General Ontology
Cosmos and Nomos

Theory of Ontological Layers and Complexity Layers

Part XXIX (Sequel-26)

Crystals and Organisms

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This document (Part XXIX Sequel-26) further elaborates on, and prepares for, the analogy between crystals and organisms.

Philosophical Context of the Crystal Analogy (III)

In order to find the analogies that obtain between the Inorganic and the Organic (as such forming a generalized crystal analogy), it is necessary to analyse those general categories that will play a major role in the distinction between the Inorganic and the Organic :  Process, Causality, and the general natural Dynamical Law.

Categorical Analysis of
Process, Causality, Dynamical Law
and Simultaneous Interdependency.


The following analyses are partly based on HARTMANN, Philosophie der Natur, 1950, pp.265.
It is fair to call all Being lying above the Mathematical Layer  "real being".  In contrast to mathematical entities, it is individual and is, moreover, characterized by the fact that Time is one of its categories. And because of this, the general form of real Being is "Becoming", which is Process.  Here  "real "  is meant constitutively, (namely) in the sense of : supra-mathematical (being), i.e. being, lying above the Mathematical Layer, but nevertheless presupposing it), or, in still other words, being in which Time is involved.
Being can come in several modalities :  possible being, real being, and necessary being.  Here "real" is meant not in a constitutive sense, but in a modal sense.
Becoming or Process pervade all Layers of real Being. Nothing is truly static in these Layers, i.e. their concreta are always subject to one or another process.

If we now confine ourselves to the two lowest Layers of real Being -- the Inorganic and the Organic -- the processes are typically spatio-temporal. Such a process is then a material process. Unless stated otherwise, when we, in the following, speak about "process", we will mean such a material process. And where, in the following, we speak about "possibility" (of something being realized, i.e. possibility in its modal sense), we do not mean an exclusively logical possibility, but a possibility of something to be realized in the course of Time, and in our particular case this something is material. So such a material being can either be (only) possible, or real, or (even) necessary (all meant in a modal sense).

A process intrinsically consists of an unidirectional succession. As such it could be nothing else then Time itself. It is, however, distinguished from Time by the fact that there is only one Time, while there are many processes. As a spatial thing (of which there are many) is not identical to Space (of which there is only one), so a process is not identical to Time.
Process is one or another real being that is extended, or 'smeared out', in Time. This real being is therefore divided into successive stages or stadia. So the extendedness in Time of some real being is its change in Time. Process is the change of some real being in Time. The stages (together making up the material real being) succeed one another other in Time.
The category of Process does, however, (still) not imply one or another type of determination (for example a causal determination), which means that the successive stages of a process-as-such (i.e. just as process) do not (consecutively) determine each other, they just succeed one another in Time.

Modal analysis of Process.

Because in a running process, (seen) from any NOW all future states are unreal (i.e. non-existent), while the process itself is real (i.e. exists), a modal analysis of Process is necessary and no doubt instructive.
At each point in Time in the process, somthing has become real, other things however, also belonging to the process, are still unreal. This approaching 'sphere' of the unreal is at the same time also, in a certain degree, undetermined, it can still turn out to be this or that. This undetermined is what lies in the future, what is approaching from the future. The fact that all the time something is under way from the future at all (and then sinking back into the past) is an essential element of the nature of process. But it does not intrinsically belong to its nature that the approaching entity is determined precisely to be so and so. For this there can exist grounds in earlier states of the process, but then another category is involved :  the particular type of determination that the process happens to possess. So the approaching entity is, seen from the reality of a given NOW-state, just (only) possible. From all this five points follow that modally characterize Process :

The next Figure depicts this graphically :

Figure above :
Upper image :  In a  process-as-such  the range of 'possibilities' as seen from one chosen NOW, gradually decreases until only one is left, which then becomes real.
Lower image :  In a process, not (only) as such, but a process possessing a determination of some kind (a determination of one state by the previous one), as, for instance, a causal process, there is, seen from every NOW, only one possibility, and this becomes real.

In all this, i.e. in the modal characterization of the process as such (i.e. only as process and nothing else), we must find out what meaning is here attached to "possibility".  As (only a) 'possibility' it is not based on our mere ignorance about what will, and what will not, be realized in the process, because the pruning of possibilities takes place in the process itself, neither is it just logical possibility, as we see it when we gradually narrow down a genus to one of its species, because this is something general and not proceeding in Time, while a process is individual and proceeds in Time.
But neither is it genuine possiblity, because when something is truly possible, then all the conditions for this thing to be possible at all must already be present (otherwise it is (still) impossible). But when something is possible in this way, then it is at the same time already necessary (i.e. the thing is not only possible, and even not only real, but even necessary). But then all other possibilities are eliminated. So this elimination of all possibilities but one, does not take place only as soon as one of them has become real, but already before that, namely when one of them becomes truly possible.
So the 'possibility' as it exists among the other 'possibilities' as we saw it in the process (as such) is not a genuine possiblity (it is not a modal category typical for one or another sphere of Being), but it is nevertheless real in the sense of :  it nevertheless occurs in the real world (as we indeed saw it in the process). It is an incomplete or partial possibility (and therefore in fact still an impossibility). And as such it figured in the above five statements about the modality of the process.
Surely it is doubtfull whether a course or flow in such undeterminateness actually applies to real processes. It would mean that, apart from its temporal succession, such a process would not possess some determinative coherence. This is very improbable, for of course there are certain specific types of determination present in all natural courses or flows, BUT THESE (types of determination) DO NOT BELONG THE NATURE OF PROCESS AS SUCH, BUT INVOLVE OTHER CATEGORIES (such as causality, substrate, etc.).
The very nature of  process-as-such  implies, it is true, a unity, in which the states are successively connected, but whether this unity is that of some general and intrinsic determination, remains open, as long as we consider the process only as process.

In the nature of  process-as-such  is not its being determined. It is just the temporally successive unity of the temporally separated states. It is unity only in the sense of internal unity, not necessarily in the sense of external closeness or wholeness. For it is not part of its nature to have a beginning and end. It can have them, but then this is the result of certain special types of connectedness, as they are expressed in the morphogenetic processes (and some other processes) in organisms. Most of the physical (i.e. inorganic) processes do not have definite limits (indicating end or beginning). There, one flow smoothly passes into another, and all of them ultimately unite, resulting in the one World process.
Because a  process-as-it-is-in-itself  is without a determination of states, it is understandable that the very existence of causality is often contested. In the same way it is well possible to doubt the existence of natural law. Indeed, before the Renaissance it was in fact unknown. And today modern theoretical physics tends to limit ordinary natural law to macroscopic phenomena only, while microscopic (i.e. quantum) phenomena follow a different kind of law. On the other hand, the  process as such  is, since the Eleatics (antiquity, denying process and change) never questioned. It is (for it to be questioned) too obviously present in the whole type of phenomena. And that is reason enough to categorically distinguish it from all forms of determination, for these themselves only make sense when they refer to it as unquestionable reality base.

Causality  ( HARTMANN, 1950, pp.325 )

The categories of Becoming (Process) and of Substrate and Constancy (treated later on) little presuppose with respect to (types of) determination.  Categorical determination does, of course, apply here as it applies anywhere from principle to concretum. In addition to it we have (as presupposed by the above mentioned categories) the formal determination of the irreversible and uniform time flow, which takes place within the concretum, and which determines the general direction and speed of processes. This determination is still not about content.
So with respect to content the  process-as-such  is still not determined by the mentioned categories. Its nature is only such that consecutively new states appear, which then link together within the temporal succession. A given state can be followed by any new state whatsover, in the absence of any rule or qualitative coherence. The consequent states are (on the basis of the category of process alone), with repect to previous states, totally fortuitous, and a prediction of future states would be impossible. But we know that real processes are not like that. They involve more categories than that of process alone. So in the process there must reign a linear form of determination that determines the temporally later, also with respect to content, by the temporally earlier. This is the minimum of ongoing (consecutive) determination and dependence, demanded by the phenomena :  a form of determination then, which follows the flow of time, goes straight with it, and which provides a first qualitative sequence of order in the process.
This form of determination is causality. It is fundamental for the inorganic process, and is presupposed by all other forms of concretum-concretum determinations.
Causality then is such that the series of states of the process is in its successive sequence not arbitrary, but definitely determined. Along the temporal sequence one state depends on the previous one, respectively one state is  produced  by the previous state. This produced state is then called "effect", while the previous state, i.e. the producing state, is called "cause".  When we realize that such a cause is itself an effect of a still earlier state, while the effect is itself the cause of a still later stage, then, instead of the bipartite determinative relationship, we have the linear determinative sequence, the causal chain or causal nexus.
This looks simple. In fact it isn't.
We should not equate the pair cause and effect with the pair  sufficient ground  and  consequence  which is a more general relationship. Sufficient ground and consequence can be encountered in a purely mathematical or logical context, or in  If / Then constants (where we have, for example material implications, like "medusae of the genus Aurelia imply D4 symmetry.", which has nothing to do with cause and effect).
To the mentioned aspects of causality -- linear sequence, following the arrow of Time, and the consecutive production -- one should add its irreversibility. It is in fact already contained in its following the arrow of Time, which is itself irreversible. The difference lies only in the fact that while nobody have ever questioned the irreversibility of Time and Process, it is questioned in the case of causality, where one sometimes spoke about "goal-causes".
Widespread is the opinion that causality not only refers to the temporal succession of states, but also to the simultaneous. We should be carefully with this. States can have duration (which can be interpreted as a short series of states that differ very little from each other), and of two such enduring states one could be the cause of the other. A good example is a metal ball resting on a pillow. The dimple in the pillow is the effect, the resting of the ball is the cause. In fact we here already have to do with another phenomenon, namely the interaction, because also the resting of the ball is in the same sense effect as is the dimple. Its cause lies in the resistence of the pillow against the weight of the ball. So the pillow and the ball interact. This interactional relationship of the simultaneous shows itself in uncountable versions. It is present in all static collocations, but also accompanies the dynamic phenomena, even those that have a pronounced process form, as for instance the motion of a bullet in the medium of air, and the air resistence which it itself causes.
Where to put this relationship is a question of classification and of the delineation of categorical concepts. If one considers it to be (a form of) causality, one must enlarge the latter's concept. But then one should adopt another, narrower, concept to express temporal linear causality. Whatever we do, these two categories (interaction and temporal linear causality) can only be separated from each other in abstraction (i.e. as concepts), their coherence with each other and with all other general categories in the same Layer cannot be removed. Nevertheless we must distinguish them.
For reasons of simplicity we (with HARTMANN) stick to the narrower meaning of causality as the temporal linear sequence of causes and effects. The simultaneous relationship will be considered under the heading of Interaction.

Linear causality does not proceed from thing to thing. Cause and effect are not things. Surely they can be tied up with things, but cannot be identified with them. Causes, and also effects, are real relationships, collocations, states, process stages. One  "state of things"  depends on another  "state of things".
But a state of things is not something simple. It has the form of a collocation of circumstances. This generally applies to all states which form the series of stages of a process, also in apparently simple processes. Collocations, as simultaneous conditions, not merely spatially undestood, are themselves systems of real relationships, whose diversity depends on the extent of the given section of the real World that is said to contain these relationships. Thus a cause is not an individualized aspect of being, but consists in a manifold of aspects, linked, in a simultaneous collocation, up into a system. The same applies for the effect. The fact that such systems can be highly complex, fleeting, one off, and uncomprehensible in their totality, does not affect this. Important is to hold on to the fact that causes and effects are consecutive process states, i.e. consecutive stages of an inorganic process  ( Here "process" in its wider sense, i.e. including some type of determination, which here is the causal nexus).
This picture one should constantly have in mind when starting with the analysis of causality. For with this the intrinsic nature of causal determination is beginning to show itself.
Essential, namely, is that to each aspect of the cause there corresponds an aspect of the effect, and vice versa. And if one calls these aspects "partial causes" and "partial effects", while calling the whole collocations "total causes" and "total effects", then we can say :

Each partial cause, while not determining in an isolated fashion, produces its specific partial effect, and the smallest change in content of the total cause entails a corresponding change in the content of the total effect, where "corresponding" does not mean a same degree of change, but a change coupled to the cause.

On this is based the well-known statement :

Same cause, same effect.

Whether there are equal total causes in the process of the real World, i.e. a reappearance or repetition of precisely the same collocation, is not decided by this. The statement only says " If " this were to happen, "then" .  .  . .  It is therefore important to add a second statement :

Different causes, different effects.

This should be understood such that even the smallest difference of one partial cause is already sufficient to have the partial effect, and with it the total effect, turn out differently. And with this we should note that sometimes a small degree of difference of a cause can entail a large one in the effect. We see this in chaotic dynamical systems. Such systems are extremely sensitive to differences in initial conditions. And even though the deviation of the next state can still be small, the system assumes a completely different course, resulting in very different states later on. To understand this, one should realize that partial causes do not determine all by themselves in an isolated fashion, but only together as a whole.
Two points can now be emphasized :

On can, however, express the causal relation in a still more general sense, and then it appears as a rigorous modality statement :

The effect is in virtue of the cause necessary. It cannot fail when the cause is present, and it cannot turn out differently from how it will be in virtue of the partial causes of its total cause. So it is necessary with repect to its being-there as well as to its being-so.

Causality is a relationship, a relational category, while this relationship has the form of a dependency. In this respect it is a category of (concretum-concretum) determination. And could it be true that Relation and Determination together are nothing else than lawfulness, i.e. a matter of (natural) rules? Certainly not. The categorical elements of Relation and Determination (resp. Dependency) are, taken together, not identical to any law or rule. Surely, the law can 'catch' or represent the special kind or species of the relation and of the dependency, but not these themselves. The relationship between cause and effect is a primordial one, i.e. one that cannot be reduced or analysed any further. Still more this applies to the determining function of the cause, and most perhaps to the modality aspect of necessity. For causal necessity is a totally different necessity than is the necessity as we find it in (natural) rules or laws. It is, like any other real necessity, in each case a different one, while the law has only the necessity of the general  ( HARTMANN, Ibid., p.331 ).
But with all this the essence of causality is not yet exhausted. What must be added is the productive or creative nature of it. For what Time alone cannot accomplish, the causal process can. It is the ongoing production of the new. Causality is characterized by two aspects :  The causal nexus and the causal sequence based on it.
The character of a sequence or series consists in the fact that every effect is a cause of further effects, every cause is already effect of an earlier cause. This linear pattern is not interrupted, it goes from each state forwards and backwards (in the sense of linking) and in principle ad infinitum.
The character of nexus consists in the ongoing production itself. The causal nexus is nothing else than a(n act of) determining, issuing from each process state, while making up the dependency of the next state. It thus consists in an ongoing producing and being produced. In fact in it also the sense of direction of the causal series as well as its irreversibility become clear.
It is evident that the causal series, together with its internal structure, the causal nexus, is far from being just a law. Rather it is the natural process itself, to which the law applies, not only insofar as it proceeds at all, but more specifically that it determines itself continually further. For the production of ever new states evidently precisely makes up the natural process. It sustains it, lets it proceed further. And that means it (i.e. the production of ever new states) lets the process endure. So the causal nexus is the internal dynamical aspect of the process itself, that aspect, namely, that cannot be apprehended from the mere time flow, the substitution of states, or from Substance ( = constant substrate).
The real process, inorganic or otherwise, requires a dynamic internal aspect. And clearly this aspect must have the form of an all-out (concretum-concretum) determination. This can be causality, but in other cases it can be another type of linear (concretum-concretum) determination  ( In the Organic we have the organic nexus, and in the Super-psychic we have the final nexus).

The disappearance of the cause in the effect. Causality as creative process.

The other side of all production or creation is destruction. What does this mean for the causal relationship itself?
From the essence of Process it was already clear that the states making up its stages, are not preserved, but transform into one another, resulting in the fact that always the one disappears in the other. What is being preserved is only the process itself. And it is Process that consists of the coming and going of states.
All this directly applies to the causal series, in whiche these same states are causes and effects. From this it follows :  What is preserved in the causal process are neither the causes nor the effects (because the effects are in turn causes of the next states), but only the ongoing production, the causation and effecting, handed on from state to state, itself.
All this is especially significant with respect to causes. The cause is not that what is preserved. It is that what vanishes in the effect. It does not pass over into the effect such that it is absorbed into the latter, but in such a way that it, while producing the effect, it is being  c o n s u m e d  and vanishes, in the same way that this cause itself was in turn produced by vanishing earlier causes. If this were not so, then two effects would result :  one from the original cause, and one from the cause as it is in the effect. Said slightly differently :  If the cause reappears in the effect, then it would once more give this effect. So the effect is, as seen from the cause, something totally new. Cause and effect exclude each other. Therefore, also the effect cannot be in the cause (also in this case we would obtain two effects). It originates as something new. We could, however, counter that although the effect is certainly not just like that already present in the cause, it resides in it in an enfolded or implicit manner. It then unfolds and appears as the effect. Said differently :  The effect is potentially present in the cause, and soon becomes actual. But it is characteristic for the causal series that it can, in principle, extend indefinitely in both directions. And when the effect is in the cause, albeit just potentially so, then this cause must potentially contain also all future effects, i.e. any given state of some causal series must contain, albeit implicitly, all effects coming after this state. This is clearly nonsense. So we must accept that the causal process is creative. The effect only then originates when the cause is consumed. Appearance of the effect and the consumption of the cause is one and the same phenomenon.

Causality and categorical NOVUM.

In causality the states not only appear after one another, but also appear out of one another. Out of, say, B (cause) necessarily (and thus in every case) follows K (effect). And out, say, C (cause) in the same way follows M.  And out of D follows .  .  .
The fact that K, and not M, follows from B, is in itself not intelligible, but known from observation. In addition, the fact that K is totally different from B (fom which it originated) is also not intelligible, but is again as such observed.
On the basis of this, we could be led to believe that the cause is indifferent as to its effect, like we saw it in the case of over-forming and over-building of categories (or category Layers). But while the nature of a category as such (or category Layer) does not imply that it must be over-formed or over-built at all (as is evident by the existence of some highest Layer, which then, by definition, is not over-formed, nor over-built), a cause necessarily has its effect.
In a physical dynamical law (see also further below), causality, and with it the total novelty of every effect with respect to the corresponding cause, is already presupposed. So all the new 'stuff ' is already present in some way in the dynamical law (when interpreted physically). Here nothing is undetermined. A cause determines its effect, despite the fact that the effect is totally new, totally different from the cause, that is to say the effect is not in any way present in the cause. So the effect is something new, but at the same time it is necessary. In this it is important to have in mind the earlier mentioned fact that a thing never is a cause, but contains a cause (or more of them). Likewise a thing is not an effect, but contains an effect (or more of them). So in the causal process we do not see things vanishing, and totally new things pop up, but only causes and effects. So all the coming novelty is already (be it implicitly) present in the dynamical law. Still more novelty cannot be contained by it. For this "still more novelty" nevertheless to occur, it is required that from time to time a NOVUM appears. So all previous considerations about the NOVUM are still valid, also in this light (i.e. in the light of the genuine creativity of the causal process).
The dynamical law (referring to a specific causal series) determines, via causality, what will be produced. In fact it specifies the relation between a state and the next state, as to their content. Only when this relation is fixed for every pair of successive states (every pair of cause and effect) we have to do with a law or (natural) rule.

The next Figure illustrates this with the help of a one-dimensional Cellular Automaton, which is an abstract finite discrete dynamical system. This system consists of a row of squares (cells). The state of such a square (not to be confused with the state of the system as a whole, i.e. system state) is expressed by its color. In the present example it can be either red or blue. We depart from a given state of the system, which is this whole row (which we imagine to be bent back upon itself) having its individual cells colored either red or blue. So any possible pattern of colors (red and blue) represents a system state. It is at the same time an  effect  of a previous state (a previous pattern of the colors red and blue) and also the  cause  of the next state (next pattern of the colors red and blue).
This dynamical system evolves according to a dynamical rule or law. It specifies the relation between a state and the next state. And it is only truly a rule or law if this specified relation holds between every consecutive pair of system states, that is to say between every colored row and the next row. In the present case the law specifies the color of a cell of the next system state on the basis of its immediate environment, i.e. the colors of its direct neighbors.

Figure above :  One-dimensional Cellular Automaton as an example of a dynamical system. The dynamical law of this system is specified by the six images in the top half of the Figure. One can see that the law is set as follows :

If the immediately neighboring cells of a given cell (thus the one cell to its right and the one cell to its left) are (both) red, then in the next system state this cell becomes blue, also when it already was blue. In all other cases this cell becomes red, also when it already was red.

In the lower half of the figure we see three consecutive system states. The top one is a given state (N), while the next one is the state (N+1) that follows from it by applying the rule to each individual cell of the given state. The third state (N+2) can now be obtained by applying the same rule to the cells of the derived system state (N+1). A fourth state (N+3, not drawn) can be obtained by applying the rule to N+2, etc. So every state is replaced by the next.
If the system is indeed such that every next state relates to the previous state accordinng to that same rule or law, then this law is truly a law, determining the system, i.e. determining the sequence of states that follows from some initial state.
The Process-as-such is just the temporal sequence of states, and nothing more. Every time the next state replaces the previous one.
Causality, on the other hand, i.e. the causal process, is this same sequence of states (sequence of rows), but now a sequence such that each state determines unequivocally the next state (and this next state then replaces the previous state, i.e. the cause disappears in its effect), that is to say, we have already causality even if there were no fixed relationship between the states (for example when the rule changes in a random way after each or several state transitions, or when it already changes randomly within one and the same state, i.e. when the rule changes randomly from cell to cell). Only when the same rule or law applies for every cell in a row and every state transition, it is really a dynamical law of the system.
A state transition in our dynamical system proceeds according to the above specified rule. That this rule is as it is, is the unintelligible aspect of causality. More generally it is the difference between one state and the next, whether according to a rule or not) that is unintelligible, especially because the next state necessarily (but not necesarily in virtue of a rule) follows from the previous state. Its necessity lies in the (supposed) fact that if we let one state reappear it will give the same next state. So when we have a system that starts from some given state (row of cells) and proceeds to produce new states in a random fashion (which is still a causal series), and happens to produce the same state as the initial one, then the same sequence of states will again appear, i.e. the system will cycle with a period equal to the length between the two initial states, that is to say between a state and its reapearance.
Because the type of dynamical system as just described is very simple, and finite, in fact very small -- a very small number of interacting elements (cells) -- it will either end up in a cycle or end up in a steady state. The latter means that the state does not change anymore. This, of course, is an anomalous situation, because we would then have a cause (state) that is identical to its effect. We know, however, that in the real World the dynamical systems are very large, implying that a sequence of identical states (steady state) is virtually impossible.
The unintelligibility mentioned above must be accepted, it is an essential element of the causal process, i.e. it is the result of its inherent creativity.
In this way we now have explained the relation between process-as-such, causality and dynamical law or rule.

In the next section we will discuss further the aspect of creativity in causality and its unintelligibility. It is important to keep in mind that the causal nexus, with its inherent creativity, lies at the bottom of every concretum-concretum determination. Also important is to stress the absolute necessity of the appearance of a definite state from a given previous state, or, in other words, the absolute necessity of the appearance of a definite effect from a given cause, in spite of the fact that this nexus is not intelligible.

Non-intelligibility of the creative act in causality.

It is understandable that in causality one has tried to explain the effect by reducing it to the cause. But this can't be done, because the effect is something entirely novel, which, by definition can't be explained, because explaining something is reducing it to something already known.
One can, it is true, empirically study the 'act of effecting' in its special forms, and then one encounters special laws (and forces). But forces and laws already presuppose the causal relationship. So with them we cannot explain this relationship, i.e. we cannot explain the act of effecting (producing). The law only specifies what precisely will follow from a specified cause (state), it does not explain why it follows from that cause. All explanation consists of the reduction of the not yet understood to what it presupposes, and the first, i.e. most basic presuppositions are either assumptions or are self-evident states of things. In both cases they remain unintelligible. Natural events are explained by unearthing some causal chain, but the connection between its elements remains unintelligible.
So it is not a contradiction that natural events become intelligible by pointing to the (underlying) causal nexus, while the internal core of this nexus itself remains unintelligible. The same applies to the majority of ontological principles. Therefore it is wrong to construct theories that purport to explain the creative production as such. Also when one would, one day, solve the problem of this production, the enigma is only moved one step backwards.
On the other hand, the creative production is not the only irrational aspect of the causal nexus. The process states, that are causally connected, generally do not show some visible distinction, in the sense of their being objectively separated from each other by boundaries, i.e. the states are generally not discrete. They form an ongoing chain that either is a genuine continuum as in mechanical motion, or proceeds by such small jumps that can only very indirectly be concluded to, as it is the case in the micro-processes of energy conversion.
In both cases the precise course, as the, from moment to moment proceeding, creative production, cannot be undestood. So we have no reason to deny or question the unintelligibility of the causal creative production.

Modal analysis of Causality ( = causal process)

The category of Process could be subject to modal analysis, as we did above. The causal nexus is the form of determination of the inorganic process. It brings into the process qualitative sequence, dependency and necessity. We can now ask whether these new elements could also be modally assessed, i.e. we ask whether also the causal process can be so assessed.
With the process-as-such we saw that in every NOW, that what is coming in from the future contains a plurality of 'possibilities', of which finally only one remains. With this was connected the successive ruling out of the other 'possibilities' and the continuous decrease of the range of the 'possible', which, as regards content, signifies the ongoing increase of determinedness or definiteness.
We saw that these 'possibilities' are neither logical nor even real possibilities, but only partial possibilities (incomplete possibilities), which consist of the presence of only some conditions. Real possibility (i.e. genuine possibility), however, requires the completeness of existing conditions.
With this it remains to be asked from where then, while the process follows its course, the other conditions come, conditions which complete the real possibility and rule out the multitude of partial possibilities. This question is identical to the other, that asks what body ('authority') lifts out the one real possibility from the multitude of undetermined partial possibilities. When one answers with "coincidence", then this means that the course of the process is undetermined, that there is no determination of the later states by the previous states. But that would mean the removal of the causal nexus.
According to all this we can indicate what the causal nexus modally means, and what precisely is added by it to the temporal sequence of states, i.e. what is added by it to the process-as-such :  The causal nexus is such that from a given process state in fact not a multitude of different states is possible, and thus also that there is not a plurality of 'possibilities' present, but always only one, and that this possibility is the one that realizes itself in the course of the process. Only then the process contains determination. See the Figure above . One can call this the modal definition of the causal nexus. It means nothing less than that the missing conditions of the real possibility must indeed already be contained in the previous state, otherwise the possibility would not be a complete one. One should be careful to realize that it is the  conditions  that are present in the previous state, not the next state itself. It is the causal nexus which leads from those conditions (which belong to the cause) to the next state, or, said differently, the conditions are each for themselves the partial causes, together making up the complete cause, and they lead, by the causal nexus, to their respective partial effects, making up the complete effect. This effect, let us call it " E ", thus is not already contained in the cause, but its conditions are. A part of these conditions could already be present in much earlier states. And the set of conditions, necessary for the later effect ( E ) to take place, as represented by a (much) later process state, gradually completes itself while the process, with its succession of states, approaches the state in question. Each such condition is itself a partial effect of a previous (partial) condition. This previous condition was different from the condition that produced it. And this produced condition itself will effect yet another condition, etc., in this way growing into the very condition that can now produce the effect E, i.e. our effect in question. And if one takes, in one's consideration, the collocation of causal factors sufficiently broad, i.e. includes a sufficiently large bundle of partial processes in the simultaneous section, then all these conditions can in principle be found, and then the production of the effect in question  ( E )  becomes clear  ( Where this "clear" means :  evident on the basis of earlier experience, where one also saw a collocation of factors like the present one, leading to a result like the present one [the one under investigation] ). This being contained of all partial conditions in the previous process state is the intrinsic proper nature of the determination mode in the causal nexus. This complies perfectly well with the earlier requirement that in the total cause all partial causes are linked up together, resulting in the unity of a collocation, where then in the total effect the multitude of partial effects corresponds to them (i.e. to the partial causes).
Evidently this does not mean, that the human reason can always unearth the complete set of partial conditions. Human reason is finite, and its causal insight only reaches the nearest and most apprehensible conditions. Also science does not comprehend the whole span of the collocations, it rather simplifies the given case and finally comprehends only the general aspect that is contained in it. But the causal nexus is a category of objective reality (a category of the objectively existing world) and as such not dependent upon understanding. The actually existing determinative coherence of the process states exists independently of knowing it.
From this position one can go still one step further. Modal analysis  ( HARTMANN, Möglichkeit und Wirklichkeit, 1938 ) has shown that all that is regular is, just because of that, necessary. This law -- the Law of Necessity (concerning the real world) -- says that the same complex of conditions that makes something possible, when it is in its completeness present, also makes that something necessary. Or, differently expressed :  When all conditions of the possibility of something are present, that something must appear. This not failing to occur (not failing to be realized) is the necessity as it holds sway in the real world.
When one applies this law, and connects it with the removal of all partial possibilities but the one that becomes real, one can give a still shorter but very precise modal definition of causality :

Causality is that particular form of determination of the real process, according to which all that becomes possible in that process, appears necessarily.

This necessity as part of the essence of the causal nexus is that which connects the total cause with its total effect, and partial cause with partial effect. For in the coherence of the consecutive collocations the real necessity means just this that something different from that what actually follows cannot follow.

The meaning of causal necessity. Limits of the inescapability.

To the nature of this necessity also belongs its negative side, i.e. its intrinsic limitation. The fact that the effect with all its partial elements is rigorously produced from the cause, only means a dependence upon the whole set of partial elements of the cause, and not a fixation towards a specific result. A body or agent which could realize such a fixation is absent in the causal nexus. It is, in all its necessity of the effect, nevertheless indifferent as to what it itself produces. This is important with respect to the higher forms of determination, that raise themselves above it. It is the other side of the ability of causality to let itself be over-formed. Surely no power in the world can rule out any one of the causal components (partial causes, causal elements), but there can be powers that add new components. And because the causal complexes in the real-world collocations are not closed systems, but take in without resistence every component that comes their way, the qualitative direction of the event can certainly be turned. In that case simply something different is produced from the altered total cause, and it does so with the same real necessity. The intervention of supra-causal factors in the process thus does not eliminate the causal necessity, but certainly can direct the process, i.e. circumvent or turn away from the original inescapability, and produce that what could never be produced by the undisturbed causal process.
If there were in the World only physical processes, then this qualification would be superfluous. The causal necessity would then apply without restriction and make up a general causal determinism. There exist, however, higher ontological Layers, and each one of them has its special higher form of determination. And for these (higher forms of determination) the Law of Categorical Freedom applies, namely that they do not, it is true, rule out the lower determination, but do autonomously apply over and above it. Therefore these higher forms of determination can add new determinants to the lower determination. After all, they represent a categorical NOVUM with its own real-world conditions of possibility and their own real-world necessity  ( HARTMANN, 1950, p.344 ). And this changes things substantially. For the causal nexus is neutral, it lets itself be forced to accept any determining component or factor as long as such a factor does not eliminate its stock. Therefore the causal nexus can be over-formed and is, within certain limits, controllable.
By virtue of a given causal complex, not influenced by any intervention, that what marches in (i.e. approaches from the future) is indeed unavoidable. But when a determining agent of higher order is present, and when it succeeds to intervene, a new real-world factor is added, and then that which was originally approaching can be turned away from. Seen in this light the causal nexus, together with its necessity, is a very harmless type of determination. And this accords well with the fact that it is the most elementary and simple type of determination, and, as it were, only a minimum of determination.
The total determination issuing from a complete complex of conditions, that is to say a total cause in the strict sense, is only present in the context of the whole-world process taken in its full and complete extendedness. In every slice transversally to Time are then also included all higher-order determinants, insofar as these are present. Purely causal determination, that is to say without intervention of higher-order determination, only rules in physical, i.e. inorganic, processes. In organic processes it is already slightly over-formed, while in the sphere of human acting, experimenting and willing there is only a mixed determination.
One can, therefore, also say :  The openess (apparent incompleteness) of the complexes of determinants in the undisturbed natural processes surely does exist untill entering the NOW, but it does not exist for the causal natural process itself, but only for real higher-order powers. This openess, therefore, certainly exists for human acting. For it only exists with respect to the possible setting-in of supra-causal determinants. And strictly speaking, also the plurality of possibilities in each phase of the causal process only exists with respect to this setting-in. In itself no causal process state is plurivocal :  From every state, as a complete collocation of factors, there is only one possibility with respect to the next state. In itself, causal determination is a complete determination. Only outwards -- or better, upwards -- the causal determination is not closed.

Partial causes. The affirmative nature of causality.

What we, in life, know as causes are always only partial causes. Among them there can well be the most essential elements of the total cause, and sufficient for a short-term causal assessment of the unfolding event. For long-term assessment they are insufficient. What will do for more or less nearby goals, is already incomplete for science. Ontologically there are no such things as partial causes.
In fact there are neither isolated causes nor isolated causal series. There only exists an interweaving of causal series, and this is very complex and obscure to the knowing mind. Ultimately there is only the one all-embracing causal real-world process, at least with respect to the natural event. In this one world process, at any given moment, everything is co-dependent, i.e. everything is connected with everything else, also the apparently far away and seemingly disconnected. Cause, in its strict sense, always is exclusively the total cause rooted in the whole of the world process  ( HARTMANN, 1950, p.350 ).
The total cause in turn is not simply the sum of partial causes, although it is composed by them. This composition itself, namely, is more than a sum. It is an interweaving of elements, a system, albeit a fleeting one, a totality, in which the partial elements are already connected to each other in peculiar way. This connectedness is a simultaneous one, and is the result of the fact that the elements have together originated in the one all-embracing real-world coherence :  they bring along the specific nature of their connection from their causal origination. But they are always differently connected than are the corresponding elements of the total effect. For the originating tranverse connections also belong to the qualitative determinedness of the effect, and are as its parial elements in no way contained in the cause. Also they are, in the overall process, time and again differently constituted.
Only the overall cause (total cause) is a truly productive cause (causa efficiens) at all, not the partial cause. We, however, never know the total cause, because of its extensiveness. In practice we automatically only consider partial causes. That's why our causal knowledge is limited.
As a result of our incomplete causal knowledge the partial causes seem to come in two types, namely positive and negative ones. When an expected effect fails to materialize, the we speak of "failing conditions" (i.e. conditions that are apparently absent), and we get the impression that the non-existent conditions, just like the actually existent conditions, contribute to the total effect. This is a typical human way to see things. It comes from partial causes that are isolated by us and made independent, it tries to construct from them an image of the total cause. But in the real-world causal connection a different rule applies :  All conditions that work together in a total cause, are wholly affirmative. They are thoroughly "effective" factors of corresponding elements of the total effect. There are no negative causal factors. Or, in older language, there is no modus deficiens among the components of the causa efficiens. There also are no actually "failing" causal elements.
Surely there are such causal factors that "prevent" something. But this act of preventing is not the negation of something that was already foreshadowed. There is nothing foreshadowed or predetermined in the causal fabric. There is only that which just actually materializes, namely that what is realized in the collective effect of all causal factors. Yes, it is already wrong to say that something determined does not come about (does not come into being), because when it does not come into being, it is not determined. For in the causal connection only that will attain determinateness what is actually effected, and not what is not effected.

Individuality of the causal nexus.

If causality were nothing else than a law or rule, then its nature would just be something general, and only something general. But neither its series as such, nor its continuum (or microscopic discretum), and neither its dynamic and its productive activity is general.
The causal nexus is rather thoroughly individual. It should already be such, because it is a real-word relationship connecting real causes with real effects. And all real-world phenomena that are ontologically independent (i.e. not, for instance, properties as they are in themselves) are one-off and do not repeat. Realizing that the causal nexus consists of the dynamic of production, it is evident that its individuality implies that its production itself is different from case to case. And this accords with the fact that it continually produces novelty.
This does of course not exclude that lawfulness is contained in the causal process. Causality is presupposed by processual lawfulness, and it is clear that thus causality is something different from lawfulness. As the process in general is not identical to the law according to which it proceeds, so also the causal process. And as the former consists in one-off courses, so also the latter consists in one-off effecting, although both do not lack lawfulness.
Generality and individuality do not go separately side by side in the one World. Rather one and the same real-world entity or being is at the same time general and individual, namely such that all its single traits reappear in innumerable other cases, and thus are general, while their combination as a whole (and within a single being) is one-off, not reappearing in exactly the same form. A different individuality does not exist. But also a different kind of generality does not exist in the real world  ( HARTMANN, 1950, p.357 ).

The nature of the categorical layering of the real World.

The causal nexus does not have limits in a negative sense. But there is limitation in a positive sense. It is there where higher-order determination sets in. This does not apply with respect to whatever different kinds of determination. Already in the range of physical Being such other kinds of determinations pop up, for instance natural law, interaction, and others. These do not limit the causal nexus, they even do not over-form it. They just complete the real-world determination of the same processes and objects from another direction. They thus simply connect with the causal nexus without changing its essentials. Said differently, natural law and interaction are categorically homogeneous with the causal nexus. But things are different with respect to higher-order forms of determination. And we mean here forms of determination that are the result of the over-forming of the causal nexus.
The over-forming of the causal nexus occurs at three points along the sequence of Layers, namely (1) at the transition from the Inorganic (which is the ontological locus of origin of the causal nexus) to the Organic (where the Layers also relate to each other as the higher over-forming the lower),  (2) at the transition from the Organic to the Psychic (where the Layers relate to each other as the higher over-building the lower), and, finally, (3) at the transition from the Psychic to the Super-psychic (where the Layers also relate to each other as the higher over-building the lower).
Because the Layers are -- by definition -- categorically (and therefore ontologically) different from each other (that is to say, they are heterogeneous with respect to each other), one could think that the causal nexus could not cross the boundary between Layers. And this would imply that it cannot and does not apply in the psychic domain, and that in the same way psychic determination does not apply in the inorganic domain. The latter determination even would not apply already in the organic domain for the same reason. From this the theory of  "psycho-physical parallelity"  emerged, i.e. the theory that physical events (in the brain) do not causally relate to psychic events, but that they proceed parallel to each other. Of course such a theory is connected with the separation of body and mind.
HARTMANN, 1950, p.359, opposes such a theory, by denying that causality cannot cross the Layer boundaries. He, however, does this in a way which, to my mind, is a bit inaccurate and needs some rethinking.
And because this rethinking turns out to be very instructive as regards to a proper understanding of the ontological layering of the real World, we will paraphrase HARTMANN on this point and add our own views on the matter (which I have done implicitly all along, but I, until the present case, seldom disagreed with HARTMANN).

Is  ( HARTMANN, 1950, p.361 )  the causal nexus able to cross layer boundaries (and especially all the way up from the Inorganic, via the Organic to the Psycic)? Can it, issuing from one Layer, be effective in another?

While writing about all this (p.359-371), HARTMANN should be more careful in formulating things :  The  Layers  as such cannot be   c a u s a l l y  related to each other, i.e. one Layer cannot  c a u s e  another, because Layers are  c a t e g o r y  layers, and categories do not cause other categories, neither are they caused by other categories. Causation is not a category-category determination, but a concretum-concretum determination. Therefore only real entities (not principles) can cause each other, or be caused by one another.
On the other hand, the category of causation, originating in the Inorganic Layer, reappears in all subsequent (higher) Layers, but (as we know) it does so in a modified way, which here means that it is over-formed each time it crosses a Layer boundary. But (as indeed HARTMANN himself has stressed)  reappearing (of causality) alone does not imply that the causal nexus can be heterogeneous -- for instance, spatial cause, non-spatial effect -- but only that a transition from cause to effect can take place in every real-world Layer (i.e. it can occur [at least] within one and the same Layer [cause in this Layer, effect in this same Layer], while this applies to all real-world Layers). Whether the connection of cause and effect can cross a Layer boundary (while going from cause to effect), or whether a cause itself, or an effect itself, can be ontologically heterogeneous (for example containing spatial elements together with non-spatial elements, or, equivalently, containing elements from the Inorganic together with elements from the Psychic), can only be decided on empirical grounds.

Can  ( See HARTMANN, Ibid., p.361 )  it  (i.e. the causal nexus) also do so (i.e. be heterogeneous) in the case where the relationship between the Layers is that of over-building (instead of over-forming), as it is between the Organic and the Psychic, where, consequently, several essential categories of the lower Layer are halted and the system of those categories does not, as matter, enter the higher? Such questions cannot be answered by just saying that the causal nexus reappears in the higher Layer, because in the higher Layer there could be a closed causal coherence of its concreta, while at the same time this causal coherence does not intervene with elements in the lower Layer, or vice versa, where the lower Layer has its own closed causal coherence of its concreta, and, (moreover) qualitatively different from that of the higher. So the fact of causality being present in both Layers, albeit in the form of different causal coherences (where, as regards content, and only as regards content, the higher one can be seen as a modification of the lower one), does not decide whether there can be (or cannot be)  c a u s a l  connections between those Layers. In the higher Layer the causal nexus is already over-formed, and perhaps it applies there only in its over-formed state (About "causal connection between Layers", see remark above).

While, according to HARTMANN, the Psychic Layer over-b u i l d s  the Organic Layer, the psychic (causal) nexus (as a single category) only over-f o r m s  the organic (causal) nexus (also according to HARTMANN). This is not without problems. The original causal nexus stems from the Inorganic Layer. There it is  s p a t i a l.  When it is over-formed at the transition to the Organic, it is still spatial (because the category of Space is not halted at the transition from the Inorganic to the Organic). In the Psychic it is (said by HARTMANN to be) once more over-formed. But here the category of Space is halted, which then implies that psychic causality is not spatial anymore. Only  causality-as-such  (i.e. a temporal succession of states as a result of states  d e t e r m i n i n g  next states) 'survives' the transition from the Organic to the Psychic, together with the potential organization of causal factors [i.e. controlled intervention of extra factors] as it is already present in organic causality). The spatial aspect is lost.  Can this psychic causality really then be said to be the result of (just) over-forming, or should one hold that it is rather the result of over-building?  ( Because there is still something surviving, it is probably best expressed by its being over-formed). Anyway, these two causal nexus [plural] are very different indeed.

It could  ( HARTMANN, Ibid., p.361 )  then be theorized that each Layer of Being has its total process and total determination all for itself, while it does not enter in any immediate causal relationship with other Layers. This is especially significant for the lower Layer  ( lower with respect to a higher Layer), because the higher is, in any case, carried by the lower. And insofar it is dependent upon the lower anyway.
In fact it is (according to HARTMANN) not possible to extend the causal isolation of the Layers this far. And indeed hardly anybody claims the causal independence of the Organic from the Inorganic, or the independence of the events of human history of geographic and climatic 'causes'. Here the intervention of clear-cut physical factors together with their causality is evident. One can only dispute the degree of their significance.
As regards to the relationship between the Psychic and the Organic, on the other hand, such causal independence is (often) claimed. This is understandable in virtue of the peculiar nature of the psychic as compared with the organic. The collective concretum of the Psychic Category Layer is consciousness, with its typical internal world, for which there is no parallel in any other category Layer.
What is often considered to be impossible, is the heterogeneous causal series (among whose members are physical as well as psychic members). The right point is that indeed there remains something not understood in this. The limit of spatiality separates the psychic from the physical. It was then asked :  How can a causal process, for instance that of observation, start within the spatial while proceeding further within the non-spatial? In such a case the cause has to be spatial-material, the effect, however, non-spatial and immaterial.
What can be brought up against this? First this :  It is not necessary that in their proper domain physical causes remain without an effect, while that effect appears instead in the psychic. The dynamic-spatial causes rather can have their dynamic-spatial effects, and likewise the non-spatial causes in the psychic events their non-spatial effects. This (according to HARTMANN) does not exclude that both of them can also have heterogenous effects, i.e. when we have a spatial cause, its effect could include both spatial and non-spatial elements, or, in other words, the range of a possible effect of a spatial cause can extend across the spatial and the non-spatial. And also the range of a possible effect of a non-spatial cause can extent not only across the non-spatial, but also, and at the same time, across the spatial, that is to say the effect can comprise spatial and non-spatial elements (i.e. spatial, together with non-spatial). This seems fairly obvious when seen from the Law saying that all real-world factors (and here thus psychic as well as physical) of the given collocation participate in producing the total effect. For a human being, together with his (or her) psychic life, is situated right in the middle of the real-world coherence, that is to say, he, and his internal life, belongs to it. So it should be clear that in such a human being, who is a (categorically) layered being, physical and psychic components are connected with each other, every time in every internal collocation.

I would like to add :  In the category Layers these components are separated (physical components belong to the Inorganic Layer, psychic components to the Psychic Layer), while they are not (separated) in a concrete human being (there they are integrated). So in a concrete human being at least inorganic (physical), organic and psychic causes are present (but belonging to different category Layers).

So while we must admit such a close connectedness of heterogeneous Layers of Being (category Layers) as that of the bodily and psychic in a single human being, it is  a priori  not credible that the respective processes and process systems would not also causally influence one another.
Higher-order concretum-concretum determinations presuppose causality (i.e. bare causality, not necessarily spatial causality). The relevant psychic processes, first of all the processes of perception, are not just like that produced by physical causes (objects that are being perceived, and the physiological machinery of perception), certainly not by them alone. And as to the role of (perceived) physical objects, the ensuing psychic processes just are elicited from them. In all this, a whole specific apparatus participates, including the mentioned psychic processes brought along by consciousness. Perception thus has its widely extended causal complex also in the psychic domain itself, and the stimulus coming from without (and which is processed by physiological processes in sense organ and brain) is only a partial cause. Without the internal psychic causal system the object (to be perceived) does not elicit (such that it leads to an internal image of that object). The proper nature of the effecting itself does not need to be a physical one. It even cannot be physical because the (last stage of the) effecting act is non-spatial and immaterial.
The decisive consideration as regards the psycho-physical problem, is, in addition to what was said above, the following :  The heterogeneity of the causal series is far from occurring only at the Layer boundaries. Also within the physical causal sequences the effect of the cause is not thoroughly homogeneous all along. It is there only categorically so. But this does not exclude other heterogeneities (i.e. it can, within the physical Layer, be heterogeneous in a different way, different from categorical heterogeneity). Causal series are -- in contrast to, for instance, mathematical series -- in themselves heterogeneous series anyway. From the mere consecutive character of causality one can never determine in advance the special content of the ensuing effect. One can do so only on the basis of extensive knowledge of the relevant laws. And also this, only within certain limits. Knowledge of laws, however, requires an extensive observational experience. In the mean time, the act of effecting itself -- the production as such -- remains ununderstood. It is presupposed.
Thus, given the fact that all cases of effecting involve one or another form of heterogeneity, why then couldn't the disparateness of cause and effect go one step further, namely beyond the limit of categorical similarity? The essence of causal production (i.e. the transition from cause to effect) does, insofar as we know it now, not restrict this.
And further :  Given that the secret of causal production remains unfathomable, what will it then mean that we cannot comprehend how something physical affects something psychic! It is the same incomprehensibility here as within the physical and within the psychic. It is more so only because of the categorical disparateness. Basically we do not understand the regular physical causal nexus any better. Only our being accustomed to it suggests its comprehensibility. And there nobody feels uneasy with it. And rightly so :  Incomprehensibility does not neutralize the existence of the incomprehensible. Limits of comprehension are not limits of being.
Evidently, the degree of heterogeneity of cause and effect does not make a difference. Moreover, how much or how little we understand causation, does not alter anything in the act itself of effecting, where and when it takes place.

The psycho-physical relationship, being itself a causal relationship (as in the affecting of the psychic by a physical cause [for instance in perception] ), does not therefore need to be a 'purely' causal one. Other forms of determination must be involved. For here we do not have to do with just the simple linear causality, but with already organically over-formed causality. The physiological processes, as functional processes, are themselves not merely physical processes anymore. The form of determination of the specifically organic kind is, it is true, not yet clear to us (an attempt to such an understanding [of the nexus organicus] was made earlier), but that it is some over-forming of causality (of causality as we see it in the physical domain) is beyond doubt.
So much we already know that in the sense organ total effects of organic systems are involved, insofar as these are geared to a very specific reactivity. Only in this way it is possible that minimal stimuli can elicit very significant and disparate psychic effects. Here, already from the beginning, there was an error in the considerations concerning the psycho-physical relationship :  It was wrong to assume that causality itself represents the whole problem. It was wrong to consider the categorical relationship directly between (inorganic) causality and a psychic determination. One should realize that something lies between these, namely the organic form of the nexus. One neglected the latter because one didn't know about it. If one restores the natural relationship in the sense of a stacking of Layers of Being, then all fear for a 'mechanizing' of the psychic is unnecessary. Already the organic process, which is the proper counterpart of the psychic event, does not exhaust itself in 'mechanical' causal determinateness. For the psycho-physical relationship it is entirely sufficient that only certain causal elements or aspects are brought along into the higher Layers. Whether they are brought along (i.e. reappear) directly or indirectly does not make a difference. Over and above that, the most far-reaching intrinsic determination within the psychic can exist. The next Figure illustrates diagrammatically the over-forming of causality. We restrict ourselves here to the Inorganic-Organic-Psychic Layer boundaries.

Figure above :  Successive over-foming of the category of Causality (causal nexus).
The Layer of origin of Causality (red) is the Inorganic Layer. There it appears in a spatial way (dark blue), because the category of Space co-determines all inorganic entities.
In the Organic Layer it is organically over-formed (light blue). Because the category of Space is retained in the Organic Layer, the spatial aspect (dark blue), as it was inherent in inorganic Causality, reappears.
At the boundary between the Organic and the Psychic Layer the category of Space is halted, that is to say, it no longer appears or reappears in the Psychic Layer. Therefore causality (red) reappears without spatial aspect. As such it becomes psychically over-formed (yellow).
So we see that causality-as-such (i.e. causality without qualification) reappears in all Layers (and also in the Super-psychic Layer [not drawn] ).

The just given over-forming of the causal nexus directly implies its reappearance and therefore the possibility of heterogeneous causality, i.e. the possibility that the transition from cause to effect not only can take place between two concreta (cause and effect) within one and the same Layer, but also between concreta of different Layers. And that indeed the above reappearance takes place can be based on the following consideration :
We can ask :  What degree of heterogeneity would be sufficient to block the nexus ( = connection) from cause to effect? Clearly only such a degree of heterogeneity that exceeds the intrinsic categorical conditions of the causal relationship itself. In that case the nexus would be broken. Which are then the intrinsic categorical conditions of the category of Causality? Apart from the all-pervading Fundamental Categories (reappearing in all Layers, including the Mathematical), these categorical conditions boil down to the categories of Time and Process. And these apply to all real-World Layers (from the Inorganic, all the way up into the Super-psychic) :  processes are present in all these Layers, that is to say, all concreta of whatever real-world Layer have a processual nature, and because Process presupposes Time, all these concreta are temporal. One of the Fundamental Categories (and thus present in all Layers) is that of Determination (in its most general form). If we then have a process in which its successive states, are not just successive, but determine each other, in the sense that each state is determined by the previous state and determines the next, then we have Causality. And from this it is clear that the category of Causality reappears (under modification) in every real-world category Layer.
The category of Space does not belong to the categorical conditions of Causality, because the above mentioned conditions are already sufficient :  The states of a process with successive determination do not need to be spatial (as we see it in psychical states, that determine each other in a succession in Time, but are not spatial).

We can now summarize briefly our findings about the ontological heterogeneity in causality (as were partly based on, and inspired by, those of HARTMANN, Philosophie der Natur, 1950 (1980)) :

The causal complex (total cause) as well as the effect complex (total effect) can be ontologically heterogeneous. If we concentrate on the psycho-physical problem and the presence or absence of spatiality in causality, then this means that there exist the following possibilities :

Causal Complex

( total cause )

Effect Complex

( total effect )

Spatial Spatial
Non-Spatial Non-Spatial
Spatial and Non-spatial Spatial
Spatial and Non-spatial Non-Spatial
Spatial and Non-spatial Spatial and Non-Spatial
Spatial Spatial and Non-Spatial
Non-spatial Spatial and Non-Spatial

This heterogeneity is in itself unintelligible, but this is not surprising, because the transition from cause to effect is unintelligible anyhow.

Unity of the real-world coherence as regards causality.

As the unity of a temporal coherence and of a processual coherence pervades the whole real World, so also the unity of a causal coherence  ( HARTMANN, 1950, p.370 ).  For this causal coherence the Layer boundaries (representing categorical heterogeneity) are -- as we have seen -- no barriers. It goes in diverse forms to and fro. A falling stone terminates a spiritual life, a natural disaster destroys a historically evolved culture, or makes place for a new one. An idea in the head of some human being transforms a country. The over-building relationships in this respect differ only little from relationships of over-forming, for always some lower categories pass over into the higher Layers, and among these is Causality. As far as temporality extends across the real-world coherence -- and it encompasses it in its totality -- also the causal coherence does not meet any borders. Surely, all the time it encounters higher-order determinations, but it does not conflict with them, integrates with them (in the sense of subordination), lets itself be over-formed.
The dualistic theories, which claim an absolute antithesis to exist between ontological domains, as Descartes' doctrine of two substances, extensio and cogitatio (body and mind), have failed to understand this. Their error was rooted in the total absence of a categorical analysis, in failing to acknowledge the stratigraphical nature of Being, and in the virtual absence of all enquiry into the forms of dependency obtaining between Layers (and also between their concreta).
As soon as one drops this false metaphysical presupposition, then also the whole bunch of self-made difficulties in the psycho-physical problem vanishes. A psycho-physical causality then is not such an enigma anymore. At least the enigma is of the same order of magnitude as that of the causal production (i.e. the creation of the effect from the cause) at all. It is only a qualitatively more complex enigma, and a more obtrusive one.

Some notes on the objectivity of Causality.  ( HARTMANN, 1950, pp.371 )

It could be imagined that causality is just a subjective way to see things, a device to explain events, and that in reality causality does not exist, or at least not in the way as defined above. It could also be that it apparently does not apply in some special cases or in some particular domain, while it does apply in others (i.e. in some area belonging to a given Layer of being, say, the Inorganic, it seems not to be valid -- as in the quantum mechanical domain -- while in many other areas of that same Layer of Being, it is valid), which might perhaps be an indication of its subjectivity :  Causality, namely, could well be just an evolutionarily developed tool for coping with everyday-reality and survival, and nothing more. It works because everyday experience goes about its business only very roughly, such that the errors, connected with the causal interpretation of the World are too small to be detected and certainly too small to be of any significance for everyday life and survival. The alleged absolute absence of causality in so fundamental a domain as that of quantum mechanics, is then said to prove that causality in its strict sense does not apply at all, i.e. even not in the macroscopic world (where it is only a fairly good approximation).
Anyway, the question of whether causality is objective and thoroughly valid (at least throughout the Inorganic Layer) and is thus a genuine general principle, or not, is certainly relevant.
There has been a lot of philosophical attempts to refute objective causality, but only little to prove it. This signifies that the adversaries of causality were much more concerned with the question of its objective validity than its supporters were. Evidently the supporters of the principle of causality did presuppose it to be certain. They were, however, not entitled to do so.
Among the few -- as reported by HARTMANN -- who attempted to give a proof is HOBBES (17th century). He argues as follows :

If  A  appears at time  t1 ,  without it being produced by any cause, then there is an equal possibility for  A  to appear at any  t,  because the points in time do not differ from each other. But the number of  t  (that is to say, of points in time) is infinitely large. Consequently the probability of  A  appearing at  t1  must be infinitely small, i.e. zero. And this contradicts the presupposition. So  A  must have a cause.

This proof indeed strikes something of the essence of the matter. But it only demonstrates that it is very improbable that everything that happens in the real World, happens by chance. And this isn't enough.
Alexius MEINONG, departing from HOBBES' proof, tried, by a modal approach, to find a better proof. Paraphrased (by HARTMANN) the argument can be summarized up as follows :

If  A  and  X  appear successively, without  X  being caused by  A ,  both are nevertheless not without any relationship. At least  X  must be possible with respect to  A ,  that is to say that  A  should not block the appearance of  X .  What in fact does this "being possible" mean? Does it mean that  X  and  non-X  are equally possible? That cannot be, because  X  becomes at the relevant moment real, but in its being realized the possibility of  non-X  is excluded. So there was in fact only the positive possibility of  X .  But that means nothing less than that  X ,  from  A ,  rather was necessary and (real-worldly) implicated. This implication is causality.

This argument at least correctly leads to the necessity in the connection itself. But apart from this it is not completely proving what it should prove. It does not clearly distinguish logical modi and real-world modi. Therefore the employed concept of possibility, from which the argument concludes, becomes equivocal (because in logic there are, from a given general concept, several (instead of just one) possibilities). In the present context only the real-world possibility counts, insofar as it, qualitative-structurally, consists in the totality of all relevant real-world conditions. Moreover, not causality is proven by this argument, but only the much more general Law of real-world determination, in which it still remains open whether the specific nexus realis about which the argument claims to prove something (namely its universal existence), really has the form of a causal nexus, or not. So only half of what should be proved is actually proved.
Nevertheless the argument has a relevant kernel. It is a modal proof of the more general Law of real-world determination, which says :

A complete complex of real-world conditions in some here-and-now collocation of factors is always the basis of the real-world possibility and at the same time of the real-world necessity of that what is produced from it.
Or, in other words :
That entity, of which all conditions are real-worldly present, not only is real-worldly possible, but also real-worldly necessary.

This is the content of the real-world Law of necessity, which content is the same as that of the real-world axiom of sufficient ground (which figures in the  If / Then constants,  where the If-component is the sufficient ground for the Then-component).
The special nature of causality, on the other hand, does not follow from the above argument (that is to say, its sequential nature, its irreversible linearity in Time, the correspondence of partial causes and partial effects, the consecutive determination of states, etc. do not as such follow).
The causal structure as such can only be unearthed from a more specific analysis of process phenomena, that is to say one can analytically 'demonstrate' the causal structure in the data of experience, not, however, prove it from more general grounds. So there can be no genuine proof of the objective existence and validity of causality.

If one places oneself more precisely within the situation of the problem, then one realizes that the demand of a proof is besides the point. In fact it is rooted in a misunderstanding. Categories (and causality is a category) are themselves ultimate presuppositions, and cannot, therefore, be derived. Their objective validity and applicability, that is to say their presence as real-world principles, can, therefore, never be recognized on a priori grounds. We can only get to them from the dependent concretum. And with respect to the latter, we can only rely on the phenomena in the field of experience.
In addition to this -- but always only on the basis of earlier conclusions taken from the concreta -- also the intrinsic connectedness of categories among themselves, i.e. their mutual implication, forms an access.
But certain residues of a hypothetical slant remain attached to all our knowledge of categories, in the same way as they are also attached to our knowledge of the general presuppositions, axioms, or basic statements in all areas of science.

Causality and Natural (dynamic) Law
( HARTMANN, 1950, p.389 )

In a causal series each state is determined by the previous state, and determines the next state. This means that each state is the cause of the next state which is its effect. Every time a state is produced by the previous state, while this latter state disappears in the act of producing. The produced state is new with respect to the producing state. If we find something concrete that survives the transition from one state into the next, then we do not have our eye on precisely a sequence of cause and effect :  The surviving element does not properly belong to the cause, neither does it properly belong to its effect. The phenomenon of the production of an effect from its cause is a truly irrational element in the processes of Nature. Only observation tells us that from a given cause a certain effect follows. And we experience some necessity in this production, because it seems that like causes produce like effects. And in virtue of this we assume causality to be a category, of which the content consists of :  Same cause, same effect.
In principle the causal sequence could consist of an irregular succession of states, but in reality, i.e. as real-world causal sequence, it turns out to be regular, which means that the succession of states is rule-based, that is to say, (it is) according to a certain law. Such a law is then a natural law. So we can state the following about the relation of causality and natural law :

A natural (dynamic) law is present (i.e. is ruling) when a causal series is regular, that is to say when there is a relationship between successive states (of the causal process) such that when any one of these states is (fully) known, all previous and all next states can subsequently be derived, i.e. known in advance, on the basis of the knowledge of the natural law (that determines the relationship between the states).

In the case of so-called  chaotic  dynamical systems the knowledge of such a state must be infinitely precise in order to make possible long-term prediction (In predicting the weather, this condition is not fulfilled).
So although the natural law (as it is in itself, not as we claim to know it) determines the relationship between states, i.e. makes a causal series regular, we still do not have any insight into the production of one state out of another.

In natural science there is an important presupposition concerning the general ontological structure of any real entity whatsoever :  Every real entity consists of two ontological aspects, viz., individuality and specifity, that is to say, every real entity is as such individual but can, in principle, be exactly repeated many times over. This is called the species-individuum structure of any real being whatsoever. In natural science all conclusions from experiments and observations are based on this presupposition ( It is described in detail in First Part of Website, Critical Series :  The Species-Individuum Structure ).  On the basis of this presupposed Species-Individuum Structure a regular causal series (which then is a dynamical system that proceeds according to a dynamical law) can be, in principle, repeated, in space or/and in time. Although in the real world such series are never exactly repeated, we often see them being approximately repeated (which itself is based on the fundamental possibility of exact repetition). And because of this we see many instances of processes that follow the same law. Surely, these processes can lead to different results, because they started from different initial states, but the relationship between successive states is the same, that is to say, the same relation (say)  R  not only obtains between (every two) consecutive states of one such process, but also between those of the other process, i.e. (every two) consecutive states of this latter process are also related to each other by the relation  R .
The Species-Individuum Structure of all real entities also means that every such entity has a definite nature (i.e. its species aspect), which means that it relates to other entities in a definite way, irrespective of whether we can actually observe or measure this. And from this it is evident that a given cause produces a definite effect. And when this same cause (i.e. a cause that is specifically identical to the first one) appears again, it will again produce that same effect (i.e. an effect that is specifically identical to the first effect).

Causality and Quantum Mechanics.

Causality is a category. So if we discuss things concerning the nature of causality-as-such, i.e. as it is in itself, then the discussion is ontological. Now it seems that causality is absent precisely in the most fundamental domain of real-world Being, the quantum-mechanical domain. If that were true then genuine causality would also not rule the macroscopic world. It is therefore necessary to discuss this problem. An this boils down to the question :  Is the quantum-mechanical domain truly the very fundament of all real-world phenomena, or is it parasitic on macroscopic entities? Well, some aspects of the ontological significance of the discoveries of Quantum Mechanics were discussed in a (still unfinished) document in  First Part of Website, Non-Classical Series :  Metaphysics and Quantum Mechanics (last document) .  From it we here reproduce the following (with some minor alterations) :

        If we agree with the Copenhagen Interpretation of Quantum Mechanics, that the wavefunction is a  complete  mechanical description of the relevant quantum-system, then a quantum entity, like an electron, is not fully determined (is not determined in all respects) until it is actually measured by a macroscopic device. Not until it is measured with respect to, say, position, does it have a (precise) position. Not until it is measured with respect to, say, momentum, does it have a (precise) momentum. Position and momentum (basic determinations within mechanics. "momentum" means : velocity times mass) moreover are so called complementary variables, which means that they cannot simultaneously be attributed to a submicroscopic entity. Such an entity cannot have a precise position and a precise momentum at the same time. The interaction of the quantum entity and the macroscopical measuring device defines certain properties of the quantum entity. We can assume that a real being should be totally determined in order to be a real being. A quantum entity seems for its determination to be parasitic on certain macroscopical entities. The latter were considered as measuring devices, because these play a role in the quantum-mechanical investigation. But of course similar situations, 'measurements', occur in nature, without the hand of a human investigator. So we can state that quantum-mechanical entities are such that certain properties of them are only defined by and in a macroscopical interaction context. So these entities partly depend on such a context. All this is more or less comparable with virusses :  They are only 'living' in the context of (which here means literally inside) some independent life form (for example bacteria).
This fact, and the fact that some properties cannot be attributed simultaneously to a quantum entity, forces us to consider the reality-status of quantum entities as a weakened, or 'deficient' or incomplete one.
Although Quantum Mechanics also applies to the macroscopic world, its effects are negligible, because of the very smallness of Planck's constant. An exception will be encountered when a quantum event is directly correlated, as a trigger, with (i.e. connected to) some definite macroscopic event, like the case of Schrödinger's cat. But although, normally, quantum effects are negligible at the macroscopic level, they are there nonetheless. So even macroscopic entities are not always completely determined, and so remain, in a sense, incomplete beings, but, we can say, they are very close to complete beings. These complete beings therefore remain our reference with respect to the ontological assessment of other beings (submicroscopical beings), i.e. macroscopical entities are "primary instances" of (known) Being (like bacteria, and all other organisms 'above' them, are primary instances of Life, while virusses are not :  they are secondary instances).

According to BOHR (and, consequently according to the Copenhagen Interpretation of Quantum Mechanics) Quantum Mechanics is about the inseparable whole of quantum object and the measuring set-up. This whole is called the phenomenon. Such a phenomenon, of course, also occurs in natural situations, for it just means :
The quantum-entity-in-an-interactive-macroscopical-context.
In order to make things more clear I will translate, from Dutch into English, some passages (p. 100--101) from Van Quantum tot Quark (From Quantum to Quark), edited by  G. 't HOOFT,  for the TELEAC foundation, 1989, meant to be an introduction to Quantum Mechanics (comments are placed between square brackets [...] ) :

" A phenomenon is not analyzable into the measuring device on the one hand and the object of which the properties are being measured. So we are not allowed, concerning the above experiment with the photographic plate [ = the measuring of the position of an electron or other quantum entity by means of the local blackening of a photographic plate ], to imagine ourselves that an approaching electron encounters the plate on its way -- and have at the back of our mind that it was equally possible that the plate wasn't there, without making any difference to the position of the electron. It is only meaningful to attribute to the electron the property 'position' because the photographic plate is there.

The idea that Quantum Mechanics is about phenomena [ in the above sense ] gives new meaning to the principle of complementarity [ complementarity in Quantum Mechanics means that there are certain pairs of variables (quantities), like position and momentum, that cannot simultaneously be attributed to a quantum entity, while in classical mechanics they can. ]. An experimental set-up cannot simultaneously function as measuring device for two complementary quantities. An instrument that is appropriate for determining positions, cannot also measure momentum. Because in the Copenhagen Interpretation the properties of a quantum object are defined by the measuring set-up that is present, the object cannot therefore be characterized by the combination of two complementary quantities.

The not-simultaneous presence of two complementary properties is not the result of a physical disturbance of the object by the measuring device. Because the properties of the quantum-system are not defined independently of the measuring set-up, it also is meaningless to say that those properties are being disturbed. BOHR arrived at a clear formulation of this matter after discussions with HEISENBERG. The latter at first believed that the measurement of position of, say, an electron, requires an interaction with the measuring device, disturbing the momentum, resulting in the value of the momentum after the measurement being unknown, uncertain (this is the origin of the name 'uncertainty relation'). In opposition to this, BOHR stated that all this does not concern uncertainties, but undefinedness. In the context of a position measurement the concept of momentum is not applicable.

If space-time concepts and dynamical concepts (energy, momentum) are not together applicable, a quantum object apparently does not follow a trajectory through space [ This is so if the quantum-mechanical wavefunction is considered as a complete (mechanical) description of the quantum system, which it is according to the Copenhagen Interpretation) ]. According to BOHR this explains why Quantum Mechanics only gives probability statements. Classical Mechanics can give exact predictions because of the fact that position as well as momentum, and with it a precize trajectory, can be attributed to a system. Repetition of the same initial conditions leads to the same trajectory. In Quantum Mechanics this does not apply. "The same initial conditions" do not determine a trajectory, and also not a unique end result.

According to the Copenhagen Interpretation the applicability of the concepts depends upon the presence of a macroscopic measuring set-up. It is not necessary that a conscious observer is involved. The physical qualities of the measuring device are decisive for the question which classical concepts apply. Whether a human being or a computer reports the result of a measurement is irrelevant. So there is no sign of an element of subjectivity within the Copenhagen Interpretation. No special part is played by human consciousness."

As has been said, the Copenhagen Interpretation assumes that the quantum-mechanical wavefunction describes the situation of a quantum system completely. Some other interpretations assume that this description is not complete.
Here I will decide for BOHR's view (i.e. the Copenhagen Interpretation), but because I am not a physicist this choice is not 'authorized'.
So we stick to the fact (a fact in the Copenhagen context) that quantum entities are not ontologically independent, although in an other way than, say, an accident is, or a principle. A quantum entity is partially dependent upon an interactive macroscopical context, it is ontologically parasitic on such a context.
The Substance-Accident Metaphysics  [ as it was developed in First Part of Website ],  is indeed an appropriate philosophical background in which the Copenhagen-view can be received, because just this metaphysics is already acquainted with GRADED being (which is equivalent with graded existence, i.e. stronger and weaker modes of existence). Its central conceps are 'analogical' (See the Document on The Analogy of Being  [ First Part of Website, Classical Series ] ),  so it can easily accomodate for beings like quantum entities, which presuppose a certain context for them to be determined.

But not only the Substance-Accident Metaphysics, but also the Theory of Category Layers, as developed here in the Fourth Part of Website, which is the present Part, is compatible with the Copenhagen interpretation of Quantum Mechanics (and its 'incomplete' beings), because also here we have an  "analogy of Being" ,  which is evident, for example, in the  reappearance-under-modification  of a number of categories.

So we can now accept that the quantum-mechanical entities, which comprise all objects from the atomic scale downwards, are deficient, incomplete, 'weakened' beings. They are not completely determined. They 'borrow' the missing ingredients from the macroscopic world. It is, therefore, not surprising when they, as they are in themselves, lack some important categories like causality. Our categorical analysis (theory of category Layers), which, by the way, is about  structure,  not, primarily, about genesis, is, therefore, first of all concerned with (categories determining)  genuine  being, which here means beings, things and their properties, processes and process states, that do not depend on macroscopic entities in order to be genuine being at all. And although, for example, a property of a macroscopic thing is itself not  an  independent being, and thus not  a  genuine being, it is nevertheless  genuine being.  We said, our categorical analysis is "first of all" concerned with genuine being. But in fact we mean that it will exclusively concern genuine being, which is macroscopic being (from the atomic scale upwards).

Category of Simultaneous Interdependency
( HARTMANN, 1950, p.424 )

Unil now we were, with respect to Process, Causality and Regular Causality (natural dynamical law) concerned with the successions of states, that is to say we were concerned with the Time dimension. But, with respect to a process, there is also a pure Space dimension (consisting of three independent directions), which stands perpendicular to the Time dimension, and is as such Simultaneity. And this is about how real-world elements of a given set can be present at the same time, i.e. about how these elements tolerate each other to be elements of a simultaneous collocation, a state of a dynamical system. The category that determines this is that of Simultaneous Interdependency.  We could call this also the 'Category of Interaction', but this is misleading, because  interaction  is action, and action takes place in the flow of Time, it does not take place in simultaneity. The interaction of elements of a state of a dynamical system eventually results in the next state, but this takes time. This interaction should therefore not be confused with simultaneous interdependency. Simultaneous interdependency has to do with equilibrium, as in the example of the metal ball resting on a pillow and having a dimple in it. In a dynamial system it is any simultaneity-section through it. Let us recapitulate the content of some categories, and see where the category of Simultaneous Interdependency fits in.
Process-as-such is extendedness of real-world entities along the flow of Time, i.e. such an entity is dissolved into a successive series of states. From any such state many 'possibilities' with respect to the further course of the process lie open.
State-as-such, on the otherhand, means that every stadium of the process is in itself a closed whole of simultaneously coexistence.
Causality means that the states of the process do not haphazardly follow upon each other, but such that any given state is, as effect, produced by the previous one (the cause) and in turn produces the next one, (where "previous" and "next" refer to the time dimension). And this means that, from a given state, not many 'possiblities' lie open, but only one.
Natural (dynamical) Law, finally, means that the causal series (in which, as we have just stated, every state determines unequivocally the next) is  regular,  i.e. according to a rule or law, which determines some definite relationship between any two consecutive states of the given causal series. HARTMANN, 1950, for example at page 432, defines Natural Law differently, namely that such a law determines that the diversity of different causal complexes is not endless, but brings about a reappearance of the similar, resulting in the similarity of the process courses themselves. We will show that this latter simply follows from our own definition of natural law :
As has been said, natural dynamic law defines a regular causal sequence, that is to say, a definite relationship between successive states of such a sequence. A random sequence (of states), when it is (in principle) infinitely long, has a zero chance to be repeated, i.e. a totally irregular causal series of states will never be repeated. A non-random sequence, on the other hand, that is to say a regular sequence, has a non-zero chance to be repeated. So the empirical fact that every natural law has ample instances, i.e. the actually ruling of every natural law is observed in many places and times ('typical forms of courses'), directly follows from the fact that a natural law is (referring to) a regular causal sequence. In principle, anything that has a species aspect -- and a random sequence has no species aspect -- can be (exactly) repeated according to the presupposition of the Species-Individuum Structure of all entities. And something to have a species aspect is equivalent to it being regular. Of course the possibility of exact repetition only applies when the entity to be repeated is considered as such, i.e. considered (only) as it is in itself. In this way we can say that the given natural law exactly repeats itself in its instances, and only in its able to do so it is a law at all.
The repetition of the law, i.e. its set of instances, nevertheless can, and often will, consist of different causal sequences. But the relationship between successive states is the same in all instances of the law.
This being the same, i.e. the repetition of this relationship between successive states in  another  instance of the process, must result from the nature of the states themselves, because this nature of a state determines the next state, and thus the relationship between them. So the states of a process must themselves represent an instance, that is to say, each state is an instance of that type of state that brings about the repeating relationship (between successive states of a process), and can occur in another process, i.e. in another instance of the same type of process (and even in processes of a different type for that matter). The relationship between successive states of a causal process must depend on the states themselves, meaning that the nature and configuration of the elements of such a state determine the next state, that is to say, determine the law when there happens to be one, namely when the series of states of the causal process turns out to be regular. And this is the case when the general nature of a state is such that a series is produced in which a definite relationship between every two consecutive states is preserved. So a dynamical system is already fully present in the collocation of the elements of any one of its states.
When the elements of the collocation interact, then time comes into play, and the state more or less gradually transforms into the next state. But the collocation of elements of a particular state, as this collocation is in itself, is a simultaneous structure. And in such a structure the elements relate to each other by simultaneously influencing each other in the sense of holding each other in check. This is simultaneous interdependence, like we have exemplified it with the metal ball resting on a pillow.
It is in this simultaneaous dynamical (i.e. including forces) relationship between the elements of a state (which itself is a cause of the next state and an effect of the previous state), where the dynamical law resides. And it so resides in every (possible) state of the dynamical system (regular causal series).  In  First Part of website ,  where we extensively considered dynamical systems, we expressed this as follows :  The dynamical law of a dynamical system is immanent in the collection of elements of its initial condition (or any other of its states).

Natural (dynamic) lawfulness is at the same time lawfulness in the simultaneous connection and collocation (of elements of a state), i.e. lawfulness in the Space dimension,  and  lawfulness in the successive connection (of states), i.e. lawfulness in the Time dimension.

Above we stated :  "When the elements of the collocation interact, then time comes into play, and the state more or less gradually transforms into the next state."
As such this is still too crude an expression of what is going on in  one state transforming into the next state,  because we suggest that within (the one) causality ( = transformation of one state into the next) there is embedded yet another 'microscopic' causality, namely that of the transformation of elements into different elements, or/and that of a spatial reshuffling of these elements, resulting in a new (spatial) configuration of them, where this reshuffling is just a moving around of elements, and thus involving causality. We must, hoewever, realize that the interactions between any two or more elements of the given state, are not isolated events, if we consider that given state as being a (complete and pure)  c a u s e  (of the next state), where 'partial causes' are only abstractions. The interaction of elements, resulting in a new state, is in fact no interaction at all, but only a convenient way to express that one state (consisting of elements) transformes into another state. Indeed, the elements of a genuine state (not a more or less arbitrary segment of the process chain) cannot interact, because they form a simultaneity-collocation. The simultaneous interdependency of the elements of a process state is making up this collocation, i.e. it is its nature. And this nature undergoes change, resulting in the next state of the process. The form or type of dependence, which rules in (the case of) Simultaneous Interdependency, is that of  c o h e r e n c e  (and, as a result, co-existence). And this means that the partial aspects of a state (i.e. its elements) are only in their being-together (i.e. not separately) causal elements in the process. Their coherence consists in mutual modification in the overall effect. Every genuine state is just a simultaneous section of the causal series, a section perpendicular to the direction of successivity. And the one co-existence is replaced by another in the ongoing flow of the causal process. The content of one state differs only infinitesimally from the next, as seen from the macroscopic point of view. From the microscopic (i.e. quantum-mechanical) point of view this content jumps or hops from one to another, because of the indivisibility of the energy quantum.
In fact there are no separate causal series, but only the one successive series of real-world states. Fortunately, however, some subseries more or less stand out in this overall process, and they can be treated by science as if they were independent processes. In every simultaneous section of the overall real-world process we have the complete cause of the next real-world state, and at the same time the overall effect of the previous state. This universal causal dependency is tied up with simultaneous interdependence as succession is with simultaneity, and process with state. For within the section itself everything is mutually conditioned (coherent and co-existent), while this whole section has this coherence produced from the previous process state on which it is causally dependent.
In itself it is possible to approach all this from the viewpoint of Simultaneous Interdependency. The cosmic diversity extends along four dimensions of extensive magnitude. Along three of them (the spatial dimensions) its coherence rests on mutual dependence (interdependence). Along the fourth dimension, on the other hand -- the time dimension -- this diversity extends in a one-way and irreversible dependency. As this fourth dimension contrasts, as real-world time, with the spatial dimensions, and therefore stands out with respect to the real-world coherence, so also does the diversity in it (i.e. in the time dimension), as process, contrast with a mere state, and in the same way the dependency in it, as causal sequence, contrasts with the mutual conditioning of the simultaneous ( = Simultaneous Interdependency).

So let us recapitulate and add things concerning causality, natural law and simultaneous interdependency :
A genuine state (i.e. a state in the strict sense) of a regular causal sequence is the smallest possible 'slice' (transverse section) of (through) it. This slice having spatial extension, does not have any extention in Time, or is at least such that 'during its thickness' no change of content takes place. This slice or state causally determines the next slice or state, i.e. the latter is creatively produced from the former, while this former is totally consumed by the latter. In a long-term view, comprising many successive slices, we can -- in order to understand, or at least describe, the successive causal production of states -- see  interaction of elements  at work in thicker slices ('during thicker slices'). Every such interaction in fact consists of two  actions,  so let us illustrate such an ACTION first :

Figure above :  Diagrammatic representation of slices (states) through a (regular) causal process. Each slice consists of simultaneous elements.
Left image :  Admissible ACTIONS of elements, i.e. an affection of one element by another.
Right image :  Non-admissible ACTIONS of elements :  (1) An action of an element onto itself is impossible. (2) An action of one element onto another, not needing time, i.e. 'simultaneous action', is impossible. (3) An action backwards in time is impossible.

Inter-action between, say, element A and element B is NOT the following :
Element A affects element B (i.e. acts on element B), while, at the same time, the affected element B affects element A.
This cannot be so, because the latter would be an action backwards in Time.  The affecting of element A by the affected element B must proceed forwards in Time, as the next Figure illustrates.

Figure above :  Diagrammatic representation of slices (states) through a (regular) causal process. Each slice consists of simultaneous elements.
True interaction between the red and light blue elements :  The red element affects the light blue element. The affected light blue element affects the red element. Everything, insofar as it has to do with ACTION, proceeds forwards in Time. Apart from this there is simultaneous conditioning and co-existence of elements of one and the same slice (state).

So simultaneous mutually conditioning is not interaction, and when there is interaction taking place, its phases are successive, not simultaneous, and also not backwards in Time. See also next Figure.

Figure above :
Top :  Element A acts on element B, and B acts on A.
Center :  How things would be, if these two actions took place simultaneously. Or, even better :
Bottom :  'Simultaneous actions' of A on B, and B on A.  It is clear that this set of 'simultaneous actions' is not action at all, but simultaneous interdependence (coherence, co-existence). An action that goes forward and backward at the same time is neutralized, and is no action at all.

So we now know what  interactions  are. And we can describe a causal process in terms of interactions of the elements of states, while these are taking place in time (i.e. they take time), implying the transition to a next state. But, as we have already seen, within our causal sequence of states there would, if this were true (i.e. if the interactions were real), be yet another, more internal causality. And if we analyse this latter causality again in terms of interactions of (deeper-seated) elements, we end up in an infinite regress, i.e. we never end up somewhere. To solve this dilemma we can assume that the many 'interactions', together making up a state transition, do not take place independently of each other, but as one single integrated whole (which is the state). They do not exist separately. In short, there are no interactions. So while there cannot, of course, be any interaction between the elements of a  genuine  state (because such a state is a simultaneity-collocation of elements), there can also not be any interaction between these elements as seen in a thicker process slice.
The fact that there is a wholeness of a complete (total) cause at all, and that this wholeness produces the wholeness of a complete (total) effect at all, is not the result of the linear nexus alone, but also of the transverse connection in the simultaneity of the given moment, that is to say, it also results from an interwoveness in another dimension. And it is this simultaneous interwoveness that unifies all individual processes into one single real-world process. And this interwoveness is, as simultaneous interdependency, the supra-causal aspect of the world process. As category it determines the fact that there are, in the Universe, no individual processes that go their business in complete isolation from all others (i.e. are totally insulated or shielded off from their surroundings).
Just like the causal production itself, this simultaneous interdependency, together with its mode of determination, is as such unknowable  ( When we come to consider the category of dynamical system [next document] we will see that, although there is only one overall real-world process, some partial processes clearly stand out against the overall dynamical background as a result of strong internal forces. These dynamical systems are in fact the concrete beings, i.e. the stable dynamical patterns like crystals and organisms, but also many more).
HARTMANN, 1950, p.438, maintains that in itself mere linear causality without transverse connections (which can be described as interactions between elements of the causal states), i.e. causality without simultaneous interdependency, is conceivable, because the latter does not follow a priori from the causal series as such. In the real world, however, so he maintains, as it just happens to be this real world's nature, causality without simultaneous interdependency does not occur, because in the real world all the simultaneous in the causal effecting itself is transversely connected, i.e. the simultaneous (section) is not just a fortuitous co-existence, but a coherence of elements. So as such the simultaneous interdependency of 'partial causes' in causality is extrinsic to it, and is thus a new categorical element alongside causality.
To all this, I would, however, like to add that a mere linear causal chain, without simultaneous interdependence, which is , according to HARTMANN, conceivable, is only conceivable when we assume simple (i.e. not composed) elements that change into other such elements, not by reshuffling (reconfiguration) of still smaller elements, but by a purely qualitative transformation of the one causal element (non-composed causal state) into the other. That this is at all possible, was demonstrated in  Part XXIX Sequel-5  of the present Series of documents, that was concerned with the Impetus Theory of motion. In that same document it was also demonstrated that the Theory of Relativity does not refute absolute simultaneity, but had showed that it cannot (even in principle) be objectively measured. But in this very argument (of relativity theory) absolute simultaneity was presupposed. And it is this simultaneity that is referred to in our discussions about simultaneous interdependency and its relation to causality.

In the next document we will continue the study of inorganic general categories. In it we turn away from the overall real-world process (i.e. the real-world process as a whole, with its causality and simultaneous interdependency :  real-world succession and real-world states), and direct our attention to those partial real-world processes that clearly stand out from their real-world process background, that is to say we will study the category of Dynamical System. This category determines concrete, finite beings.

In the document(s) after those concerned with the crystal analogy (coming up later) we leave the investigations into the latter, and, based on the results of these investigations, now accept this analogy as a general context for the previous and ensuing work.  This ensuing work will be a continuation of our investigation into the promorphs of two-dimensional crystals, but now explicitly involving their internal symmetry (plane group symmetry). In addition, the crystal analogy could point (if it allows to be so interpreted) to two different Layers of Being, that are either distinguished from each other by a (mere) jump in physical complexity (and nothing else), or by some really fundamental ontological NOVUM, resulting in the organisms to be  elevated  or over-formed (non-equilibrium) crystals.

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To continue click HERE for further study of the Theory of Layers, Part XXIX Sequel-27.

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