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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 :

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."

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 :

• The actual unity (a being-so-and-so, as such determined by the modified Category of Unity) of an  o r g a n i s m  has not (necessarily) actually evolved from the actual unity (a being-so-and-so, determined by the non-modified Category of Unity) of  a  c r y s t a l.
  ( The crystal is a true individual intrinsic inorganic being, and may even represent the only kind of inorganic intrinsic being at all.  The organism is a true intrinsic organic being.).

• Actual regeneration (which is a being-so-and-so, determined by a modified category) in an  o r g a n i s m  has not (necessarily) actually evolved from actual regeneration (which is a being-so-and-so, determined by the corresponding non-modified category)  in  c r y s t a l s.

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 :

• Space Group
  Mathematical Layer.  Point Lattice + symmetry of motifs.
  It is purely mathematical, and therefore not involving stability or instability.

• Crystal Lattice
  Inorganic Layer.  Point Lattice + motif symmetry + atomic aspects.
  A crystal lattice is an aspect of the internal structure of a crystal, and so it is a property of an inorganic object. Issues as energy, stability and instability are involved.

• Organic Lattice
  Organic Layer.  Over-formed crystal lattice. Involving compensation reactions, etc.
  Aspect of the internal structure of an organism.

• Inorganic Growth
  Inorganic Layer.  Steady and regular increase of the volume of an intrinsic being while the latter's specific structure is preserved. The increase in volume takes place by selective apposition of particles (i.e. the selective deposition of particles from the environment onto the surface of the intrinsic being). Example :  Crystal growth.

• Organic Growth
  Organic Layer.  Overformed inorganic growth (over-formed crystal growth, in the case of the correctness of the theory of organic lattices). Organic growth takes place by selective intussusception of particles, that is to say, particles from the environment are selectively taken up into the interior of the organic being, and then further processed.

Growth
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 :

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 :

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.

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.

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.

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).

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).

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

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.

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.

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).

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 Law of Principle

• The Law of Layer-applicability

• The Law of Layer-bound Applicability

• The Law of Layer determination

• The Law of Categorical Connectedness or Union

• The Law of Layer-unity

• The Law of Layer-wholeness

• The Law of the Limits of the Range of Mutual Dependence

• The Law of Implication

• The Law of Categorical Reappearance

• The Law of Modification

• The Law of the NOVUM

• The Law of Layer-contrast

• The Law of Strength (Categorical Basic Law)

• The Law of Indifference

• The Law of Matter

• The Law of Freedom

The common principle of these laws is

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 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).

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 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.

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.

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.

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

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.

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.

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 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 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.

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.

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

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.

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 :

• Time involves Process, because time originates from processes.

• Process involves Time, because a process is a succession of states in time.

• Process involves (physical) Space, because process (as it is in the Inorganic Layer) involves material bodies and these in turn involve physical space.

• Space involves Time, because (physical) space involves material bodies (empty space cannot physically exist), while these in turn are products of generative processes, which latter involve time.

• Process involves Substance and vice versa.

• Process involves Causality and vice versa.

• Causality involves Time and vice versa (that is to say, time involves process and process involves causality).

• etcetera.

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.

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).

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.

The first Law of Categorical Stratigraphy is :

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.

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 :

• Reappearance (with concomitant modification) of general categories results in the over-forming of Layers of Being.

• Breaking off of general categories (i.e. their not reappearing again) results in the over-building of Layers of Being.

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)

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.

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).

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.

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.

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.

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 ).

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.

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.

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

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.

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 :

• There exists a categorical dependency of Layers upon one another, but only in a one-way fashion, as dependence of the higher upon the lower Layer (in the sense of resting upon or being carried).

• This dependency not only exists there where we have reappearance (of categorical elements), i.e. where we have a relationship of over-forming, but also there where this breaks off, that is to say where we have a relationship of over-building. Also there the higher rests on the lower.

• The dependency of the higher Layer of Being is never a total dependency. The higher Layer's NOVUM is and remains independent (autonomous) with respect to the lower categories -- regardless whether these reappear in this higher Layer or only supply the base on which to rest.

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 Super-psychic category Layer is the Objective Spirit.
• The specific collective concretum of the Psychic category Layer is Consciousness.
• The specific collective concretum of the Organic category Layer is a lower animal, for instance a herring.
• The specific collective concretum of the Inorganic category Layer is a Crystal.

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.

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 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).

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