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Sequel-5 to the Summary and Evaluation (of the documents XVI -- XXVIII concerning the promorphology of complex-shaped two-dimensional crystals).
This document (Part XXIX Sequel-5) supplements the ontological discussion of the previous document. It tries to demonstrate the impetus of a material entity as a variable quality of that entity. If it succeeds we possess an important metaphysical indication that points to the existence of holistic aspects in Reality.
Overview of the Argument
The argument, leading to the demonstration of the existence of at least one variable quality is structured as follows :
The complete argument, leading from the ens extensum to the existence of the impetus as a variable quality, will now be presented :
With respect to the material world the subjectively and objectively first datum is the ens extensum , i.e. the spatial being, the spatial thing (whether it is a simple particle, a complex thing, or a physical field, and whether it is an intrinsic thing or aggregate). The term "ens" (latin) means "being" in the sense of " any (particular given) being insofar as it is being" . The term "extensum" stands for the english "spatial extendedness" (in Dutch : "uitgebreidheid").
The study of the general ens extensum (but then just) as extensum, and as extensum alone, is the province of Geometry. In the present document, however, we study the extensum as ens, and that means we are doing metaphysics.
Because of its primary nature the ens extensum cannot be defined, because every 'definition' of it will already contain directly or indirectly the concept of ens extensum (To see this, just try it!).
An ens extensum can come about in two varieties, viz. a contiguum or a continuum (and we have already shown that the latter can be heterogeneous).
An (ens) extensum is a continuum if it is intrinsically one. If it is not, then it is a contiguum.
In the previous document we have established that every given intrinsic being or ens per se, or, equivalently, every 'totality' -- which kind of being is, in what follows, the focus of the discussion -- is a (local) continuum, and in most cases it is a heterogeneous continuum. Our ensuing discussions will relate therefore to (physical) continua, homogeneous or heterogeneous.
Possibility of penetrable continua
The concept of extensum, and by implication that of continuum, implies the concepts of inside and outside. So, when not speaking metaphorically, only with respect to extensa (plural of extensum) we can talk of impenetrability of one body A with respect to a body B (which means that the body B must stay outside A), or of penetrability of a body A for a body B (which means that body B can go inside A).
Consider a moving body that meets another body, and collides with the latter (We here speak about central collision).
If they are mutually penetrable then they would continue their course, they fly just through one another. If, on the other hand, they are not mutually penetrable they are, when colliding, being deformed, resulting in so-called restoring forces (elastic forces) acting on them and changing their motion. So the primary cause of this change of motion is the impenetrability, and this entails an a c t i v i t y . What we see is that impenetrability of something (for something) has an effect on the situation and motion of another thing. And this is not possible without an effective cause.
From this we see that an extensum (and by implication a continuum) alone is, it is true, a condition for impenetrability, but it is not a sufficient condition, because it also demands activity. On the basis of this, the possibility of the absense of such an activity in or at an extensum is given, which means that there are no a priori objections against the existence of an extensum that is penetrable. This is an important result.
Place and Space
From the primary notion of ens extension some possibilities can be derived. In a spatial world (here we're not talking about space, but of a world of spatially extended things or bodies), which indeed is 'our' world, the capacity for contact is automatically given : two bodies can touch each other. They are then in each other's immediate neigborhood. They can touch a third body on either side (i.e. such that this third body fits exactly between the two other bodies). They then are at a certain distance from each other. If this contact changes continuously (i.e. when there is flowing contact) then there is motion. The general study of these relations is the philosophy of Place (in the sense of the location of something) and Space (the latter is a (further) derived concept, derived from the concepts that flow from the concept of ens extensum).
Relativity of place.
Contact Theory of Place
Investigation of the contact theory.
Again, it is immediately evident that from this double contact a distance results, which has the length of a face of the parallelepipedum, i.e. a distance between the contacting faces of the two cubes.
And yet another case is equally possible :
Two cubes A and B are in contact with a rectangular bar C, such that the two faces of the cubes, facing each other, are parallel. Again it is immediately clear that the mentioned faces of A and B (or there mid-points) have a distance from each other measured by the length a. This distance again results from the contacts.
Now let the contact of A with C be changing smoothly (also this possibility is immediately clear, and we can call it a flowing contact). Again it is clear that motion of A with respect to C results, and also, because there is indirect flowing contact, motion with respect to B. The distance from A to B becomes larger or smaller. Purely mathematically this motion can also be described such that the system BC moves with respect to A. Whether this (equivalence) also holds physically, will be looked at later.
Let us again consider this system of three bodies, A, B, and C. And let us suppose that no other bodies exist. Then between A and B there 'exists' an empty space of certain dimensions. But this 'existence' should not be taken literally, because space is not an ens, i.e. it is not a being, which is so because we had supposed only three beings (three entia) to be present. And that this space is not a being whatsoever, means that it is nothing. And a nothing cannot exist. So with this "empty space -- being nothing -- between A and B " we, in fact, mean the following : Between A and B we can place a fourth body (if available) with a maximum length of a . If this length is greater, then it cannot be placed (i.e. it cannot exist) between A and B, if it is smaller, then still an additional body can be placed there. Also this is immediately evident.
Also outside this 'three-body universe' an empty space 'exists' which potentially extends into infinity. But also this statement means the following : The number of bodies can be increased and brought into physical contact with the three bodies already present, and this potentially into infinity.
Indeed, all fundamental relations, that are found with respect to place, space and motion, are completely intelligible within the framework of the contact theory. And they are intelligible from the primary datum, the ens extensum or spatial thing (HOENEN, 1947, p.140). And, especially, these things remain intelligible when we advance the ether of Lorentz as a universal medium of localization (in our above example of a three-body universe the bar C could represent this ether, while the cubes A and B represent bodies that are in contact with this ether. And when we assume the contact with this ether to be total, i.e. such that the bodies are totally submerged in this ether, the contact is three-dimensional, because the ether is assumed to be penetrable for all bodies, the possibility of which was established above.
A possible difficulty of the contact theory, and its solution.
The position theory.
The contact theory wins.
Ihm (dem Raume) geht die Bildung der objektiven Körperwelt voran. Ich kann Körper durch sinnliche Merkmale wiedererkennnen, ohne sie bereits räumlich zu erfassen. Ist in solchem Sinne der Körperbegriff gebildet, so zwingt uns die sinnliche Erfahrung dazu, Lagen-Beziehungen zwischen den Körpern festzustellen d.h. Relationen der gegenseitigen Berührung. Was wir als räumliche Beziehungen zwischen Körpern deuten is nichts anderes. Also : ohne Körperbegriff kein Begriff räumlicher Relationen zwischen Körpern und ohne den Begriff der räumlichen Relationen kein Raumbegriff.(The italics are from HOENEN)
Let us translate this important passage into English, and provide it with some comments, placed between square brackets :
The objective world of bodies [which we can represent by the ens extensum] precedes it (space). I can recognize bodies by means of sensible features, without grasping them spatially [here meaning : without presupposing space]. When in this way the concept of body is formed, then sensible experience forces us to determine local relations between the bodies, i.e. Relations of mutual contacts. And what we signify as spatial relations between bodies is nothing else. So : without the concept of body there is no concept of spatial relations between bodies and without the concept of the spatial relations there is no concept of space.Some might argue that this is all about concepts, but the reference to sense experience says otherwise.
The Ether of Lorentz
One of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest.From this statement of LORENTZ it is clear that his ether neatly fulfils the demands of place. And this we consider to be a fairly good indication of its actual existence. So although it cannot, it seems, make motion with respect to it observable, its existence as a medium of localization is now fairly well established.
HOENEN, pp.150, sets out to demonstrate that physical motion is not necessarily symmetrically relative, which means that although mathematically it makes no difference when we say A moves with respect to B, or B moves with respect to A, physically it makes a difference. However, he does this by invoking the ether of Lorentz, i.e. he presupposes the existence of this ether. We cannot accept this as a demonstration that motion is not symmetrically relative.
Fortunately there is a metaphysical indication that points to this asymmetry, when we consider uniform motion : When a particle moves uniformly (i.e. with the same velocity), no force is acting upon it (otherwise the motion becomes non-uniform). But motion is change, namely change of place. And, moreover, the body-moving-uniformly is something passive (and it should therefore, to express this, be called "body-being-moved-uniformly"). So there must be an active cause. But this cause cannot be a force. And it must reside either (1) in the body's surroundings, and then moving these surroundings (with respect to the body) or (2) in the body itself, and then moving the body (with respect to its surroundings), or (3) in both, body and its surroundings. I think it is fair enough to rule out the first and third possibilities, because they imply a large extension or realized expansion of this cause, affecting many many bodies or particles. So when a body is moving uniformly, it does so in virtue of an active cause residing in the body, not in the surroundings ( this active cause will later be identified with the impetus).
All this is at least some indication of motion not being symmetrically relative, without invoking an ether like that of Lorentz.
The contact theory, which we have found to be correct, demands an immobile and unchangeable medium as a medium of localization. And if we look for such a medium we see that the ether of Lorentz fits these demands. It is pervading all non-ethereal bodies, and so is indeed a medium for them, implying three-dimensional contact with every such body. It is permanently at rest (according to LORENTZ's hypothesis), which means that the place of any non-ethereal object immersed in this ether is immobile. It is the non-ethereal object that moves and therefore changes place.
However, this ether, in its function of universal localization medium, must be specified further, for its own sake as well as in order to assess the plausibility of its existence :
Ontological analysis of the Ether as universal Medium of Localization.
Every real full-fledged being can be considered to consist of Substance and Accident, or, in other words, of properties (accidents) plus that (substance) of which they are properties. If it were not so constituted, it would be difficult to consider it as real. The ether, if it is to be a medium of localization, must be a real being (as established earlier). So it must ontologically be constituted by substance and accident. But as such the ether can change, and would not be an appropriate localization medium. A way out of this dilemma could be the following : Precisely the 'naked' substance, i.e. its substance without accidents, i.e. that which remains the same during (accidental) change, is the medium of localization. This medium would not be real if it did not have accidents (properties). But it does have accidents. It is only that these accidents do not participate in the ether being a universal medium of localization. Only its substantial aspect does. That this, not seen as a being, but as an aspect of a being, is real enough can be illustrated by the substantial aspect of any ordinary physical body that is an intrinsic being. Let's take snowflakes. They all differ in appearance, even when grown in uniform conditions. Especially they differ in morphology. But their chemical composition is the same, and also their crystallographic symmetry (expressed by their Space Group) is the same. As was established in First Part of Website (Crystals and Metaphysics) the Essence of a single crystal is its Chemical Composition plus its Space Group (symmetry). And this Essence represents the substance and was called the genotypical domain of the given being, which here is a crystal. From this Essence flows part of the crystal's phenotypical domain, consisting of intrinsic properties, like the crystal's point symmetry, its electrical and other physical properties, and also its chemical properties. In addition to these properties the crystal also displays extrinsic features (constituting the other part of its phenotypical domain) such as resulting from irregular growth, caused by fortuitous irregularities of the growing environment.
This description should, however, be a little amended : In fact the mentioned crystal's chemical composition plus its space group symmetry -- because as such this is already a full-fledged physical structure -- already belongs to the crystal's phenotypical domain, the domain of the observable consequences of the crystal's Essence (its genotypical domain), and the latter can be identified with the particular relevant crystallization law (as dynamical law of a dynamical system, which is the growing crystal in its nutrient environment). It is this crystallization law that, as Essence of this particular crystal, cannot change, because in that case we would obtain a specifically different crystal (Realize that the Essence, insofar as it is this particular Essence, cannot change. Only the crystal can change, and when this change is a substantial change -- and thus not an accidental change -- we have to do with a specifically new Essence of the crystal. This could happen, for instance, when a given crystal metamorphoses its intrinsic structure as a result of change of certain external conditions like temperature and pressure.). In the same way the direct (phenotypical) consequences of the Essence of the crystal, for example the space group symmetry and point group symmetry as intrinsic properties (and only as intrinsic properties) remain the same, while other features like the particular shape and morphology that the crystal has actually taken up, changes, when say, ice crystals are concerned, from snowflake to snowflake. Of course the intrinsic properties could change, but only as properties, not as intrinsic properties of the initially given crystal, and then they become intrinsic properties with respect to another species of crystal, for instance, with respect to chemical composition, when Oxygen is replaced by Sulfur (at low temperatures), or, when its space group symmetry turns into another space group symmetry ( These are substantial changes, about which we spoke just above). But in a snowfall this does not happen. And it is this case we consider illustrative for something remaining the same within something that changes constantly. And the ether is now considered to be something that remains the same -- and can as such serve as a medium of localization -- within an ontologically broader entity that can and does change all the time. This ontologically broader entity, which as such must be a full-fledged being, is composed of (a particular) substance plus (its) accidents, intrinsic or extrinsic, and could, or even should be -- because a universal medium of localization not only demands just extension, but extension in and around all objects that obtain place -- some physical field. Maybe several physical fields are involved, that, however, ultimately unite to be one field after all, and the ether would then be that aspect of this field that remains the same. And this aspect will then consist of the (unified) field's Essence plus that what necessarily flows from it, i.e. that which is immediately implied by it, which is the set of intrinsic properties. What we observe however, is neither this Essence, nor the intrinsic properties insofar as they are intrinsic properties, but only actually existing features. The Essence plus intrinsic features does not change as long as the substance does not change, i.e. is not annihilated. This means that our unchangeable entity, demanded by the contact theory, is a theoretical construct, not a physical entity. And this goes someway to explain why the Michelson-Morley experiment failed to demonstrate it : Motion can only be measured when it is motion of a body, i.e. of an ontologically complete entity, with respect to another such body.
This interpretation, here presented, of the nature of the localization medium differs from that of HOENEN, because he maintains that this medium is a full-fledged substance, i.e. a complete being, its substance plus its accidents. We say that the medium of localization is only an ontological part of such a complete being. It is the theoretical construct (or, equivalently, the ideal entity) as outlined just above. And its reality wholly derives from the reality of the complete being of which it is an ontological part.
If our medium of localization by means of which a body obtains its place, were uniform and homogeneous, then every place would be the same, which means that motion with respect to this medium would be impossible. But our medium is not necessarily homogeneous. We have said that this medium of localization (insofar as it is a universal medium of localization), is the constant structure that is immediately implied by the Essence or intrinsic nature of the complete entity of which the medium is just an ontological part. And if we now assume that this constant and permanent structure is non-periodic (otherwise many places separated by certain distances are exactly the same with respect to local structure as well as to orientation), then our medium is a true universal medium of localization. It is an abstract heterogeneous continuum.
If there really exists such a universal medium of localization, then the place of a body is a unique place when it is related to this medium. But can a place really be unique, i.e. can we demonstrate this without assuming this medium ? Yes we can. We will derive it from absolute simultaneity. So the first thing we must do is to derive the latter :
The Theory of Relativity presupposes the possibility of Absolute Simultaneity.
If something is not intelligible, then it cannot exist.
We will now show when the first mentioned philosophical position applies, and when it does not.
Suppose there is something of which we definitely (i.e. in the sense of direct intellectual insight) know that it has quantity. And suppose we can establish that this quantity cannot, even in principle, be measured, while this impossibility is neither caused by imperfect measuring devices, nor by fundamental physical constraints, but comes about by a cause within that entity itself, then such a something (i.e. this entity) is unintelligible. And, according to the just given principle of intelligibility, it then cannot exist. So in this case the first philosophical position --- not observable in principle ==> cannot exist --- is valid.
Indeed this position is only valid if the "in principle non-observability" relates to the object itself, i.e. to the object in question.
It is not valid when this in principle non-observability relates either exclusively to technical imperfections of the instruments (but this is aggreed upon by everybody), or exclusively to absolute, i.e. in principle, physical impossibility of observing and measuring, because here we can imagine cases where we know beforehand the presence of, say, a property (of something) by evident intellectual intuition, while this property is not observable because of fundamental physical reasons. And in such a case the philosophical position --- not observable ==> cannot exist --- does not hold. A simple example could be the following : Suppose that it is impossible, even in principle, by physical reasons, to position measuring devices such that they can inspect the rear side of the moon. Then we cannot conclude that the moon doesn't have a rear side, because we intuitively know, that the moon, being an extensum, i.e. a spatial thing, must necessarily have a rear side.
Let's continue with the problem of the existence of absolute simultaneity.
We should realize that we here are trying to determine something of the nature of time, not how it can be measured. What is then time? Well, we could, with ARISTOTLE, define time as follows :
Time is the numerable aspect of change (for instance motion) with respect to the before and after.
Let us supplement and elaborate on this definition.
Every change unequivocally determines an order of before and after. This temperal order does not exist apart from of the different changes, it is within these changes, but is not a privilege of some particular change or motion. When a given moment of one or another change (motion, or, generally, process) corresponds, i.e. is simultaneous, with a certain moment of another change, then all that precedes that moment of the first change, also precedes that same moment of the second change. And if the end of a given change coincides with the beginning of another change, then the whole order of before and after resulting from the second change, comes after the order of before and after of the first change. In this way all changes contribute to one and the same order of before and after in the whole universe. It is because of this that we are entitled to speak of one universal time, one universal order of before and after. This does not mean that time proceeds independently from change. What exists is nothing else than the order of before and after in concrete moving or changing matter.
The above given definition of time and also the just given elaboration on it, seems to be contradicted by the theory of relativity, especially the notion of simultaneity. But, there is a caveat here : While the philosophical definition of time admits of the possibility of the existence of objective and absolute simultaneity and therefore holds that there is just one universal time, the theory of relativity says, and rightly so, that absolute simultaneity cannot, even in principle, be measured. And, as has been said, it is now important not to jump to the conclusion that it then doesn't exist. On the contrary, absolute simultaneity, is, although not measurable, presupposed by the theory of relativity :
This is because in the theory of relativity the possibility of transformation is assumed. Transformation here means that the location (place) and moment in time of a given event, i.e. one and the same event in the universe, can be determined in more than one system of reference (coordinate system). And this means that observers in different systems of reference that move with respect to each other, all can observe and record this event, be it that they will find different values of place and time, at which this event takes place. Transformation formulae admit to express time and place as measured within one particular reference system to be expressed in terms of another reference system that moves with respect to the first one.
The ensuing argument, demonstrating that absolute simultaneity is -- because transformation is (by the theory of relativity) supposed to be possible -- presupposed in the described situation, was first given by Van MELSEN, A., 1955, Natuurfilosofie (written in Dutch). There is an English edition of this work -- not a translation -- preceding Natuurfilosofie : Van MELSEN, A., The Philosophy of Nature, 1954).
If we, for the sake of convenience, limit ourselves to two systems of reference, I and II, that move with respect to each other with a uniform motion (i.e. with constant speed), then the possibility of transformation presupposes that every event, recorded in I, can also be recorded in II. The transformation equations then exactly determine what the values of registration in II will be, when given in I, or vice versa. One can now express the presupposition, based on every transformation-possibility, also as follows : The two systems (which move with respect to each other) should be constantly in contact with each other (i.e. penetrate each other), otherwise not every event could be recorded in I as well as in II. This being constantly in contact, however, means that at whatever chosen moment of time all points of II coincide with certain (though unknown) points of I. After all, there must be a constant correspondence ( = transformation possibility) between the two reference systems.
Precisely the existence of such correspondence presupposes something with respect to time, still apart from its measurement. It is, namely, presupposed that at the same moment when, say, point P1 in system I coincides with point P'1 in system II, another point P2 (in system I ) necessarily coincides with one or another point in system II. Otherwise the two systems would not be in contact with each other at that particular moment, implying that there does not exist any sensible application of the transformation equations. See next Figures.
Figure above : Two systems of reference, I and II, moving with respect to each other. Both systems must be imagined to be extended indefinitely. See also next Figure.
The systems of reference (with respect to the assessment of place) should be understood as coordinate systems (For three-dimensional reality they must be three-dimensional) :
Figure above : Two systems of reference, I (black) and II (red), moving with respect to each other. Both systems must be imagined to be extended indefinitely. They are coordinate systems, each provided with an origin (indicated by a green point). From such an orgin the location of some object can be indicated (with two coordinates), i.e. it can be measured.
So the application of the transformation equations presupposes that at every given moment, let us say the moment that is marked by a certain event at point P1 in system I, all points of I, whatever their distance is from P1 , coincide with certain points of system II. And in this fundamental sense (and only in this sense) one can legitimately speak of absolute simultaneity. This simultaneity does not mean that clocks indicate a same point in time. It means that a given moment in time is not limited to one place, one point in a system. Or, expressed in other words : Absolute simultaneity, according to its fundamental philosophical meaning, expresses nothing more than the fact of the coexistence of the parts of the universe (Van MELSEN, 1955, p.236).
REMARK : In the above argument we considered two events that occurred simultaneously, viz., the coincidence of point P1 of system I with point P'1 of system II on the one hand, and of point P2 of system I with point P'2 of system II on the other. But these are not really events in a physical way. So one could conclude that the implied simultaneity is not of a physical nature either, and therefore not real. And thus the argument, which was supposed to be about real simultaneity, seems to be invalid.
However, I don't think that things are that bad. The systems of reference, I and II, of the argument, m o v e with respect to each other, making them enough physical for the argument to be relevant.
Moreover, we could tentatively add the following : Suppose that at the location and moment of the coincidence of point P1 of system I with point P'1 of system II, there happens to take place some physical event, and that at the location of our point P2 of system I, while coinciding with point P'2 of system II, there also happens to take place a physical event. Then from the fact of the simultaneity (here in the sense of [mathematical] coexistence) of the two coincidences (P1 with P'1, and P2 with P'2 ) it follows that also the two physical events took place simultaneously.
It is of great importance to realize that the above described presupposition (present in the theory of relativity, and based upon the supposed possibility of transformation) of the simultaneous coincidence of points of one reference system with those of another (that moves with respect to the first), does not mean that this coincidence can be objectively registered. To see this, let us analyse the following case :
Suppose we have two systems of reference, I an II, as described above, which uniformly move with respect to each other. If we take into account the possibility that the (constant) speed involved in this motion can be very high, i.e. can approach the speed of light, then the transformations that relate these two reference systems must be (according to the theory of relativity) the so-called Lorentz transformations for place and for time.
Suppose further (see this Figure above ) that at a certain moment point P1 of system I coincides with point P'1 of system II, while this moment of coincidence is recorded as t1 . If we further, for the sake of convenience, suppose that system II moves in the direction of the x-axis of system I, then, with respect to the position of P1 in system I only the x-coordinate counts. We suppose that, by measurement in system I, it is assessed that the involved coordinate is x1 . And now, according to what has been said above, at the same moment when t1 is measured, another point P2 of system I will necessarily coincide with one or another point of system II. Let us call this point P'2 . (a little later we say something about its position). The difficulty, now at hand, is that observers in I and II will not agree among each other as to which points P2 and P'2 of both systems will coincide at the time t1 . The position of point P2 of system I and with respect to I, at the time t1 is measured to be x2 . This point will coincide with a point P'2 of system II. This point thus becomes identical to the point with location x2 , but the location of this point as assessed within system II is different. It is different according to the Lorentz transformation of a coordinate. The new coordinate (x'2) then is :
So indeed we see that the necessary presupposition of the existence of objective simultaneity, in the sense of being implied by every accepted possibility of transformation between systems of reference, namely that the places of one given coordinate system are continually in contact with those of another coordinate system, doesn't say anything about the possibility to actually and objectively measure this simultaneity.
There is no possibility to measure this simultaneity. And this is a true result of the theory of relativity. Therefore the concept of simultaneity does not make sense in natural science, but it does make sense as one of its presuppositions, and as such it is a truly philosophical concept.
So in our metaphysical (and thus philosophical) analysis of reality, which is a consideration of the way and status of Being and beings, we can accept the existence of absolute simultaneity.
And such a simultaneity implies the existence of absolute place (absolute position), because of the following reason :
If at location x1 an event g1 takes place, then a simultaneous event g2 cannot take place at location x1 . It can, however, in principle, take place at any other location (i.e. at any location which is not x1 ). And this shows that the location x1 is unique with respect to a given event. In the same way we can couple a different event to another point, say x2 , and so on with respect to every point whatsoever. All this means that place is something absolute. And this means that we have found with all this a second indication of the truth of the contact theory ( The first indication was conceptual in nature, it drew from the concept of ens extensum). And after having established objective place, absolute motion follows as a consequence, because motion is continuous change of place.
As we have said, absolute simultaneity cannot be objectively measured, and so, consequently absolute place and absolute motion cannot be so measured. And that's why the outcome of the famous Michelson-Morley experiment was negative.
Now that we have, finally, established the absolute nature of time, place and motion (and knowing that they cannot as such be objectively measured, but are necessarily presupposed), we can turn to the phenomenon of the impetus . We will show that it exists, and that it is a variable quality (And all this is done to obtain, by means of the demonstration of the existence of at least one variable quality, another indication of the existence of h o l i s t i c a s p e c t s in the fabric of Reality).
The Impetus as a Variable Quality.
The motion is uniform, if in randomly chosen equal time intervals, equal distances are traversed (HOENEN, 1947, p.287).
We shall now work towards a definition not involving time.
Suppose we have two bodies, say two metal spheres, that are moving in such a way, that they begin to move together, and end their movement together, or, if we do not want to involve the complexities of the starting and ending of movement, we consider just a segment of this movement, cut out out somewhere between begin and end. The motion of the two bodies is further supposed to be such that they always stick together, resulting in the fact that the motion of the one is an exact copy of the other. We will call these two motions congruent. That this is possible is immediately clear. It is also clear that these two motions can be connected to each other, end of first to begin of second, resulting in one motion. While the first case can be observed and verified easily, the second is harder to observe unequivocally. But here we're talking about concepts, and these are clear. The possibility of the second case results from the fact that the successive continuum, like the static extension, is, what could be called a principle of individuation in the following sense : It is immediately clear that a figure, that is here realized in an extensum, can also be realized in another extensum, or in another appropriate part of the same extensum, which means that congruent figures can exist. These figures only differ with respect to position, that is to say, they only differ individually or (equivalently) numerically. And the same holds with respect to the flowing continuum (dynamic continuum), which is motion (also in its broader sense of change). So evidently motions are possible that only differ in successive position, i.e. they only differ purely individually or numerically. These motions then are mutually congruent.
Well, what is valid for two (or more) motions, also holds for successive parts of one and the same motion. And again, evidently, a case is possible where two or more of these parts only differ with respect to successive position, i.e. they can be congruent. And this evidently holds for larger and smaller parts. So a motion is possible of which randomly chosen parts that are equal among themselves are, no matter how large or small they may be, congruent. The equality of these parts is defined by the equality of corresponding pieces of the trajectory. And such a motion we define as uniform. And then we can, now without circularity, define uniform motion by involving time (as in the definition given above ) : equal parts of time correspond to equal parts of a uniform motion.
Now the principle of inertia.
This principle, consisting of two parts, reads as follows :
If a body is not subjected to any external factor, then it will, if it is in a state of rest, remain in that state. And if a body, that is not subjected to external factors, (already) has a velocity, then it will have it continually, with the same direction and magnitude, i.e. also in this case it will remain in the same state of motion as it initially was. This motion, then, is uniform motion..The first part of this definition of the principle of inertia, does not raise problems. But the second part does. First of all we will ( following HOENEN, 1947 ) argue that the principle of inertia is not an a priori principle, but in fact an empirical principle, i.e. it follows from and is confirmed by, observation.
Our result so far is that motion, also uniform motion, must have an active cause, in order for it to be intelligible (and thus in order for it to exist), while this cause is not a force (in its technical sense). But what then is this active cause?
In finding this cause we must adhere to the principle that there is no action at a distance. This is why in physics the field concept is introduced. Further, the active cause does not seem to reside wholly in the medium of motion, because it does not exert a noticeable influence onto other bodies as long as the moving body doesn't collide with them. So this cause must reside chiefly in the moving body.
So we have found that the active cause of sustained motion, as this motion is expressed by the empirically verified principle of inertia, lies chiefly in the moving body, and that this cause is not a force, but a quality. Further we have learned that when a force is applied to the moving body it accelerates if the force is applied in the direction of the initial motion, or decelerates if it is applied in the opposite direction. Such a force thus changes the speed, and consequently changes the momentum and kinetic energy which are the aspects of the active cause. So this active cause itself increases or decreases when a force is applied to the moving body, which means that this active cause is a v a r i a b l e quality of the moving body. And this variable quality as the active cause of motion (not the cause of change of motion) is called the i m p e t u s of the moving body. This impetus, thus, belongs (mainly) to the moving body, which implies that the motion of this body is asymmetrically relative (i.e. the impetus is asymmetrically distributed among the body and its surrounings whatever these surroundings may be). And this means that we cannot maintain that we could equally say that these surroundings move with respect to the body in question. And this asymmetrically relative motion demands a universal medium with respect to which the body moves, which in turn implies the existence of absolute place. And for this a universal medium of localization is demanded. And we found this medium earlier. It was the ether of Lorentz in the form of the theoretical construct given above .
So now we've finally found at least one variable quality, and this fact refutes all forms of Mechanicism (and probably also all forms of Reductionism) in their sense that ALL complex entities are mechanical, respectively reductionistic, i.e. totally reducible to simpler entities. This is because the increase of such a quality, such a variable quality, is not exclusively dependent on the increase of the number and of the arrangement of relevant particles or elements. An entity having such a quality, can acquire an augmented 'version' of this quality. This means that inner change of such a particle is possible, which is denied by Mechanicism.
Let us specify this a little more.
The total impetus of a body consisting of many particles of course increases when, while everything else remains the same, this number of constituent particles increases, say by accretion of additional particles initially outside this body. But this does not refute our position, because of two reasons :
In the next document we pick up our investigation of snow crystals again : Their significance for the holistic ontological theory is further examined.
To continue click HERE for further study of the Theory of Layers, Part XXIX.
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