General Ontology
Cosmos and Nomos

Theory of Ontological Layers and Complexity Layers

Part XXIX (Sequel-24)

Crystals and Organisms

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This document (Part XXIX Sequel-24) further elaborates on, and prepares for, the analogy between crystals and organisms.

Philosophical Context of the Crystal Analogy (I)

Philosophical context :  meaning and purpose of the Crystal Analogy

The ensuing exposition of the "crystal analogy" (later documents) will be largely based on the lines laid down by PRZIBRAM, 1926. But this analogy of his is in fact for a large part just a mere Inorganic--Organic analogy (as distinguished from a Crystal-Organism analogy, which is a crystal analogy proper). Nevertheless the comparison of crystals and crystallization on the one hand, with organisms and organic processes on the other, represents the focus in PRZIBRAM's analogy.
Our exposition has as its goal or purpose the comparison of the Inorganic and Organic domains. Originally crystal analogies were -- as in HAECKEL, 1866, 1917, and in PRZIBRAM, 1926 -- meant to demonstrate that organic objects do not fundamentally differ from inorganic objects, especially not from crystals. For example the colloid state is not something typically organic, but can be found in crystallization phenomena as well. Further, curved surfaces, so typical for organisms, are also found among certain crystals, for instance Diamond. Still further, the phenomena of intrinsic shape, symmetry and promorph, as well as the phenomena of growth and regeneration, so typical for organisms, are also found in crystals (Such analogies could, as PRZIBRAM was the first to point out, demonstrate the presence of an organic crystal lattice in organisms). And also the thermodynamics is the same in both domains. So organisms are, according to these analogies, just complex inorganic beings, not involving any non-physical directing force. Also the work of D'Arcy THOMPSON (1917, 1942, and abridged edition 1961) is aimed at showing that many an organic structure or form can be recreated by means of purely physical forces and processes.
However, it turns out that these works for the most part (or at least for a substantial part) only reveal analogies, some more or less remote, others more closely so. This fact that only analogies could be revealed could mean something with respect to the true similarities and differences between 'inorganisms' and organisms.
We want to know more about these similarities and differences. Especially we want to know whether they are fundamental, or, maybe better (expressed), which one of them are truly fundamental. In order to know this, it is clear that a mere inspection of inorganic beings (for instance crystals) and organic beings (plants, animals) is not sufficient. Organic beings can as such differ strongly from inorganic beings, while at a more fundamental level they may not be so different.
All this boils down to the realization that we must investigate the  p r i n c i p l e s  governing the Inorganic World and compare them with the  p r i n c i p l e s  governing the Organic World, and this means that we must investigate the ensemble of determinants -- Categories,  If / Then constants -- of the Inorganic Layer of Being, and compare them with those of the Organic Layer of Being.
The Ontological Theory of Layers of Being and their inhering principles (categories,  If / Then constants) was developed in Part I and Part II of the present Series of Documents. Because these Parts are a long way back, the reader is advised to consult them (again) before proceeding with the ensuing crystal analogy  (The author did this also!).
While the previous documents constitute a physical, chemical and biological preparation to this crystal analogy (embryology, thermodynamics, crystallization, surface tension, etc.),  Part I, Part II, and the beginning of the present document, constitute the philosophical preparation to, and context for, it.
The crystal analogy (but, as has been said, being largely a mere inorganic-organic analogy) as it is presented by PRZIBRAM (and which can be supplemented with material from D'Arcy THOMPSON and some from HAECKEL) will be studied in the context of  categories  (If / Then constants) of the Inorganic Layer and of the Organic Layer, and will, it is hoped, reveal the qualitative identities, similarities and differences between these two Layers.
With HARTMANN we will assume the presence of some categorical NOVUM, i.e. a totally new (new, as compared to the Inorganic Layer) principle or set of principles appearing in the Organic Layer, which NOVUM is responsible for genuine novelty to ensue in the Organic Layer (novelty, as compared with things in the Inorganic Layer), together with corresponding modifications of inorganic principles. It is responsible for, or embodies, the appearance of new categories, and -- as has been said -- for the modification of some inorganic categories that reappear in the Organic Layer. What exactly is the nature of this NOVUM, we can only speculate, and in doing so we repeat a section from Part I :

Preparation and motivation to study Hartmann's theory of layers

In what follows we will try to get as close as we can to HARTMANN's theory of the ontology of the Temporal World, i.e. of the whole system of layers above the mathematical. This system of layers is his 'Real Sphere of Existence'. In this we will not follow in all rigor the above expositions about the derived and the cognitive non-derivability, and with it about the 'definition' of the "new" (the novum). Our demand of consistency of the whole exposition, i.e. consistency between what follows and what went before, will be somewhat mitigated. This will give us room for  d e v e l o p i n g  a theory about the existence and content of the layers instead of just  p r e s e n t i n g  it fully-fledged (which is, after all, not even possible). However, we will in a stronger fashion emphasize the dependence of the higher upon the lower, i.e. stronger than HARTMANN already does, implying that the higher categories ( If / Then  constants) are not absolutely fundamental, but only relatively so, resulting in the fact that the whole set of layers, including the mathematical one, is ontologically homogeneous.
The whole theory of layers (or levels) is meant to give some preliminary understanding of the ever increasing wealth of structures and subtleties as we ascend from the purely physical (ultimately from the purely mathematical) via the organic and psychic (subjective spirit) to the super-psychic ( The latter is the supra-individual layer of human culture and institutions -- the objective spirit).
It cannot be expected that the above given inherent problems of such an investigation will be solved, certainly not by one writer all by himself. The only intention is to trigger further thought and discussion with respect to those problems.

The NOVUM (i.e. the genuinely new feature), appearing in a higher layer (and representing this layer) consists in a very special complexification. The latter results not only in a highly complex structural unit, but also complexifies its relevant surroundings in such a way that that unit obtains a specific  m e a n i n g,  like we see in DNA molecules. Just for themselves these molecules are just complex chemical structures, and as such belong to the physical layer. But their having acquired a specific meaning elevates the whole system (DNA + its chemical environment) onto a higher structural and functional level. The mentioned meaning consists of certain definite  r u l e s,  determining  from now on  the whole structure. This is the NOVUM and leads to Life, provided this kind of meaning-generating complexification is such that the whole structure is not only determined by the new rules, but only by these new rules, i.e. when it can now go its business all on its own (which means for example that it also takes care for the selective import of matter and energy, and the selected export of matter and entropy, and thus guaranteeing its own continuation as a process).

The dependency of the higher upon the lower is a consequence of the higher having emerged after, and in virtue of, the entanglement of jumpy (i.e. more or less abrupt) complexification of (domains of) the lower layer. So without that lower layer there will not be any entanglement of complexification and consequently no emergence of a higher layer. Thus the (presence of the) (next) lower layer is in any case a  conditio sine qua non  (i.e. a condition that must, in all cases be satisfied [there could be more such conditions that should be satisfied, and only when all such conditions are satisfied we have  sufficient ground,  and the consequent will then necessarily follow.] ) for the higher layer to exist at all. And, what is important, the lower layer determines the higher layer ONLY as a conditio sine qua non, and certainly we here have not to do with a determination by a category of its concretum (but with a  concretum--concretum determination [which itself stands under a certain category] ).
The lower layers, determining -- as we now know -- only as a conditio sine qua non, are  i n d i f f e r e n t  as to  what  higher layer can emerge after the entanglement of complexification, i.e. whether it be Life, Consciousness, or whatever. A layer all by itself does not have a tendency to complexify, i.e. self-organize into a higher layer, it only has the ability, the potential, to do so.
Something comparable (with that what was exemplified for the case of the emerging of the organic layer) is the case with respect to the emergence of the psychic and the super-psychic layers from their respective lower layers. They go their business according to special rules, however, not contradicting the lower-level rules.
The fundamental (and thus most general) laws of Nature (not necessarily as they are described by science, but as they really are) have room for such high-level special rules. The same goes for the case of more special natural laws, like crystallization laws or laws of other types of dynamical systems :  Also they leave room for high-level special rules. Those low-level dynamical systems are then selectively fed with certain ingredients, which deflect their course, and become moreover included into a larger (i.e. high-level) dynamical system, while those same special low-level laws are at the same time constraining those high-level rules, but only as a conditio sine qua non for them.
The indifference of a layer with respect to the content of higher layers and also to their appearance at all, also implies a certain independence of the higher layer with respect to the lower, because the latter does not determine the specific content of the higher layer, apart from it being a conditio sine qua non. The only dependency of a  particularly structured  higher layer upon the next lower layer is the  p l a y  that is allowed by the lower layer. The lower elements, in the sense of lower-level laws or rules, cannot be trans-formed, but only be  o v e r - f o r m e d.

HARTMANN, discusses also the possiblity -- as it is supposed to occur at the transition from the organic to the psychic -- of becoming  o v e r - b u i l t,  in which case the lower layer remains only in its function of being the carrier of the higher. The latter is then only dependent on the capacity (of carrying) of the lower layer. But because we here entertain just a mitigated version of the NOVUM in general, we, for the time being, do not consider a layer to be over-built).

Life as a definitively  n e w  phenomenon is affirmed not only by philosophers but also by many natural scientists, so for example DAVIES, P.,  The Cosmic Blueprint,  1987/9, p. 101 (1989 edition) :

"Biology will never be reconciled with physics until it is recognized that each new level in the hierarchical organization of matter brings into existence new qualities that are simply irrelevant at the atomistic level."
Every lower layer co-determines, it is true, the next higher layer, but at most only as its matter (i.e. its substrate), matter that becomes in-formed. The independence of higher layers (and ultimately the independence of their corresponding categories -- their nomos) is only a  partial  independence, generally because of the mentioned conditio sine qua non  o n l y,  that the lower features are for the higher, and, more specifically, because of the dependence of their content on the degree of available play  o n l y,  (a play) that is allowed by the lower categories (which in most cases are laws). And this only partial independence (and thus not complete independence) causes the higher categories not to be absolutely fundamental. The only categories that are truly fundamental are those of the lowest layer, namely the mathematical. So insofar as absolute fundamental categories are concerned, the whole layered system of the World is ontologically homogeneous, as found out earlier.
But the higher layers can nevertheless not be fully understood when we only consider the lowest -- and absolutely fundamental -- categories, because the lower layer, as it is in itself, is always  o p e n  with respect to the presence (at all) and to the content of some possible higher layer that can appear on top of it. That is because of the  i n d i f f e r e n c e  of the lower layers and their categories as to the specific content of the higher layers that can come next and which are then being carried by them.
The higher categories, say higher forms of concretum--concretum determination, cannot in any way act against the lower categories, but only with them, i.e. having them for themselves (to 'exploit' or harness them), they can assume whatever quality that fits into the available play of lower categories. But despite this autonomy of their's they remain in a certain dependence upon the lower. They are thus 'free' within their dependence ( HARTMANN, Der Aufbau der realen Welt, p. 548 ).

An instructive example is the  o v e r - f o r m a t i o n  (not trans-formation) of the  c a u s a l   n e x u s,  i.e. the repeatable connection between states (of dynamical systems). The causal nexus as such is not a whole series of states, but just the generation of one state (effect) out of another (cause). In itself the causal nexus is not directed to predetermined end states :  If the cause changes, for example when it is perturbed, a different effect will ensue, while the original effect will not take place. So causality does not lack direction, but lacks direction to a specific target. This indifference of the causal nexus as to the final result makes it susceptible to be harnessed, i.e. to be over-formed, which means that a definite influence can be applied to the cause resulting in a corresponding effect, i.e. a definite specific target.
In an organism we have causality, and this causality, in itself -- as we saw -- not being directed to a specific end result, is susceptible to noise (perturbations) coming from outside the organism. The latter, however, blocks this noise and posits its own causal factors, resulting in a specific outcome. In this way a specific structure- (or behavior-) generating law appears, which is, however, fully compatible with causality. The latter is just over-formed (not trans-formed). Of course here the ability of the organism to discriminate between factors that are relevant to it or irrelevant or even noxious, is already presupposed. But this ability can initially be in a very primitive state, i.e. just a physical function, and not yet (requiring) an organic function. In a later stage of organic constitution this ability will become more subtle and effective. It is best to assume that both phenomena (over-forming of causality, and the mentioned ability of discriminating between the self and the not-self) go hand in hand, and represent in fact one and the same event of jumpy complexification.
In this way we get systems in which the elements seem to 'cooperate' in such a way that causality is, in a sense, masked, and that a specific goal is being realized by the dynamics of such systems. Such goal-oriented directiveness (as if teleology came into play), although compatible with all physical laws (Again, the laws how they really are in themselves, not insofar as we suppose to know them), is irrelevant to physics, but relevant to biology.
What is needed is a comprehensive theory of organization, a theory that investigates and explains emerging structures and laws, already apparent in the crystallization process and in some other inorganic dynamical systems, and that goes all the way up to investigate the staggering organizational processes that take place in living beings.
The recent dynamical systems approach has entered this line of research, but is still a long way from explaining fully even the crystallization process, let alone those of organisms. And, the investigations of Nicolai HARTMANN (in the 1930's and 1940's), which are conducted at a very fundamental and general level, already are, despite the mentioned inherent difficulties, very providential in this respect and should be studied by at least all philosophically minded biologists and physicists who want to place their subject into a broader context. And, above all, it should be studied by philosophers, which has -- as far as my knowledge goes -- hardly taken place.

Let's now return to our main concern with respect to HARTMANN's ontological layers (which we will interpret -- for the time being -- as complexity levels), namely the vexed problem of the NOVUM (i.e. the "new"). We again try to illustrate it -- but now in some more detail -- in the case of the  o r g a n i c,  in which we do not present a reconstruction of its actual origin but of its constitution. Some aspects of the foregoing discussion will be more or less repeated, while others are added.
In the physical layer the mode of determination is causality [where "determination" does not mean a category--concretum determination, but a concretum--concretum determination (in the present case standing under the category of causality) ]. In the complexification that will eventually lead to the organic layer to emerge, complex molecules will be formed by the above described harnessing (over-formation) of causality, and the physical laws based on it. These molecules encode blueprints for the synthesis of proteins, in definite amounts and temporal order. These proteins assist in the realization of biochemical reaction chains, etc. By means of feedback loops the whole system is then controlled. All this results in the fact that the organism grows and maintains itself (under import of matter and energy and export of matter and entropy) according to certain intrinsic rules that are only relevant (i.e. geared to) large organic units that play the role of system elements and that interact according to these rules, which are consequently high-level rules or laws, only as such appearing at high structural levels, and not present at lower levels. And such a rule is not just the result of a simple summation of lower level rules, they are of a different nature all together, i.e. their qualitative content is different.
High-level rules can also be observed in inorganic systems, but in organisms they imply dynamical (sub)systems [A rule implies a dynamical system, because a rule or law of such a system is, in a dispersed fashion, immanent in the elements of the system.] that show a resistance against perturbations, i.e. those systems are not allowed to be fed by alien elements. As has been said, this can initially be just some purely physical function, but should further be sophisticated, hand in hand with the origin of the higher-level rules themselves, into the ability to discriminate between Self and not-Self (which is, by the way, the essence of Life). And in this way there is just a selected set of causal factors admitted, while others are neutralized. And only in this way we have a self-contained set of rules (and with it a self-contained dynamical system) that connect certain specific high-level states to subsequent states and, finally, to certain special high-level end states. Organisms are therefore called  autopoietic systems,  i.e. systems that 'produce themselves' (that do themselves, in contrast to them being done [by something else] ). Such self-contained sets of high-level rules (or laws) and the corresponding dynamical systems do not occur in the inorganic world, where dynamical systems can and will accept in principle any alien factor coming in its way. Under circumstances such factors can be damped by such an inorganic system, it is true, but when the system is unstable it will alter its course in virtue of such an incoming factor. Such inorganic systems are, because of this, in many cases not precisely repeatable in the 'wild'. One of the exceptions are presented by the formation of crystals, which, however, involve relatively simple equilibrium systems.
So the above discussed (strongly) self-contained high-level dynamical laws, though not occurring in the inorganic world, are completely compatible with causality and with the fundamental physical laws based on it :  When we examine the  e l e m e n t a r y  state transitions (of which the high-level state transitions are composed of), we will see that they represent each for themselves purely causal connections. The NOVUM thus consists of the fact that these elementary causal connections stem from a highly selective, i.e. choosy environment (within the system itself), resulting in the organization of particular causal connections, in turn resulting in a particular and stable succession of complex high-level states, leading to some specific end state or cycle.

With all this we have, in a crude and more or less vague way, described the  o v e r - f o r m i n g  (not trans-forming) or  h a r n e s s i n g  of causality. The latter is, as it were, the 'matter' for the former, which then is its 'form'. And so, with the presence of such high-level laws -- which, taken all by themselves, represent a qualitatively different type of NEXUS, different from that of causality -- pure causality still exists at the lower level, while at the higher level it is over-formed. And, as has been said, in the same way physical laws presupposing causality, can be over-formed. And because the resulting law is of a different type (namely a different type of nexus, and, moreover, self-contained and high-level), we call it  a  n e w   c a t e g o r y  (i.e. a new determinant in HARTMANN's sense), a  c a t e g o r i c a l   n o v u m,  as such responsible for the appearance of the organic layer -- which has taken up many categories from the inorganic layer, but more or less being modified by the novum -- on top of the inorganic (physical) layer.

One must realize that the "organic layer" does not as such consist of individual organisms :  In each individual organism (including humans) we find both layers, the inorganic and the organic. And in some higher organisms yet another layer appears in addition to these two.

And, as is clear from the above, the appearance (emergence) of the NOVUM, and with it of the new layer, is accomplished by a leap-like increase in functional complexity of physical matter ( This increase of complexity follows a very long and highly entangled path compressed into a very small 'reaction-container').
The foregoing complicated and more or less unclear discussion that tries to explain the phenomenon of over-forming, is no more than an attempt to get rid of the awkward notion of the NOVUM as something not being produced somehow but coming out of the blue.

About the  h a r n e s s i n g  or over-forming of existing physical laws, see also DAVIES, 1989,  The Cosmic Blueprint,  p. 143 and p. 149.

So in the foregoing we have 'explained' the appearance of the NOVUM, namely as the result of over-forming. HARTMANN, however, postulates the appearance of the NOVUM as something totally new without antecedents. And this NOVUM is responsible for the modification of many categories of the lower layer reappearing in the next higher layer, i.e. is responsible for their over-forming.
Maybe this is true, and we keep it in mind (i.e. we accept it for the time being). But it implies the NOVUM coming out of the blue, which assumption causes the theory to come close to those that assume some non-physical directive that is responsible for the organization of many -- in themselves -- physico-chemical units into functional high-level 'routines' as we find them in organisms. But, as hinted at already, maybe we should try to assimulate with the idea of the appearance of something totally new, of a totally new principle or set of principles.

Turning our attention for a while to the  m a t h e m a t i c a l  non-physicalized  l a y e r,  we see something similar to harnessing. For example, we begin with considering a most primitive starting point, the topological space. This is a collection of points endowed with only very basic properties such as connectedness and dimensionality. Such a space can be seen to be gradually enriched with new properties, eventually resulting in a metric space, where the concepts of distance and angle have full meaning. So we have then ascended from the primitive topological level to the higher level represented by metric space. The latter is not reducible to topological space, because new features have appeared in metric space, but it is fully compatible to the former. We have witnessed a (modest but genuine) increase in complexity with respect to mathematical entities. If we now deduce the relevant theorems, then we make explicit the complete content of the newly added features.
Something similar can be done with primitive arithmetic.

We should understand that the higher-level laws, as they occur in biology, must have been in some way actually  o r i g i n a t e d  from lower-level physical laws (in the way tentatively described). But because the latter offer play for several different possible high-level laws, the particular high-level law, that had actually originated from a lower-level law, is not as such deducible from the latter (as is claimed). But of course if we take the originating process, that actually happened -- and that has lead to these higher-level laws -- into account, which in fact means, that if we take the whole Sphere of Being into account, then it is more difficult to claim the mentioned irreducibility (in an ontological sense, not concerning our ability to actually derive). So we have to be careful in this respect. We should come to know what exactly happens during a 'complexification leap' creating a new and higher layer of existence.

We have differentiated Reality into a series of Layers. If we ascend from the most fundamental layer up to successively less fundamental layers, we see an increase in wealth of content. In this sense we can speak of 'lower' (less content) and 'higher' (much content) layers. The Mathematical Layer is the lowest Layer of Being, then comes the Physical s.str., i.e. the Inorganic, Layer, then the Organic Layer, then the Psychic Layer, and finally, the Super-psychic Layer. Their respective (determining) principles or categories are (1) original categories (called so, there, where in the stack of Layers, they appear for the first time), further, more or less modified categories (called so where they reappear in another Layer), and finally a categorical NOVUM specifically belonging to a given Layer, determining the latter's specific nature.
Loosely we can speak, in addition to  "higher and lower Layers",  of  "higher and lower categories",  expressing whether they belong to higher or lower Layers. And most generally we can speak of  "the higher" and  "the lower",  while this still refers to the wealth or degree of content.

In Part XXIX Sequel-4 of the present Series of documents we discussed these Layers of Being, and (as a hypothesis) integrated them with the theory of the Implicate Order (originated by David BOHM) and also with the theory of Holistic Simplification (originated by MEYER-ABICH). As such it was summarized in the following diagram :

All such theories are concerned with the 'higher' and the 'lower', and their interrelations, especially whether the one originates from the other, and if so, in what order.

The lower is indifferent as to it giving rise to the higher. So in whatever a given Layer, there is no tendency whatsoever to give rise to one or another higher Layer (on top of it, where  "on top"  expresses the substrate function of the (lower) Layer). So there exists no preformation whatsoever (if we exclude from our discussion the hypothetical existence of an Implicate Order, in which holistic symplification takes place). If this is correct, then the appearance of a higher Layer must involve something entirely new, i.e. a categorical NOVUM.
Of course we could say that although the lower (for example the inorganic) does not, it is true, in any way have  a  tendency  to give rise to the higher (for example the organic), it does possess the  ability or potential  to do so. But this is preformation all the same, which destroys the lower Layer's indifference as assumed above. This indifference is manifested in the relatively rare occurrence of Life in the Universe (as far as we can tell), and on the Earth itself for that matter  ( There life only occurs in its peripheral parts).
Totally in itself then, that is to say, wholly due to itself or wholly of its own, the lower Layer does not possess the ability to let it be over-formed (let alone over-build) by a higher Layer. Or, in other words, the lower Layer cannot, all by itself, create a higher Layer. For this over-forming (and as such creation) a NOVUM is needed.

There are two more arguments in favor of the appearance (and of the possibility at all) of a true NOVUM in the Organic Layer :

The first runs as follows :
If our conjecture, that holds that the Inorganic Layer is not the lowest Layer, but lies on top of a purely mathematical substrate, which then can be called the Mathematical Layer, is correct, then we are sure that the Inorganic Layer, i.e. the Physical Layer in the strict sense, contains among its principles a genuine NOVUM. This is evident from the fact that the  ' material ',  the spatial and the temporal aspects, as we find them as typical for the Inorganic Layer (and the next Layer), is in no way whatsoever anticipated in the Mathematical Layer. So the possible existence of a NOVUM at all, cannot be denied beforehand, that is to say it is not a priori impossible that a NOVUM is present in the Organic Layer, letting it fundamentally differ from the Inorganic Layer (meaning that it is not wholly reducible to the latter), because the appearance of a NOVUM had already occurred 'earlier' (i.e. at another occasion), namely at the transition from the Mathematical to the Physical or Inorganic layer.

A second argument in favor of the possibility of a true NOVUM could be found implied in the theory of the origin of the physical Universe :  At least its temporal aspect 'came' from something absolutely atemporal.

So it is not too speculative to accept HARTMNANN's categorical NOVUM, marking the presence of a new Layer of Being. This NOVUM is neither a force, nor a non-physical force, but a (new)  p r i n c i p l e  or (new) set of principles, that is to say a new category or new set of categories.

While in the  Substance-Accident metaphysics  (as was done in First Part of Website )  the intrinsic beings (like individual crystals or individual organisms) are central, and in  Natural Science  beings (not necessarily intrinsic), phenomena, processes, and in particular the generative relations between them, are central,  in the  Ontology of Layers the  If / Then constants  (categories) are central  (Intrinsic beings, unqualified beings, processes and generative relations are positively involved in this ontology, but are not central). In this way totally disparate beings could be (seen as) connected with each other by together constituting the If-component of an entitative constant (We return to this topic further below).

Categories  ( If / Then constants)  are rational structures in the sense of ontologically sufficient grounds. They are not concepts (although they are expressed [by us] in the form of concepts and other logical elements). As has been said, the comparison of ontological layers, say the Physical s.str. (i.e. Inorganic) Layer and the Organic Layer, takes place by comparing their respective principles (categories,  If / Then constants). Often the higher layer can be seen to contain categories of the next lower layer but in an over-formed condition (Sometimes even in an over-built condition, which we shall not deal with here because this does not occur if we go from inorganic to organic [which is the main topic of the present document] ).  An original category and the corresponding category that is an over-forming of it have (only) some rational kernel in common (i.e. the content of their kernel is identical). In fact the original category consists of this kernel only, while the derived category contains something in addition to it. So the latter category is a modification of the former. And such a modification is brought about by the NOVUM of the higher layer, i.e. of the layer where the category reappears,  reappears, it is true, but in a modified form. So the category and its modification belong to different Layers of Being.
It is not necessarily so (but could sometimes be the case), that a modified category (that is to say an over-formed category, or a category that is the result of over-forming) determines something (to be so and so) that has actually evolved from something that is determined by the corresponding non-modified category. For example :

Things, determined by original categories, and (other things) by corresponding modified categories, thus do not necessarily relate to each other 'genetically'. These things relate according to some  c o n t e n t  they possess, and the categories themselves (the original and the modified) relate to each other by their common kernel. The NOMOS is not a process-world (and does not necessarily and exclusively result in 'genetic' relations), but a non-spatial and timeless world of determining constants, and as such representing the rational structure of the COSMOS, or, in other words :  while the COSMOS is, at least in its lower material layers, spatial and temporal, and thus extensive, the NOMOS is non-spatial and non-temporal, and thus intensive  (Realize that the Category of Space is not itself spatial, and that the Category of Time is not itself temporal).
In the psychic domain (the Psychic Layer of Being) things are also intensive  ( They are extensive only in Time). Perhaps this points to some kinship between the world of determining constants (NOMOS) and the world of thoughts. In both cases their 'substance' is noetic  ( ' think-stuff ',  as contrasted with spatial stuff or physical matter).

We will now, in a preliminary way, compare the Inorganic Layer with the Organic as to their categorial contents. All this to prepare for more detailed discussions later on, and to see the significance of the crystal analogy.

The categories determining atoms, molecules (as to what they are), and all the laws (which are also categories) that determine their possible interactions,  categories that is to say, that first of all belong to the Inorganic Layer,  are retained (i.e. reappear) in the Organic Layer. They apply in organisms as regards their individual internal processes which constitute their being alife. But the special structure of these internal processes, the selection and filtering of initial conditions (of the corresponding dynamical subsystems), the equilibrium of these processes, and especially, their combination and their fine-tuning with respect to each other, do not stem from those physico-chemical laws. They represent high-level structures, or holistic organization. These higher-level processes do, however, not violate the physico-chemical laws (i.e. the laws that govern things in the Inorganic Layer), which is a clear sign that the Inorganic layer is a necessary  substrate  for the Organic Layer. So, to take an example, the organism's motion in space is subject to gravity, inertia and physical energy. This depending on, and complying with, the laws of the Inorganic Layer, is also evident in all phenomena of chemotaxis and the like. But the purposive function (as a result of the harnessing of these physico-chemical processes) of the organs, and the behavior as we see it in organisms, are a purely  organic  matter (HARTMANN, Der Aufbau der realen Welt, 1940, p.542). The being organized of physical and chemical processes -- their being harnessed -- or, in other words, their being over-formed (or over-built), is determined by new categorical elements, which stand under the general NOVUM.

A category (If / Then constant) has a certain  range of relevance . So we can say that, for instance, at least the whole Inorganic Layer is the range of relevance of the category of Causality. In this case the category (causality) is realized (that is to say, is a controlling factor) everywhere in the Layer, which means that, if it were limited to this Layer, it would be a mark or identifying feature of that Layer. Certain other categories, however, although having the same range of relevance, are not necessarily realized -- i.e. do not necessarily determine things -- everywhere  in this range. For instance for the category of D3 symmetry (which can be exemplified by a regular three-fold pyramid) the range of relevance is also at least the whole Inorganic Layer, but it is not actually (and therefore not necessarily) realized (i.e. determining something)  everywhere  in this Layer (as is evident from the fact that not everything in this Layer necessarily possesses this symmetry). Indeed, this is the mark or fingerprint of the Special Categories (at least the very special categories), that is to say categories that are first of all not relevant and active in the whole set of Layers (i.e. they do not determine in every Layer), but also not so with respect to just some of these Layers or to one such (whole) Layer.

There are certain categories that play an important role in the crystal analogy. To mention but a few :  Lattice (s.l.), Growth and Regeneration.
Of each of them we can indicate (but do that succinctly) their modification as they pass from one Layer to another :

As for Lattice :

As for Growth :

It is perhaps instructive to dwell a little longer on the important phenomenon of  growth  and add a discussion about  regeneration  which is closely connected to growth, and is, like growth, in addition to being observed in organisms also observed in crystals.

A process (taken generally) is a regular sequence of states. It is determined by a special nexus category (which is a particular dynamical law, and itself is based on the causality nexus Cause ==> Effect).
Growth is a (special) process (an activity of an intrinsic being), and as such, that is to say, as a process, determined by its corresponding nexus category. The latter is an aspect of the dynamical law that generates and maintains the given intrinsic being. But growth is not just the necessary succession of system states :  it is a process that results in a steady and regular increase in volume of some intrinsic being while its specific structure is preserved. It can be interrupted (as in Amphibians) and terminated (as in Insects) by metamorphosis. So growth is only that part of the dynamic trajectory where a steady increase in volume takes place. Accordingly the whatness category or If / Then constant determining the content (or the being-so-and-so) of Growth (or of Growing) reads :

Category of Growth  (whatness category)

If an intrinsic object (organic or inorganic), while being generated or dynamically maintained, is presently passing through a series of states in which its volume steadily and regularly increases, while its specific intrinsic structure is preserved thereby, then  the object  g r o w s .

Growth will ensue when certain conditions are satisfied. These conditions differ strongly from object to object (i.e. from being to being).

The ability to grow is a  property  of certain (classes of) intrinsic beings. A being has this ability, when, finding itself in certain states and (appropriate) external circumstances, it will necessarily grow. Let us call such a being G.  We can now state the corresponding entitative If / Then constant as follows :

Category of Intrinsic Ability to Grow  (entitative category)

If we have a being G (must be specified) that is such that it will necessarily grow when finding itself in certain specified states and in specified external circumstances, then  the  a b i l i t y   t o   g  r o w   i s   p r e s e n t  in this being (i.e. it has this ability as one of its properties).

The If-component consists in fact of the disjunctive set of all beings that are such that, when finding themselves in the mentioned conditions, will necessarily grow.

Regeneration (of parts)
The whatness If / Then constant determining the content of the phenomenon of regeneration (inorganic or organic) reads as follows :

Category of Regeneration  (whatness category)

If in a given intrinsic being or thing there is a local (with respect to some site of that thing) growth process going on, such that a part of that intrinsic being, which should already be present were the dynamical succession of states of that thing  (and as such representing the states of the corresponding dynamical system [generating or maintaining that thing] )  not have been altered by extrinsic agents (perturbations), but which is, because of such agents, still absent or lost,  is being recovered under full preservation of the specific intrinsic structure of that thing,  then  there is  r e g e n e r a t i o n  taking place in that intrinsic being or thing.

There are many conditions (internal and external circumstances) that must be satisfied for regeneration to ensue, and the pattern of such conditions depends on the type of intrinsic being. Regeneration, although being local growth (or locally speeded-up growth), does not necessarily increase the overall volume of the given intrinsic being.
The ability to regenerate, which is, as stated, dependent on certain conditions and type of intrinsic being, is  a  p r o p e r t y  of certain (classes of) intrinsic being. It could be limited to certain developmental stages or to certain parts of such a being. The corresponding entitative If / Then constant can be formulated as follows :

Category of Intrinsic Ability to Regenerate  (entitative category)

If an intrinsic being R is present that is such as to regenerate missing or lost parts as soon as it finds itself under certain specified conditions,  then  it has the  a b i l i t y  o f  r e g e n e r a t  i o n.

Rational connection of things by categories

Growth and regeneration (but also a multitude of other phenomena, in fact all phenomena, insofar as they are objective), when expressed as If / Then constants, especially as entitative, material and whatness categories, are in themselves rational structures, or contents, that can be, and indeed are, realized in many intrinsic beings or materials. The totality of the constants, including nexus categories, constitute the NOMOS, and in the COSMOS they connect things (i.e. beings -- and beings do not exist in the NOMOS), not necessarily genetically, but with respect to content (rational content, qualitative content). They are constitutive constants  ( There are constants that are not about content, but about 'strength of existence', for example some one being could exist either potentially, or actually or necessarily. This concerns categories of modality.).
Considering constitutive constants is to place pure qualitative content in the center of the exposition. And when considering the categorical make-up of several distinct Layers of Being, for instance the Inorganic and the Organic, we compare them not genetically, but with respect to their qualitative or rational content, and also not with respect to the different things or processes those Layers embrace, but to their ensemble of (basic) principles, that is to say we look first of all to the latter as they are in themselves, and only then insofar as they result in different things and processes.
In this way, for example, an Aurelia (which is a common medusa) is connected with a crystal of the mineral Diaboleite  ( Pb2 Cu (OH)4 Cl2 ),  because the structure of both involves  4mm  symmetry (which can be represented by a quadratic pyramid), while apart from this these two beings have nothing whatsoever to do with each other, that is to say they are not in any way genetically connected. They both imply 4mm symmetry, but obviously in virtue of totally different generating processes (but maybe with some small identical kernel). The one being has not aquired its symmetry from the other.
The If / Then constant that connects them is the entitative constant of intrinsic 4mm symmetry (where 4mm can grouptheoretically be denoted as D4 ).  It reads :

Category of Intrinsic D4 symmetry  (entitative category)

If we have an Aurelia then  intrinsic D4 symmetry will be present in it (i.e. this symmetry is necessarily implied by it as one of its intrinsic properties).

It can also read :

If we have a crystal of Diaboleite then  intrinsic D4 symmetry will be present in it (i.e. this symmetry is necessarily implied by it as one of its intrinsic properties).

In addition to an Aurelia individual and a Diaboleite crystal, there can be many more intrinsic things (specifically different from the latter) that also necessarily imply the property of D4 symmetry. In fact the total  disjunctive  set of all such intrinsic beings forms the If-component of the category. If we call this set T, then the category reads :

If we have T (i.e. if whatever element of this set exists),  then  intrinsic D4 symmetry will be present.

So all these (often disparate) objects that are (by definition) elements of this set T, and consequently also our Aurelia and our Diaboleite crystal, are connected by this entitative constant.
The complete  concretum  (i.e. that which is determined by the category) of this category is the conjunctive set (i.e. A and B and C and D and .  .  .  ) of all beings (A, B, C, D, .  .  .  ) having this symmetry, beings that actually exist (not 'exist' as :  If . . . exists). More strictly the concretum is :

object-intrinsic D4 symmetry.

The category presupposes the pre-existence of a certain intrinsic object, and also the analysed whatness of Ditetragonal-Pyramidal symmetry. This analysed whatness is the group table for the symmetry group D4 ,  which determines what Ditetragonal-Pyramidal symmetry (the unanalysed whatness) in itself is.
The connection of an Aurelia and a crystal of Diaboleite by the entitative constant of intrinsic D4 symmetry is symbolized in the next Figure.

Figure above :  Diagram depicting the connection of an Aurelia and a crystal of Diaboleite by the entitative constant of intrinsic D4 symmetry. The Aurelia and the crystal of Diaboleite are but two intrinsic beings, out of the whole set of beings, implying (as indicated by the arrows) D4 symmetry.

Connection of things (beings) is also accomplished by nexus categories (and the underlying category of Causality) :  Two or more things are connected in Time in the form of a succession of states, where each state is a here-and-now being. And precisely such a connection is determined by a nexus category.
On the other hand, whatness categories do not connect things :  they only make it possible for our investigating reason to collect them into concepts or classes. Ontologically a whatness category connects a being or property with itself, and thus forms a loop.

Most whatness categories pertaining to intrinsic beings (i.e. determining what a given intrinsic being is in itself) do not spill over (i.e. reappear) into the next higher Layer of Being. Such a whatness category is a dynamical law of a particular totality-generating dynamical system. And when such a particular system is found, say, in the Inorganic Layer, it is not expected to be encountered again in the Organic layer. But if the whatness category, concerning intrinsic beings as to what they are, is more general, then we can expect it to reappear in the next higher Layer after a certain degree of generality is attained. For example something to be a 'dissipative dynamical system' is at home in the Inorganic layer, but reappears in the Organic Layer.
Whatness categories of  properties,  on the other hand, are expected often to reappear in the next higher Layer, either modified thereby or not, for example  D6 symmetry  and (as a second example)  ability to regenerate  are at home in the Inorganic Layer, but spill over into the Organic layer, where the former reappears unmodified, while the latter becomes modified.
Modification of reappearing categories, is the sign of crossing the boundary between two Layers of Being.

Categorical Laws

In Der Aufbau der realen Welt, 1940, p.412, HARTMANN presents his Categorical Laws, that is to say he discusses the fundamental relations either (1) between categories of the same Layer of Being, or (2) between those that govern all the Layers above the Mathematical (All the non-mathematical Layers -- i.e. all Layers involving Time -- together form the "reale Welt" of HARTMANN as contrasted with his "ideale Welt" which is atemporal and is very close to the Mathematical Layer as accepted and characterized on the present Website), i.e. (relations) between the  Fundamental Categories,  or (3) (relations) between categories that reappear in a next higher Layer, or (4) between category and concretum (i.e. between the determining and the determined). So of all the categories HARTMANN only considers the Fundamental (appearing in all temporal Layers) and General Categories (determining everywhere in one given Layer). (As far as I know he didn't consider special categories (in our sense of the term) at all. What we have called "general categories" he calls "special categories ).  So his  categorical laws  only involve Fundamental and General categories. Indeed, to expound the system of Layers, their distinguishing marks and the relationships between them, only those (fundamental and general) categories are needed. By investigating te categorical laws he is able to characterize those categories more fully, because according to several such laws the content of a fundamental category is co-determined by that of all the other fundamental categories, while that of a general category by all other general categories of its Layer.
The Special Categories, viz., special whatness categories, special entitative categories, special material categories (material constants) and special nexus categories (all of them -- as has been said -- not considered by HARTMANN), generally do not follow these laws, because of their specific (in contrast to general) nature.
We will list and explain HARTMANN's Categorical Laws, which -- as has been said -- are about the Fundamental and General (constitutive) categories, and will add the appropriate considerations concerning the Special Categories. We will further discuss all categories in the form of  If / Then constants  (initiated by WOLTERECK, 1932, not done so by HARTMANN).

Summary of Categorical Laws

There are four groups of categorical laws :

  1. Laws of Applicability

  2. Laws of Categorical Coherence

  3. Laws of Categorical Stratigraphy

  4. Laws of Categorical Dependency

The first group consists of four laws (which are summarized in the General Principle of Applicability).  These four laws are named :

The second group consists of five laws (which are summarized in the General Principle of (horizontal intercategorical) Coherence).  These five laws are named :

The third group consists of four laws (which are summarized in the General Principle of Stratigraphy (Layering) ).  These four laws are named :

The fourth group, finally, consists of four laws (which are summarized in the General Principle of Dependency).  These four laws are named :

We will now discuss the categorical laws of each of these groups, and see how they constitute the ontological layering. We also discuss how the Special Categories behave with respect to these laws, and see all categories (fundamental, general and special) as having the structure of an  If / Then constant.

Laws of Applicability
  ( HARTMANN, Ibid. p.412)

The common principle of these laws is

The General Principle of Applicability :

Categories are what they are only as being determining principles of something, where the latter is called their concretum.  They are nothing without their concretum, and the concretum is nothing without them.

This General Principle of Applicability can be analyzed into four laws, which will now be dealt with one by one.

The Law of Principle

The beingness of a category consists in its being-a-principle. Something being a principle (i.e. a determining principle) of something (else) means nothing else than that it determines unequivocally certain or all features of this (latter) something, that is to say that it  a p p l i e s  to it (where the latter "it" refers to precisely that feature that is actually determined by the category, and which is its concretum).

When we have some intrinsic being (say a given organism or crystal), we can say that it is determined by several different principles or categories, each determining some feature of this being. But we can also say that this intrinsic being is determined by one 'master' category which then implies the applying of many other categories. But however this may be, the category has no other beingness or existence apart from its being-a-principle-'for'-its-concretum. This is evident from the intrinsic general structure of a category, namely its  If / Then  structure. The category contains already its concretum because the latter is contained in the Then-component (while the If-component represents the sufficient ground for the When-component, therby together making up the category).
Of course all this is valid for all sorts of categories :  Fundamental Categories, General Categories, Special Categories, Whatness Categories, Entitative Categories, Material categories, and Nexus Categories.
The category determines its concretum. So in a way, the category is independent from its concretum. But this doesn't mean that its existence, beingness or its essence is independent of its concretum. So category (principle) and concretum form, what can be called, a Strange Loop. They involve each other. And thus there is no separate world of categories or principles, that (moreover) enjoy some higher-order beingness.
The relation between a category and its concretum is an  non-causal  determination :

In the laws to come we must discriminate between the  Range of Applicability  of a category, and its  Range of Relevance.

The Law of Layer-applicability

The determination, issuing from a category, is, within its Range of Applicability, i.e. within the limits of its actual applicability, absolutely binding upon its concretum, that is to say it does not, in any way whatsoever, leave room for exceptions. No power, outside or next to it, can neutralize this determination.

The General Categories of a given Layer control (always together with the Fundamental Categories) all beings, materials, processes, etc. that belong to that Layer. In this does consist their Layer-applicability.
A special category on the other hand, controls one or more entities (beings, materials, etc.) within its range of relevance, while many other entities within this same range are not controlled by it, but are controlled by other special categories.

The Law of Layer-bound Applicability

The absolute applicability of a category exists only with respect to concreta of the Layer to which that category belongs. Beyond this Layer this applicability -- if existing there at all -- can only be a limited and modified one.

This law does not apply to many a  special  category :  For instance the (special) category of  intrinsic D1 symmetry (bilateral symmetry) does, without it being a Fundamental category, apply (to some entities) in the Inorganic layer (for example to crystals of the mineral Hilgardite (Ca2 Cl B5 O8 (OH)2 ) (HURLBUT & KLEIN, Manual of Mineralogy, 1977, p.64), but it does also apply in the Organic Layer (for example to Vertebrate animals, Insects, etc.), without being modified :  because, first of all. whether a given symmetry is implied by an  inorganic  (intrinsic) being or by an  organic  (intrinsic) being, it is the same symmetry. So in any way the whatness category of D1 symmetry is not being modified when crossing the boundary between two Layers. Secondly, as an  entitative  category, i.e. as a category of intrinsic D1 symmetry (i.e. in contrast to a category determining the  whatness  of something), the (D1) symmetry is an implied symmetry (implied explicitly by some intrinsic being, or implicitly by some material), and whatever the way in which this implication is brought about, its being implied is always in precisely the same sense, namely that this symmetry is part of the Essence or overall whatness of the object. So not only as whatness category, but also as  entitative  category it is not modified by crossing the boundary from the Inorganic to the Organic Layer.
But  general  categories are being modified if they appear at all in the next Layer of Being. And if we 'apply' such a modified category, or (what is worse) a totally new general category, to the Layer below (or above) its appropriate Layer, then we are 'guilty' of letting apply categories to the wrong concreta, as we see it happening when applying, say, strictly Inorganic categories to the Organic (when explaining the Organic wholly in terms of the Inorganic ( = the doctrine of Mechanism)), or when applying, say, strictly Organic, or strictly Psychic, categories to the Inorganic (when explaining the Inorganic by (i.e. in terms of) the Organic (radical Organicism), or respectively by the Psychic (Psychologism)).

The Law of Layer-determination

Of a given concretum all its general features -- which here means all features that are commonly possessed by all entities of the Layer to which that given concretum belongs -- are absolutely determined by the categories of that Layer. So in its generality every entity of that Layer is  c o m p l e t e l y  determined by the categories of that Layer. The concretum belonging to a certain Layer is thus categorically saturated and has no need for other general (in the sense defined above) determination.

Strictly speaking, a  concretum  of a category is precisely that (and no more) what is actually determined by that category. In the above statement of the Law of Layer-determination the term "concretum" is used in the sense of a collective concretum, i.e. some actually existing entity that is determined by a multitude of different categories.

But although any entity ((collective) concretum) of a given Layer is categorically saturated (completely determined), it is as such not yet completely determined in an absolute sense, because special features, determined by special categories -- special all the way down to individuality -- must be, and indeed are, added to its general features.
The  concretum  of a nexus category is a nexus ( = connection) between different beings through the time dimension. The nexus category determines the  kind  of nexus. This nexus itself is in turn also a determination, but not a categorical determination (i.e. not  a  principle-concretum  determination), but  a  concretum-concretum  determination. The category determining the specific kind of concretum-concretum connection is in fact a whatness category, because it determines what this connection is. And because it is about a connection we call it a nexus category.
The general nexus category, namely causation, belongs to the Inorganic Layer (as one of its general categories), and every entity in that Layer is co-determined by causality, i.e. for every entity in that Layer causality is in some way involved with respect to its determination. So the category of causality belongs to the ensemble of General Categories of every entity in that Layer.
Special nexus categories, on the other hand, for example special dynamical laws, do not enter the ensemble of categories of  every  entity of that Layer, but do only enter that of some entities of that Layer, where such an entity (i.e. the category's concretum) is a specific connection in time of several beings or (system) states.

Laws of Categorical Coherence
  ( HARTMANN, Ibid. p.432)

Only the Fundamental and General Categories, that is to say only the categories that either do apply to all entities of all Layers, or to all entities of one and the same whole Layer, are subject to the Laws of Categorical Coherence.
The mentioned categories of a given Layer are connected with each other. The type of this connectedness is a specific one. It will, in what comes next, as distinguished from other types of connections, be called  categorical coherence.  It lies at the base of a certain regularity (lawfulness), that essentially reappears in all Layers, with only little modification. As has been said, in addition to the General Categories of a given layer, also the Fundamental categories show the same type of mutual connectedness. The laws of this connectedness are therefore general and can be uniformly grasped in all the levels represented by the Layers. They represent as laws of coherence the second group of categorical laws.
Because the relation of the categories of one and the same Layer exclusively is about the categorical diversity of one and the same 'hight of beingness', the play of the laws of coherence only spans within the 'horizontal' dimension of the system of categories. Therefore this play has still nothing to do with the stacking relations (stratigraphy) of the (four) Layers of Being, and can only mediately influence the latter relations. But this influencing already acts in the 'vertical' dimension, which is governed by another regularity or lawfulness. So here we shall not refer to it.
As compared with the Laws of Applicability (considered above) the Laws of Categorical Coherence are something totally different. They do not in any way involve the relation to the concretum :  They presuppose it already. They cannot, therefore, follow from just the essence of being-a-principle. They are laws concerning the connectedness of categories with respect to their intrinsic content. They are bound up with the intercategorical relations, and can only be grasped as a result of the latter's qualitative exposition.

The common principle of these laws is

The General Principle of (horizontal intercategorical) Coherence :

General categories do not exist individually for themselves, but only within the framework of the given categorical Layer (which itself is the collective general principle of the corresponding Layer of Being which is the categorical layer's collective concretum). They are bound by that framework and co-determined by it.

This General Principle of Coherence (of General and Fundamental categories) can be analysed into five laws, which will be discussed one by one.

The Law of Categorical Connectedness or Union

The general categories of a given Layer of Being do not determine their concretum (i.e. their collective concretum or concrete being) in an isolated fashion, that is to say they do not each for themselves and independently of the other categories (also determining that same concretum) determine their collective concretum, but do it together in unison. Together they constitute a unit of determination, in which, it is true, the several categories dominate or recede differently, but in which they cannot determine independently.

All general features of a given concrete being are determined by the Fundamental categories and by the general categories of the Layer to which the concretum belongs.

One should understand that  a  c o n c r e t u m,  as the term is used here, is not necessarily an individual (actually existing) being or thing, like a crystal or an organism. It is just that particular being-so-and-so that is as such determined by the corresponding category.

A genuine being, which as such is a concrete being, like a crystal or an organism, generally is  a  c o l l e c t i v e  concretum with respect to a great many different determining categories, where each category determines one of this being's different features (which feature is then -- when taken generally [i.e. over all possible cases] -- the  concretum  of such an individual category), but does so in harmony with the other determining categories of that being. An intrinsic being possesses an Essence, which is the dynamical law of the dynamical system that has generated that being, and which at the same time is the whatness category of that being, determining what that being is all by itself. The actual dynamical development of this being, that is to say the generation of it from the materialized dynamical law (which materialization is equivalent to an initial condition of the dynamical system) involves still many more different categories. So a genuine being is determined, not by one category only, but by a complex of them. Every (Fundamental and) General category of the given Layer of Being, determines a corresponding feature in every concrete being of that Layer, that is to say the (Fundamental and) General categories determine that what is commonly possessed by every concrete being of that Layer. And it is clear that the determination of such a being by all the general categories is still an incomplete determination, and it is here where the Special categories come into play.
HARTMANN, Ibid., p.436 gives the following example :
Suppose that "Space", " Time", "Process-nature", "Substance", "Causality", and a number of other principles, are indeed the determining General categories of bodily physical beings, i.e. are the general categories of the Inorganic Layer of Being. Can we then think that a given physical body finding itself in some of its possible conditions or states, is, in that state, unspatial or atemporal, while at the same time materiality and causal dependence intrinsically belong to it?  Or would it be possible that one of its states of motion appear without a cause, and disappear without giving off some effect?  When indeed the mentioned general categories are those of the Inorganic Layer of Being, all that would evidently be impossible. For a material physical being not any such category can be missing.
In every concrete special case the coherence of determination is a complex of the same basic elements. In this, the individual categories can show up in different proportions of dominance. Is the concrete entity to be determined a process, then we see a different pattern of dominance as when it is a material body. But never a (general) category is missing, as is also evident by the fact that  process  and material  body  are not really separated :  any material body finds itself in one or another process of change.
So one can legitimately speak of the general identity (seen as we go from case to case) of the categorical elements that enter into the complex -- but still general -- determination of the diverse concrete cases of a given Layer of Being. This identity (same set of general categories determining each individual concrete case) is only then violated when passing over into another Layer of Being, either downwards or upwards. But then the same applies with respect to the general categories of that new Layer. In fact things are as follows :  That there are Layers of Being at all, each with a typical coherent ensemble of categories or categorical pattern, and in this way differing from each other, is already a function of our (presently being discussed) Law of Categorical Connectedness or Union (First Law of Categorical Coherence).
The first Law of Coherence is a basic law. But because it deals with the phenomena of categorical coherence still from the (standpoint of) determination that takes place upon a concrete case (thus fully involving  principle-concretum  determinations), its nature is still close to the Laws of Applicability (that have been discussed earlier). The first Law of Coherence, therefore, represents the transition from the Laws of Applicability to the true qualitative mutual connectedness of the (general) categories (of one and the same Layer of Being). The fourth Law of Applicability says that all general determination of concrete cases comes from the categories of  their  Layer, while the first Law of Coherence says that all general categories of the given Layer are involved in the determination of each concrete case (of the Layer). So these two Laws supplement each other. Taken together, they say that the whole of the general elements contained in the overall pattern of determination of a whole Layer of Being is based on the all-pervading identity (from case to case) and coherence of the corresponding layer of categories.
The Special Categories, on the other hand, are more or less dispersed across the total field of concrete beings of the given Layer. They determine further the already generally determined collective concretum. Generally, the If-component of a given particular special category does not, when satisfied at all, pervade by implication the whole Layer, despite the fact that this Layer is that category's range of relevance. Whether the If-component is satisfied or not -- i.e. whether a sufficient ground for the Then-component (which component is a particular being-so-and-so) is present or not, present in the sense of actually existing or not (so existing) -- depends on the actual state of the totality of concrete beings and processes, representing the concretum of the (whole) categorical Layer. This state implies certain specific local patterns to be present, some of which might represent a sufficient ground of the Then-component of the category, resulting in the realization of the category's concretum.
Let us now discuss the second Law of Coherence :

The Law of Layer-unity

The general categories of a given Layer of Being, form a coherent unity, not only by their determining in unison, but also in virtue of themselves (i.e. in virtue of their own content, nature or structure). A single (general) category only can exist (which here means :  only can apply) insofar as the other general categories of the Layer exist (apply). Their connectedness in their acts of determining is based on their own qualitative or structural connectedness. There are no isolated general categories.

The Law of Categorical Connectedness expresses the coherence (first Law of Coherence) as it were from 'without', namely as complex determination (determination in unison). Such a way of determining (complex determining) must, however, already be based on an all-out relationality within a category Layer. The present Law of Layer Unity, and the next two Laws of Coherence, deal with this relationality in the framework of the general categories of a given Layer of Being. These three Laws of Coherence can, therefore, in contrast to the first Law of Coherence, be denoted as 'coherence from within', or as Laws of Intercategorical Relation. So with respect to their content the general categories of a given Layer of Being belong together. They do not have independent contents.
Also here this does not apply to the Special Categories. Their content is largely independent of the content of the other special categories. However, it is to be expected that the content of any given special category presupposes all the content of all the general categories of the Layer in which that special category occurs.

The third Law of Categorical Coherence is the following :

The Law of Layer-wholeness

The unity of a Layer of categories, i.e. of the total set of general categories of a given Layer of Being, is not the sum of its elements (not the sum of those individual categories), but an indivisible wholeness, that is prior to its elements. The Layer-wholeness consists of the  mutual  dependence of its elements.

Such a wholeness is not the same as unity. It is unity in a much stronger sense. The general categories of a given Layer are not just dependent on some other categories, they are mutually dependent on each other, which means that they can only originate all together at once.
Although mutual dependence as such, and thus the wholeness of the set of (general) categories, could be the case also beyond the given Layer, it does not do so. That is to say, it does not extend beyond a given Layer of categories (determining the corresponding Layer of Being), which limit is expressed in the fourth Law of Coherence :

The Law of the Limits of the Range of Mutual Dependence

The mutual dependency of the non-special categories and their structural mutual connectedness do not extend beyond the limits of one and the same Layer of Being. They are limited to the totality of categories of precisely one Layer.

This means that, although categories of other Layers could be more or less similar to categories of the given Layer, they are never identical. So non-special categories always are  general  categories, but general only with respect to precisely one and the same Layer. All this further implies that the Layers of Being are fundamentally different from each other. They extend, each for themselves, precisely as far as mutual dependence and structural mutual connectedness of their categories extend.
If this Law would not hold, then all categories, that is to say all categories of the whole of Reality, would be mutually dependent and structurally connected (i.e. having similar structure). Then also higher categories, for example those that are specific to the Psychic or (still) higher Layers, would co-determine lower beings, resulting in, say, a mechanical motion additionally governed by purpose, intention, predestination, etc. And in the same way Inorganic beings would then considered to be alife.

Finally, we have arrived at the fifth Law of Coherence :

The Law of Implication

The wholeness of the given Layer of categories reappears in every one of its members. Every individual general category implies the other categories of the same Layer. Every individual general category has its essence outside itself in the other categories, as well as within itself. So the coherence of the category Layer is present in every one of its members as well as in the whole. The whole (set of categories) is, as it were, present in every individual member.

This Law does, of course, not hold for the Special Categories. The latter exclude each other (instead of implying each other).

Implication of categories is the functional intrinsic structure of Categorical Coherence.
The implication is not an implication as it is used in Logic. Were that the case then the mutual implications of categories would mean their equivalence. Categorical implication of one category by another means in fact that the one category necessarily  involves  the other. In a way such mutual involvement of categories, i.e. the involvation of all general categories of the given Layer by every one general category of that same Layer, is fairly evident in itself :  Speaking about general categories, these categories are general with respect to a given Layer, which means that they all enter the set of categories that determines any given collective concretum of that Layer. Only then this concretum is generally determined and only then it truly belongs to that given layer. If, in some one set of categories determining some collective concretum, one (such general) category were missing, then this category would not be a general category. But what we have demonstrated here is the coherence of general categories from (the standpoint of) their determining a concretum. The Law of Implication, however, means that the categories also  qualitatively  (i.e. as to their intrinsic content) involve each other, which should be shown for every general category of a given Layer.
We will do this for a few instances.
Well, then, let us again suppose that  "Space" (spatiality, i.e. something  is  so-and-so, in this case it  is  spatial), " Time" (temporality, i.e. someting  is  temporal), "Process" (process-nature, something  is  such that it has process-nature), "Substance" (something  is  that which remains identical and present during a process of change), and "Causality" (some pair of entities  is  the necessary and repeatable succession (in time) of two states :  cause and effect), and some more principles,  are  general categories  of the Inorganic Layer of Being. Then the following implications (in the sense of involvations) are directly evident :

Let this be, for the time being, enough to illustrate what is meant by the qualitative connectedness of all the general categories of a given Layer of Being.

As has been said, the Special Categories do not follow the Laws of Coherence. They generally exclude each other. It is true, however, that the general nature of a given Layer -- as it is determined by its corresponding ensemble of General categories -- sets limits as to what special categories can occur at all in that given Layer. So we do not expect, for instance, that symmetries, as defined by geometric symmetry transformations (rotations, reflections, etc.), occur in the Psychic or Super-psychic Layers of Being. The mentioned geometric aspect of true symmetries (as defined by geometric transformations) assign such symmetries to either the Mathematical Layer or the Inorganic Layer or the Organic layer. So there is some connection between General categories on the one hand, and Special categories on the other.

Laws of Categorical Stratigraphy
  ( HARTMANN, Ibid. p.472)

According to the third Law of Applicability every Layer of Being has its own categories. Further we know that the coherence of general categories has its seat in the 'horizontal' dimension (of the system of Layers), that is to say, it only reigns within a given Layer of Being. Seen so far, the Layers would be totally independent of each other, which obviously is not the case, because all the Layers together make up the one World. So there must be certian relations between the Layers, based on certain 'vertical' relations between their corresponding categorical ensembles. These relations cannot consist in coherence again, because then the Layers would vanish altogether, resulting in one 'Layer' only, which itself is then based on one single coherent ensemble of categories. So there must be stratigraphical laws (laws about the relations between layers) that are independent from implication (which latter is the functional intrinsic structure of categorical coherence). And while indeed the existence of a system of Layers was presupposed in the previous categorical laws, we must now investigate what precisely this layering of the World is all about, and this boils down to inquire into the mentioned 'vertical' relations between the categories of different Layers of Being, which relations we just had called 'stratigraphical laws' (still other vertical relations between categories are the Laws of Categorical Dependence, which will be discussed later on).

Next we will give the common principle of the Stratigraphical Laws :

General Principle of Categorical Stratigraphy

General categories of lower Layers of Being are often contained within those of the higher Layers, but never the other way around, that is to say, categories of higher Layers are never contained in those of lower Layers.

This General Principle indicates that the vertical relations between categories are totally different from the horizontal relations (coherence), because the latter are mutual, i.e. reciprocal, relations while the former are one-way relations.
The General Principle of Categorical Stratigraphy can be resolved into four Laws of Categorical Stratigraphy, which, like the Laws of Coherence, only together form a single uniform but complex regularity. Separated from each other, they remain one-sided and could result in confusion, masking their content.

The first Law of Categorical Stratigraphy is :

The Law of Reappearance

Lower General categories reappear in the higher Layers as kernels of higher categories. They are categories that, once having appeared in some Layer, do not disappear again in the subsequent higher Layer or Layers, but pop up again (and again). The whole line of such reappearance presents itself as an uninterrupted passage through the higher Layer(s). This reapperance, however, is a one-way phenomenon :  The higher categories do not reappear (as elements) in the lower categories (and thus, in the lower Layer). The categorical reapperance is irreversible.
Moreover, not all general categories reappear in all subsequent higher Layers. Some break off somewhere along the line.

Let us give some preliminary examples of the reappearance (and breaking off) of general categories once they have appeared (for the first time) somewhere in the Layer sequence (as seen from the Mathematical all the way up to the Super-psychical).

A particular process (actually going on) is determined by a particular nexus category. Such a category connects different states or stages in a particular and regular way, and is as such a special (nexus) category. As analysed it is a dynamical law of a particular dynamical system. This special nexus category determines a particular  being-so-and-so  represented by the actual process that is going on, that is to say this  being-so-and-so  is a certain sequence of states and as such represents the category's concretum.
Generalizing all this we can say that a certain not further specified collocation of actual existing entities has process-nature. And this means that that collocation is determined by the General Category of Process (which is the general nexus category [where every two consecutive states, taken all by themselves, represent Causality] ).  The concretum of this General category is a regular succession of states, which is a case of something being-so-and-so.
A sufficient ground (in fact the disjunctive set of all equally sufficient grounds) for this  being-so-and-so  to be realized, is the If-component of the category of Process, while this  being-so-and-so,  i.e. a regular succession of states, is the Then-component of that category.
This category, that is to say the category of Process, is indeed a General category, because in the Layers where it appears, it is involved in the determination of every collective concretum of the Layer :  Every concrete being or material (as distinguished from just a property), which as such is a collective concretum (i.e. a concrete entity determined by many categories), is involved in one or another process.
This category is not only a General category of the Inorganic Layer, but also of the Organic Layer (and probably beyond). So, after appearing (for the first time) in the Inorganic Layer, it reappears in the Organic Layer. But, and this is important, it reappears not as something identical. It reappears as  a  modified  category of Process.
The living cell provides an instructive example.
The thousands of chemical reactions taking place at any moment within the living cell constitute a complex interacting web. Having studied each individually, the logical approach of the reductionist is to attempt to build them up into sequential chains, recognizing that the products of one enzyme-catalised reaction will immediately serve as the substrates for another. But all this is too simple to reflect the reality in a living cell :  One cannot abstract an individual enzyme reaction from the whole metabolic dance of the molecules, so one cannot abstract any single reaction pathway. What this implies is that many of the substances participating in a certain reaction chain participate not in one but in many interacting pathways, and the factors which may influence the rate of any individual enzyme reaction then multiply dramatically. Once the metabolic web reaches a sufficient degree of complexity, it becomes strong, stable and capable of resisting change. The stability no longer resides in the individual components, the enzymes, their substrates and products, but in the web itself. The more interconnections, the greater the stability and the less the dependence on any one individual component. This is 'molecular democracy'. The cellular web has a degree of flexibility which permits it to reorganize itself in response to injury or damage. Self-organization and self-repair are its essential autopoietic properties ("autopoietic" means self-making). The metabolic organization of a cell is not merely the sum of its parts, and cannot be predicted simply by summing every enzyme reaction and substrate concentration that we can measure. For us to understand them (as to their significance and function), we have to consider the functioning of the entire ensemble. It is discovered that there are intracellular messages, carried by the ubiquitous signals provided by the calcium ion, and that they are propagated as waves pulsing through the living cells. In the open system of the cell, with a flow of energy passing through it and continual deviations from thermodynamic equilibrium, choreography is all (See for this :  ROSE, S., Lifelines, 1997, p.162-166). If we look to one or another biochemical reaction in isolation, we are not looking to the cell, resp. organism, anymore, but have returned to the Inorganic Layer.
In the dynamical systems and subsystems, special parameter values (constants for specific dynamical laws) and special initial conditions are set by the organism, resulting in directed pathways.

All the above shows how different a biological process is from an inorganic process. Some features, like 'repair' as we see them in organic processes, can be recognized also in the Inorganic, as for instance in the regeneration of damaged crystals, but these are only analogies, albeit important ones.
The organic process, taken generally, is an inorganic process that is over-formed, resulting in a robust goal-oriented (organic) process. The overall metabolic process in a living cell is holistic. Of such an holism we only encounter faint images in the Inorganic, like we saw in snow crystals.
So although the General Category of Process, appearing in the Inorganic, reappears in the Organic, it does so in a modified way.

Categories can, in this way, reappear in the next higher Layer.
Some of them keep on doing this, resulting in their presence in all the Layers above the Layer of original appearance. These Layers then come to relate to each other as matter and form :  The next higher Layer is an over-forming of the present Layer.
Other categories, however, seem to break off, i.e. in the next Layer they fail to appear again, and also never return in the subsequent higher Layers. Where this is taking place the relevant Layers of Being do not relate to each other as matter and form. The one is not an over-forming of the other, but over-builds the other. In this latter case the Layer that is over-built is not the matter of the aforementioned matter-form relation, but only a material carrier. We can compare this with music that is recorded on a CD.  The CD itself is not in any way part of the music (which is evident by the fact that a grammophone record or a magnetic tape can also carry this same music). So although the music must have a carrier (in order to be displayed), the latter can be of any appropriate type or material.
Because we are mainly concerned with the transition from the Inorganic to the Organic, and because here only  over-forming  takes place, we shall not deal extensively with the phenomenon of  over-building.  The latter is to be expected in the transition from the Organic to the Psychic Layer. To give an example, in the latter Layer the category of Space is missing, i.e. this category, while still present in the Organic, has broken off in the transition to the Psychic. This case of not at all reappearing of a certain general category is sufficient to let the Psychic Layer of Being be not an over-forming but an over-building (of the Organic Layer of Being).
Generally we can say :

We can visualize the system of Layers geometrically by means of horizontal dividing lines (i.e. lines dividing the consecutive Layers from each other). The categories going through these Layers, can then be symbolized by vertical lines, starting somewhere in the system and going upwards. It is then easy to represent the breaking-off of categories by the terminations of lines at one or another layer-dividing line.
With such an image it becomes clear what decisive role in the categorical constitution of the World the reappearance of categories plays. Nothing less than the unity and intrinsic connectedness of the World (as collective concretum of all these categories) amidst the diversity, and seemingly dissolving heterogeneity of Being, is dependent on this reappearance of categories. The main force in this respect is exerted by the Fundamental Categories. They pass through every Layer from the very first onwards, albeit necessarily accompanied by the respective modifications.
But the World's connectedness is not limited to these (Fundamental) categories. Also the (General) categories undergoing interrupted reapperance (i.e. breaking off somewhere and not returning anymore) play an important part in this connectedness. Although they only pass through a part of the system of Layers, they at least connect some adjacent Layers with each other. By the totality of such interrupted general categories the World is held together, also without the Fundamental Categories, because the 'clamps' alternate, that is to say, where one terminates another begins. So the World would, as has been said, just as well be connected into a unity without the Fundamental Categories, but with them the form of the connectedness is at the same time also uniform.
So we cannot doubt that the Law of Reappearance is, in yet a different way as are the Laws of Coherence, a fundamental principle with respect to the constitution (basic structure) of the World. Without this Law there would be no observable connection between physical matter and life, life and consciousness, psychic and spiritual creation.
A layered or stratified structure can, it is true, also exist without any reappearance of categories, but true interstratigraphical connectedness (i.e. connections between layers) cannot do without it. The World would be just a jumble of heterogeneous domains of Being, having nothing to do with each other, when reappearance of categories would be entirely absent.
The World in which we live has unity. But this unity is neither that of a principle (say a master category), nor that of a center, but the unity of an  o r d e r  and of a coherence (the latter taken in a general sense). The form of the World's order is its layering, while the form of its coherence (generally meant) is its categorical reappearance (of all Fundamental categories in all Layers, and of General categories in some Layers).

The stratified structure of the World is a one-way increase of categorical structure from the elementary and simple to the differentiated and complex. Were the complex already contained, in some way, in the elementary, the latter would not be elementary at all, and the layering would not have the character of a structure that step-wise increases its content, because then  everything  would enjoy the same structural height, or possess an identical general categorical make-up (as we see it in fact only in one and the same given Layer).
A step-wise increasing structure can only come about when the higher Layers possess additional categorical determination as compared with lower Layers. They could not have this extra determination, were the domain of their general categories extending into that of lower Layers.

Although we concentrate (on this website) on the transition from Inorganic to Organic (expressed by the crystal analogy), where all general categories of the former reappear in the latter (but in a modified condition), resulting in the  over-forming  (in contrast to over-building) of the Inorganic Layer, it is nevertheless instructive to again briefly consider the  over-building  of Layers of Being, as we see it apparently at the boundary between the Organic and the Psychic (subjective spirit), and between the latter and the Super-psychic ( = objective spirit, consisting of human institutions and history). It is instructive, namely, to realize (in learning) the precise difference between collective concreta (concrete individual beings or materials) on the one hand, and the several Layers of Being (with their respective categories) on the other. HARTMANN (Der Aufbau der realen Welt, 1940), discusses this on p.494-498. The kernel of this difference between concrete entities on the one hand, and Layers of Being on the other, is that the concrete entities are themselves layered. And this means that in every higher  concrete entity  all lower general categories, i.e. all general categories determining the lower concrete entities, reappear, while in the higher  L a y e r s  of Being  (the Psychic and Super-psychic) only a part of the lower categories reappears.
So although not all, but only relatively few lower general categories are contained (in modified condition) within the categorical ensemble of the higher Layers, the ontological sub- and infrastructure of these Layers contains all general categories from the bottom up, where all lower general categories are concentrated in the substructure of these higher Layers, that is to say in their ontological base. And the higher Layers cannot exist without this ontological base (HARTMANN, Ibid., p.498).
The study of categories should concentrate on the  Layers of Being  as such, and not on the sequence of concrete entities (inorganic thing or material, organic individual, human being, society). The step-wise increase of the latter's complexity expressed as an internally layered structure should be seen as a consequence or expression of the overall Layering of the World as a whole. And it is this stratigraphic aspect of the World, whose regularities are expressed by the Laws of Categorical Stratigraphy.

This discussion is in fact about the relation of over-building of one Layer by another :  Whereas reappearance of categories (but always with concomitant modification of them) results in over-forming of one Layer by another, the breaking-off of categories results in over-building of one Layer by another. The question (in the present discussion) is whether such over-building really exists at all in the World. This over-building allegedly takes place, first of all, at the transition from the Organic to the Psychic. Here the category of Space is said (HARTMANN) to break off (implying the absence of physical [and organic] processes, of materiality, etc. in the Psychic Layer). But isn't it more evident that all the General categories of the Organic (and therefore also all those of the Inorganic) cross the borderline between the Organic and the Psychic, because it is for sure that any psyche (i.e. any consciousness) presupposes a material organic substrate?
If we were asked what concrete entity (collective concretum) represents the Inorganic, then we'd come up with crystals or materials.
If we were asked the same question with respect to the Organic, then we, of course, will come up with individual organisms of the plant or animal type.
And with respect to the Psychic (which can be called :  subjective spirit) we will point to higher mammals like chimpanzees.
Finally, with respect to the Super-psychic (which can be called :  objective spirit), we will point to humans, especially to their latest descendants.
The following diagram depicts all this.

Figure above :  The stratigraphical range of concrete entities, each one of them representing (which does not mean identity) a Layer of Being :
A human being represents the Super-psychic Layer of Being (category Layer).
A chimpanzee, and like higher mammals (but excluding man), represent the Psychic Layer of Being (category Layer).
A herring, and any other lower animal (but also all plants), represent the Organic Layer of Being (category Layer).
A salt crystal, and any other crystal, represent the Inorganic Layer of Being (category Layer)

This scheme as such is certainly correct and reflects the fact that Life presupposes the Inorganic, Consciousness presupposes the Organic, and Social Institutions presuppose the Psychic. Nobody will deny this. Therefore it is to be expected that all the general lower categories reappear in all the higher Layers. HARTMANN, however, maintains that the transition from Organic to Psychic (and also from Psychic to Super-psychic) is fundamentally different from the transition between the Inorganic and the Organic, by the alledged fact that some general categories break off during the former transition. He bases this on the nature of the psychic acts, which are devoid of spatiality and of all that the latter entails.
I doubt whether such isolation, when we talk about 'psychic acts', is admissable. Maybe this is a case of misplaced concreteness. Maybe we just still cannot adequately characterize a 'psychic act'. The connection of psychic acts or psychic processes with organic and inorganic basic features appears to be  inextricable,  and so the organic and inorganic general categories are expected to enter necessarily into the ensemble of general categories of the Psychic, that is to say, it is expected that all general inorganic and organic categories reappear in the Psychic (and also, together with the psychic general categories, reappear in the Super-psychic). Also our above diagram points in this direction. If it is true, we do not have to do with relations of over-building anymore, but only with relations of over-forming, implying that all general categories, once having appeared somewhere in the Layer system, keep on reappearing in all the higher Layers (accompanied, however, by modifications), and never break off.
We will not bring this discussion to a final conclusion, but leave it open to further inquiry.
Anyway, it is important to distinguish between Layers of Being (and their respective category ensembles) on the one hand, and the concrete entities (crystals, materials, organisms, etc.), representing in some way these Layers, on the other.
These concrete entities again come into the picture when speaking (further below) about the Laws of Categorical Dependence.

The Law of Modification

The categorical elements are being modified in diverse ways when they reappear in higher Layers. The special status that they obtain when taken up into the coherence of such a higher Layer, results in their being modified from Layer to Layer.
For such a category this modification is accidental, but for the constitution of the World it is as essential as the reappearance as such.

As far as the transition from the Inorganic to the Organic is concerned, we have with this Law of Modification arrived at the kernel of the crystal analogy. We can see the modification taking place in many special categories when crossing the Inorganic-Organic boundary, such as (the condition of) Growth, (the condition of) Regeneration, etc., when we investigate them as they are in the Inorganic Layer and in the Organic Layer.
The Law of Modification in fact already follows when one substitutes the Law of Implication (fifth Law of Categorical Coherence) in the phenomenon of reappearance. The reappearing category (which we also called 'categorical element') enters into the framework of the higher Layer-wholeness. But in doing so it comes to be subject to that higher Layer's coherence. And because this coherence consists in mutual implication (in the sense of involvation), the lower incoming category must somehow going to get connected with the categorical elements of that higher Layer. After all, this Law of Implication said that the whole categorical framework of a given Layer reappears in every individual categorical element of that Layer. Therefore a category, that penetrates into higher Layers, must experience some modification with respect to its content. We then see some lower category reappearing within a corresponding higher category (i.e. a corresponding category of the higher Layer). For instance, lower categories of Unity only reappear in higher categories of Unity, lower categories of Continuity only reappear in those of higher Continuity, lower (dynamical) system types together with their elements, that is to say, together with their basic structure, only reappear in higher types of (dynamical) system, etc. But precisely those higher types are different structures, and this difference feeds back to the reappearing categorical element. In virtue of the categorical coherence of the given (higher) Layer (in which some categorical element reappears) the reappearance indirectly feeds back to the rest of the categories of the Layer. But this coherence of the higher Layer is at the same time different from that from which the categorical element came frome, and accordingly feeds back onto that element.
In the case of the Fundamental categories new coherence and modification coincide, because they are the general basic elements of the categorical structure of the World at large.

The total picture of reappearance and modification shows itself, when one inspects them with respect to a given group of categories as they extend through the system of Layers, as a bundle of divergent lines, intersecting the Layers. Thereby the uniformity of every such line is the expression of the reappearance itself. The progressive divergence, on the other hand, expresses the modification. Qualitatively this divergence consists in increasing differentiation. From Layer to Layer new structure under new coherence appears. Within this progression the original nature of the (reappearing) categorical element is more and more masked, because of the superimposition of higher structures. It can eventually become so poorly recognizable, that special analysis is needed to reveal or retrieve it.

In this way reappearance and modification together result in a categorical connection that not only intersects the coherence of the Layers, but also being co-determined by it. But also in turn this categorical connection (having resulted from reappearance and modification) co-determines equally essentially the categorical content and coherence of the Layers. In fact, despite all heterogeneity, both types of connection -- the horizontal and the vertical -- integrate into one categorical system (HARTMANN, Der Aufbau der realen Welt, 1940, p.499-500).

Reappearance together with modification is also to be seen in  special  categories. We saw it above with respect to  Growth  and  Regeneration ,  when we compared them as they are in the Inorganic on the one hand, and in the Organic on the other. But there are also special categories, like those referring to  Shape,  Symmetry  and  Promorph,  which are, where they reappear at all, not modified. First of all they do not do so as whatness categories, secondly they also do not do so as entitative constants. In the latter case the If-component contains, in a disjunctive way, all entities that intrinsically imply a given shape, symmetry or promorph. And all these entities are scattered all over the Inorganic as well as over the Organic domains.

Of the Fundamental categories instructive examples are those that are relatively simple, but at the same time not directly self-evident. Such is the oppositional pair Continuum--Discretum.
It is easy to distinguish continua and discreta in the sequence of Numbers (Mathematical Layer), for instance the series of real numbers, representing a continuum, and the series of whole numbers, representing a discretum, on the one hand,  from the continua and discreta in, say, physical motion, and dynamical process (Inorganic Layer), and (all this) from the continua and discreta in the Organic. In the latter we see development, which consists of form-generation and dissolution at the same time (i.e. where existing forms are broken down in order to build up others). We see here continuities and discontinuities as the stages of development succeed one another within one and the same overall organic process. But this series is definitely bounded in the case of the ontogenetic developmental process (i.e. the embryological plus postembryological development) :  It generally starts with the fertilized egg cell and terminates with (natural) death. In phylogenetic development (evolution) on the other hand, such a boundedness does not occur :  When circumstances permit, this process (that is to say, evolution) can go on indefinitely. But again it shows a definite system of discretions (discontinuities) in the form of relatively constant (biological) species, genera, families, etc., not as such known in the (dynamical) systems of the Inorganic. So the face of organic continua and discreta is quite different from that of either inorganic or mathematical continua and discreta.

The wealth of modifications (of reappearing categories) increases when one traces several lines of category modification and sees that they are different from each other, that is to say that each category describes its own line of modification, that cannot be reduced to other such lines, and that consequently the lines of a bundle of reappearance and modification not only are divergent, but are structurally different as well. Each category shows in its way of reappearing the special regularity of its own modification curve (HARTMANN, Ibid., p.502/2).

The condition for such specific modification cannot wholly consist in the reappearance itself, neither can it consist wholly in a different pattern of dominance and recession of reappearing categorical elements, or in their sheer combination. Rather it is evident that behind the modification (of reappearing categories) is something else, in virtue of which it is already essentially determined. This other is the Law of the NOVUM.

The Law of the NOVUM

By reason of the reappearance every higher category is constituted by a multitude of lower elements. But this sum does not exhaust it :  The higher category is always more than just this sum of lower elements. It contains a specific NOVUM, that is to say a categorical aspect or element that is  n e w,  and appears together with the reappearing category. This new element is neither contained in lower elements (elements of lower categories -- where "lower categories" means :  categories of lower Layers of Being), nor in their synthesis, and doesn't allow to be resolved into them.
The NOVUM, as present within such a category, determines the dominance or receding of reappearing elements of it, and of other categories of the same Layer, as well as the modification of, in this Layer, reappearing categories.

The theoretical acceptance of such a NOVUM is very difficult. This is because the World is obviously one coherent whole. And this whole would be disrupted by the appearance of something entirely new (and thus, in fact, not coming from this world). We have discussed this problem earlier in the present Series of Documents, and have provisionally accepted the NOVUM, and with it, consequently, the whole theory of ontologically distinct Layers of Being, to begin with in the form as it was originally proposed by Nicolai HARTMANN in his Der Aufbau der realen Welt, 1940, and subsequently modified by me here and there  (especially the characterization of categories as  If / Then constants  and the inclusion [into the discussion] of very special [as distinguished from general] categories, and in addition to that, the introduction of whatness categories).

Because we are concerned mainly with the relation between the Inorganic Layer and the Organic Layer, we will concentrate on the problem of the NOVUM as it is supposed to appear in the Organic Layer. While such a discussion should in fact need the space of a whole book, we will be as succinct as possible in order not to interrupt the considerations of the Categorical Laws for too long (although the ensuing discussion is in spite of this still fairly long because of its importance). This relative succinctness is also meant to express the fact that we are still unable to formulate in an appropriate and clear way this organic NOVUM, that is to say we actually don't know how precisely Life differs from non-life.

Discussion concerning the Organic NOVUM

( Nexus Organicus )


One of the General categories of the  I n o r g a n i c  is the general inorganic nexus category, which is a dynamical law in its most general form. It is the general law of inorganic change. It is itself based on Causality.
This general nexus category can be analysed into two distict types :

  1. A (general) continuous nexus category.

  2. A (general) discontinuous (discrete) nexus category.
The discontinuous inorganic nexus category can be symbolized by a general formula

Xn+1 = f( Xn )

( This formula means :  The next state of the system is a function [not specified, because the dynamical system is genera] of the previous state.)

Turning now to the  O r g a n i c :  in the development of a given individual organism we have to do with a regular succession of states or stages, leading from the initial generation of that organism to its (natural) death. The category determining this succession is a special (organic) nexus category, which is in fact a special dynamical law. This law can be assumed to be discontinuous (certainly in the case of multicellular organisms, because the smallest growth increment is still far from being infinitesimal, namely the cell).
We can further assume that all the many special organic nexus categories have a certain kernel in common, and this kernel is then the General Organic (discontinous) Nexus Category, or Nexus Organicus for short.
Well, this Nexus Organicus, generally determining the genesis and maintenance of individual organisms, can be seen as an over-forming of the General Inorganic (discontinuous) nexus category, or, equivalently, of the General Inorganic (discrete) Dynamical Law we saw earlier :  Xn+1 = f( Xn ).  This over-forming is brought about by the NOVUM of the Organic Layer. In fact it  is  the NOVUM.
All this can also be expressed in the following slightly different (and maybe more correct) way :
We can, to begin with, assume the existence of a truly general inorganic nexus category, general in such a way as to not discriminate between continuous and discrete processes. When this general nexus category is over-formed it results in a general organic nexus category that generally determines organic development. We can further assume that this general organic nexus category contains, in addition to rather dominant discrete aspects, also continuous aspects. If this is correct the over-forming indeed involves  general  categories, that is to say, not only is the organic nexus a general category (of the Organic Layer), but the inorganic nexus category, of which it is an over-forming, is a general category as well, this time of the Inorganic Layer. And in this way we indeed have a truly general inorganic category that is over-formed, resulting in a truly general organic category, where in both cases "general" means general with respect to the given Layer, which in turn means that every concrete entity in such a Layer, is, without exception, subject to this category.

In First Part of Website we have argued that the dynamical law of the dynamical system that generates  a  b e i n g  is equivalent to the ESSENCE of that being. In fact such a dynamical law is, when that being is an organism, a special case of the (general) Nexus Organicus. So the Nexus Organicus is the  g e n e r a l  ESSENCE of an organism, which in fact means its being alive. So indeed the Nexus Organicus is the genuine NOVUM of the Organic Layer, because it  is  the  l i v i n g  condition. The kernel of this Nexus Organicus is the General Inorganic (discrete) Nexus Category.  As over-forming of the latter the Nexus Organicus is the NOVUM of the Organic Layer of Being.

In what comes next we will try to point out the nature of this over-forming, and especially which types of (concretum-concretum) determinations are involved.
The successive states or stages of the morphogenetic process (individual organic development) relate to the final result -- the generated form -- as if they were a series of selected means, means for the realization of the mentioned form. This phenomenon has led to the doctrine of Vitalism. This doctrine, however, assumes a categorically too high a type of determination (in morphogenesis), a type that is taken from the domain of human acting. The obvious difficulty of involving in all life processess a consciousness setting goals, is then circumvented by such concepts as 'immanent goal'.
Mechanism on the other hand, assumes too simple a scheme by introducing inorganic categories into the Organic without any concomitant modification.
But it is clear, while assessing the type of determination in organic morphogenesis, we do not have to choose between either Mechanism or Vitalism. There are other forms of determination apart from the causal nexus and the final nexus ('final causality', as distinguished from efficient causality or causality proper) (See for all this :  Nicolai HARTMANN, Philosophie der Natur, 1950, pp.692). Already more or less intermediate between causal nexus and final nexus we see a type of determination going on in the higher-order morphogenesis as it takes place in phylogeny, namely natural selection. Here we have the generation of the functional or goal-oriented aspect from non-goal-oriented beginnings, as DARWIN has teached us. Something like this we must look for in the complex morphogenetic process that is involved in the development of an individual organic being. Here we see, to begin with, two factors at work :

  • The function of the position in the whole, where parts are determined by their position within the whole, which we shall call wholeness determination.

  • The determination issuing from the genetic initial condition, which we will call centralized determination.
Especially the latter is still not sufficiently understood, that is to say we do not know how precisely genes eventually determine macroscopic features, i.e. how they determine beyond their determining specific proteins (mostly in the form of enzymes that catalyze certain biochemical reactions). While the phylogenetic process (evolution) is open-ended, the individual morphogenesis has a beginning and an end. This latter process is reproduction, not production. Production is in fact much simpler than reproduction, because in the latter the seemingly teleological factor is present. So it is  reproduction  which, as a process, distinguishes itself strongly from any inorganic process. Consequently this organic morphogenetic process (leading to the generation and development of an individual organism) represents, as a mode of determination, the kernel of the Nexus Organicus, i.e. of the organic NOVUM.
Just like in the case of genuine final causality -- namely in human acting -- there is (efficient) causality (going on) at the base (Indeed, in the realization of goals, the (chosen) means work as causes), so also in the Nexus Organicus there is (efficient) causality (going on) at the base.
It is the initial very special arrangement of causal factors that constitutes the over-forming of causal relations, and with it, of inorganic dynamical laws (In fact it is the latter that are over-formed, in virtue of arranging of causal elements). In the final-nexus this is also the case, but here it is consciousness that arranges these causal factors (in fact, which let the causal factors be arranged by material means), and therefore a final-nexus cannot be the organic nexus (because a final nexus only holds for human beings). So what in the individual organic morphogenesis arranges these causal factors, which then drive the organic system towards specific end-goals? First of all the boundedness (begin and end) of the process must be taken into account, that is to say, the wholeness of the intrinsically segmented and closed dynamical system appears here as categorical NOVUM, which in turn results in the rhythm of differentiation and articulation, in short the process-curve as temporal wholeness. It is a process that spans between two identical forms -- parent and offspring -- but it does so mediately :  something different is inserted between these two identical forms, namely the genetic blueprint, of which the determinative function is the reproduction of the species form in the individual. The problem of the Nexus Organicus is just how such a disparate system (the genetic blueprint), that is inserted between the two identical forms, can bring about a form so different from itself. It is the vexed problem of genetic determination (or expression). The latter determines the constitution and function of cells, but at the same time depends on the actual position of these cells within the organismic body, that is to say the differentiation of the cells is co-dependent on where they are within the body. This position (location) of a cell is probably assessed by means of inhering chemical gradients, as we have discussed in earlier documents (Part XXIX Sequel-11 and Sequel-12).
The genetic expression (i.e. the expression of the genetic blueprint in visible and macroscopic form and function) can be called (with HARTMANN, 1950, p.699) "centralized organic determination".
In every stage of individual organic development centralized organic determination and wholeness determination ( = the feed-back of the here-and-now whole to its parts) interpenetrate each other. The centralized organic determination (determination by the genetic blueprint, where genes also interact among themselves), however, is the most important, that is to say, the most fundamental. The genetic germ is a special and closed complex of causes. Only then it can lead to a specific end-goal. In all this the closeness of the complex of causes means that this collocation of causes denies additional alien causal factors to be taken up. It isolates and protects its own causal factors against influences from the rest of the World. And this exactly is absent in the inorganic causal nexus or inorganic dynamical system. The latter happily and indiscriminately takes on board elements (including causal factors) from the outside world. It is simply not geared to a specific end-goal, and doesn't have a closed ensemble of determining factors.
How did such a specific closed ensemble of causal factors come to be present in the genetic germ? This ensemble can be compared with the chosen means as it is in the final-nexus in the Psychic Layer. In organic development, however (thus in the Organic Layer), these choices came about by  selection  during  phylogenetic  development, in the concurrence of organic individuals within the common life of the species. Every individual of such an organic species is carrier of the genetic blueprint, and the latter has phylogenetically come into existence. It is therefore the result of selection processes (natural selection) in which its expediency has formed. And it is evident that it (i.e. the genetic blueprint) can only maintain its continuity through the series of consecutive individuals when it tightly holds on to a reproduction process that is exact, so that it continually generates individuals of the given species.
But in all this the genetic blueprint, which is here supposed to come about by natural selection, is in fact already presupposed when considering the phylogenetic process. This is indeed true, but we must realize that the genetic blueprint of higher species (representing higher organisms) has  originated  (via selection) from that of lower and lowest species. And it is this origination of the genetic blueprint we're talking about. The genetic blueprint of higher organisms is 'bread' along their lines of descent, and only the expedient versions will survive. And what matters most is the closeness of the complex of causal factors in the genetic germ, because only such a closed complex can be geared to some specific end result, without being 'consciously resolute' (as it is the case in the final-nexus).
This complex of causal factors, that is to say the genetic blueprint, is, however, far from constituting the totality of conditions leading to the development of organic form. It is one of the three basic factors. Also the function of position (wholeness determination :  dependence of a part upon its location within the whole) and external conditions belong to this totality of conditions for organic development. Also these carry the mark of over-formed causality. So although the complex of causal factors, constituting the genetic blueprint, is 'closed', it is nevertheless not the total or sole determining factor of that to which it is geared. It interacts with the other two factors mentioned.
The centralized determination issuing from the genes continually co-determines the selection of those external causal factors that are involved in the wholeness determination (i.e. the determination issuing from the whole thus far developed, onto its parts) of the here-and-now wholeness (i.e. the given developmental stage) and (co-determines the selection of those factors) that are involved in the developmental stage's interaction with the external world. The determining genes are thus at the same time a selective principle of those conditions of development that do not explicitly reside in them.
The process that is governed by the genes is determined such as to take up, during given developmental stages, certain specific external influences into the course of development (and reject others). And in this way it comes about that the genetic blueprint is -- indirectly -- a system of causal factors with a remarkable degree of closeness anyway, a closeness that is to say, for the whole of the morphogenetic process with all its subordinated processes. As to the degree of closeness this type of determination in many respects surpasses the teleological determination as we know it from human acting (HARTMANN, Philosophie der Natur, 1950, p.703). This is of course only possible if the external conditions indeed can deliver the corresponding factors to the successive and advanced developmental stages  ( The early stages are largely independent of external factors). And here we have a precondition that no genetic blueprint can create or guarantee. But generally the organic system is adapted to be able to damp perturbations within certain limits.

In addition to the reproduction of an organic individual we have the reproduction of  cells  ( These two coincide in unicellular organisms). Here wholeness is directly transformed into wholeness, that is to say a cell generates a cell without an intermediate and different state. So the type of determination in cell reproduction is mainly wholeness determination (where the position of parts plays a role). The genetic blueprint must be copied exactly, and some new organelles must be formed in order to arrive at two identical sets of them. Centralized determination is here in essence absent  ( There is in cell reproduction no generation of macroscopic structure from a microscopic blueprint, this latter is just being copied). The wholeness determination (in the cell reproduction) is as type of determination still very close to causality, albeit a causality that is bound up with interaction of partial causes, and is as such at least in principle intelligible. And this process (of cell reproduction) is close to just the process of assimilation of substances. Also here we have a form of wholeness determination effected by the existing cell-whole, and pattern and positions of cells. So in assimilation, as in cell reproduction, all parts of the organic structure directly cooperate, a phenomenon that is not present anymore in multicellular organisms (that is to say, all three determinations are doing their job, it is true, but not all parts of the multicellular organism are equally involved anymore) (HARTMANN, 1950, p.705).
But the morphogenesis of multicellular organisms is based on virtually the same cell division as takes place in unicellular organisms, namely the continued division of the fertilized egg cell, with the only difference that the newly formed cells stick together, forming tissues. In this way a higher-order whole ensues in which there is now the continually changing function of position (parts influenced by their position in the whole so far formed).
Another feature by which multicellular organisms differ from unicellular organisms is the  differentiation  of cells. But this largely depends on the here-and-now-generated higher-order whole insofar as this whole gives off the functional stimulus of position within that whole.
All in all it is evident that genes do not immediately and exclusively determine tissue and organ forms, but only mediately so. So their way of determining becomes, because of this, more intelligible. For directly determined by them are the just appeared daughter cells (that is to say these cells are determined by genes, but not as centralized determination as it is the case for the genetic germ generating a whole organism). Indeed the fact that the overall cell structure remains the same also when differentiation of the newly generated cells has taken place in this process, makes the latter very well intelligible. So at least the determination of a cell aggregate, as a tight living community of kindred cells, by the genetic germ, can be understood (making the phenomenon of the Nexus Organicus less mysterious). And such living community of cells is nothing else than a multicellular organism.

In the process of Life the levels of assimilation (of substances), reproduction (ontogenesis [= embryology + postembryology] )  and species formation (phylogeny) condition each other mutually. Something like this seems also to be the case with respect to the several types of  determination,  that come together in the organic nexus. In the individual development (embryological and postembryological) of multicellular organisms centralized determination (issuing from the genetic germ) and wholeness determination (issuing from the function of (the) position [within the relevant whole] )  intermingle with each other (HARTMANN, 1950, p.707). But the genetic germ directly determines only the cells, that is to say, their general structure and general function. But because those cells' multiplication depends on division, and this in turn has the form of a wholeness determination (where here wholeness is a single given cell that is about to divide), it follows that we have here a higher-order centralized determination (the [general] determination of cells by the genetic material) based on a lower-order wholeness determination (cell divisions). But the cell differentiation depends on (or is at least co-determined by) the stimulus that is given off by the position (location) of the cells in the here-and-now whole of the organism, which is higher-order wholeness determination. And so it seems that three determinations are integrated :  A higher-order centralized determination ( = determination of general cell structure by the genetic blueprint) partially based on lower-order wholeness determination (cell division), crosses with a higher-order (same level as the centralized determination) wholeness determination (cell differentiation).
And because this whole system of determinations has been originated phylogenetically, its generation stands under a determination of still higher a level, calibre or status, namely that of the organic stem or phylon ( = high-level taxonomic or classificatory unit) and its form-flow. This latter determination, however, is neither centralized nor wholeness determination. The only aspect of it that we can presently comprehend categorically is the principle of natural selection (in DARWIN's sense). This principle can perhaps be further analysed along the lines of, for example, Stuart KAUFFMAN's 'fitness landscapes' (KAUFFMAN, 1995, 1996, At home in the Universe, The Search for Laws of Complexity) and should as such (i.e. as analysed) be taken up in the configuration of organic determinations. And selection involves the reproduction of organic individuals (so we are back again at ontogenesis).
All in all our system of determinations is thus four-fold. Right from the beginning four types of determination intermingle, distributed over several different orders or levels of form-generation. In the life of multicellular organisms they all interpenetrate in such a way that no one single determination can function without the others.
One comes closest to the content of the Nexus Organicus if one considers it in the light of the just discussed interpenetration (integration) and mutual dependece of the four modes of determination. It is not to be found in only one of the four types of determination. Precisely the highly complex synthesis of heterogeneous forms of determination is characteristic of the Nexus Organicus. The categorical NOVUM, represented by this synthesis, is, however, still in need of a well-structured appropriate comprehension, that is to say of an adequate expression within the categorical language (See HARTMANN, 1950, p.707/8).

We have finally concluded our discussion concerning the organic categorical NOVUM, which was called the Nexus Organicus (still in the context of an exposition of the Law of the NOVUM (third Law of Ontological Stratigraphy). This discussion, whose length reflects the importance of expounding the organic NOVUM, is partly based on HARTMANN's, namely in his book "Philosophie der Natur", 1950, p.692-708. To summarize, it shows that the overall dynamical law of the dynamical system that generates (and maintains) the organism, that is to say that gets individual organic morphogenesis going, is a typical organic nexus category, called the Nexus Organicus.
While a given particular organism is generated in virtue of a particular dynamical law, which as such represents -- as is argued in First Part of Website -- the ESSENCE of that particular organism, the  general  organic dynamical law -- the Nexus Organicus -- represents the ESSENCE of an organism in general, that is to say it represents Life as a feature, characteristic of concrete beings of the Organic Layer. The goal of the above discussion was to say more than just :  " The categorical NOVUM of the Organic Layer is Life."

The Nexus Organicus is the result of over-forming of the general  'nexus inorganicus'  or general nexus category of the Inorganic Layer.
What is  n e w  in this nexus organicus is the  s p e c i f i c  highly complex and  o r g a n i z a t i o n a l  synthesis of the four types of determination.
Indeed it is  organization  at the categorical level that has created this NOVUM.

Let us further elaborate on the general nature of  a  NOVUM   ( HARTMANN, 1940, Der Aufbau der realen Welt, p.503-505 ).
Without the appearance of a categorical NOVUM in each new Layer, the wealth of forms of modification is not intelligible. But also the specific nature of the higher categories themselves, as well as that of the concrete entities (collective concreta, such as crystals, materials, organisms, etc.), cannot be understood without the appearance of a NOVUM.  If, when we go up from Layer to Layer, truly new categories would not appear, then the higher (collective) concretum would be in principle intelligible by appropriate knowledge of the lower categories alone :  The organism would then be in principle understood from the principles of the material (i.e. the physical), consciousness from those of the Organic, etc., because the higher categories themselves would then be nothing else than just combinations (not organizations) of lower categories.
This, however, does not seem to be the case in our observed world.
Organic nature as reducible to physical nature, psychic nature to organic, etc., seems to be utterly unintelligible, not only because we (as observers and investigators) happen to be unable to grasp the combinations of structural units, but because in reality the higher does not exhaust itself in sheer combination of lower elements. The idea of 'combinatorics' which truly underlies all such attempts to explain (that is to say, reductionism), is, when referring to the categorical layering of the World, a dead end. It is an artificial simplification, an imposed unification, that conflicts with observed diversity. It is a denial of categorical basic relations  ( HARTMANN, Der Aufbau der realen Welt, 1940, p.504 ).

As I have pointed out earlier, the assumption of a genuine NOVUM, could represent in fact a capitulation of scientific explanation, because genuine explanation is only felt as such, when the complex is reduced to the simple, or the higher to the lower.

Surely there are the always new combinations of reappearing categorical elements in the layering of categories. But neither are they a function of the elements themselves, nor selected from them, but evidently a function of the  higher categorical structure,  that as such is independent, and in the same degree original as these (categorical) elements, and so not a product from their sheer combination, but a fresh unity, that is all-out whole. That's why it will never succeed to fully explain higher beings in terms of the regularities or the laws of lower beings.
And that is it what is meant by the Law of the NOVUM :  Because of the reappearance, the higher categories contain within themselves, it is true, a diversity of lower elements, but are not only not exhausted by their sum, but are, as to their content, always already determined by the appearance of a categorical NOVUM.
The Law of the NOVUM is not a limitation of the reappearance -- as we see it, for instance, in the case of over-building -- but the positive counterpart to it. It does not impede the passing of lower elements through consecutive Layers, but holds against it another basic property of the World :  The aspect of categorical independence (not existential independence) of the higher Layer with respect to the lower. It is precisely this aspect that cannot be co-expressed by the fact of the inclusion of lower categories within the higher, but which (aspect) is nevertheless presupposed in this inclusion, because without the periodical appearance of the NOVUM, the Layers of Being could not distinguish themselves according to their height (which is their wealth of content). But because the modification of reappearing categories depends upon these differences in height, we can say that also this modification depends on the appearance of the NOVUM.

The NOVUM is always specific with respect to the Layer in which it resides. As a phenomenon it is first of all connected with a single category. But because such a category involves all other categories of the given Layer  ( Throughout this discussion it is general categories we're talking about.), so also the totality of the corresponding Layer-coherence shows an overall NOVUM -- we could call it a Layer-NOVUM -- NOVUM, that is to say NEW, with respect to the whole of the Layer beneath. And in accordance with the Law of Layer-wholeness this overall NOVUM has categorical priority over the individual NOVUM of the member-categories of the Layer.
Here it is clear that both groups of categorical Laws, viz., that of Coherence and that of the Stratigraphy, intermingle with each other. They constitute a system, in which reappearance and Layer-unity come together and keep each other in check. The NOVUM of the higher categories with respect to the lower categories is the point of departure of the autonomous regularity of coherence right in the middle of the layer-relationship, because it primarily is a matter of the business of the whole category layer.
Between these two groups of categorical Laws (Coherence and Stratigraphy) there is, in all this, no opposition. Such opposition would also already not occur, were the reappearance nowhere whatsoever interrupted. On the contrary, the Layer-coherence, together with its NOVUM, is itself rather taken up by reappearance and carried further up into the higher Layers.
Because every modifying categorical element (i.e. being modified when it reappears higher up) carries with it the coherence of its Layer of origin, it transfers it to the categories of the higher Layers, as far as its reappearance reaches. It is true, however, that it does so in a modified form, and so indeed it is not only itself a modifying element, i.e. a categorical element undergoing modification, but the transferred coherence is transformed as well. But this doesn't change anything of the transference itself, as can be seen clearly in the case of the Fundamental categories, that do indeed not suffer any interruption of their reappearance.
So as far as the reappearance of the categorical element reaches, it also turns its coherence into an aspect of the higher and more complex Layer-coherence. And because this (higher-layer-coherence) is the overall NOVUM of the higher Layer, it super-ordinates the coherence of the reappearing elements and includes it into itself without neutralizing it. This relationship is limited only by the limits of reappearance. Where the latter fails, that is to say when even only one of the lower general categories does not reappear in the categorical ensemble of the higher Layer, matters become different. In that case the coherence of the lower categories cannot be transferred to the higher Layer together with the remaining lower categories that do reappear in the higher Layer. There the original connection is resolved and gives way to another connection. But such limitation of the reappearance and such resolution, is not determined (i.e. not 'caused') by the NOVUM of the higher Layer, but by the limitation of the over-forming, i.e. where it gives way to over-building.
The total picture not only shows an integration of both types of categorical regularity (coherence and stratigraphy), but also a high degree of interpenetration. Both are independent, heterogeneous and at the same time fundamental. But this heterogeneity does not impede them to close-in into a higher overall regularity. And only then they together form a multidimensionally complex regularity of connectivity of the domain of categories. At the same time one sees how the perpendicularity of the two basic dimensions of categorical connection is not just an image, but expressing a genuine intersectional relationship, in which also the implication of coordinated categorical elements co-reappears and modifies, while the reappearance and modification of the elements in turn become the substrate of categorical implications  ( HARTMANN, Der Aufbau der realen Welt, 1940, p.507 ).

Having extensively dealt with the Law of the NOVUM, we will now turn to the fourth Law of Stratigraphy.

The Law of Layer-contrast

Reappearance and modification do not progress in a continuous fashion, but with discrete jumps. There is no continuous modification of categories, progressing that is to say with infinitesimal steps. These discrete jumps moreover take place at a common level of attained complexity, that is to say at one and the same horizontal level of the system of category Layers. Where one or more general categories do not reappear, a definite level is marked. Modification of categories that do reappear takes place at a same level, where this level is moreover the level where other categories break off (insofar as they do this at all).
In this way uniform incisions in the categorical system result and so give rise to genuine layers. In this uniform stratigraphic system of categories each higher Layer has a common NOVUM with respect to the previous lower Layer. Such a higher Layer contains the modified Layer-coherence of the lower Layer, and this higher Layer in turn pops up with its Layer-coherence in the next higher Layer, again in a modified way. So such a Layer as a whole, behaves, as a consequence of the Laws of Coherence, in the same way as do the individual categories. And as a result of all these ways of behavior, the system of categories consists of definite and contrasting Layers.

This fourth Law of Categorical Stratigraphy, viz., the Law of Layer-contrast, is not at all self-evident. It is only more or less so in the cases of over-building (provided they actually occur). First of all we must again distinguish between the collective concretum (i.e. some concrete existing being) on the one hand, and its ensemble of determining categories, on the other, and with respect to such a concretum, we must focus especially on that collective concretum that includes all concrete beings of the World. There must be some relationship between all these concrete beings on the one hand, and the set of categories determining them, on the other. In this it could well be that the set of all concrete beings shows continuity  ( This continuity could be either typological or genetic [i.e. phylogenetic]. The latter continuity is especially evident in organisms [see also below] because they have actually evolved from each other),  while the corresponding set of general determining categories is definitely discrete, the latter reflecting as such at least an aspect of the Law of Layer-contrast
because this Law is a law of (general) categories, not of concrete beings. In fact, laws of concrete beings are only 'laws' about how these things look like, i.e. whether they differ in their appearance, and if so, whether these differences come in discrete steps or are the result of continuous sequences. The genuine laws of concrete beings are about what and how these concrete beings really are, not only how they look like. In fact the latter must be the result of the former. This means that the genuine laws of concrete beings are their determining categories and the (regular) relations between them. So there are no two sets of laws, one for concrete beings and one that only involves their determining categories.).
Thus when we see continuity along all concrete beings (going from one to the other) in the way they look like, we must investigate whether or not their corresponding system of principles (categories) is continuous as well. And again, it is perfectly possible that a discrete system of determining categories results in a continuous system of concrete beings, or vice versa.

Above we spoke about the system of organisms as  c o n t i n u o u s.  What we meant was not strict continuity, which definitely isn't the case in the system (typological or [phylo]genetic) of organisms. What we mean is that we could assume the absence of large steps, while admitting a multitude of very small steps.

As to the relation between  inorganic  beings and  organic  beings, we can -- as a hypothesis -- assume that their transition (from inorganic to organic) is discontinuous, and takes place with the appearance of the Nexus Organicus, which is the categorical NOVUM of the Organic. Indeed it is the appearance of a NOVUM that results in discontinuity between category Layers.
Every Layer then has its own specific NOVUM, and because of the coherence between the categories of one (complexity) level, such a level obtains a face of its own, which means that we have a Layer of categories that contrasts with other such Layers. Such Layers, i.e. such category Layers, are Layers of Being. Concrete entities (like an individual human) can extend across several such contrasting layers of being.

It is now time to deal with the last group of Categorical Laws.

Laws of Categorical Dependence
  ( HARTMANN, Ibid. pp.512)

There are four Laws of Categorical Dependence, that can be summarized in the

General Principle of Categorical Dependence :

Categorical dependency is a one-way phenomenon only. It is that of the higher categories upon the lower. It is, however, just a partial dependency, that is to sat it still admits of broad play for a degree of independency of the higher categories.

We have seen that the reappearance finds its natural limit where over-building sets in. Spatiality and material substance -- to take an example -- do not return above the Organic. And -- to take another example -- the act characters of the Psychic do not return in the objective spirit (the Super-psychic). But in addition, and apart from this, the reappearance of categories as we follow it bottom-up becomes more and more limited, because the further upwards in the overall system of categories a category appears, the smaller becomes the play of its modification, in virtue of the fact that less and less Layers are left to be available to create such modifications. And this limitation is not only extensive, but also qualitative. The power of reappearing becomes weaker in higher Layers, it recedes more and more against the power of the NOVUM. The higher up a given category appears for the first time, the easier the structural complex of its elements in its inclusion into the higher structure dissolves again. The structure of the category originating higher up is already more complex, it has more bolts and nuts, and these can be more easily dissolved in the process of modification. With respect to the degree of dissolvability the modification approaches its disappearance.
On the other hand we saw that all limits of reappearance vanish if one considers the series of concrete entities (collective concreta) instead of the Layers of Being. The higher members of the concrete entities (human beings, society, history) are themselves layered (stratified), which means that they also contain the categorical layering from the bottom up.
This change of view (Layers ==> concrete entities) is not arbitrary, although it is not very well suited to clearly illustrate the stratigraphical structure of Being with respect to the contents of the Layers. But it is the more suited to show the existence of the stacking of Layers (in terms of dependency). And all this is of paramount importance for our step to be taken, namely the transition from the Laws of Categorical Stratigraphy to te Laws of Categorical Dependence, because in the higher concrete entities we can, by virtue of their being layered, directly see relations of dependency between Layers of Being. The highest Layer of Being is that referring to the objective spirit, namely the Super-psychic Layer (of which some concreta are :  human ethical, social and political institutions, and human history, together forming the objective spirit). This objective spirit (Geist), as actually existing, is evidently carried by non-spiritual being, namely by the whole layering of lower being. It is real only when real humans, of which it is the objective spirit, exist. Therefore it refers back to actually existing consciousness, and in this way presupposes it according to its categories. And although its content does not contain these (lower) categories (because here we have to do with over-building), the objective spirit contains them insofar as they reside in the very foundation of its beingness or actuality. But because the actual consciousness in turn cannot be without an organic living substrate (a body), and the organism in its turn cannot exist without a physico-chemical substrate, it is evident that the whole sequence of lower categories is necessarily presupposed in the objective spirit and its categories. This sequence of lower categories is, however, not observable in the objective spirit  as isolated phenomenon. When one describes ethical or judicial phenomena as such, one would, of course, never encounter physiological or mechanical events. But in the actual  being  of spiritual life (i.e. in the actually existing objective spirit) the whole sequence of lower categories is present, be it in a more or less hidden way, because precisely its real being rests on the being of the lower Layers of Being. The objective spirit itself, however, i.e as it is in itself, does not -- as has been said -- contain the lower (general) categories. But it does, of course, contain the Fundamental Categories, because they penetrate all Layers.
Not the fact that one can consider whole concrete entities instead of Layers, and then extend the Law of Reappearance, such that in such a consideration all lower general categories reappear in all higher Layers, is the most important, but the fact that there actually exists a relation of dependency between the Layers of Being, letting the whole existence of the higher be dependent on that of the lower. And this relationship also refers to the corresponding individual categories (without having to assume an all-out reappearance of categories). The fact that spatiality and physical process are not features of consciousness and objective spirit, does not prove that they can exist without them. It only indicates that spatiality and physical process do not enter the specific nature of consciousness and objective spirit. In the layered make-up of a human individual and human society they have degenerated to subordinal conditions. They nevertheless stay what they are, namely conditions. They are just over-built and, as it were, covered or concealed by structures of a wholly heterogeneous nature.
If one, however, pulls away, from the higher concrete entity, these lower structures (spatiality, physical process, etc.) right from under its feet, then at the same time this higher concrete entity vanishes too. And even when one does not appreciate such argumentation, it is trivially true that all real existence of consciousness and objective spirit in the World is thousand-fold connected to lower-order dependencies, that in turn are not only temporal and causal, but also wholly spatial and dynamic in the sense of having a dynamical-process nature. As nobody (according to HARTMANN) would seriously try to explain, say, the objective spirit from these dependencies, so also should nobody deny the dependence itself  ( HARTMANN, Der Aufbau der realen welt, 1940, p.515/6 ).

In the system of Layers we have, then, relations of dependency. And although these are already more or less implied in the Laws of Stratigraphy, they mean something else. That a system of Layers contains dependency relationships at all, is in itself not self-evident. Layers could be stacked in a neutral fashion. It becomes different when the layering has the special form of reappearance and modification of elements passing through it. And a relation of dependency is eventually necessarily involved, when the lines of modification have a definite direction, that cannot be reversed. If only the lower categories reappear in the higher, and not vice versa, then this implies that the higher categories necessarily end up in a certain state of dependency upon the lower ones, because elements as such (i.e. as elements) are necessary conditions of the complex in which they are contained. This dependency is a specific one. Another (type of) dependency we saw in the relations of coherence (as expressed in the Laws of Coherence), which was a mutual dependence of categories of a given Layer. But precisely because of this mutuality the dependency as such is neutralized. The equilibrium between the conditioning and the conditioned remains, as we saw it in the Law of Implication. For genuine dependency, on the other hand, the dominance of the conditioning is characteristic. Well, such dominance automatically reigns vertically within the system of Layers, because here the dependency is one-sided, corresponding to the fact that the reappearance of categorical elements is irreversible  ( The reappearance, as one-way reappearance, is only one aspect of the vertical dependency. The latter has other aspects too, not brought about by (irreversible) reappearance.).
The preponderance of the lower categories -- not referring to their sense or significance, but surely to their ontological weight -- precisely corresponds to this irreversibility. It even still corresponds there, where, at the pronounced incisions in the sequence of Layers, the reappearance of many lower categories breaks off.
So categorical dependency follows the stratigraphy, and (it follows it) rather wholly generally so, irrespective of the limits of reappearance.

For the  concepts  that should express the categorical dependency, a certain difficulty inheres in it. The image, underlying the concept of dependency, is a spatial one (something hangs on something else, like a piece of lead on a rope). And in this image, that on which something depends (from which it hangs) is seen as the 'higher', while that which is dependent (is hanging) is seen as the 'lower'. In this sense dependency still applies to the relation of logical subsumption (i.e. the subsumption of a special concept under a general concept) :  the higher concept (for example "animal " ) is independent (from the lower), while the lower concept (for example "vertebrate animal " ) is dependent upon the higher, because it contains the higher ( "vertebrate animal " necessarily containes "animal " ). But in the relationship of categorical stratigraphy its sense of direction is reversed, because in this stratigraphy the status of ' higher' takes on a different meaning, namely a status according to content, which is not taken from that spatial image, it even opposes it (the independent is the higher in the spatial image, while it is the lower in the categorical stratigraphy). In logical subsumption the higher is the more general, having least content with respect to the lower, which is dependent upon the higher because it necessarily contains the higher and thus presupposes it, while in the ontological layering (stratigraphy) the higher has more content than the lower. In the ontological stratigraphy the lower is the elementary, and is therefore independent, while the higher is the complex state, and therefore dependent (because it necessarily contains the lower). It is, therefore, necessary that the direction of categorical dependence follows that of the ontological stratigraphy.

We can (HARTMANN, 1940, p.519), to begin with, summarize the content of the Laws of Categorical Dependence in the following three points :

To grasp this last point one should recall that even reappearing (and therefore co-determining with respect to content) categorical elements within the NOVUM of the higher Layer are down-graded to subordinated aspects. So in all cases the  categories  of the higher Layer are autonomous, regardless their dependence upon lower categories, and not only when they over-build these lower categories, but also when they merely over-form them.
All this refers to dependency of categories upon other categories, and with them of Layers of Being. For concrete entities (collective concreta) it does not hold (also according to HARTMANN). They generally are layered entities dependent on all lower Layers, i.e. dependent upon all lower general categories.
Let's take an example :  Consciousness, which is as such the collective concretum of the Psychic Layer [ = Layer of psychic categories],  is, for it to exist at all, dependent upon an actually existing organism, and thus dependent on all general organic categories. And because any given organism is for its existence dependent on all general inorganic categories, consciousness depends at the same time on all general categories of the Inorganic Layer).
The next two diagrams illustrate overall concrete (layered) entities and layer-specific concrete entities, their relation to the category Layers and to the relationships of over-forming and over-building.

Figure above :  Overall (i.e. expanded) concrete (layered) entities representing category Layers. While themselves (also) being layered (except the lowest one), these overall concrete entities represent (but are as such not identical to) the highest Layer into which they reach (See also Figure higher above ).

Figure above :  Every Layer of Being (category Layer) has its specific collective concretum :

The specific collective concretum of the Inorganic Layer extends across two Layers (the Organic and the Inorganic). This is because the Organic Layer only over-forms the Inorganic, while the Psychic and Super-psychic Layers each over-build their respective lower Layer.

Apart from the  c a t e g o r i c a l  dependence (which is a category-category dependence, and as such contrasted with categorical determination, which is a category-concretum determination)  of  concrete entities (in the sense of collective concreta),  i.e. as this dependence can be deduced from them,  there is also the dependence of them from specific values of the fundamental physical constants of Nature (the value of the gravitational constant, of the constant of Boltzmann, of the speed of light, etc.). These latter dependencies clearly belong to the category-concretum determinations (i.e. principle-concretum determination).

Let us now consider the four Laws of Categorical Dependency one by one.

The Law of Strength
(Categorical Basic Law)

The higher categories always presuppose a series of lower ones, but not vice versa.
So categorical dependency applies without exception from the higher to the lower (the higher [partially] depends on the lower).
When one indicates this  "being-a-fundament-or-being-a-condition"  of a given category as its "strength", while its dependency as its "weakness", the Law can be succinctly formulated as follows :  The lower categories are, within the ontological stratigraphy, always the "stronger" ones, while the higher are always the "weaker". This relationship is as such irreversible all over the whole sequence of Layers. In the domain of categories (Nomos), strength and height are always inversely proportional.

This Law is directly evident there where we have reappearance and modification of categorical elements. This is because the reappearance consists in the inclusion of lower categories in higher categories. And this inclusion involves dependence of the higher categories upon the lower ones. That is, it is true, only a modest and partial dependence, but certainly an undestructible and irreversible one. The reappearance is, as we know, also not reversible. A complex item (as we can view a higher category), how far it is elevated above the elementary (a lower category), remains nevertheless in a certain state of dependency upon it.
This state of affairs is not, however, sufficient for an all-out dependency of the higher upon the lower, because the reappearance itself is not universal across the system of Layers. One could, it is true, think of the Fundamental categories, whose reappearance and concomitant modification takes place in all temporal Layers (i.e. they apply already in the Mathematical Layer and then reappear in all subsequent Layers). But also this is not sufficient, because many other categories fail to get through at the natural limits of over-forming. And indeed it is the dependence of categories of which it is all about. Surely, some categories, other than Fundamental ones, cross this boundary too (i.e. cross the boundary between two Layers in spite of the presence there of a relation of over-building [instead of over-forming] between the two Layers separated by this boundary), for example the category of Time. But with this we still don't have an all-out dependency of higher categories upon lower ones. So reappearance is indeed not sufficient to fully account for the dependence of all higher (general) categories upon lower ones.
Here a different factor comes into play :  It is the all-out resting (or being carried) of the higher Layer of Being, together with its ensemble of categories (which makes it up), on the lower Layer. This relationship is more general than reappearance :  It is also present where the latter fails. It passes beyond the limits of over-forming, because also the ontological 'super-structure' (as this overbuilds a lower Layer) -- which does not, by its nature, take up a great many categorical elements (i.e. it rejects those elements) -- remains retrospective towards the lower Layer of Being and its categorical make up. It rests on it.
To these relationships one is forced to conclude when studying the concrete entities, like crystals, materials, organisms, etc.
Dependency that originates from reappearance, is only one kind of dependency. In itself, categorical dependence can do without reappearance. A lower Layer can be a necessary condition for higher being also without its categorical elements being contained in that higher being. It can be its necessary condition in the sense of ontological base. And this base, as base, does not by itself imply a penetration of its elements into the next (higher) Layer. Its function is only to carry the latter. Here we can again think of the CD analogy. The material of the CD carries the music. Categorical dependency of the higher upon the lower, respectively the being-stronger of the lower categories, therefore, is indifferent as to whether reappearance of lower categories takes place or not, where the latter means that for the higher categories these lower categories are only an ontological base.
From all this it is evident that the Categorical Basic Law (the Law of Strength) is more fundamental than the Law of Reappearance. It is not bound by the limits of reappearance within the system of Layers. It expresses a basic relationship nowhere interrupted along the sequence of Layers. So it penetrates deeper into the very essence of the layering than the stratigraphic Laws themselves do.
Considering only the four main Layers of the World (thus not considering possible subordinated layers), the content of this Law (i.e. the Law of Strength) can be expressed as follows :
The organism is nothing more and nothing less than the result of over-forming of the physically material (i.e. of the inorganic).
A consciousness is nothing more and nothing less than the result of over-building of the organic.
In the same way there is only objective spirit as super-structure of the psychic, i.e. as result of over-building of the psychic.
Always the higher level of being is carried by the lower. Never does it just hover in the air without ontological base. And this relationship continues, regardless whether the higher categories absorb lower categories or have these latter only as their ontological base.

Although we concentrate mainly on the Inorganic-Organic, we will relate what HARTMANN tells us about the objective spirit (Geist) at page 524-526 of Der Aufbau der realen Welt, 1940, because these considerations are of general significance to a good understanding of the doctrine of categories.
The  objective spirit  is the collective concretum of the Super-psychic Layer of Being. It consists of the ethical person, human history, human society and institutions (like science or religion), etc. The corresponding category Layer, the Super-psychic Layer, lies on top of the Psychic Layer, the collective concretum of which is consciousness. The objective spirit or spiritual being(ness) is not identical to psychic act, and its laws are different. But the executional nature of the psychic act is contained in it, the act just grows into a system of a different nature with respect to content and significance. This different system is itself in no way psychical act anymore, it extends far beyond the limits of the act-executioning consciousness into a sphere of common spiritual life, that uniformly continues to exist and develop within the continuous alternation of individuals. But also this higher system always remains bound to consciousness and psychic act as to its carrier. Without the latter it cannot exist.

The Dependency of Spiritual Being(ness) and the Categorical Relationship

( Ontology of the Objective Spirit )


The "strength" of a category, in the context of the Laws of Categorical Dependence, is thus not identical with its power of reappearance. This power or capacity is, it is true, tied up with this strength :  Indeed, the case of the Fundamental categories (which do pass through all Layers) clearly shows that precisely the lowest categories possess the greatest penetration power. But that is only one aspect of the Law of Strength. There is still a more general sense of being-stronger.
This is best seen when departing from the objective spirit. Spiritual life not merely rests on consciousness and mediately on organic and physical being, but also has much to do with it :  The (human) spirit interferes, transforms and evaluates, it create things according to its goals, things unknown to Nature. It breeds plants and animals, and transforms its own psychic life. But in all its activities it remains dependent upon the inherent laws of those entities that it so transforms. The (objective) spirit cannot change the laws of the material, of the physical processes, of the organic. They stay what they are. The spirit has no dominance over them. On the contrary, it is these natural laws that set specific limits to its acting and planning. Those laws also apply in its own domain of life, because the latter is not free-floating, but resting on a substrate. A falling stone can terminate the life of a genius, on whose activities was dependent an intellectual enterprise that would change history. The supremacy of man does not come from ontological independency, but from his knowledge, conscious adaptation and goal-oriented evaluation.
The positive aspect of this relationship is clearly illustrated by technology. The latter cannot influence the natural energies and their behavior. All it can do is understand their underlying laws, and use them for achieving certain specific goals that benefit humans and their society. Technology (which is one of the features of the objective spirit) consciously takes into account the being-stronger of lower categories. It adapts to their rule in a docile way. And all that it creates, is based on guessing or fathoming that rule. At the same time technology also consciously takes into account the indifference of such natural powers or rules with respect to all over-forming or over-building. For falling water it is even, whether it falls freely or through a turbine channel. But that it falls anyway, the spirit cannot change.
This relationship is something general. Spiritual life is a constant adaptation to the framework of spiritless powers. The care for habitation, clothing, warmth, etc,. sticks with people at all levels of cultural elevation. The spirit is hooked back to the rules of Nature of which it is a member. These rules themselves are not in any way bound up with it. In this way, the dependence, the susceptibility to possible injury and the destructibility of spiritual beings, yes even of the merely living beings, stand in stark contrast with the independence and supremacy of the cosmo-physical conditions. This is impressively evident when one imagines the vanishing smallness of the human world with its temporally limited history :  how it, while clinging onto a, it is true, relatively stationary, but nevertheless transient condition of a planet surface, has an ephemeral existence, not knowing whether in some remote corners of the Universe there exist something similar under comparable conditions.
Here the relationship of strength of the lower and dependency of the higher is evident in the concretum itself. It is the well-known basic fact of human existence that in every-day events is as clear as in the bodily and psychic functions that are resting on it like breathing and eating, working and entertaining. The adequate ontological expression for all this is to be found in the dependency relations of the categories :  What the higher categories perform is limited to those things that are permitted by the ontological basis formed by lower determinants. In this sense the lower categories are the stronger.
The human organism has, in many respects, adapted itself to the exigencies of the objective spirit, but this adaptation has definite limits. Spiritual or intellectual development of the individual needs a longer life-span than the higher animals. Within the limits of the organically possible, the vital life-curve of the human body is adapted to this purpose. Perhaps this adaptation can be improved, but it cannot do so indefinitely. It is limited by the law of the organic, that every organic species can only continue by change of individuals, that is to say from one individual to the next. And as the psychic life separates the individuals, i.e. that consciousness appears anew in each human individual, so also the spiritual development must start anew everytime. The spirit can, it is true, as objective spirit form an existing background for a given human individual, within which it develops, but spiritual development itself, the processing of earlier accomplishments, must always depart from a more or less empty beginning.

No matter what examples are chosen, all of them show the same basic state of affairs. In addition, they show the independence of categorical dependency from the reappearance, and at the same time that both are irreversible. Strength and height of categories are inversely proportional to each other.
The Categorical Basic Law (the Law of Strength) expresses nothing else than the uniform direction of dependency throughout the sequence of Layers. This dependency of higher categories from lower is as such not directly visible. We deduce it from the collective concretum :
In a human being we see that his consciousness is dependent on (certain parts of) his organic body, and that his organic body in turn is dependent on certain physico-chemical processes and materials. This visible dependency should be accounted for by a principle, that is to say by a category, or maybe several categories.
What is the concretum of this category?  It would be :

The psychic depends on the organic, which itself depends on the inorganic".

We see that this 'concretum' is in fact a dependence relation between principles (instead of concrete entities) :  indeed, "the psychic", "the organic", and "the inorganic" are not as such actually existing concrete entities. Therefore we should formulate things as follows :

The psychic as such depends on the organic as such, which itself depends on the inorganic as such".

And this means :

The principles (categories) of the psychic depend on those of the organic, while the principles (categories) of the organic depend on those of the inorganic."

This indeed is the concretum of the first mentioned principle or category (as answer to the above posed question). And the latter is the first Law of Categorical Dependence, viz., the Law of Strength (Categorical Basic Law). So we see, when generalizing, that categorical laws, that is to say laws about categories, are categories themselves. And so that particular category that is represented by the Law of Strength determines the dependence of psychic categories from organic categories, and of organic categories from inorganic categories, or, more generally, expressed :  the dependence of higher categories from lower categories.
So what we mean to convey here is that we cannot in fact say, without qualification, that the psychic is dependent on the organic and the organic is dependent on the inorganic. Expressed in this way, it refers to a dependence of certain principles (categories), i.e. to a category-category dependence. But this dependence of psychic principles on organic principles, etc., undoubtedly involves many concretum-concretum dependencies, which we can see in all the processes that are going on in either of these three domains of Being. And a concretum-concretum dependency is determined by a category, namely a nexus category. Such a category connects concrete states in a definite and necessary way. Only in such cases we can legitimately say the one (state)  depends  upon another (state). The dependence is between concrete entities, instead of between principles.
So from the fact that (1) for the objective spirit to exist at all, consciousness is indispensable, (2) for consciousness to exist at all, an organic body is indispensable, and (3) for an organic body to exist at all, physico-chemical processes and materials are indispensable,  we deduce a corresponding dependency of principles (categories) that determines these indispensabilities. And this particular dependency of principles is itself a principle or category, namely the Law of Strength (text continued in next document).

The next document continues the discussion of Categorical Laws, (this discussion) as such belonging to the philosophical context of the crystal analogy.

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