saw, partially intelligible, but not completely so. Accordingly, it [i.e. motion as such] will derive its intelligibility -- which it must possess because it is real -- partly from something else. And that something else is the  active cause [of the motion. In this, one should realize that "beginning to move" is in fact a change of the state of motion, and this is caused by a force, as it is mathematically described in classical mechanics. Hoewever, the persistence, and thus continuation, of the motion, bringing the body successively from one position to another with constant speed, after the force has ceased to be applied to the body, demands a continuous cause, other than a force.]  Generally :  A thing being  such  does not make intelligible that it later is  different,  i.e. that it changes. Surely this is clear :  That something is  such, under the condition that it will change when subjected to a foreign influence, explains that it has become that certain other thing. [So the initial nature of a thing together with a known foreign influence on it, explains the result (in dynamics we say that the outcome is determined by initial condition and dynamical law)].
And so we have, while already merely considering regular motion, insight into the famous principle of Aristotle :  omne quod movetur ab alio movetur, all what is moved is moved by something else.

Aristotle uses this priciple in his "Proof of God, derived from the nature of motion". Modern scholastics have decided to abandon this proof because of the inertial motion [regular continued motion without participation of some force] out of respect for the usual view of classical mechanics. Unjustified, as is evident from these lines.

Apart from "body L in motion" (with respect to a place) -- that is the only thing we contemplate of that body if we take it purely passively -- there is something else (perhaps  in  the body itself, this isn't yet determined) that moves the body  actively.  Motion by itself is pure "becoming", pure passivity. This passivity demands, in order for it to be completely intelligible, a corresponding activity. To describe all this we need many words. And we realize that these words are very poorly expressing things. They only mean to arouse motions in our head which come to rest when suddenly this simple insight emerges :  "becoming" demands, in order for it to be intelligible, yet something else. Precisely that is, we believe, what's going on even in a child's mind, who opens up its toys to see what is "hidden behind" some unapprehended motion of this or that part. It wants to know, what is "behind" it :  the first glimmer of the principle of causality.

Second reason.
Our second reason we partly obtain from experience. Afterall, it teaches us that a body in its motion, and  on behalf of,  i.e. in connection with its motion, shows activity. When it collides with another body it exerts a force and when it carries with it an electrical charge, it causes a change somewhere else, and so on. So the body unifies with its passive "becoming" of the motion [not the beginning of motion, but its persistence, i.e. motion as becoming] also an active capability. And both are connected to each other. Two aspects of this activity are important quantities in mechanics :  momentum or [equivalently] amount of motion (mv) and kinetic energy (1/2 mv2) [where  m  is the mass of the moving body, and  v  its velocity.  mv  is what all is moving, i.e. how much mass is moving, and how fast all that is moving.  1/2 mv2  is the amount of energy partaking in this motion.]. Both aspects of this activity (we do not say that they are two "things") are connected with the velocity of this "becoming" with which they together increase and decrease. Now, either this activity depends on the motion, or the motion depends on that activity (or both depending on some not mentioned third party). The first case supposes dependency of an activity upon a purely passive "becoming", which is absurd. So the second assumption remains (or the third, being equivalent to it [a motion, directly depending on the activity, and via this activity also on a third party] ).  Motion, also regular rectilinear motion, accordingly depends upon an active cause, which was to be demonstrated.

What cause?

Where is the seat of this active cause? An answer to this question was given by the impulsus- or impetus-theory of the Middle Ages, which also today is worth the trouble to be investigated. For in the main, the medievals have correctly seen things and have, by their theory, become the founders of modern mechanics.

But first we must consider Aristotle's reply to this question. The stagirite asks himself in what way to explain the continuous motion of bodies thrown forward, such as a stone or an arrow. The explanation of such a motion brought with it a special problem. Not a problem, though, as long as the thrown body is in contact with the agent that throws it :  the arrow with the bow in the hand of the archer. But after it [when the arrow is finally flying] the difficulty appeared. After the agent has ceased to operate, the arrow keeps on flying for a time. For this continuous [i.e. flowing] motion Aristotle demands a continuously operating cause, and precisely a cause that remains in contact with the arrow. The first demand [agent during flight] must, after the above exposition, be posited also by us. And the second demand [agent during flight in contact with the arrow] will find support especially in modern physics, a physics that has, rightly, rejected all sorts of  "actio in distans", immediate action at a distance, i.e. not mediated by some medium. The field theory is nothing else than a consequence of the rejection of this "actio in distans". Accordingly, we must, with Aristotle, find an agent which is in immediate contact with the flying arrow. Here, then, is Aristotle's solution :  The arrow cuts through a medium, which offers not too much resistance :  air or water. This is necessary, because otherwise too great a friction would suspend all movement. But this still does not yet explain the active, that has to  support  the motion. Well, Aristotle was looking for it also in these same media. And he had to do something like this according to the principles that we saw above [agent active on arrow during flight, agent in constant contact with flying arrow], because these demand an agent in immediate contact. See here the hypothesis Aristotle has set up :  The first agent, the archer, not only moves the arrow, but also the surrounding air. But he not only sets this air in  motion,  but provides it with moving  activity,  which Aristotle clearly distinguishes from the  motion  of the air [because motion, i.e. to be in motion, is passive]. So it is not the  motion  of air-particles, by which [motion] they, colliding with the arrow from behind, move it further (this hypothesis was proposed by other Greeks, perhaps also by Plato). This is explicitly denied by Aristotle, and in its place he proposes the hypothesis of an active power distributed to the surrounding medium. The hypothesis, that air is a suitable medium for all this, might seem to us, who know the properties of gasses so much better, improbable or rather impossible, but does not contain the absurdity that Duhem [writing on the development of physics] sees in it. Might we perhaps think of another medium, which certainly is the carrier of activity, of fields, the aether of Lorentz?
Aristotle proposed yet another thesis concerning this motion, a thesis that turned out to be false, namely this one :  That this motion, also when there was no friction, eventually becomes exhausted. After some time it automatically stopped, when, namely, the farther-away parts of the medium could not pass on any  activity  of motion anymore. He thought that experience forced him to assume it. And it is only the more sophisticated experience, enclosed in Newton's planetary theory, that gives us certainty as to the principle of the "conservation of energy".

The Middle Ages.
Later aristotelici have rejected the theory of the master. Not the whole theory though :  The two principles, namely, that an active cause was necessary, and that no "actio in distans" must be assumed [but direct contact], they kept on adhering to. They also adhered to the position -- being evident in itself -- that that activity must eventually have its origin in the first agent (the archer, in the case of the arrow). But they held that this activity was not passed on to the medium, but to the arrow itself. The first, who, in sharply critisizing Aristotle, defended it, was the cristian aristotelicus Joannes Grammaticus Philoponus in the 6th century. His exposition is not too clear, and, moreover, takes over the error of Aristotle, or, if not [Joannes] himself, then certainly the ones who had followed him :  They held that this active power, which the arrow, in order for it to be able to continue its motion, receives from the archer, would decrease in the course of time alone, i.e. without friction or other forces being involved, and finally would cease to be at all. So "conservation of energy" was unknown also to them. And here also they were loyal to the data of an insufficient experience.
But in the Middle Ages, already in the 13th century, but especially in the 14th, the theory of Philoponus was worked out to great perfection. Especially this is to the credit of the Parisian school of nominalists, first of all Buridanus. And the theory became a common position of the scholastics ever since. So also Buridanus accepted the two metaphysical principles from which Aristotle took his point of departure. But he placed the active cause of the continued motion in the missile [arrow] itself, in a quality, being passed on to the missile by the first agent [archer]. He further assumed that it persisted unweakened (so the motion remained regular) if no other  forces  acted on the missile from without. Did such forces, for instance gravitation, act into the same direction, then that quality would, as a result, continually increase, and so the movement, caused by it, would become faster. And in this way it became, among other things, possible to understand the laws of free-fall. With this the foundation of modern dynamics was laid down. The quality in the body-having-speed got the name "impetus", but was also called "impulsus" and also"nisus", and kept on living in scholastics under these names.

May one accept this theory? As to its largest part surely we should. It satisfies the metaphysical principles that rightly were Aristotle's point of departure :  There is an active cause of the continuous motion that finds its expression in the experimentally verified principle of inertia [because precisely this cause is sustaining the contiued regular motion, i.e. it sustains the movement of inertia], and this cause doesn't lie at a distance from the body-in-motion. It even lies mainly  in  this body, for it has no detectable influence on other ponderable bodies, in whose vicinity the body passes by without touching them.
'Mainly', we said, for shouldn't we also partially return to the position of Aristotle and attribute an active role [also] to the medium? That medium, then, is, of course, not the air, but the aether of Lorentz, playing already the role of universal medium of localization anyway. And the impetus is then an active principle that moves the body with respect to the aether. Shouldn't then the aether, as a result of some sort of reaction, also be active? The regular motion of the electron is already so explained, why not that of the gravitational mass? [This makes it probable that the impetus has a  configurative  nature. And precisely a figure (expressing this configuration) intrinsically is an extensive quality.]. One might hypothetically go further and bring this play of action and reaction into connection with "undulations" (waves) in the aether. When doing so, one comes wonderfully close to the modern view of duality of wave-motion and material-particles-flying-forward, for not only electrons, but also "molecular rays" of hydrogen and helium seem to satisfy the equations of  L. de Broglie.

The dynamics of Aristotle and the earlier scholastics has failed. But in what does consist their failure? Not in that, as one often hears, that for regular motion they demanded an active cause. This is, as we saw, a clear demand of metaphysics. Even not [were they at fault] by the fact that they placed this active cause into the surrounding medium. This seems at least partially to be true. That they had taken the air as this medium is an error [namely as an absolute medium for all motions], but this was not an obstacle for the development of dynamics. Their failure consisted in the fact that they, as a result of insufficient experience, were of the opinion that this cause of motion decreased in the course of time alone, up to its disappearance, resulting in a denial of the conservation of energy. Only the acceptance of the conservation of the "impetus" made possible the progress of the science of dynamics. Apart from these, there are other faults in the mechanics of the Stagirite. Especially these :  His distinction between "natural" and "violent" motion, and his opinion that the motions of the "sublunar" bodies are governed by other laws than those of the celestial bodies.

With the "impetus" we have discovered the first genuine variable, intensive qualityOf course there are more such qualities. However, natural science has problems with quality as suchQuality as such cannot be measured (and positivistically it is then said that they therefore do not objectively exist. So natural science tries to reduce existing qualities to quantity [i.e. saying that they are in fact quantities], and quantity can be measured. So with extensive magnitudes there is no problem, they can be measured with appropriate standards of measurement. But if qualities do actually exist as such, then all mathematical formulas featuring not only true quantities but also qualities-reduced-to-quantities, then, although they are consistent in themselves, do not truly represent the part of Reality which they are supposed to represent. This not only is the case when true qualities are concerned, but also in, for example, the scientific exposition of space and time, as laid down in the theory of relativity. The purely mathematical formalism of such theories obscures many truly existing features and differences in nature. And a philosophy of nature rightly wants to include  a l l  features and differences insofar as they are basic and general.
HOENEN, whose text we were following, has keenly seen these shortcomings of natural science when it expounds its results in terms of objective reality. Its theories correctly relate various measuring results. These results appear as numbers and in turn appear as numerical variables and constant numbers (natural constants) in the mathematical equations of natural science. In this way, results of measurement on several different natural phenomena are correlated to one another. But when it comes to the
  interpretation  of these formulas, some not accounted-for and implicit philosophical suppositions are smuggled in, for example the principle "what cannot at least in principle be measured, i.e. observed, does not, and cannot, objectively exist". And it is natural philosophy that is scrupulous as soon as philosophical principles are concerned. It wants to represent things how they are in themselves, independently of actually being observed or of their being observable at all. And it is metaphysics, as the theory of Being, that will decide whether certain unobservable things do exist (have being) or not, because metaphysics is about the general and necessary conditions of Being (qua Being).
Apart from HOENEN, all this is also stressed by Nicolai HARTMANN, a contemporary of HOENEN. But while in HOENEN, as it is typical in Aristotelian-Thomistic metaphysics, concrete things, especially substances (in the metaphical sense, i.e. as true beings) are central because they are supposed to be the very basic entities or representatives of Reality,  in HARTMANN his "categories", i.e. the ontological conditions of possible general constitutive elements, in addition to his modal categories of the possible, real, and necessary,  are the central elements of Reality.
So before we continue in following HOENEN's text concerning the nature of "space" and "quality", (and "time") it is good to include an introductory exposition of them, largely taken from HARTMANN, but including ideas of ourselves [JB] as well. In all this we try to integrate, as far as possible, Aristotelian metaphysics with (1) our theory of the Implicate/Explicate Orders of Reality and [with] (2) the hartmannian doctrine of categories (categories, that is, in the hartmannian sense, not necessarily those of Aristotle, and not those of KANT).

Introductory exposition of Quality and Space-and-Time, i.e. the intensive and the extensive, as to what they are, how they are known, and how the Implicate and Explicate Orders are involved in their constitution.

In our hypothesis we hold that the Explicate and Implicate Orders are mutually immanent domeins of Being. And Being-As-Such is, as it were, distributed among the two Orders, i.e. it involves both Orders as to its constitution. Certain aspects of Being may, of course, be proper to one Order only. Thus, the  extensive  is present (i.e. is as such expressed) in the Explicate Order only. There it appears in the form of structure, length, distance, volume, (local) motion, etc. In the Implicate Order, the extensive, and thus the spatial and the quantitative, are present merely as noëtic descriptions, being themselves not extensional entities. But the Implicate Order is the exclusive seat of the  intensive,  i.e. of the qualitative. The Explicate Order cannot reproduce or display intensionality. It must transform it into the extensive.
The holistic constitution of material objects (for instance atoms, molecules, crystals, and organisms), that is, the holistic nature of all true substances (in the metaphysical sense), is completely and exclusively accounted for by the Implicate Order :  The alleged material parts of such a substance, are, through the Implicate Order, i.e. mediated by the latter Order, connected to each other in a non-local way, and are then, as seen from the whole of the Expl-Impl Order, no concrete parts, but qualities of the substance. The latter thus forms a heterogeneous continuum instead of a mere aggregate of material parts. So a material continuum (a substance) is a continuum only in virtue of the fact of having the Implicate Order involved in the constitution of substance. Seen exclusively from the Explicate Order, the parts of a substance are separate material contigua (such as atoms in a molecule). These material contigua are contiguous things (together forming a contiguum, a whole consisting of contiguous, adjoining, things), and are structurally such that they are, in the Explicate Oder, perceived as having different qualities, while in the Implicate Order they  are  qualities, not of these parts but of the substance itself. And because the Implicate Order is more fundamental (in the sense of origin, not in the sense of ontological aspiration) than the Explicate Order (which forms the ontological aspiration of the Implicate Order), we may say that, seen from Reality as a whole, a substance does not consist of actual parts, but is a pattern of actual qualities (and quantities, etc.), qualities of this substance. So qualities, as they are in themselves, do not occur in the Explicate Order. Nevertheless, although we cannot directly measure them (i.e. measuring their degree of intensity), we can, as it seems, perceive them, perceive them, that is, as intensive qualities.
How, then, can we perceive them?
To explain this, we start with a passage taken from  LOGIC, formal elements of cognition, Part II, at the end of the Section  "The nature of first intentions" (i.e. logical tools or intentions)  in  Fifth Part of Website  :

So what we have so far is that extramental objects can, and do, have qualities, and these qualities can be -- each for themselves -- objectively detected by the sensory apparatus of at least higher animals, that is, the latter can be objectively aware of (sense) qualities insofar as their sense organs are sensitive for that which transmits these qualities. Further we know that awareness of a quality (of an inspected physical body) cannot just be the physical effect of the influence of the inspected physical body on the perceiver, otherwise a steel bar that is heated in a fire would not only get hotter, but would feel the heat, and this is absurd. The effect of the influence is just a genuine part of the receiver and is therefore subjective. In order for a perceived quality to be objective, the receiver must decode it, and after this is accomplished the receiver has become, in a way, the quality. As for sensing the blue copper sulfate crystal :  The blue, which is actually present in the crystal, is encoded (we can also say enfolded) in the light illuminating the crystal. This light interacts with the retina of our eyes, but not in such a way that the retina or other bodily parts of us become blue. The neurological machinery of the faculty of vision now decodes -- retrieves or unfolds -- the blue, i.e. it reads the blue from the coded message. And in doing so we  see  the blue of the crystal. Indeed, generally, nothing happens with the form 'blue' when it is encoded, transmitted, and decoded, that is, the form is not (necessarily) perturbed or distorted during these processes, and therefore it is perceived objectively. The form is now  shared  by the sensing organism and the sensed thing, and this is the relation of  formal identity  in (sensory) cognition (it must be only formal, because the sensing organism cannot become numerically identical to the sensed thing). Let us clarify things further with the following diagram :

Qualities (in the broad sense of formal contents) and, concomitantly, quantities or, generally, mathematical relations in things, are apprehended by the senses. The proper object of any given sense organ (color for the eye, sound for the ear, etc.) is infallibly and objectively known by means of these sense organs. The concomitant objects of the sense organs (all quantitative and mathematical features) are not always infallibly perceived (as we see it in the case where distant objects appear smaller), but can be corrected by the cooperation of all the senses together, finally resulting in these features also being apprehended objectively as they are in the (external) thing.  (end of quotation, and added diagram, from Fifth Part of Website)

Continuation of the  introductory exposition of Quality and Space-and-Time  (before continuing -- much later -- with HOENEN's exposition of Natural Philosophy :

Qualities and quantities as they have their seat in the duality of Explicate and Implicate Orders.
In the Explicate Order there is only extensionality, spatial structure, configuration. No intensionality can be sustained there. So there (intensive) qualities are not as such present in things.
In the Implicate Order there is no extensionality. And only there is the seat of (intensive) qualities.
In the Explicate Order, a quality of a thing is represented by a determined extensionally structural aspect in that thing. Light waves can record this aspect by coding for it (as explained above). In the sensory apparatus this structural aspect is decoded again, resulting in us to experience it as a quality, for example a color. This quality thus is -- through coding and decoding -- recorded in our sense apparatus, and, precisely, unchanged, and thus is its perception in principle objective. The same with changes in intensity, corresponding with structural changes in the object. But, intensity is, ex hypothesi, not present in the Explicate Order, and so neither are true qualities. They may be present in the Implicate Order, and so we must, in perceiving a quality and the changes of its degree of intensity, have insight into the implicate-order part of the object. Indeed, we may say that quality and its changing degree of intensity are present in objective reality, but this, then, is now taken as the Explicate / Implicate Orders as a whole.
So through the Implicate Order we perceive certain structural aspects of a material thing as intensive quality. A given quality is a quality of something, ultimately of a substance (in the metaphysical sense). The relevant structural aspect of an object, which (aspect) is 'responsible' for a given intensive quality of that object inheres in this object (in the substance), and if we now include the role played by the Implicate Order, i.e. the implicate-order part of that object, then we can legitimately say that the quality (corresponding with that structural aspect) is inhering in this object, in the substance. The relevant structural aspect (which itself is extensional) is, in the Implicate Order (the implicate-order part of the material object) represented by the corresponding intensive quality (i.e. is in the Implicate Order an intensive quality). We might say that the decoding of the sense-datum, in the case of intensive quality, takes place  through  the Implicate Order, i.e. through the implicate-order part of the object. And as a result we indeed experience it as intensive.

Now, while still discussing quality as to what it is ontologically, we introduce the concept of  dimension.  Holding that such an introduction of a new ontological entity is  not  a mere superfluous complication of the supposed ontological constitution of things, is based on the following preliminary consideration :

As to the extensional dimension, any spatial extension in material things needs a scale in which it can be and vary. And, as to the intensional dimension, any intension of any quality of material things also needs a scale in which an intension is determined and in which it can vary.

In order to apprehend and ontologically asses (intensive) quality and (assess) quantity (which is extensional), we must discuss the different types of general  substrates  carrying them, and further assess the ontological seat of them in the Explicate - and/or Implicate Order, and with it, in substances, including the aether of Lorentz.
(This aether of Lorentz is a universal medium of localization (of ponderable objects) and the substantial carrier of the varying electromagnetic and gravitational qualities. More precisely, the latter are carried by special substrates in the aether-substance, while other such substrates in the aether carry quantities.)
These substrates of qualities and of quantities (of all substances) are the special  dimensions.  Some of these dimensions are dimensions of extensive magnitude (such as length, volume, etc.), while others are dimensions of intensive magnitudes (such as the impetus, color, temperature, etc.). A dimension has being, i.e. its exists, but is not a being of any sort.
Dimension  is the play and ordering of opposites (before-after, larger and smaller, warm-cold, etc.). It has the nature of substrate (carrier). Every property (in the broad sense) varies in a, for it proper, dimension. The common substrate of properties is substance (while the primary instance of substrate is the Materia Prima in Substance). So the "being a substrate" of substance is expressed in the collection of dimensions inhering in substance. So these dimensions inhere in substance, but not in the same way as accidents (such as quantity, quality, relation, etc.) do :  Although they have being, they are not beings, not even secondary instances of Being as are the accidents.
A dimension, or dimensional system, is unequivocally ordered to that what is 'localized in it', but must also be distinguished from it. An extensional dimension is the ontological condition of measurability (a condition of the metrics of the property). Or, we might say :  a determined kind of dimension has its own metrics. The dimension itself is not measured, because it has no boundaries (is not partitioned). Measurement can only be done on something that has limits (boundaries) in such a dimension. The dimension is that 'in' which the measurable is limited (bounded), in which the measurable is truly measurable, for the limits of the measurable are are precisely the limits 'in' a dimension, as well as also is the metric standard with which we measure. The (type of) standard is 'in' the dimension and refuses to be carried over into arbitrarily different dimensions, but only into those dimensions which are isometric with it.
Dimensions are the substrates of the measurable, because they are substrates of possible limits. And therefore they are mediately also substrates of possible measurement.
A dimension is a continuum of possible transitions that are extended (not spatially) between opposites. It is, however, not so that in every such continuum an  extensum  would be present. Take, for instance, the special dimensions of weight, pressure, and speed :  In them there is nothing that is spatially extended. Every speed is just a point ('strength') on the scala (dimension) of speeds, not an extensum (such as a distance in space, or a duration in time) in this scala. The same goes for every pressure-strength, every weight, every force, every impetus, and every energy-quantum (these can be measured along their respective extensional effects). There surely are magnitudes and standards of measurement of speed, pressure, weight, the force, energy, etc. But these magnitudes are not extensive, but intensive magnitudes, and also the continuum-of-gradation, which is the dimension, is a dimension of intensities. A given intensity is, as has been said, simply a point in the dimension, it does not, filling it in, occupy a part of it. The intensity does not spread from one point of the dimension to another. All stepping off beyond the point on the scala is here much more a matter of varying of the degree of intensity, a change, a transition to another degree, or, seen from the viewpoint of statistics, a scatter of values. In all this, the intensional dimension lacks the complement 'extension'.
On the other hand, the extensional magnitude is the filling of the dimensional continuum with content, the occupation of the dimension by a being, which [being], together with its determinations and relationships, and precisely because of them, is localized in its [proper] dimension. This being is a true ens extensum, it is not, for example, the being : "1.85 meter", which is but a secondary instance of Being, i.e. an accident of substance, and which itself certainly isn't 1.85 long, while the corresponding substance is. It is the substance itself which is extending in its extensional dimension. "Extending itself" is, by itself, nothing else than the extension, and its magnitude is extensive magnitude. Therefore extension does not belong to the dimension, but to the qualitatively and quantitatively determined being, which extends itself in it.
As to the very being of a dimension (its ontological status) we may consider the following :  Although we can logically impeccably say :  "Socrates  is  1.85 meter (long)", implying that "1.85 meter" really is a true being, albeit a secondary instance of it, we cannot so say :  "Socrates  is  its extensional dimension". This at least suggests that a dimension is not a being.  But because it is an ontological condition (for something to be extended) it certainly  has  being, i.e. exists, everywhere where its concretum (that what it determines) exists. And, of course, the concretum can only exist where its condition exists. All this, about the status-of-being of all extensional dimensions also holds for all intensional dimensions.

The part played by the Explicate and Implicate Orders in the being of dimensions.
The intensional dimension of a quality, and thus of a substance, cannot be in the Explicate Order, because the latter Order cannot sustain intensionality. So the intensional dimension must have its seat in the implicate-order part of the substance concerned. But the (specific)  extensional effect  of the quality has its seat in the explicate-order part of that substance. In the next diagram the intensional dimension is drawn vertically, and the extensional dimension horizontally. Three possible degrees of intensity of a given quality are depicted :

The mapping of the intensional dimension (in the implicate-order part of the substance)  onto  the corresponding extensional dimension (in the explicate-order part of that same substance) is mediated by  projection  and  injection  of them from the Implicate Order into the Explicate Order and vice versa.
And, as has been said, measuring [with an instrument] the degree of intensity of such a quality takes place (and only can take place) in the corresponding extensional dimension of the quality's effect in the explicate-order part of the substance  ( like a thermometer in fact measures the extensional effect of the intensional quality "heat" to which its liquid is subjected).
The dimension of an extensive magnitude (such as length), on the other hand, is directly, and exclusively, seated in the explicate-order part of the substance having the quantity, and is measured 'in' that dimension.

The dimensions of Space and Time.
The only  extensional  dimensions are those of space and time. In fact, this way of expressing things suggests that space and time  have  dimensions. But this is definitely not so :  space as such and time as such  are  dimensions themselves (real space consists of three aequivalent dimensions perpendicular to each other, while real time is one dimension only). And because they are dimensions, they are not beings of any sort, but they nevertheless exist alongside, and in connection with, their respective concreta.
Space and time dimensions thus distinguish themselves from all other dimensions by the fact that in them we essentially have to do with extension (spatial and temporal extension). For, although themselves not being extension, they are nevertheless that 'in which', primarily, extension only is. They are precisely those dimensions in whose range extensive magnitude and extensive proportions of measure reside.  N.HARTMANN, Philosophie der Natur, 1950. p. 68, writes (translated) :  " With this a first ontological basic assessment of space and time is obtained. It concerns the categorical nature of their dimensions [which they themselves are], in which they, as to their common nature, distinguish themselves from all other dimensions."  This result runs parallel with the fact that in the space-time dimensions the nature of [the] opposites [i.e. the opposite nature of that what is in such a dimension] between which the dimensions stretch out [which stretching-out is at the expense of these opposites, not of the dimensions themselves, which are merely conditions] almost disappears. Opposition is here only visible in that of direction in each of these space-time dimensions. The extensional determinatedness [definition] of magnitude is to initial consciousness [i.e. in unreflected awareness] precisely as being the primary and immediately intellectually visible one, while the  intensive  only becomes intellectually visible (clear) after mediation through the extensional, and even in natural science [the intensive] is depictable only through reduction of it to spatial and temporal magnitudes. Immediate intellectual vision of proportions of magnitude are connected with the aspect of extension. All schemata in natural science (coordinate systems, diagrams, etc.) are representations of whatever real magnitudes in the dimensions of space (where also time is spatially depicted).

Dimension as such, intensive and extensive magnitudes, measurement, standards of measurement, space-time dimensions, and numbers.
A magnitude is always a magnitude of something (for instance of something that has volume, length, or duration), and in measurable intensive qualities "magnitude" is the result of transformation of the intensive into the extensive :  So is the magnitude of weight, of pressure, of speed, etc. Numbers are not magnitudes of something. They simply are schemata of possible magnitudes. Although dimension is not size, yet measurability belongs to that what extends in this dimension, and in this way measurability all the same belongs to the essential aspects of the dimension. And even in dimensions of intensive magnitudes things are not so different :  everything that is localized in such dimensions has its measurability too, albeit in the dimension of the extensive effect only.
Measure and magnitude stand close to each other. Human standards of measurement are, it is true, arbitrary, but they stand under this law of categorical connection, which one may express as follows :  Every kind of magnitude is measurable in the measure of its dimension only, and every measure refers to magnitudes of its dimension only.
In order to further clarify the essence of  measurestandard of measurement,  and  magnitude (quantity), we give an example of each one of them :

Measure :  unit of length.
Standard of measurement :  inch.
Magnitude :  length.

To knowing consciousness, through spatial and temporal magnitudes, the connection is made of physical relationships  to  quantitative determination. This connection is the foundation of exact science. This also with respect to intensive magnitudes. For mediately even something of the intellectual visibility of the space- and time-magnitudes is carried over to the diversity and mutual relatedness of all intensive magnitudes, as they are indeed in science made visible by its measuring instruments onto spatial dials.
As to the objectively existing real relationships [as contrasted with how things are to the knowing consciousness] themselves, on the other hand, we may at least say that their quantities are always correlated with the space- and time-magnitudes. Afterall, the nature of process in those existing real relationships is a spatial-temporal nature. The mathematical, in itself empty, relationship (as in a formula) is not, it is true, carried over exclusively into these space- time-dimensions [for many variables intend features with a content other than that of space and time]. But surely, this empty mathematical relationship is primarily apprehensible in space- time-dimensions, insofar this empty mathematical relationship actually reaches into the real world só far as does the 4-dimensional structure of space-time events and things. Also the heterogeneity of intensive and extensive magnitude doesn't change this. Intensive magnitudes are not free-floating without being tied to something that has extension in space and time :  Forces have their range of action, their field, their temporal beginning [to act] and their cessation [to act], and precisely with these their intensity is rendered apprehensible [In short, it is apprehensible through it extensional effect]
[A force is the action of something onto something else. A body as such does not have physical force, but is subjected to it through the activity of another body].
Every intensive magnitude is ordered into the configuration of extensive magnitudes. It can be obtained from this connection only by the mental act of abstraction.
Within the confines of our theory of the Explicate / Implicate Orders, the intensive dimensions of substance (in the metaphysical sense) are, as has been said, situated in the Implicate order only. And as a result of  projection  such an intensive dimension becomes visible in the Explicate Order as filled extensive dimension.

Space-time dimensions and the aether of Lorentz.
The 'empty' space between (ponderable) bodies is, as it seems, a stretch of unoccupied, unfilled, space-dimension (or dimensions). The (three) space-dimensions  as such  are, however, not real, but are aspects of substance [i.e. of the many existing substances), that is, they are intrinsic conditions of the extensional content in it. So extension is only to be found in substances. From this it follows that substances cannot be separate from one another, they must touch, be in continuous physical contact with each other, without interruptions, in order to be able to form a single system of spatial dimensions. This all-out physical contact of substances is finally realized by the aether of Lorentz. And the latter is demanded by the definition of place anyway. Even already in general terms a universal medium of localization (aether or no aether) is demanded by the absoluteness of place and by the objective existence of absolute simultaneity (as it is demonstrated in  part XXIX Sequel-5 in Fourth Part of Website ). And what precisely then might be that universal medium of localization surely is best shown by the properties of the aether of Lorentz. So the space-dimensions, as aspect of all substances and as condition for the existence of extensional things, are completely filled with the latter (including the aether).

Again, the way of being of dimensions.
The way of being of a dimension (and that of all "constitutive categories" as described and defined in HARTMANN) is that of a  principle (a category) :
The principle does not exist (has no being) without its  concretum,  and the concretum does not exist (has no being) without its constitutive  principle.  "Existence" here primarily refers to "intrinsic consistency" (secondarily it refers to extrinsic conditions, existential conditions). So a dimension (which is a category sensu HARTMANN) does not exist without something that properly resides 'in' it.
Specifically, things hold for extensive respectively intensive dimensions (or system of dimensions) as follows :

An extensional dimension [which itself is not an extensum) does not exist without something that extends 'in' it. Already the fact that something extends in it is sufficient, that is to say, the dimension does not require, in order for it exist, to be  completely  occupied. The concretum is here present as something extending.
An intensional dimension, on the other hand, does not exist without the fact that one point in it is occupied as a step of the ladder of possible increase or decrease of a given magnitude that is ordered to this dimension. Of course for this it doesn't matter where precisely on its scale one of its points is occupied. The concretum here is always present simply as a point.

Of course principle and concretum are not symmetric to each other in all respects, otherwise they would be equivalent :
The principle, the category, is that what ontologically determines, while the concretum is that what is determined. And the principle cannot be without that what is determined by it, i.e. its concretum. And the concretum cannot be without that by which it is determined.

Critique of the Theory of Relativity as to the way of being of space and time.
The theory of relativity (as established by  EINSTEIN  in 1905 (special theory) and in 1916 (general theory)) unjustifiably transfers its theses  from  the measurable and the qua magnitude computable  to  the ontological conditions of possible magnitudes and measurability.
Space and time are dimensions, i.e. dimensional categories. So exclusively as such they do not exist. They are not beings and so also not accidents (of substance), but are  ontological  conditions of the being of extensional magnitude and duration (which also is extensional). They ontologically determine the being or possible being of their concretum, but cannot exist (cannot have being) without that concretum which ontologically is determined by them (as its categories). Said differently :  With or without their concretum they (all categories, and thus all dimensions) are not beings, but may have being. Without their concretum they do not have being. The same goes for the concretum with respect to its ontological determinant. It is as a result of this transfer that the theory of relativity maintains that there is no absolute simultaneity, and that the speed of light (in vacuo) is constant. Space and time would then be relative with respect to the constant speed of light, expressed by the Lorentz-transformations. The theory of relativity has transferrred the observable or the non-observable to the categorical (sensu HARTMANN), that is to say, to the ontologically determining and fundamental. And this is the great fault of the theory of relativity. Categorically seen (and thus not simply form observability alone) there must be absolute simultaneity, and time must progress everywhere in the same degree, independently of the state of motion (i.e. independently of the degree of motion) of the physical body to which this time is valid. So there is one universal real time.

In the space-time system, time is fundamentally different from the space-dimensions. It represents one dimension only. In contrast to space it flows, and in this flow it is irreversible. And this flow itself of time is an irreducible fact.
Space as such is not a coordinate system, because in it there is no fixed point of reference and no determined preferred direction. Space as such is a system of (three) dimensions in which arbitrarily many coordinate systms are possible. Also real time (as contrasted with time in intellectual vision, subjective time) is not a coordinate system, but by another reason :  it has (is) one dimension only. For a coordinate system more dimensions are required. Quite surely, though, real time rudimentarily has the nature of a coordinate system. It has, as contrasted with space, fixed points of reference, namely the NOW's. These NOW's are all ontologically equivalent and replace one another continuously. The single dimension of time may be taken as the single abscissa of possible ordinates of other dimensions. And indeed, such a role it plays everywhere where it combines with other dimensions into a single system of dimensions.

Extensa (i.e. extensional things) can move in space (having a trajectory or rotating about an internal axis). In this, "space" is not a receptaculum (a container) of these extensa. This means that space itself is not spatial, but in virtue of it things can be spatial, i.e. be spatial extensa, and in virtue of it they can move  'in'  it  [Here, as in all 'ins' with respect to dimensions, "in" should be taken in the sense of "carried by an ontological substrate", the dimension]. Space is, as a system of three dimensions, ontologically determining. So space is a system of three extensional dimensions, and these dimensions are such that they make possible extension  'in'  them, just like the one time-dimension is such that a process can spread itself  'in'  it. So it is not space itself that is, or may be, at places curved, but the radiation or field of force finding itself in it. So there is no "curved space" of general relativity (but curved light-rays in a straight (linear) space). Space can also not move, and it can also not expand, because space as such has no extension. The aether, extending 'in' its dimensions is expanding. Space itself has no boundaries, but boundaries, if present, are in space itself, i.e. 'in' its dimensions. Space, taken all by itself, is not more than an ontological condition of the being of its concretum. And this concretum is the spatial nature of things (including the aether). These things extend 'in' space, i.e. 'in' the system of the three spatial dimensions.
Space and time are thus, as dimensions, ontological conditions of respectively spatiality and temporality of things and processes, they are "categories" in the sense of HARTMANN.  But as such, all categories, as defined by HARTMANN, are aspects reigning through whole sections or layers of Reality, and as such they are not individualized, i.e. not defined as individualized, and certainly they are not beings of some kind. But in things they are individualized. For example, individual things can move 'in space' because all things (i.e. substances or aggregates of them) are spatial. Every such thing contains in it the ontological condition "space-dimensions" by which this thing is an extensum and can therefore be of a certain size. Therefore, contact (of its surface, or its volume) with (the surface or volume of) other things is possible, and with it  changing  contacts are possible as well, and this means that it can have motion with respect to these other things. Space itself, i.e. as a system of dimensions, is not a separate thing in and through which other things move. Space, is, as a category, i.e. as an ontological determinant, residing in every extensional thing, every extensum :  Space is as a category recognizable as residing in such a thing because we see that that thing has spatial extension. The same goes for every other category as ontological determinant.

Substance and Substance. The two senses of  "substance" and  hartmannian categories.
"Substance" is taken by HARTMANN as to refer to "that which remains the same during change". And this only refers to accidental change, in which indeed the substance itself always remains unchanged. It does not refer to so-called "substantial change". So HARTMANN, following KANT, defines "substance" differently from how it is defined in aristotelian metaphysics. In the latter, substance cannot only change accidentally, but can change itself as well. It can change into another substance.  Substance,  as defined in aristotelian metaphysics is not only a "category" in the aristotelian sense, and particularly the "first category" of Aristotle's list of  "categories" or "predicaments" (the other categories are called "accidents"), but is at the same time, in that same metaphysics, an ontological determinant. It is the ontological condition, a substrate, of accidental change and determination. And this makes "substance" a hartmannian category as well. And as such, i.e. as hartmannian category, it has no being, except together with its concretum, its proper garnish of accidents. In fact, in (further developed) aristotelian metaphysics, substance all by itself, i.e. 'naked' substance, can also not have being, but only in the sense that it cannot as such actually exist as an individual thing. In original aristotelian metaphysics "existence" is not explicitly dealt with. In that metaphysics it is only something like  intrinsic consistency  that counts, and this is called "being" or "beingness". The entities listed in Aristotle's "categories" are true beings, together forming a group of so-called "pros hen equivocals", and of them "substance" is the primary instance, i.e. the primary instance of Being, while the acidents are secondary instances of Being.
So as hartmannian category, "substance" all by itself has no being. But in every individual thing it does have being (but is still not "a being"), because in such a thing it is together with its concretum. It shares the being of that individual thing, although not its being "a being". And the same holds for the extensional and intensional dimensions which are hartmannian categories and only hartmannian categories. They represent a part of the substance-as-substrate, in this case substrates of, respectively, extensive and intensive magnitudes.

Continuing the critique of the theory of relativity.
The fact that the principal idea of the theory of relativity is not breached is clear [because it is still adhered to by physicists today, and confirmed by many observations]. The point is simply what one takes to be its principal idea, its theoretical kernel. If one confines this to its mathematical relations of data obtained by measurements in space and time, from which alone the theory takes its point of deparure, the theory is correct. If, on the other hand, one takes the categorical (i.e. ontological) consequences drawn in it, consequences as to the nature of space and time themselves, then the theory is false (N.HARTMANN, 1950). The fact that the theory itself does not acknowledge this limit which should be drawn here, not even seeing it, no mention of this limit's unequivocal determination in it, is its failure. Its point of departure directly leads to a relativistic mechanics, re-shaping by the Lorentz-transformations, taken up in its formulas, classical mechanics. It remains questionable what precisely ontologically follows from the constancy and non-surpassibility of the speed of light in all metric relationships. We may say :  The relativity, attributed to space and time actually refers to the dynamic behavior of matter and (its) fields of force. This does not, however, justify any further conclusion. Rightly assumed that in all systems regularly moving with respect to one another the laws of mechanics and of electrodynamics are the same, the relationships between the measured magnitudes in these systems must have the form of the Lorentz-transformation. From this follows, for all measurement of length and duration -- but only for that measurement -- the relativity of the interval and simultaneity. What from all this follows is nothing less than precisely the placing of limits, which the theory (of relativity) does not. It can be expressed in two statements :

If the theory of relativity transgresses these two limits, it becomes equivocal and endangers its own sense and significance. The transgression consists in the extension of relativity (of things being relative) onto the categorical (i.e. the ontological) essence of space and time.

With all this, we conclude our Introductory Exposition of Quality and Space-and-Time, i.e. the Intensive and the Extensive, as to what they are, how they are known, and how the Implicate and Explicate Orders are involved in their constitution.
It is essential to the setting up of a Natural Philosophy, and forms a preliminary context of our reproduction of, and our commenting on, the text of HOENEN, 1947  ( Philosophie der anorganische Natuur).
It is interesting to note that certain of the above conclusions about the objective, and especially, ontological, validity of the theory of relativity, drawn from HARTMANN (1950) are basically the same as those drawn by HOENEN (1947) and also by Van MELSEN (1955). While the philosophical background of especially P.HOENEN is that of Aristotelian-Thomistic metaphysics (Substance-Accident doctrine), the background of N.HARTMANN principally is from a critique of KANT's metaphysics, and not at all from Aristotelian-Thomistic metaphysics or from any other scholastic tradition for that matter. While for HOENEN (individual) SUBSTANCE is the central element of Reality, for HARTMANN it is the CATEGORY, as ontological determinant, that is central. But both share a realistic view of knowledge. So it is significant, encouraging, and stimulating, that our main theses or opinions coming from within our theory of the Explicate-Implicate Orders largely coincide with those of the three mentioned authors.

We will now continue our exposition of the philosophical theory of HOENEN in his Philosophie der anorgnische Natuur, 1947.  And it is "space", as it is, according to HOENEN, that will now have our attention.



Earlier we said that Aristotle and St Thomas were speaking a lot about "place", but little about "space", in contrast to modern philosophers, speaking much about "space", and little, or rather not at all, about "place". We then have investigated the most important problems to which these notions have given rise, the problems of nearness and distance and motion, while in fact using here almost exclusively the notion of  "place", and hardly a word about "space". We did not do this simply to follow Aristotle (anyway, we opposed him by assuming a real extensum which is penetrable :  the aether of Lorentz), but only because years of pondering have teached us that this approach is the only rational one. We now have to devote some attention to "space", partly because of its historical significance, partly in order to somewhat deepen the above. However, we must limit ourselves.

Space and place.

What is meant by the notion of  "space", and in what does it oppose the notion of  "place"? Before we can answer this question we have to specify things a bit more, because, unfortunately, the word "space" is used in several meanings.
One speaks of space in the following connection :  Geometry is the science of space. Then the word means nothing else than :  the extensionality, the extensive, as such [i.e. not the extensionality of the (one) time-dimension, but the spatially extensive]. And about this we have said enough. The word is also used in a second meaning, namely in following connection :  this storeroom is spacious, it offers much space. In this sense it entirely belongs to the sphere of our problems. It means :  where a certain volume of bodies can be stored. The walls of the storeroom are at a certain distance from each other, resulting in it to have a certain capacity to store extensa. In this sense the notion of  "space" hardly differs from that of  "place" as defined by Aristotle.
The third meaning, the only one we will discuss here, is connected with the second, yet also differing from it significantly. One, namely, wants to place [store]  all  real extensa [all real material things] into a single universal storeroom, capacity, recipient. That, then, is "the very" space, of course not enclosed by walls. Sometimes one demands, explicitly or implicitly, that an extensum, for it to be able to exist, must be included somewhere in that space, and for it to be able to move, must move in that space. And so we see that this notion entirely belongs to the sphere of problems investigated earlier. We may call this space universal or also absolute space. It is a universal capacity to include real extensa, bodies.
Now, however, one is of the opinion, and perhaps this is very consequential, to attribute to this space a set of very peculiar properties, if it wants to properly fulfil its function of universal capacity. It, of course, has extensionality. A none-extensum is not a recipient of extensa [except when it is merely an ontological condition for something to be extensive]. It, i.e. space, is penetrable by bodies, otherwise it would rather be an obstacle instead of a capacity to contain [bodies]. These two properties, and especially also the second, do not cause trouble anymore. For Aristotle the second property constituted a difficulty against the assumption of an aether as real place, as we saw when dealing with impenetrability. That space may not have boundaries, it must be infinitely large. For also when the world has boundaries, it can nevertheless be larger, for from the notion of finite extensum necessarily follows that a larger extensum is [logically] possible. So necessarily new bodies may be added to the finite world, and this ad infinitum [i.e. without limit]. So if space as capacity to include these bodies is as such presupposed, then it must be there already beforehand without itself having any limit. It is by this that space generally is described as to be infinite.
And in this way we arrive at the most peculiar properties of space [so conceived] :  Because it is prior to the bodies, if not in time, then according to nature [meaning that it is supposed to be more fundamental than are the bodies contained in it] -- it is afterall the capacity to include bodies -- and thus being independent of these bodies, one often attributes to it the following property :  also when all bodies would be destroyed, space -- capacity for new bodies -- would nevertheless remain. It is indestructible. It keeps on existing. It is by its nature eternal and uncreated and incorruptible.

Space, a being of reason.

But with this, space as reality is also condemned. It is a mere being of reason, an "ens rationis", as the scholastics say. And with this,   basically,  all philosophers agree. But see, in many of them difficulties against this thesis come up from [considering] other, true, and supposed, data. And if one does not have the means to solve these difficulties, one arrives at desperate theories, attempting nevertheless to attribute to this non-real being of reason a reality of whatever sort. Then they assume, [we] using KANT's words, an "Unding" [absurdity], because it only exists (without something real existing) to eventually contain all the real. Others, so KANT himself, see themselves forced with the reality of space also to deny the reality of the spatial, the extensum. Both parties have made the error that they did not depart from the first given in all this, namely from the extensum, from the body, from which then first and immediately (as we has found above with Aristotle, St Thomas, and Einstein) as a result of contact, resting and flowing contact, automatically derive the spatial relations of nearness, distance, and motion. And then Nature does not need "space" as recipient anymore, and when this space, the notion of which has been introduced  after  these data, turns out not to be real, we avoid the desperate result of the first, who yet accept a contradictory real space (the "Unding"), because we, in order to understand Nature, do not need real space. And we avoid the error of the others, because the rejection of space as real does not imply the rejection of the spatial, of extensionality, of nearness and distance, and of motion. These are prior to the notion of space, do not depend on it, do not become unreal when "space" becomes unreal. [This is certainly true when "space" is taken as an existing thing, i.e. as a being. Such a thing we do not need. And if we take "bodies" as substances (in the metaphysical sense) or aggregates of them (such as rocks, logs, etc., but also planets and satellites), then these are, as material things, prior to space, because space derives from the spatiality of them. If, on the other hand, we descend into Substance itself, and consider its ontological constitution, we may legitimately ask for the ontological condition of the substance's spatiality (extensionality), and this condition may well be "space", but now certainly not in its meaning as container of things, but as a set of (three) extensional dimensions that are substrates of extensa. As such "space" is a hartmannian category which as such (i.e. even without its proper concretum) "has being" in every individual material substance, but is not "a being".
Perhaps something similar is the case with "time" :  While the sizes (i.e. volumes) of all things (substances or aggregates of them) differ, they do not result in as many different sets of space-dimensions, i.e. they cannot be conditioned by as many different sets of space-dimensions. They are conditioned, carried, by a single set of three space-dimensions present in every substance. And, more specifically, as to the length of things :  Longer and shorter things are carried by the same dimension present in every substance. All the different cases of length are carried by the same dimension present in all substances. Well, perhaps, analogously, all the different cases-and-sorts of "change" in and of substances (i.e. all cases and sorts of replacement of one form by another), as each sort of them has its play in its own proper dimension (such as : the dimension of temperature-change, the dimension of pressure-change, the dimension of energy-change, the dimension of impetus-change),  [all the different cases-and-sorts of "change"] possess a common element, an element that is present in all change, an element that is the very essence of all change, so (that) there is in them (i.e. in all cases of change) something like a "change-as-such". And this commonly-possessed change-as-such has its own play, and thus its own dimension, a dimension present in every substance, and this dimension is time. It is the dimension of the one universal time. This universal time is not itself in motion, does not itself flow. It is the universal dimension, present in every substance, that carries the "change-as-such", commonly present in all cases of change.
In this way, we [JB] in our own and independent speculations, consider  t h i n g s,  i.e. substance or substances, to be prior in nature to "space" as well as to "time", because their respective dimensions reside and are sustained in every substance, and thus presuppose this substance.
We said that time does not move, not flow. This is because there is nothing relative to which it might flow. The only candidate we might come up with to which the flow of time would be relative is the NOW.  And although the NOW is itself flowing with time, flowing from past to future, or coming down from future to past, it might be a point of reference with respect to which time flows. However, the NOW is as such not different from time itself, and cannot, therefore, be an entity with respect to which time moves. Moreover, the NOW, is a product of human perception, not something objectively existing independently of being perceived. Only from the ability of things, that is, of substances,  to be  different from one another (i.e. having a different content) does the phenomenon of things  becoming  different derive, and so does time.

[returning to HOENEN's exposition] Elucidation [of space being a mere being of reason].
Let us clarify it a bit more. We said :  basically  all philosophers agree that space is not a real essence. Only in human imagination it is so that if we remove all real bodies, something remains that resists being removed, namely our own body as a center, surrounded by an extensum. Precisely that is there, in our imagination, real, because it cannot imagine the nothing. There we have in fact not removed all bodies. There, in addition to ourselves, a homogeneous background remains, and the bodies are only apparently absent, because we have removed precisely that what qualitatively differed from that homogeneous background. If we really want to  think  "space", that what remains when all bodies have been removed, then also that graphic, homogeneous, dark-colored, extensum of our imagination must be  thought away [intellectually removed]. Also the aether, of course, has been removed, because it is a real, physical, extensum, a body, as well,  just like the ponderable and visible bodies are. The aether is not the "space" that must be left over when all bodies have been removed. But what then remains, really is :  nothing. And that basically is what all philosophers hold and rightfully so [and therfore space is just a being of reason].

Newton and Clarke.

But the  condition, making possible the existence of real extensa, of physical bodies, still remains, one might maintain. And this surely is true when considering the active potency of the Creator. But as to the passive potency it is merely an abstract condition, not a really existing recipient having to include the bodies. If one would demand such a real recipient, if physical bodies, real extensa, in order for them to be able to exist, had necessarily to be included into a real recipient, this recipient should in its turn have to be included in another recipient, and so ad infinitum, which is absurd. So a really existing recipient - space - is impossible. But one might hold that while space itself, as a result of its infinity, does not need a recipient, a finite body does need such a recipient, because such a body has to be "somewhere". But this second reason to suppose a real recipient is also invalid because a finite body [or group of bodies] doesn't need to be somewhere [Indeed, the universe as a whole even cannot be somewhere. The assertion that a body must "be somewhere" follows from a wrong interpretation of the datum of our imagination. And then, as already remarked by Leibniz in his famous polemics against Newton's pupil Clarke :  This space would then be an eternal and necessary being. But only God is eternal and necessary, and space is definitely not identical to God. It is an attribute of God, as maintained Clarke, namely "His Immensity", which [assumption], however, is likewise impossible. Afterall, to space necessarily are attributed mutually different parts. It has extension, it must serve (as it was held) to include bodies, in order to be able to explain distance and nearness of them. But to assume parts in God's Immensity is absurd [because then these parts would be prior to God himself]. Nevertheless, these properties of necessity and eternity, together with extension, do belong to the concept of this "absolute space". So it cannot be real. It is, to use Kant's expression, an "Unding". So one now understands that, as we said, basically all philosophers saw space, not as a reality, but as a being of reason, and, consequently, in itself as a nothing. It is more difficult to understand, how some of them -- Clarke is an instance of it -- came to "realize" space in one way or another. Let's consider some more points.
Clarke defended in fact the ideas of Newton. Well, Newton thought that he was, as a result of some experimental data, forced to assume the existence of absolute space. It concerned the phenomena in rotating bodies (for example our Earth is, as a result of its rotation, flattened at the poles, and Newton performed experiments with water in a rotating bucket)  letting him assume an absolute motion, i.e. a motion that is not relative to bodies in its surroundings. So such a motion was, as he thought, a motion relative to space itself. Now Newton was well aware that absolute motion in the sense of being "motion relative to nothing" is absurd. Therefore he wanted to grant space a certain degree of reality. Once he called it the "sensorium" of God -- about which vague expression the polemics between Leibniz and Clarke blazed up furiously -- but in the "scholium generale" at the end of his great work (in the edition from Amsterdam of 1723, p.483) we read that space is constituted by God's infinity, which was also the position of Clarke, defending the opinion of his master. So it is more or less understandable that Newton came to his desperate thesis. The properties of rotating bodies we now know better to explain, as we saw earlier. According to Mach it is a motion relative to the stars. Still better is the view :  it is a motion relative to the aether of Lorentz. And in this way the desparate attempt to explain rotation as a motion relative to space which then would have to be identical to God's Immensity, which it cannot be,  is avoided.
So absolute space, this necessarily existing, uncreated extensum, indeed is only a mere being of reason. In Nature it indeed is, as we said :  nothing. And this is the great difference from the notion of  "place". This is a reality. And we do need a reality as medium of localization :  Place may be, as we saw, the enveloping real surface [surrounding the body-to-be-placed] according to Aristotle, or it may be, which is undoubtedly better, the parts of the aether of Lorentz [which is the ultimate medium of localization]. With the help of the reality "place", through contact, the spatial relationships can be realized, and not with the help of the unreal "space". That the notion of space as being of reason may well be used to  describe  these relations, we shall see later on. First we must touch upon several other attempts to "realize" space.

The atomists.

Also the ancient atomists, Leucippus and Democritus, ended up into an antinomy regarding the notion of space by the same reason as Newton did, because they thought that they needed an absolute motion, a motion relative to space, to nothing. They wanted to unify with the metaphysics of Parmenides, the metaphysics of unity and of unchangeableness of Being, yet the world of plurality and changeableness, and then so constituting the real world. Plurality then is there only in the form of a plurality of atoms, differing in size and figure. Changeableness merely consists in the motion of atoms. But also this plurality and this changeableness was excluded by Parmenides. For, as he had argued, this plurality would demand separation of things (the full[ness of Being] )  by empty space. Motion is hindered by the full [i.e. by the one uninterrupted Being] and so in turn demands empty space :  but [the] empty space is [the] nothing i.e. the not-being, and the not-being does not exist. Leucippus cut the knot with his famous thesis :  [the] not-being does exist just as well as [the] being does.
And see :  also here space is delared to be nothing -- afterall, all philosophers do it basically -- but at one stroke existence is attributed to this not-being. Joël called this desperate solution a "salto mortale in negation", and we can now better judge about the desperate. The solution must be rejected according to what we found out above. Afterall, nearness and distance and motion can only derive from contact, immediate and mediate, resting and shifting, contact of a real extensum with another real extensum. But let us also salute the insight of these ancient Greeks, who did understand, and in distress -- they had to save the world of plurality and change -- grabbed this life line :  Then even this unreal extensum, empty space, must exist. Of course this solution is unacceptable, and in this way these first principles of Greek atomism as a solution of the problem of plurality and change should already as such be dismissed.


In an analogous fashion Descartes (1596-1650) wanted to explain change in the world :  with motion only. But he wasn't an atomist, his matter is divisible without limit. Also in an other respect he differs from Democritus :  To him, empty space is a contradiction in terms, because space is an extensum, and extension is to him the essence of matter. So space is  per se  the full[ness of material being]. Descartes had a problem presented to him :  " If in a container the content is destroyed without becoming replaced by a new content [matter], then there would be realized a vacuum" [and thus empty space nevertheless]. His weird solution was :  " No, in the supposed case the walls of the container would touch one another, because nothing is between them". Here the thesis that space is nothing is urged too strongly, or rather, wrongly applied [HOENEN apparently means :  "the thesis that space is not only material but also "the full", i.e. matter everywhere, is urged too strongly, resulting in denying the possibility of isolated and partial gaps of contact between material bodies.] The supposed case seems to us perfectly possible (perhaps not in our natural world in which the aether cannot be removed by natural forces). And if it is realized [emptying the container of its content], the walls will not touch each other. Yet, actually there is no matter between them (except for those walls connecting two other walls separated by a distance, and this is essential [for (1) the contact of the separate walls with the connecting walls and (2) the size of the latter determine the distance between the former, and in this no space is needed, only contact-throughout of bodies with one another.] ),  but a body of precisely  the right size  m a y  be placed between them, completely filling the container. This is not an abstract possibility, but a very concrete one, resulting from the shape and size of the real container. Here it makes real sense to speak of :  Between these walls there is space having this size and shape. And this is a first example in what way the being of reason "space" can be applied to express real truths [So the being of reason "space" is convenient in descriptions, in precisely the sense that space is there first and that then things can be placed into it. But "space" here is meant to be not completely empty space, but as isolated gaps between parts of bodies otherwise touching other bodies, bodies that are in real physical contact with other bodies resulting in the world being one single contiguum - a whole consisting of parts (bodies) that touch one another.]
As a result of Descartes' space-theory he was led to yet another weird conclusion. The world must be infinitely big, or, rather, indefinitely big. A finite world would yet have space to be left outside it. It, afterall, can indeed be bigger, but that space again is extension and thus matter. And, consequently, for Descartes, and according to him, with absolute necessity, the world becomes infinitely big, or, rather, because he allows the infinite only in God and His attributes, the world becomes indefinite, which is in the case of a really existing being absurd [every existing essence or being is completely determined, definite. That's why this conclusion was said to be "weird"]. [...] The solution of the difficulty presented by a finite world with an infinite space around it is evident. The proposition "beyond the world a space exists" is, if it be taken litterally, absurd, because then to "space", to the nothing, "existence" would be attributed. But this proposition should not be taken litterally. It is a circumscription of the following  truth :  With a finite world may  per se  be connected (and indefinitely so) newly created bodies by means of contact. ["there is space enough for all these new bodies"] And in this way the being of reason "space" can once more be used in a proposition expressing a real truth. [This proposition was :  "beyond the world a space exists."]

The full[ness of Being] and the possibility of motion.

Concerning the possibility of motion in a world without vacuum, four theories have been developed in the course of history. The first one is the Eleatic, denying the possibility of motion in a full[y occupied] world. Therefore, Parmenides denied motion itself and declared the impressions of our sense experience, observing motions in Nature, as mere appearance. Democritus also defended the Eleatic theory of the impossibility of motion in a full world, and this precisely was the reason why he assumed the existence of the vacuum [local vacuum], and constructed a world in which free atoms moved in empty space. When considering the theory of distance of bodies, we saw that this only becomes intelligible by mediate contact of real extensa, rendering the distance between atoms in a Democritean world [i.e. free atoms moving around in empty space] impossible.
The three other theories construct the possibility of motion in a full world, and so escape from the above difficulty. Descartes did this by postulating that every motion is part of a total motion along a closed trajectory, which also was already assumed by te Greeks in the "antiperistasis". This does not give problems, as long as that total motion is one of matter contained between two perfect concentric circles, which, of course, is only exceptionally the case. When the motion is some arbitrary different one, then deformations of shape must take place in matter, namely, generally, continuous deformations. Now, in the system of Descartes, however, deformations can only occur as a result of  division  of matter. And when, consequently, this deformation is continuous, i.e. goes its way gradually (from a straight plane must, for example, be produced a curved plane as a result of division and rearrangement of the particles), in some matter-particles an actually-infinite division, a division down to a powder of mathematical points, must be assumed, and from this be made up a continuum again. Both operations (the division and compounding) are impossible. Descartes himself sees the problem, and in fact says that he doesn't have a solution of it. Also this theory is unacceptable [Indeed, a division into actually infinite parts is impossible. The division will never come to a conclusion, and however far it has proceeded, the number of resulting particles is still finite. And a construction of a new particle out of (dimensionless) points is impossible as well.]
A theory of a world without vacuum, as Aristotle had developed it, prevents these difficulties. Aristotle assumes that the bodies are subjected to densification (condensation) and rarefaction (dilution)  in the strict sense,  i.e. not only apparent condensation and dilution occurs, as is known in classical physics, which consist in coming closer respectively dispersing of separate particles which each for themselves retain their volume unchanged, but one single continuous body, i.e. without pores, is not tied up to a determined volume (why should it be, it may potentially have different volumes). It, accordingly, may have different volumes in different circumstances [Up until neutron stars and black holes]. In this, no penetration of parts of the body is presupposed [i.e. it is not presupposed that parts would mutually penetrate one another], but if the whole body may have a larger or smaller volume, then also every infinitesimal part of it. With this, both changes, condensation and rarefaction, may be accompanied by changes in the geometric form of the body, for example in the curving of the surface, without division taking part therein. In a theory that is able to explain intrinsic change [qualitative change, change of intensive quality] with the doctrine of potency and act, all this is simply following from that theory. This theory has, in modern physics, found an application in the theory of electrons of  Lorentz :  electrons in motion are subjected to a flattening (the effects are observable at high speeds) [I am not sure whether this is still unequivocally confirmed today, 2010, however], which [flattening] includes both changes [condensation along the axis of rotation, rarefaction along all axes perpendicular to it]. It is clear that in the theory of Aristotle a world without vacuum does not exclude motion [because condensation and rarefaction are motions, at least insofar as geometric deformation is concerned. But because geometric deformation here is supposed to take place as a result of corresponding deformations of the smallest parts, the latter deformations must then be qualitative changes, because they cannot be the result of again a rearrangement of still smaller constituent particles in the body. The above mentioned electrons indeed are particles of smallest size, they cannot divide anymore and do not consist of still smaller parts. So their deformation is a qualitative change.].
The most perfect theory rendering possible motion in a full world is the aether-theory of  Lorentz. This it owes to the fact that it has demonstrated the existence of a real extensum, the aether, which is penetrable to ponderable bodies. And in this way it delivers the perfect explanation of the possibility of motion in a full world. The derivation of distances and motions as a result of intrinsic contact with various parts of the aether is immediately clear. The aether is a perfect medium of localization. The penetrability of the aether to ponderable bodies removes all obstacles to their motion. That what renders the theory of Democritus and that of Descartes unacceptable is in the theory of Lorentz replaced by something from which the possibility of motion precisely becomes understandable. In this aether systems of bodies can be found which are similar to the democritean world of separate atoms. Discontinuous systems of ponderable bodies are possible. A gas, for example, surely is a swarm of countless small separate particles, which are, as the atoms of Democritus, in a state of violent motion, colliding countless times with one another. Now, the discontinuity of these particles, the molecules, is no longer a difficulty. They all move in a real continuous medium, the aether, which itself is the condition of the possibility of distances and motion.
This same aether also has an  active  function in the motion of ponderable bodies. It serves as a substrate of electromagnetic and gravitational fields, in which forces reside that give bodies acceleration. It also appears, as we saw, to play an active role in motion of inertia. Remarkable, in the aether of Lorentz we recover a property which Aristotle also attributed to "place", when he declaired that this [place] also has an certain active capacity.
One more remark will be made here in passing :  If we will ever possess a good theory of the notion of "mass", making clear the"ponderous" and "inert" mass of Einstein, but also the "active" and "passive" mass, and the connection of these four aspects, then "mass" in these expressions, include, we believe, a relation with the aether  (For an attempt, see later on).

Space as a well-founded being of reason.

So space is a pure being of reason only [Indeed, space is not real, while the spatial is (spatially extended bodies, extensa)].  In Nature there can be no reality (something really existing) combining in itself all the properties attributed to the notion of space. We said that all philosophers basically accept this, but also saw that there were some who felt forced to look for real space nevertheless. Others, on the otherhand, went too far into the opposite direction and together with the reality of space also rejected that of the fundament onto which the notion of space rests, and so arrived at the denial of all what is spatial, of extensa, of nearness and distance, and of motion. Here we have one of the brands of idealism. For a large part this came from the difficulties of the continuum, which we have already discussed. Without repeating things again, we only want to recall that these difficulties have their complete solution in the potency-theory of Aristotle, and that the reasons to also reject the existence of bodies and motions turn out to be worthless on closer scrutinity. If indeed real extensa did not exist, then "space" not only would be a mere being of reason, but would even lack any fundament in nature. This not being the case, the notion "space" does have such a fundament.
The difficulties of the continuum were for Leibniz the  only  reason to reject the reality of the spatial, and with it to limit all this to the world of mere phenomena [i.e. the world of mere sensory and/or intellectual perception] :  extensionality, distance, and motion. Nevertheless Leibniz is not an all-out idealist, we rather would call him semi-idealist. For Leibniz still assumes that to all relationships of the phenomenal world known and derived by us, there do exist analogous relationships in the real world, resulting in the fact that we, in our knowledge of the spatially-phenomenal do possess an analogous knowledge of the non-spatial real. Kant went even further and in fact denied also this analogy of our knowledge. For him the  " the thing as it is all by itself " (das Ding an sich) remains unknown in our world. In the present context it is interesting to scrutinize Kant's argument [saying] that he could legitimately conclude from the truth that "space" is a being of reason also the truth that all the spatial has no reality. Here he made the mistake in viewing "space" as a fundament, as a first datum, and the spatial as the derived. And this error became fatal to this thesis. Indeed, if the relationship were truly such, then the unrealness of space would imply the unrealness of the spatial too. But the relationship is the other way around :  The first datum and known as to be real is the extensum (the spatial body). And from this follows :  possibility of physical contact, and from this in turn nearness, distance, and the possibility of motion. And only then the notion of "space" appears. And if, on further scrutinity, the latter appears to be a mere being of reason, which moreover is unnecessary for [deriving] those [allegedly secondary, but in fact] first known realities and relationships [extensa, and what follows from them :  contact, distance, motion], then, evidently, it does not follow that the extensum and its effects are mere beings of reason, for not space is the fundament of the spatial, but the other way around. If one installs in Kant's reasoning in the  Transzendental Aesthetik  this necessary correction, that not space, but the extensum [as  ens  extensum] is the first datum, it automatically falls apart.

So "space" is a being of reason, but, as the scholastics declaired unanimously (apart from deviations in special questions), "a being of reason based on Nature itself ". What this precisely means we, above, had indicated with two examples. "Space in itself " is nothing. So a proposition as this :  "a space of three dimensions exists", is, litterally taken, nonsense. But above we saw in two cases (space in an empty container, space beyond a finite world) that we may use this notion in propositions describing a reality. Let us add some more examples. The proposition, that we, just then, called nonsense if taken litterally, may be used in a good sense and is often so used. One wants, namely, to express with it :  There is a world, made up of bodies, which are real extensa in three dimensions. In mechanics one speaks of  "degrees of freedom of motion of a material point". And thus the same proposition also means this fact :  In our world a freely mobile material point has a motion with three degrees of freedom. The fact that some particular "being of reason" may nevertheless be founded in Nature, and in fact is so founded, now means :  It may in such a way be used in meaningful and true propositions.
Let us compare this case with another. If someone denies that bodies of four dimensions are possible, and so also a world, composed of them, cannot exist, then he may express this by saying :  A space of three dimensions exists [first proposition], but there is no such space having four dimensions [second proposition]. If one takes these propositions litterally, also the first one should be denied, because a "nothing" as space cannot exist [i.e. departing from the thesis that space is a mere being of reason only, then also, of course, a space with three dimensions is such a being of reason only.]. But if one understands them in the sense given above, then the first proposition must indeed be affirmative, while the second (if indeed no four-dimensional things are possible) negative. [In this sense "n-dimensional space" in fact refers to n-dimensional bodies.]

A space of four dimensions would "exist" if our world of three dimensions were curved [Because it must be curved within something, i.e. it must be curved relative to a four-dimensional space]. In such a case -- the theory of relativity deals with it -- a world without a boundary and nevertheless not being infinite is possible. An example is delivered by an extensum having two dimensions. If this is curved (the surface of a sphere, for instance), then it may be without boundary -- a whole surface of a sphere  h a s  no boundary, but it surely  i s  a boundary -- and yet it is finite. If something like this holds for our world, it would be curved and presuppose a space of four dimensions. [A curved two-dimensional world must be in a three-dimensional world. And in the same way, if our (three-dimensional) world were curved, it must be in a four-dimensional world.]

Such beings of reason also occur in other sciences, but their [cognitive] theory has been hardly or not at all worked out. So, in projective geometry one speaks of  "the straight line at infinity" [a sort of "horizon" one might say], and "the straight plane at infinity". These are not "existing" things, not realizable boundaries of a plane or a space [because they are supposed to lie at infinity]. They are, litterally taken just as impossible [to exist] as "space" is. They simply are just beings of reason (which the figures in projective geometry are not), precisely as is "space. But they may be introduced in propositions (which one doesn't interpret litterally too) expressing very real relationships between figures, provided they are understood. And then they are well-founded beings of reason, for they render formulations and reasonings to become wonderfully succinct and elegant. Such a being of reason now is "space". But with this restriction that its usefulness is much more limited. With the notion of  "place", to which directly corresponds a reality, one may, without significant loss of succinctness or elegance, express almost all relationships from this sphere of facts and problems. And the introduction of the notion of "space" -- the history of philosophy is there to prove it -- may lead to disasterous errors. So we may conclude :  Aristotle, and after him St Thomas, were very wise in speaking much of the reality of "place", and little about the being of reason "space".

[Earlier we have found out, following HARTMANN, that indeed "space", as it is in itself, i.e. with nothing else, does not really exist. But this here means "does not exist as a being of some kind". It does exist, though, as a "category" in the Hartmannian sense, but only together with its proper (type of) "concretum". As such "space" is an ontological condition of the spatiality of things (where space itself is not spatial) :  "space" is a system of three "dimensions", and 'in' them things can vary in their sizes. So the system of space-dimensions is a category in the Hartmannian sense, meaning that they do not exist without the proper type of concretum, and then only really exists in each particular individual instance of an extensum (a spatial body). But still, such a category is not a being. So space in the Hartmannian sense is ontologically prior to spatially extended bodies, while for Hoenen the latter are prior to space, which is only a being of reason, albeit founded on extended beings.]


About the Relativity of local Motion, and about Motion as to what it precisely is.

With HOENEN we have discovered that a body in regular rectilinear motion needs, for such motion to be intelligible, an active cause  in the body itself.  This cause is a genuine intensive quality of that body (i.e. of every substance making up this body, if it is an aggregate of them), and was called the "impetus". But this finding brings us to the alleged fact that all motion is relative.
It is said, that motion is "relative". In certain senses of "relative" this is entirely true. But the presence of an impetus in a given moving body, including the case where this body moves in a straight line and with constant speed, an impetus, itself an intensive quality, that causes an extensive effect in the body :  motion,  attributes motion to that body, and to that body alone. This impetus has been brought in by the extrinsic cause of the beginning of motion (for example a thrust). W'd better say that the extrinsic cause (thrust) has as its effect in the body to which the thrust was delivered :  the body now having an impetus of a certain intensity proportional to the thrust. And when the thrust ceases (to be applied), the body nevertheless keeps on moving thanks to its having the impetus. A subsequent application of a force into the direction of the body's motion will increase the intensity of the impetus, and thus will increase the speed of the body. Seen things in this way, motion of a body is something absolute, it is the possession by the body of an impetus, while for a body at rest the intensity of its impetus is zero. This means that motion and rest of a body are not relative in the sense that they are in fact not different states of a given body because observation cannot tell them apart.
It is interesting that the critique of the all-out relativity of motion has not only been brought foreward from Aristotelian-Scholastic circles, but also from philosophers not arguing from Aristotelian-Thomistic positions and principles. One of them is Branislav PETRONIEVICS, in his extensive work  Principien der Metaphysik, ALLGEMEINE ONTOLOGIE UND DIE FORMALEN KATEGORIEN,  1904.  As far as I know, this work (written in German) is little, if not, entirely unknown to, at least, metaphysicists and philosophers of Nature (including HOENEN (1947), Van MELSEN (1955), and, as far as I know, N.HARTMANN (1940, 1950)).
Petronievics gives a very clear and convincing account of the alleged relativity of motion, and demonstrates that motion and rest of a body are absolute states of that body. In what follows we quote and translate him [comments between square brackets] from page 314 onwards in the work mentioned.

If two matter points A and B (because ultimately it is such points that move, because they together constitute the moving [macroscopic] object) move toward each other in a straight line, i.e. approaching each other, or moving away from each other, then this same change of distance [from each other] may be accomplished by the fact that A moves and B is at rest, as well as by the fact that, the other way around, A is at rest and B moves, and also by the fact that both points move. So one sees that the same change of spatial relationship can be produced in three ways, resulting in the fact that it is not clear to an observer which point is resting, and which point moves, and one in this way arrives at the peculiar assertion that motion and rest are purely relative states, that every object may be considered to be at rest as well as in motion, that this change in spatial relations is a mere extrinsic relation to the things concerned, that not any object as such originally possesses motion or rest.
This assertion of the relativity of motion and rest does contain severe intrinsic contradictions and severe intrinsic misunderstandings. Such an assertion is to a critical understanding, demanding clear concepts, a first-rank monster, and one can only wonder how one can proclaim such impossible assertions with exampleless levity as scientific truths. May the difficulties of assessment of a precise difference between motion and rest be great indeed, one may not derive from these difficulties this evidently false assertion. Asserting that the change of spatial relation as such is a real event -- and no one has doubted this, for one indeed does depart from this fact in order to conclude the relativity of motion -- is as such correct, but that in it neither the one nor the other object may be considered as originally being moved or resting, is clearly so incorrect as it possibly can be. For every change of spatial relation certainly is a change of relation of both objects and not something that is so to say floating between the two, without having anything to do with them. It is the objects themselves as such who approach one another or move away from one another, resulting in the reality of this approaching or moving away of them to be accomplished by themselves. It is them, the objects, that move or are at rest. It clearly, then, is an open contradiction to assert the reality of change of spatial relation, effected by motion, and to deny the reality of the motion itself, what (assertion) takes place precisely in the case in which no absolute difference between motion and rest is admitted. If things are indeed so -- and I don't know how one could overlook such simple truths -- then a real difference must exist between motion and rest. In reality one must strictly distinguish between the case in which this one object is moving and the other is at rest, from the two other cases  [  (1) the second object is moving and the first is at rest, (2) both objects move.]. Motion and rest must originally be states of the objects themselves [independently of whether this can objectively be observed or not].
And indeed, when we take a closer look to these three cases of change-of-spatial-relation of two points, we can easily discover objective criteria distinguishing between motion of the one point and rest or motion of the other. If, in the above example, one point is moving, then the direction of its motion is always opposite to that of the other point when one of these points is at rest [If one point is at rest, then the relative motions of both points are opposite. "Relative motions" here refer to the motions purely phoronomically seen, i.e. as changing spatial relatations between, not material, but mathematical points]. If, on the other hand, also the other point moves, then its motion may proceed in the same direction or in the opposite direction, and one may then clearly indicate -- of course under the general condition also holding for the first case that the change of spatial relation is one and the same -- whether really both points are actually moving :  If both points have the same speed, then they must move in opposite directions [otherwise the spatial relation between the two would not change at all]. If they, on the other hand, move into the same direction, then they must have different speeds in order to produce the same change of their spatial relation. So we see, there do exist true objective criteria residing in motion itself -- direction and speed -- distinguishing the moving point from the resting one, and which clearly determine which one of the two is the moved one and which one the resting, and that only one of them is resting (for if both were resting, no change of spatial relation would take place).
The fact that one doesn't see this chief contradiction included in the notion of purely relative motion [the contradiction is :  in relative motion  rest and motion are the same, i.e. opposites are equals], and the fact that one has not considered these objective criteria discriminating between the state of motion of a material point and its state of rest, which [criteria] therefore are enough to remove that chief contradiction, [these two facts] are the result of the diverse misunderstandings concerning on the one hand the notion of relative motion, which, in a sense, surely is a meaningful notion, and on the other our subjective observation of objective motion, and we now want to expose more closely these misunderstandings and show their invalidity.
"Motion" and "rest" are undoubtedly in a certain sense relative concepts. First they are so in an all-out general sense of that expression ["relative concepts"], in precisely the same sense in which, say, white and black, delight and unease, etc. i.e all pairs of opposites, are relative concepts. Rest and motion, namely, stand to each other in a positive-contradictory relation. The concept of  "rest" lets itself only be apprehended as a state opposite to that of motion, and "motion" as a state opposite to that of rest, about the same as we can think about the "black" only as the opposite of the "white", and vice versa, and think about "unease" only as opposite of  "delight", and vice versa. In this first sense "rest" and "motion" are relative concepts (notions) insofar as they are relational concepts. But from this relational nature we evidently cannot deduce that sort of relativity of motion that removes the difference between motion and rest, because then, we, for the same reason, must doubt the real difference between white and black, delight and unease. But in yet another much narrower sense "rest" and "motion" are mutually dependent states. Let us think of a completely isolated single unique material point [making up all of Reality], then we can only ascribe motion to this point when somewhere there is something which remains at rest and with respect to that the lonely point changes its relation, and because this other something cannot be, say, empty space, because such a space is impossible, it can only be another material point. So motion is undoubtedly also in that sense a relative concept that a moved object can as such be apprehended by reason only together with a resting one, and that "motion" loses all sense when "rest" is not presupposed as really being present. And this relationship between rest and motion is something which is not to be found in the relationships of those opposite qualities mentioned earlier, for the existence of the black is not in such a way dependent on the existence of the white, that everytime when the white is given in our consciousness also the black is there [in the sense of both of them being present], and the same goes for the qualities delight and unease [they even cannot be present together at the same time], while, on the other hand, the motion of a real point is always dependent on the rest of another. ["The material point moving relative to the resting point" here refers to the possibility, not of its motion as an event, but of understanding its motion, and only of understanding it. So in order to "motion of a point" to be intelligible, the presence of at least one other point that is in a state of rest must be presupposed. The resting point is not supposed to cause the motion of the other point.]  [PETRONIEVICS, here, speaks of the "existence of qualities" as [these qualities] being present in consciousness. And, indeed, perhaps that is their only true seat in what we call the Explicate Order [i.e. they reside in the Explicate Order, it is true, but then only in the consciousness of certain organic beings, or, perhaps, the only true seat of qualities is the Implicate Order when we consider consciousness itself to reside in that Order, especially because consciousness as such is not an extensional, but ban intensional entity.]
While from the first mentioned relation of motion to rest [being relative conceps such as delight and unease] one cannot derive a purely relative difference between the two [i.e. one cannot derive from that first relation that motion and rest do not differ absolutely from each other, but only relatively so], it is precisely this second relationship [between motion and rest] from which this purely relative difference (between motion and rest] was derived. If the motion of a material point cannot be conceived without the rest[ing state] of another material point, then precisely the undeterminedness as to which one of them is resting and which one of them is moved, is what may lead us to this conclusion [of the mere relative difference between motion and rest]. But we have shown that the undeterminedness is not so great as it looks, that there are objective criteria clearly distinguing between motion and rest. The fact that one doesn't see this ultimately results only from another confusion, a confusion that is evident, but also easily removable. One confuses, namely, objective motion, which [in itself] is unequivocally determined by these criteria, with our perception of it, without realizing that our perception does not contain the objective things as such. Mere appearance in perception can be reduced to an incongruence of this perception with the corresponding external objects, but perception all by itself, as well as the real objects all by themselves, do not contain any mere appearance. And the same holds for motion. To my subjective perception, when I observe two objects changing their spatial distance from each other, it may be totally immaterial which one of them will appear in my perception as moving and which one as resting. But to themselves this is not immaterial at all. One of them is resting and the other is moving.  I can, when I am sailing with a boat along the coast, perceive either the boat or the coast moving, respectively resting. But from this it doesn't follow at all that it also is objectively and in itself (an sich) entirely immaterial which one of them moves and which one of them rests. When I, in my perception (observation), perceive that it is the boat that moves and the coast that rests, then my perception is, at that moment, as perception, entirely correct and in no way a mere appearance. And the same goes for the other case, namely when I preceive the coast moving and the boat resting [Also this is in itself, i.e. as perception at that moment, entirely correct]. My perception does, however, not coincide with the external things as such, and one of the two observational facts apparently must, with respect to these external objects, be false :  In the objects themselves, i.e. in the objects as such, motion and rest cannot replace one another so quickly as it can in objects-as-perceived [coast moving / boat moving may alternate quickly during a single period of perception]. If one strictly distinguishes objects-as-perceived from the [corresponding] external objects, then one neither has reason to assert a relativity of motion and rest in the objects-as-perceived, nor [has reason] to assert it of the external objects.
Following on these considerations concerning the dependency of motion on [the state of] rest, we want more closely to assess the relationship of the moving point with the resting point. In our above example only two material points were considered of which one was supposed to be moving and the other supposed to be in a resting state. We now may ask whether motion, when only two points are supposed to exist, is actually possible. And it is easy to rightfully deny such a possibility. It would only be possible if empty space is supposed to exist, in which the two points would then be given :  but then, however, also only one single point could be given, for the existing empty space as such could, in this case, in virtue of its immobile place, fulfill the function of precisely the unmoved point with respect to the moved point. It would, afterall, represent the [required] resting and unmoved [state]. If, on the other hand, empty space is impossible [which it is, because space itself is only a form of extensional ordering of things], then we evidently must presuppose the existence of a whole multitude of material points [together, in touching each other, making up "space" (in fact "squeezing out" empty space). And many such contacting points are needed to create distance.], making possible the motion of that one point. For in order for the one point to be able to move away from the other point, it is wholly necessary that there is a multitude of places which may be passed-by or visited  by the moving point, and because empty space is impossible, these places must be occupied, i.e. defined, by real points, that is to say there must be a multitude of real points defining real space.
If empty space were possible, then, as just said, also motion of a singly existing material point were possible, for, on the one hand the immobile places of this empty space would represent (after the findings of Newton) the necessarily to be presupposed rest[ing state], and on the other hand a multitude of places in it [empty space] is  eo ipso  given. Well, in real space the multitude of places is  eo ipso  given, but these places, as defined and made up by real points, are not immobile, and we may now ask how, in this case, we must think the necessarily to be presupposed rest[ing state] to be. The conclusion that in this real space, in order for a material point in it to be able to be moved, necessarily there must be unmoved real points, fixing by their unmoved state the places and with them space itself, is beyond doubt [So space is constituted not by partly filled empty space, but entirely by material (in the sense of "having qualitative content") points (touching one another)]. For if we whished to suppose that at one and the same moment all real points in real space can be in a state of motion, this would mean that space itself was cancelled at that very moment [For when, at some moment, no points are in a state of rest, there are no places anymore, so space is not fixed (i.e. intrinsically defined) anymore]. And may, in the next moment, a space be fixed again [i.e. a space is again intrinsically defined] -- which certainly could happen -- the fixed space would be an entirely new one, differing toto genere from the space of the previous moment. And between them -- the old and new space -- there would not be any community, and there could be no talk of motion of material points. One can only speak of motion when the space, in which that motion takes place, is and remains one and the same, and we have only to ask when and how this unity of space, if space is real, is possible. Here we cannot yet give a specific answer, we can only determine that this identity of space [from one moment to the other] also then is guaranteed when in the two successive moments in time in which the motion takes place at least one real point in space remains unmoved, without it being necessary that in the next moment of the motion it is the same point that remains at rest. Undoubted is only so much that space must remain identical in time for motion in it to be possible, and this identity is only then guaranteed when at least in every moment of motion one point remains at rest. Whether this is always the same point, whether it is one point only or a whole system of points, whether this system of points lies at the centre or at the periphery of the world, or somewhere about in the middle, all these questions are of a special nature, and one can only answer them when the intrinsic structure of the world-monads, constituting empty space, has become known, which will be accomplished later. Here we are satisfied with the general finding that in real space there always must be at least one point in a resting state, in order for motion of the others to be possible.
One at first sight totally different question, but in reality immediately connected with the finding of [at least] one stationary point, concerning whether that resting point, spatially conditioning the motion of the moving point, must be in the immediate vicinity of the moving point or not, can perfectly be answered here. As is well known, it always has been one of the greatest difficulties for those who identify space with matter to establish a precise definition of the place that has been relinquished by the motion, respectively occupied. So, as is well known, Descartes has defined such a "place", a bit differently from Aristotle's definition, as the boundary-surface of a body [in Aristotle it is the boundary-surface of the surroundings of that body, i.e. something different from the body itself] in relation to the surrounding bodies, and "motion" as the going-away of a body from the neighborhood initially constituted by the [initially] surrounding (resp. immediately touching) bodies, which are then supposed to be in a resting state. The assertion that, for the one material point to be able to move, the immediately touching points must be in a state of rest, could only have been made on the basis of a misunderstanding of the above found necessity that every motion spatially presupposes the resting state. The place of a material point is, on the one hand, insofar determined by this point itself as such, as that point does represent the place in space. On the other hand, the position of this point in the whole of space is determined by other points (also Descartes makes this distinction by distinguishing between the "internal" and the "external" place), thereby not only [is position determined] by the immediately surrounding points, but by all points indeed, constituting space, so that, when, during the motion of the one material point the immediately surrounding points should remain stationary, then, for the same reason, also all other points should remain stationary. However, if the position of a material point is determined by the position of all other points in space, then, the other way around, also the position of all other points is determined by that same one point, which is directly evident as soon as one thinks space as really composed of points, as soon as space is really discrete [instead of continuous]. One then understands that when only one point is given as fixed, also the position of all other points is completely unequivocally determined [this at least holds in "discrete space" in which there are, nevertheless no gaps, thanks to the existence of several different supposed types of points], so that the stationary state of only one point is sufficient in order for space to be there and with it the motion of all remaining points.
After having in this way determined the reality of motion [as it differs from that of qualitative change] and the dependence of motion from the stationary state in space, we now have arrived at the exposition of the second essential nature of motion, its relation to time. We now want to determine the dependency of motion on rest also with respect to time. Whether motion is continuous [i.e. a flowing phenomenon, absolutely with no interruptions whatsoever (excluding, of course, its beginning and end] or discrete [and thus consisting of non-zero indivisible parts] is a question that now has to be answered. In this, it is clear that the continuity, respectively the discreteness, of motion depends on the continuity, respectivey discreteness, of space and time. Are space and time continuous, then also motion must be continuous, are they discrete, then also motion is discrete. And it is, first of all, only the discreteness of time from which the discreteness of motion depends, while the discreteness of space only indirectly determines the discreteness of motion. [At this stage of the discussion (p.321) PETRONIEVICS has already demonstrated that space and time are indeed not continuous but discrete. That this is so, chiefly follows from the inherent contradictions in the concept of continuity and (actual) infinity.]. But what exactly does it mean to say that motion is discrete? No more and no less than that motion is constantly [i.e. again and again] interrupted by rest, and that a given motion, lasting for some time (i.e. not being confined to a single moment), contains rest as an integral ingredient. This  discreteness of motion  immediately follows from the discreteness of time :
Time consists of the filled [i.e. having content] timeless NOW-moments and the unfilled [i.e. lacking content] temporal moments-of-change. [i.e. time consists of an ongoing alternation of timeless and temporal moments.]

For  local motion  the following correspondences with Time may be noted :
To the filled timeless NOW-moment of Time corresponds in Motion the stationary state.
To the unfilled temporal moment-of-change of Time corresponds in Motion the state of motion in the strict sense, i.e. the act of motion itself.
In  qualitative change  things are as follows :
To the filled timeless NOW-moment of Time corresponds the existence [we may say, the endurance] of an object as such [i.e. the object as it is here and now].
To the unfilled temporal moment-of-change of Time corresponds the origin, respectively the vanishing, of the object.
In accordance with this, in the  change of place (motion)  we have :
To the filled timeless NOW-moment of Time corresponds the existence of an object (respectively a material point) at a place.
To the unfilled temporal moment-of-change corresponds the placing of the object into a place, respectively the removal of the object from a place.

Because, now, the stationary state is nothing else than the residing of a material point at some place, it is as impossible to conceive Motion without rest, as it is to conceive Time without filled timeless NOW-moments.
Anyway, one may conclude the discreteness of motion also directly from the same basis from which the discreteness of time can be concluded, namely from the necessary discontinuity of change, for motion, as itself being a form of change, clearly must consist of simple absolutely indivisible acts of motion, and that what separates these simple acts of motion must itself be simple, and these are the stationary states.
[So, according to PETRONIEVICS the discretenes of Motion consists in bits of motion separated by stationary states, while the discreteness of Time consists in bits of flowing time separated by timeless NOW-moments.  Although a timeless NOW-moment is a temporal duration, it is not time-flowing, i.e. it is not the result of time-having-been-flowing. The timeless NOW-moment is the unit of duration, it is the smallest possible duration, it is not divisible into smaller durations, nor is it the result of a concatenation of such smaller durations. This, indeed is the atomic nature of time :  The extensivity of time has true minima, and these minima still have temporal extension (duration), although they cannot be further divided anymore.]
Indeed, it is demonstrated that  time is a discrete phenomenon  [and from here the discreteness of motion can be demonstrated, as PETRONIEVICS shows (1904, pp.134) (and reaching the same conclusion as some earlier authors already did) :

If the parts of time [in contrast to the parts of space] are after one another (and indeed they are, as contrasted with the coexistence of the parts of space [embodied in the extension of simultaneously existing material bodies] ),  then there can be no simultaneous parts of time, i.e. only a single part of time can be really-given. For if more than one part of time could be given, then they would no longer be after one another, but coexistent, because only that is really-given what is given simultaneously (in the "after one another" the past part is not given anymore, while the future part is not yet given, and only the present part (the NOW-part) is given, i.e. only the present really-given part). But if the one given part of time contained in itself parts, i.e. if it were composed of still more simple parts, we may ask whether these parts are coexistent or are after one another. They cannot be coexistent, because there is no coexistence in time [only in space]. They also cannot be after one another, because then they could not all of them be real [always only one of them can be really given, the others are past or future]. So in the one really-given part of time there can be no still simpler parts, it must itself be simple and indivisible. [And thus, the NOW-moment of time is simple and indivisible.] [And these parts, when they together constitute time, cannot be unextended (like mathematical points on a line are supposed to be) because then they could not together constitute extended time. If time consists, in addition to NOW-moments also one or two other types of indivisible parts, then at least one type of them must have (temporal) extension, in order to together constitute the extension of time. And precisely the presence of indivisible but extended parts in time means that the latter is discrete. Time is divided in at least actual successive NOW-moments, and because it is actually so divided it cannot be a continuum, because a continuum is only potentially divided into parts.]
When an extensive series is composed of only non-extended elements they can never together constitute the extensive series. So when the time-series consists of non-temporally extended NOW-moments only, they cannot together from the time-series. How the latter can nevertheless be built up, PETRONIEVICS, 1904, pp.138, explains as follows :
First, purely mathematically seen, the assertion that an extensive magnitude cannot be composed of simple units is false. It would only be correct if the definition of "quantity", saying that it is that what has parts and is divisible, were itself correct. This is, however, not the case. In pure arithmetic, when we exclude from it fractions and irrational numbers, and then having only the set of integers, there is between the first composed numerical-magnitude (numerical multitude), the 2,  and zero (as the absence of numerical magnitude) something in between which is not a multitude anymore and thus not divisible anymore, and which nevertheless is a quantum. And that is the absolutely simple undivisible numerical unity, the One. When we, accordingly, can legitimately think some given arithmetic magnitude as to be composed of simple parts of magnitude, why couldn't we in the same way legitimately think an extensive magnitude [for example a length or a duration] also being composed of simple units? The example of the arithmetic numerical magnitude shows that such a magnitude composed of simple indivisible units does not express a conceptual impossibility :  If it is, accordingly, conceptually possible to think of a discrete magnitude composed of simple units, then also such a real magnitude will be possible as soon as anywhere in the realm of beings there is given a real correlate of that simple conceptual unity. And such a real unit is indeed given in and around the time-series :  It is the really-given absolutely simple NOW-moment, which is filled with real content. And further, in the pure arithmetic magnitude [and thus not as mapped onto a line], for example the number 5, all simple units composing it, are so much connected with each other that they, in the one numerical magnitude (for example 5) have lost as it were their independence, i.e. they are not separated anymore. On the other hand, the real moments of time, coming one after the other, are given in a separate fashion (i.e. they are given as independent moments) [meaning that here the simple units are not 'mixed up' together but are given separately, i.e. one after the other], they are separated by real transition-acts which themselves are not filled with content, and so constituting [i.e. by separation of the NOW-moments] the extensivity of time, i.e. the extensivity of the time-series. Why, then, should the extensive time-series, as the simple concatenation of the simple, filled-with-content, successive NOW-moments, separated by simple transition-acts, not be formed? It can be formed :  The magnitude of the simple filled [with content] NOW-moment surely is 1, not 0, while the magnitude of the transition-acts separating these moments is 0 :  the transition-acts, not being filled with real content, surely each are, as compared with the filled NOW-moments as to their magnitute, equal to zero. [And indeed, a concatenation of ones and zero's always results in some composed magnitude larger than 1]. [The here mentioned "transition-act" in the time-series is the same as the above mentioned "unfilled temporal moment-of-change"].
We must now clarify in what sense, precisely, that which has just been stated is meant, because the transition-acts represent a special reality-species, and are thus themselves filled with a particular content, and so [are] not to be represented by absolute zero's, but themselves representing special units, not comparable with the units of real content. So when we say that the transition-act as such is not filled with real content, we mean that it is not filled with the primary qualitative-quantitative content, but not that it has no content whatsoever. The past and future moments, of which the time-series is composed, may, because they, respectively, once were recent [current, present] moments, and will be recent moments, in this sense just as well be considered to be filled moments [filled NOW-moments] as is the true recent NOW-moment. One may now ask whether the transition-moment, lying between the filled NOW-moments [i.e. alternating with these moments], itself belongs to this time-series [of NOW-moments] or not. For if the transition-act itself as such belongs to the series of filled moments, we may in fact consider the transition-acts not as zero-magnitudes of the time-series anymore, but must consider the time-series as an extensive magnitude consisting of two entirely heterogeneous unit-species. [So the one time-series might consist of two different (parallel?) but highly correlated sub-series].
In the space-series we will, later, see that the simple negation-acts, separating the real space-points from one another, are as such not given in this series itself, and, therefore, may certainly be viewed as empty gaps in this series, gaps lacking being, having zero-magnitude. In the time-series this is also the case [i.e. the case that the transition-acts, separating filled NOW-moments, are as such not given in the time-series itself.]. [It is further dealt with, later in PETRONIEVICS' work.]  [...]. But even when transition-moments would belong to the [same] series of filled NOW-moments, there would still exist the extensive magnitude of time, [this magnitude] consisting of simple units. But it [the extensive magnitude of time] then would consist of two heterogeneous species of simple units, and not of units of one and the same species.

(After having dealt, more or less preliminary, with the nature of time, as viewed by PETRONIEVICS, we continue the latter's exposition of motion, which is, of course, closely connected with that of time.)
That  motion  has a discrete nature, also is indirectly confirmed, when it can be demonstrated that the empirically given diversity of speeds of motion cannot be explained when motion is continuous. The demonstration to be made here is purely empirically, beause, abstractly taken, "motion" only expresses a change of place, without expressing anything as to whether this change itself may proceed in several different ways (without containing in itself the aspect of speed) [So when we want to ascribe something -- in this case discreteness -- to the nature of motion, i.e. to really  p r o v e  that this nature is so and so, we, in fact, should not involve variable speed of motion, because this is only empirically given, rendering the argument empirical instead of deductive]. Whether the speed of motion can be different or not [i.e. whether  d i f f e r e n c e  of speed is possible at all] is rather entirely dependent upon the nature of space and time. When we now demonstrate that continuity of space and time completely excludes any difference in the speed of motion, the relevant facts of experience (different speeds) evidently will form a decisive empirical basis of confirmation of the discreteness of motion, of course under the supposition that these data of experience follow from the discreteness of motion. [So, if the facts (data) of experience (which are the different speeds of motion) do follow (i.e. are explainable) from the discreteness of motion, the latter is then empirically demonstrated by these facts.]
Is, then, difference of speed of motion possible when the continuity of space and time is presupposed? To this question we answer with a definite No. Apparently, two cases, corresponding to the two main theories of space and time, must be distinguished in discussing this problem. We must, namely, distinguish the case that space and time are considered to be independently existing entities alongside the other things (Newton and Kant) from the case in which they are held to be mere frames of ordering of things (Aristotle is the first explicit representative of this view). Two points of view in fact distinguish between the two cases. In the second case "speed of motion" cannot, or at least not easily, be viewed as a purely dynamical aspect entirely different from space and time and residing in the moved point as such, while in the first case this is, purely formally, possible :  In the first case [space and time both independent entities] namely, matter and space are different from each other, and, in line with this, speed of motion seems to be a genuine intrinsic aspect of the moved material point itself. In the second case [space and time frames of ordering], on the other hand, the material point as such is at the same time space-point, and one had to suppose that it is more than a mere space-point if the speed is a special factor independent of space. And, further -- and this is much more important -- in the first case, together with the difference and independence of matter and space, there seems to be possible also a corresponding difference and independence of speed from time. While, namely, matter at different places in space may be of different density (the latter taken purely extensively), in the same way the speed may be of different magnitude at different periods of time, and so a difference of speed would be possible. The representatives of the theory of the independent existence of space and time [independent from other entities] are quite aware of the fact that they as genuine continua must everywhere be uniformly extended, and that there can be no question of different densities of space at different locations, and also not of a difference of speed of time in its various sections. But precisely by the fact that space and time as continua are uniformly extended, they must be different from matter, because only then matter can be dispersed differently in space, and only then the speed of the individual parts of that matter may be different in time. Or so it seems.
This last assertion, now, is -- and with it we enter the problem itself -- a veritable confusion. The different density of matter in space can only be conceived as such, because matter is discrete and space [supposed to be] continuous, so that nothing precludes to have these discrete parts of matter to stand in arbitrary distances from each other [making different densities possible]. Motion, on the other hand, [conventionally] is not supposed to be discrete but itself supposed to be continuous, and as a result, difference of its speed is absolutely impossible. [Conventionally, space, time, and motion, are supposed to be continuous, and thus, especially time and motion. And a continuous motion cannot unevenly be dispersed in a continuous time, meaning that difference of speed is impossible when motion is supposed to be continuous.] The empty entity of time, be it stationary or flowing, cannot give motion any possibility to be different in different sections of its temporal trajectory, for as being a continuum, motion is just as homogeneous as are all other continua, as are space and time. The moved material point on the one hand describes [traces out] a spatial trajectory, and, on the other hand, a temporal one (this expression wants to indicate that time is a special entity, distinguished from motion and change), and it [the material point], therefore, must run-through every determined spatial distance [every spatially extended piece or section] in a determined temporally extended section, so that one and the same spatial distance can be traced out apparently only in one and the same temporal section [implying the speed of motion cannot change]. For if one would suppose the opposite of it, then it would mean not more and not less that space and time are not uniformly extended everywhere. Space and time as extended continua surely must be extended in the same way, meaning that one and the same spatial section contains as many of the continuous extension as the same section in time contains continuous extension [the amount of extension measures length in space and duration in time] -- because one surely doesn't want to deny that measured by their extensive magnitude the same sections are present in space and time -- and the same, evidently, will also hold for motion if it too is continuous. And because motion consists in nothing else than that one and the same material point traces out an extended section in space and time, it is clear that the same space- and time-sections always correspond to the same motion-sections (motion as continuum also is extended and thus has sections of extension), implying that any difference of speed of motion is absolutely out of the question, for this difference doesn't mean anything else than that one and the same section (distance) of space may correspond to different temporal- and motion-sections, which, evidently, is impossible. [So it is established that when space, time and motion are continuous phenomena, a difference of speed of motion will be impossible. But difference of speed of motion is clearly observed to be the case in the natural world, meaning that space, time, and motion cannot be continuous. And here especially, that motion cannot be continuous, because it could not as such be unevenly dispersed. Motion must be discrete, and may as such be unevenly dispersed, either when space and time are continuous, or when one of them or both are discrete.]. And may one, in this, even so explicitly presuppose that motion is not the simple unification of space and time, that, accordingly, motion is something that immediately flows from the material point as such, i.e. flows from ints intrinsic powers, all this doesn't help, for were one nevertheless to presuppose such intrinsic powers in the atom, from these powers only so much will enter into motion as is permitted by the general nature of space and of time in which motion takes place. This speed of pure motion cannot, apparently, be greater than the speed of the pure flowing time itself is -- if this is thought as flowing -- because then this surplus could, evidently, not be present anymore in pure time as such, which is impossible, because motion takes place  in  time, and likewise it [the speed of pure motion] cannot be greater than the corresponding section of empty resting time, because it then would again not be dependent on it [i.e. on time]. And smaller than the speed of time this speed of motion can, apparently, not be, because motion is -- ex hypothesi -- supposed to be continuous. It must, as being continuous, extend itself in the same degree as time itself does.
Much easier as it was in this first case, is it to find out the impossibility of differing speed in the second case [the Aristotelian position, and also the position of continuous space and time, i.e. in fact the position of continuous motion]. In this second case time and motion coincide, and it is then clear that of the intrinsic powers, determining the speed of the moving material point -- when we permit this also in the present case -- only so much can be realized as is permitted by the general nature of time, because in this case time, motion, and speed, coincide. If time were continuous, then a difference of speed of motion in this case would mean that time would have different speeds in its different sections, which in turn would mean nothing else than that it is not everywhere uniformly extended. So if time is not a special entity alongside the changes, then the impossibility of different speeds becomes automatically evident, and one only needs to apply the same principle, which in the present case is decisive, also in the first case, to see that continuous motion is not compatible with different speeds of motion.

While we now have established that motion, if it is continuous, cannot have any difference of speed, we must now demonstrate how this [empirically verified] difference is possible when motion is discrete. If motion is discrete then it is, as we have seen, always momentaneous, and each longer lasting motion consists of a determined number of these absolutely simple motions respectively acts-of-motion, namely in this way that each single simple motion is determined by the stationary state, i.e. that the resting state precedes each simple motion. The difference of speed of motion is now based on the fact  that the temporal magnitude of the moments-of-motion is always the same, while the moments-of-rest have a different temporal magnitude.  Each act of motion, as a simple act of change, lasts, namely, a single moment only, while the resting-state -- because it is, as in its essence, timeless -- may, as to its duration, have different magnitudes. What this duration of the timeless moments of rest actually means, we have seen earlier, pp.164 (1904) :

Negation-acts transform [in time or merely in space] one entity into its opposite. They are, according to PETRONIEVICS, fundamental species of Being. In the time-series there are two types of negation-acts, viz. simultaneous and successive negation-acts. The simultaneous negation-act is a timeless negation-act, while the successive act-of-change is a temporal negation-act. Timeless interruptions of the time-flow turn out to be necessary in order for difference of speed of local motion to be possible. It can be established that different speed of motion is nothing else than the timeless interruption of the on-going flow of time in which the motion takes place. The flow of time would be on-going if upon every moment of rest immediately would follow the moment of motion (i.e. of the act-of-motion). As soon as this does not happen, as soon as the moving real point in the space point (space location) rests during  several (i.e. more than one) moments, the on-going flow of time is interrupted, and the motion has a different speed. (p.158/9). [In this way, time is dependent on material processes, especially on motion. It is not a separate entity alongside material processes.]
As soon as the timeless NOW is seen as the timeless absolutely partless act-of-positing [an act, not composed of parts], or, the other way around, as soon as the absolutely simple positing-act of the negation, from which originates the temporal act-of-change, is identified with this timeless NOW, this simple timeless part of time is there. The timeless negation-act [and thus the simultaneous negation-act], when it transforms itself into the temporal negation-act [and thus into the successive negation-act], ceases to be :  If we now imagine that while the one timeless negation-act in things transforms into the temporal negation-act, another negation-act at another place in the thing remains unchanged, then, evidently, the non-temporally extended section of duration, i.e. the timeless magnitude of duration, of that other simultaneous negation-act coincides in this case with the sought-for simple timeless part of time. (p.164).

The capacity of transformation of the timeless act (positing rest) into the temporal [act, positing motion] -- in which transformation, as we will see further down, does consist the intrinsic essence of motion -- makes possible the comparison of the timeless rest with motion as to its temporal magnitude. It makes possible the difference between (1) just one single moment-lasting stationary state and (2) a several moments-lasting stationary state of a moving point. If a material point must rest at a place before it ends up at the next place as a result of the act-of-motion, then it may, when the motion lasts a longer time, at each given place, rest either only a single moment (i.e. precisely as long as does last the simple [i.e. elementary] act of motion), or rest in more of them [in a consecutive series], and it may in every place rest with the same or different duration. If the moving point rests for the same duration in each [successively visited] place, then its speed will be uniform, and it will depend on the magnitude of the duration of rest whether it is greater or smaller. Does the moving point rest at different points not a same number of moments, then the speed of its motion will not be uniform, i.e. one and the same [material] point will have in different sections of its trajectory different speeds.
It is now clear -- and that is one of the most important consequences following from the above expositions -- that motion necessarily must have  an upper boundary (a maximum) of speed.  Does the moving point at each place of its trajectory rest just one single moment, then its speed will, in addition to that it is evidently uniform, be a maximum, because every other speed is lower, for smaller resting breaks than are the elementary ones are not possible. This result of there being a maximal speed of motion appears at first sight to be paradoxical, yet, it is easy to demonstrate that maximal speed is also necessary when motion is continuous. If we, per impossibile, admit difference of speed also in presupposedly continuous time, it surely is clear that this speed could not surpass the speed of time itself. If, on the other hand, time is viewed as resting, then, again, as explained above, the speed must have a maximum, because this speed depends on the continuum of the resting time. But the maximal speed of discrete motion is entirely different from that maximal speed (which at the same time is also the minimal speed) of continuous motion, if in both cases possible difference of speed is assumed :  The maximal speed of continuous motion, namely, would be an infinite maximum, which no finite speed is able to reach. The maximal speed of discrete motion, on the other hand, is itself finite and is the greatest finite speed.
In the investigations so far of the concept of motion we have found a dual dependence of motion upon rest :  First, motion spatially depends on rest in virtue of the fact that motion of a moved material point presupposes unmoved points which determine and make possible the identity and integrity of one and the same space in which motion takes place [already one stationary material point defines space]

Of course, this identity and integrity ("continuity") of space should not be understood such that the whole space in one moment is identical with that of another, but only such that in virtue of the unmoved space-points the spatial position of the moved points is unequivocally determined in both moments.

And, secondly, motion depends on rest also in temporal respect, because the motion at a determined moment demands the stationary state in the previous moment, and only consists in the negation of it [i.e. in the negation of the stationary state]. As one can see from this, motion is much more dependent upon rest in temporal respect than in spatial respect. In spatial respect it is, as it were, only a single time dependent on rest, while in temporal respect motion depends on rest all the time :  The stationary state as spatially determining motion does not have to be in the neighborhood of motion, while the stationary state as temporally determining the motion is in immediate temporal nearness to it, immediately precedes it.
We, now, only have to ask whether this dependence of motion upon rest is an absolute dependence, i.e. whether, as indeed every single motion in a certain moment is determined by the stationary state of the previous moment, likewise motion-as-such depends on rest, whether the motion in the world is preceded by the stationary state absolutely, whether before motion in the world was possible at all, the world was in a atate of absolute rest. Earlier we indeed had concluded from the essence of time itself and as such, that change (and the same evidently also holds for motion, because motion is a species of change) in the world has had an absolute beginning. The same conclusion can now be drawn from the nature of motion. If motion is negation of rest, and an act of motion, if not being determined by the stationary state of the material point moved by that act, being impossible, then, evidently, motion cannot have been since eternity, for every motion presupposes the stationary state, while the stationary state does not presuppose motion, because if that were the case, the stationary state would necessarily be just as temporarily-momentaneous as motion, which clearly is not the case. Only when motion does presuppose rest and rest does presuppose motion in the same degree, the conclusion of the absolute beginning of motion would not be stringent, for in this case its series must be merely infinite and without beginning [chicken-egg-chicken-egg-chicken ...] because none of the two may be thought as being the first. But it is an entirely different matter if motion depends on rest, but that rest is not at all dependent on motion :  Were motion eternal and without beginning, then that would evidently mean that the stationary state, preceding a motion, were itself preceded by motion, etc., ad infinitum, which would imply mutual dependence of rest and motion, contradicting the assumption. So motion must have had a beginning (because its series must begin with the stationary state).

As a result of these findings of the temporal dependence of motion on rest and the, with it immediately connected, finding of the instantaneity of motion, we seem to be in direct conflict with one of the best founded principles of modern mechanics, and of all of science for that matter, namely with the principle of inertia. The principle of inertia, as is well known, says that a material point in the condition of rest (in the stationary state) or in a certain state of genuine motion (i.e. of motion with a definite speed) remains in that state as long as no external (extrinsic) factors {forces] change that state [that is, that state is not changed as long as no external forces act on that material point]. According to this principle the stationary state as well as the state of motion as to their nature are lasting states [meaning that they have longer or shorter duration]. Every physical body, finding itself at rest or in motion, remains in them as long as external factors do not force to change them (from rest to motion, and vice versa, from one motion to another). Consequently, then, motion would be as continuous [in the sense of tending to keep on] a phenomenon as would be rest. But according to our above findings, motion is purely momentaneous [everytime receiving an internal 'push', so to say]. In its nature, motion is not a lasting state. It rather is its opposite :  At the same moment motion begins, at that same moment it also ceases to be. As to the stationary state it cannot, it is true, be denied that it is a lasting state, rather it is undoubtedly such a state, and even in a still stricter sense than usually thought, for it is not lasting in a temporal but in a timeless sense. But, taken in a strict metaphysical sense the principle of inertia does not hold for the stationary state either. For the stationary state the principle only holds in mechanical Nature, because that state may be negated as a result of  i n t r i n s i c  factors (the principle of inerta only refers to external factors), but this kind of negation by intrinsic factors, because it has consciousness as its condition, does not occur in unconscious Nature, implying that here the stationary state is really a lasting state as long as no external forces are applied to the resting point. The timeless negation-act, positing the stationary state, may transform itself :  This it does by itself in consciousness [i.e. in the world of immediate experience] and without any extrinsic agent. On the other hand, in the domain of unconscious Nature, this extrinsic agent is necessary in order for it [the timeless negation-act] to change into the temporal act-of-motion or act-of-change. [So in a metaphysical sense, i.e. in a most fundamental sense -- the phenomenon as to its very essence, i.e. as to what it intrinsically is -- the principle of inertia does not hold. But as to observation and observability, i.e. in natural science, the principle does hold.] As it is here, i.e. in the unconscious world, that, as to the stationary state, it is the nature of the particular conditions of reality that determine that the resting state is subjected to the principle of inertia, -- although it isn't so subjected in the metaphysical sense [i.e. metaphysically seen] and [thus] not so subjected as a result of its most fundamental essence, -- in the same way it is also special conditions of reality subjecting the state of motion to the principle of inertia, the state of motion, which originally wasn't inclined to follow up that principle, as it is the case of the stationary state, which is a lasting state. Although motion always remains, metaphysically taken, a simple act-of-motion, nothing does prevent to presuppose that the nature of world-elements in the once started motion of a world-element does demand the repetition of the simple acts-of-motion as long as it is not hindered by special circumstances, as is also the long time-flow of worldly changes itself determined by the nature of changing world-elements only. We cannot now go into the nature of these world-elements, we do that later. Here it was sufficient to determine that the metaphysical invalidity of the principle of inertia does not need to exclude the empirically-physical validity. It will mean that the principle of inertia may well be a composed fact and not necessarily needs to be a simple fact [That is, the principle of inertia may well be of a secondary nature only]. All this may well indicate that in the principle the very essence of motion and rest is not necessarily expressed. Without digging deeper into the matter, I'd like only to note that the continuation of a once started motion of a material point is simply necessary because the same relation of the material point to the surrounding points -- and only this special relation can cause motion in the unconscious world -- having generated the one motion of that point, will also generate it in the next moment when the material point has the same relation to its, in that new moment, surrounding points, the same relation that is, with the points that surrounded it in the previous moment, etc. in indefinitum. So not the nature of motion as it is in itself turns the principle of inertia into a necessity, but the nature of the moving material point as a member of the relational world does turn it into a necessity, which precisely is overlooked when the theory of discrete motion is rejected by reason of the principle of inertia [Discrete motion is intrinsically interrupted motion, that is, it is repeatedly interrupted by stationary states of the shortest possible duration followed by renewed motion. This discrete nature, (appearing) at motion's deepest level, violates the principle of inertia].

Two questions concerning motion still remain. The first one of them is about how motion is possible at all in a discretum-without-gaps [i.e. in a discretum in which there is no room for movement], because its possibity is so often denied. The second question is about how motion is possible if rest precedes it, how, at all, motion could begin there where previously was rest. This second question evidently is immediately connected with the ultimate essence of motion itself. Its answer in itself at the same time contains the assessment of the ultimate essence of motion. The first question is insofar connected with the second as, as a result, the possibility of motion in the discretum will be established [before answering the second question]. But motion is in temporal respect only then discrete (and containing rest as integrating part) if space is itself discrete, space that is, in which motion takes place.
So we first ask whether  motion in discrete space  is possible. If empty space is impossible and space coincides with real matter, then motion as such seems to be absolutely impossible. It does, namely, seem to be that if space is, without gaps, filled with matter, a material point is not at all able anymore to relinquish its place and to occupy a new one, because every other place as such is already occupied by one and thus not able to receive a new material point. This is one of the oldest and most important reasons to presuppose [patches of] empty space, and yet it clearly rests only upon a confusion of the absolute continuum with the gap-less discretum. In real space surely every place is occupied with a material point [including points of radiation, gravitation, etc., or, one might say, at least with points of imponderable matter, the aether]  [of which it is, currently, the place]. If, however, in all this, every material point is really taken to be a point, i.e. when real space is taken to be discrete [a continuum cannot be made up by (dimesionless) points], then we are free to suppose that at the moment at which a material point relinquishes a given place and is in the process of occupying another, the material point, originally occupying that other place, relinquishes it and necessarily has to occupy a new one, and so on, and so on, rendering in this way motion to be possible as a result of the simultaneous relinquishing of places by many material points. Descartes is the first thinker, who, while identifying matter and space, determined in this way the possibility of motion in real space. Only he had, peculiarly, taken space not as a gap-less discretum but as an absolute continuum, which is, however, impossible, because in an absolute continuum no separate parts do exist [while in the gapless discretum they do] and, therefore, motion in it of individual parts is as impossible as, say, a qualitative difference of such parts [here, I presume, we must identify "absolute continuum" with "homogeneous continuum" as contrasted with a "heterogeneous continuum" in which qualitative difference of regions of such a continuum are possible.] Only the confusion of the absolute continuum with the gapless discretum is to blame for not seeing the possibility of motion in discrete real space  ( Descartes, determining the way of motion in real space, was not bothered by this principal difficulty). As soon as one has recognized this difference, motion becomes possible in real space when one takes space as did Descartes. And yet another very important consequence which Descartes himself has drawn from his determination of motion, must be reckoned with to understand the possibility of motion.  Every motion whatsoever must proceed along a closed trajectory.  This rule applies to real space quite independently whether it be taken as infinite or as finite (upwardly), for because a material point can only take up a new place when the original point relinquishes it, the same applies to the latter, and so on. If, now, the series of these material points, successively giving up to one another their places, were not a closed one and [thus] the last point of it not occupying the relinquished place of the first point (starting the motion), may the number of points in that series be infinite or finite, then, on the one hand, the place of the first point would remain empty, which is impossible [under the supposition that space and matter coincide], and, on the other hand, the last point of this series has yet to expel a material point from its place, and when this latter material point would not take up the empty place of the first point, it would, so to say, fall out of real space, which is impossible. Do we, on the other hand, suppose that the empty place of the first point becomes occupied by the material point of another motion-series and that the material point having been expelled from its place by the last point enters the empty place of the first point of yet another motion-series, then -- in order that the same difficulties being present in the first motion-series will not partly repeat in both new series -- both these series must merely be parts of the first series, i.e. the motion-series always must proceed along a closed trajectory. But this closed trajectory in discrete space does not need to be regular (as soon as the intrinsic geometric structure of discrete space is known), and only because Descartes confused the spatial continuum with the discretum, and not bothering himself with the intrinsic geometric structure of the discretum (his corpuscula were meant to possess the most diverse geometric shapes, because they were taken as extended [and not all geometric shapes are possible in discrete space] ),  he was able to declare this closed trajectory to be a circle and base upon it his whirl-theory.
After having established the possibility of motion in real discrete space, we must now determine how motion is possible when the stationary state necessarily precedes it. All points of the closed motion-series must, before their motion starts, be at rest, and we now ask how one of them can at all initiate motion, and then let participate in it all other points simultaneously. Earlier we already have stated that the change of place of real points is impossible without the real negation-acts lying between them. Here we want to base this finding in a rigorous way. The necessity of real negation-acts between the real points becomes an absolute necessity when these points must be necessarily at rest before they enter into a state of motion.
Let us, for this, look to the motion of the points  A, B, C, D, E, F  in the triangular point-net of the next Figure  [The points of this net are the geometric points of triangular discrete space separated by non-spatial points (negation-acts). The lines in the Figure connecting these points are imaginary and express the triangular nature of this brand of discrete space. Each geometric point of this space is the "place" of a material point which may leave it.]


which [moving points] are ordered along a closed line [trajectory] [green in the Figure] (the periphery of a regular hexagon), along which they carry out their motion, when one of them is set to move. If these points are stationary, their motion, taken metaphysically, cannot originate by absolute, absolutely unmotivated, chance, it must come from the nature of these (material) points themselves to be able to start motion. Now, in fact, this ground for starting motion cannot reside in the single point because the point as such is without parts and thus in its interior containing nothing what might generate this motion, if it were not for pure forces, which should be rejected as mere mystical and mythological beings by any rational metaphysics. The motion of the point may also not taken to be a fundamental property of it. This not only by reason of the fact that it would violate the logical principle saying that only precisely that [entity] may be taken as an ultimate simple [i.e. not composed] fact or property of a thing, that stands in a transparent conceptual connection with precisely that [thing] of which it is supposed to be the property -- which here [i.e. in the case of the motion of a material point] is not the case, because it is entirely obscure how and why the individual point has itself moved all by its nature -- but the discrete nature of motion as such already forbids this entirely. The discrete nature of motion brings, on the one hand, with it that the motion in every single moment is entirely impossible without the resting state in the previous moment, and, on the other hand, that motion at all in the world is not possible without the previous stationary state of the world as a whole. As a result of all this, motion is not and cannot be the original property of the material point, because it is, on the one hand, at every moment interrupted by the stationary state, and, on the other hand, motion cannot belong to the material point from eternity, but has come to it at a certain moment.  [ For an  ens  (a being) to be in a state of motion,  is, -- with respect to  ens  only insofar as it is  ens, -- per accidens,  not  per se,  not flowing from its nature as  ens.  Expressed a bit differently :  the connection between ens and motion is  per accidens.]  Were every single real point existing only for itself and [thus] without any relation to other points (i.e. were the world non-relational), then motion of them evidently could not originate, and to be stationary would be its eternal unremovable state. It is clear that the possibility of every real point's motion must come from its relation with other points, and we now ask ourselves how this negation-relationship between them should be taken (should be thought of), in order motion to become possible by it.
If we would presuppose that the negation-act, separating, for instance, point A from point B in the above Figure, were a purely formal act, then still no motion of point A and its shift to the place of point B could take place, because a purely formal act has no entitative content, and its removal does not at all entail real change, because the "nothing" -- and the negation-act indeed is in this case a pure nothing -- cannot undergo any change at all. It is clear that in this case [negation-act being a formal act] motion of the point A cannot get started. It is, however, an entirely different matter when the presupposed negation-act is real, for in this case from its removal surely something real, a real change, would ensue, and then also the motion of point A may take place. How, then, does this motion take place? The answer to this question will reveal the ultimate essence of motion and its difference from qualitative change. If both real points A and B  ( Figure above )  are really separated from each other by the real negation-act, and as two, as separated [points], only exist in virtue of this act, they evidently would not remain what they were after the removal of that act. They cannot remain separate, cannot remain two anymore. They, accordingly, would, after removal of this negation-act, seek to unify with one another. Evidently, they have to leave their place [in order to accomplish this unification]. If there were only one single species of negation-act in the world, i.e. if only quantitative negation-acts existed, then, apparently, their removal would entail also the removal of the real points as such, that is, they would all come together and unify [in fact they would  be  together, i.e. simply coincide, without previous motion] (sinking back into the absolute substance [prime matter] ),  and the absolute removal of the real negation-acts would at the same time mean the absolute removal of the real points, and then, in the realm of Reality, only qualitative change were possible. But this is not so [i.e. it is not so that only quantitative negation-acts do exist]. In addition to quantitative negation-acts there do exist also qualitative negation-acts [ rendering points to be qualitatively opposite :  " X is, qualitatively, not Y " and " Y is, qualitatively, not X "], and when we presuppose the unremovability of the latter during the time that the quantitative are changing [are removed], then the mysterious phenomenon of motion finally becomes clear, and its possiblity acknowledged. So when the points A and B do not depend solely on the quantitative negation-acts, positing their numerical difference, but at the same time also on qualitative negation-acts, distinguishing them from other real points qualitatively, the removal of the quantitative negation-act would not entail anymore the removal of the real points, if the qualitative negation-act, positing these points originally, is [supposed to be] unremovable [After removal of the quantitative negation-acts the material points nevertheless do not coincide because they remain qualitatively separated from one another]. What, then, would actually happen? As a result of the removal of the quantitative negation-act between the points A and B these points must evidently relinquish their place -- because only by this act they are held at their respective places -- but, because they are not going to coincide thanks to the steadiness of the qualitative negation-act, positing them as real qualities, their motion will be just the common resultant of these negation-acts acting in opposite directions :  The real material points must, without themselves becoming cancelled, give up their respective places. And because the real [material] points A and B cannot simply exchance places, because they then would have to penetrate one another [on their way towards each other], which is impossible -- quite apart from the fact that this penetration truly would mean their absolute unification -- they must force other points in their vicinity to give up their places, and so on, as long as the motion of all these points does not become closed as was indicated above.
On first inspection it might seem that this enforcement of the motion of the other points would not in their turn need the removal of the negation-acts between them, so that all other points in the closed trajectory may be set in motion purely mechanically by reason of the fact that the necessary giving-up of the place of the first [two] points simply renders vacant the place of the other points. To suppose something like this would be to declare clearly composed facts of sensible experience to be fundamental simple facts of Being :  Nothing seems to be more clearly understood as once a given body is set in motion, the other bodies encountered by it in space must make way for it because two bodies cannot simultaneously exist at one and the same spatial place. As to the simple material points of which we here speak, we do not deny the latter statement about impenetrability, but metaphysically taken, such a transmission of motion from one point to the other can as less take place purely mechanically than the first 'push' of motion had taken place mechanically (the  first  push of motion, would it be really mechanical, truly should be reduced to absolute chance), but [should be accomplished] truly again by the removal of the real negation-act separating two points. So the transmission of motion [to the points having their initial places in the spatial trajectory of the motion] can again take place only by the removal of the real negation-acts residing between the real points, and the whole difference between the first point giving the 'push', and the other points receiving this 'push' only boils down to the fact that the removal of the real negation-act at the beginning [of motion] takes place spontaneously, while the others passively.

As a result of these expositions about the possibility of motion as compared to qualitative change, we believe to have indicated clearly and precisely the difference between them. Frankly, these expositions still contain many gaps, which definitely cannot be circumvented, because motion, as the last one of the formal categories [following upon time and space], forms the transition to the [so-called] real categories [centering about quality].  Time and space as such, i.e. as forms of ordering, are pure relationships and therefore belong to the formal categories, although standing, as relationships, in close connection with real negation-acts, by which they are posited (which, however, as such, as we have seen, do not belong to these series themselves, rendering their abstraction from them a natural one).  Motion, on the other hand, is, as a form of change, itself real, surely rendering it as such to be a real category. What is formal in [the phenomenon of] motion are the spatial and temporal relations without which motion is incomprehensible. As a formal category motion is to be taken by reason of, on the one hand, it being a change of place, where place is a formal spatial relation, and, on the other hand, because it, as being a change, belongs to time. As a real category motion is to be taken because it is, as being a change, a real negation-act. In the same way the stationary state as such is a real category because it consists in a real simultaneous negation-act. The stationary state is a formal category insofar as the place resides in space and insofar as the stationary state as timeless act resides in time itself, as explained earlier. So while the category of state as such, i.e. seen as it is in itself, is a real category, the category of ordering is a purely formal one, and while motion and rest are formal categories only insofar as they presuppose the categories of ordering, it is also clear why we, in this chapter, came to questions immediately reaching into the domain of real categories. The difference of motion from qualitative change, and the possibility of their coexistence, will only become entirely clear, when we learn to know the intrinsic real structure of Being. With all this we [PETRONIECICS] hope to have laid down the foundation [in the sense of having worked out the formal categories of Being :  time, space, and motion] for the solution of the qualitative world problem.
(end of quotation and translation of, and commenting on, PETRONIEVICS's text (1904) on the essence of motion.)

It has been very instructive to include in the present document on motion, and thus on the principle of inertia, on the impetus theory of motion, on space, place and time, on dimensions, and on quality (more of it in the next document), the long, but interesting section on motion, written by PETRONIEVICS. In it, time, space, and motion, are held to be discrete (instead of continuous) phenomena, which means that they are constituted by the smallest elements of their species, elements which, although they are non-zero entities, are nevertheless absolutely indivisible. And these elements of either time, space, or motion, are qualitatively or numerically separated from one another by so-called negation-acts. With "material points" (quality points) [together forming physical bodies or patterns] these negation-acts are principal species of Being in the "space-theory" of PETRONIEVICS, principal species of Being, distributed as points in extended and/or non-extended space (involving intensive dimensions), in fact these points directly forming discrete space.
So it was indeed instructive to present an alternative view, alternative that is, with respect to that of natural science, that of Hartmann, and that of Hoenen, in order to demonstrate how complex and diverse the seemingly simple and familiar notions of space, time, and motion really are. It should stimulate the reader to further ponder about the true nature of these categories.

* * *

With all this, i.e. in the discussions of the present document, we have, largely following HOENEN, 1947 and also PETRONIEVICSconcluded the exposition about  PlaceSpace  and  Motion.  In the next document we will, again largely following HOENEN (but also Nicolai HARTMANN, 1940, 1950 (1980)), consider the nature of  q u a l i t i e s  and their dimensions, and integrate the results in our theory of the Explicate-Implicate Orders. Especially, we will discuss the ontological seat of  intensional dimensions  in which all (variation of) intensional qualities reside as to their substates, and these dimensions are then contrasted with extensional dimensions.

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