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Revised Ontological Interpretation of the Determinations ('Accidents') of a Substance [ Part Three ]

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That what is fully determined, i.e. completely specified, is real, and that what is real is fully determined. That what is fully determined is individual, and that what is individual is fully determined. And when it is moreover not only individual but also an individual, it is subsisting out into Reality.

Remark: As I noticed earlier, the discussion throughout relates to the possession of a determined length, say, 60 cm, i.e. a completely specified determination.
LENGTH-AS-SUCH has a different nature. LENGTH-AS-SUCH has the nature of a principle : Every real subsistent being (that could be a Totality or an aggregate) possesses (a) length. Expressed more generally : Every real being is quantitatively determined. Those items that are signified by the highest, i.e. most general, 'accidental ' genera, accidental categories, --- the "accidental genera " are terms signifying determinations --- namely (those items) signified by the terms Quantity, Quality, Relation, etc., are not only not complete beings, but are no beings at all. They are just the most general determinations of a Substance (a Totality), or equivalently, the most general ways of being. Every real subsistent being is determined according to these General Determinations. But this does not apply to the complete determinations ' narrowing ' the General Determinations down (i.e. having them turned into special fully determined determinations), to, for example, 1.50 meter long, because not every being is 1.50 meter long. Among these full-fledged special determinations we can discriminate between per se determinations and per accidens determinations, with respect to the Essence and so with respect to the dynamical law.

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The Nature of the Elements of the Dynamical System and of those of the Totality, and their Relation with the Dynamical Law

Totalities can be actually or conceptually, generated from elements in several ways, depending on the type of Totality. The most important of these types are :
• Molecule
• Crystal
• Organism
It is important to emphasize that -- when we speak about " generation (or formation) of a Totality " -- we do not have in mind a natural or industrial manifacture of this (species of) Totality. For example many kinds of molecules are actually produced (synthesized) by the coming together of already complete atomic complexes, or by breaking down already existing larger molecules. So a dynamical system which actually produces such molecules in Nature or in the chemical industry often consists of already larger and more complex components (larger and more complex than single atoms). But those larger components must once have been synthesized somewhere, ultimately from single atoms. So we can, in the context of locating the Essence (of, for example, a molecule), legitimately think of the single atoms as the system elements of a dynamical system that can in principle generate that molecule. Moreover in most chemical reactions catalysts play an important role. But they do not actually take part in such a chemical reaction, they only speed up the reaction. So the dynamical law of, say, a certain molecule, is here viewed as the dynamical law, not necessarily of an actual concrete dynamical system, that had generated that molecule, but of a conceived dynamical system that could in principle generate that (species of) molecule directly from a collection of single atoms under appropriate external conditions. Consequently the dynamical law is, throughout this website, first of all an inferred entity, a (special) principle, inherent in some very implicit way in a certain collection of atomic species. Such a collection can harbor a great many such laws. Which one (of them) will actually operate depends on several external conditions.

Molecules

Say we have a molecule, indicated by its empirical formula as A4BC, and by its structural formula as :

(and thus a molecule consisting of a chain of four atoms of species ' A ' with an atom of species ' B ' attached to the second member, and an atom of species ' C ' to the third member). The generation of such a molecule will normally take place via the disintegration of other molecules and subsequent recombination, finally resulting in that molecule. But, as has been said, if we focus our attention on the ONE dynamical law, ultimately responsible for the formation of such a molecule, we must conceive such a molecule as directly being formed from its constituent atoms. We must conceive these atoms as initially freely existing, and subsequently entering into a definite structural pattern. As has been stated, the initial set of freely existing atoms admits, on the basis of their properties (their intrinsic determinations), of (the potential presence of) different dynamical laws. Which law (from this set of possible laws) will start to operate, is dependent on some external conditions like temperature, pressure etc.
When the atoms (because of the operation of one of those laws) enter into the structural molecular framework, they are in fact being integrated into a (larger) whole and become virtual. They are turned into determinations of that whole. The degree of virtuality is directly proportional to their degree of integration.
When such a whole, such a molecule, is itself going to be engaged in subsequent chemical reactions, it will normally first disintegrate up to a certain degree, and this means that the virtual elements become actual again, and / or certain complexes of virtual elements (those complexes being themselves also virtual) become actual, and subsequently are now able to react, either with each other again, or with other freely existing (and thus actual) atoms or atomic complexes, to generate another molecular species, or several other molecular species.
In locating the dynamical law for (the generation of) a particular molecular species (always comprising identical individuals) it is clear that this dynamical law (among some other possible laws) was inherent in precisely the set of free atoms, that entered the molecular structure. In the case of the aforementioned example that is the set {A,A,A,A,B,C}.

Remark: Another of the possible laws could have generated the molecule

which is a molecule formed from the same set of atoms, but now arranged in one chain without side chains. It has the same empirical formula, namely A4BC, as the previously considered molecule.

As the examples show, every molecule points to a definite set of atoms, definite in the number of its elements, and definite with respect to the atomic species involved. This set is indicated by the empirical formula of the relevant chemical compound. But for this set to constitute a dynamical system that can (albeit just in principle) generate the molecule from the elements of the set, a macroscopical, i.e. more or less bulky, context seems almost certainly required, which means that the atomic set, as described by the empirical formula, should be multiplied such that the resulting set now has macroscopical, or at least submacroscopical, dimensions, but is still qualitatively identical to the initial set.
Because -- as we see in the physiology and biochemistry of organisms, especially very small organisms -- chemical reactions can take place at very small scales, the factor of the just mentioned multiplication needs not be very large. Maybe, and at least for convenience, we can forget about this multiplication all together, and consider just the set of atoms as indicated by the empirical formula as the complete set of system elements of our conceived dynamical system that can generate the given molecule under appropriate external conditions.

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SO IN MOLECULES THE DYNAMICAL LAW IS NOT INHERENT IN THE MOLECULE JUST LIKE THAT, BUT IS TO BE LOCATED ONLY BY REFERRING BACK TO SOME PROPERTIES OF THE INITIALLY FREELY EXISTING ATOMS (i.e. conceived as freely existing) FROM THE ABOVE DESCRIBED SET, OR FROM AN EQUIVALENT SET,--- PROPERTIES, WHICH MAY NOT EXIST ANYMORE IN THE MOLECULE.
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The existing properties of the molecule and the conditions in which it finds itself, together are the determinations of the Totality represented by that molecule.

Crystals

The case of the formation of crystals is slightly different.
Here also the dynamical law is inherent in the set of initially free atoms (or ions, or molecules -- and these refer back to their constituent atoms). This set, representing as it were the dynamical law, must contain all atomic species that finally enter the crystal structure, but the number of individuals of each atomic species (going to make up this set) is not fixed beyond a certain minimum. That's why a crystal can grow more or less indefinitely. The initial set of atoms, i.e. of system elements, should accordingly be bulky in order to generate a macroscopical crystal.

ALSO IN THIS CASE THE DYNAMICAL LAW OF THE CRYSTAL IS NOT INHERENT IN THE CRYSTAL JUST LIKE THAT, BUT REFERS BACK TO SOME PROPERTIES OF FREELY EXISTING ATOMS FROM THE ABOVE DESCRIBED SET.

The existing properties of the crystal and the conditions in which it finds itself, together are the determinations of the Totality represented by that crystal.

In both cases, molecules and crystals, no reactions take place anymore inside the generated Totality. Only vibrations, and -- sometimes -- rotations do occur.

Also in both cases we have to do with a certain initial collection of elements. In the case of these elements forming a dynamical system, this collection contains more (potential) energy than some possible chemical configurations of these elements do, in wich (configurations) they are bonded chemically. Now as soon as these elements get the opportunity, they will spontaneously assemble into one of those configurations that contain less (potential) energy and are consequently more stable. I.e. those elements will interact. And they get the opportunity to do so when they are sufficiently close to each other.
Out of the many possible element configurations, that one will be 'selected' which contains the lowest energy in the given external conditions.
So the whole system spontaneously flows to a lower energy state, and this is equivalent to saying that a certain dynamical law spontaneously starts to operate among the elements (when certain conditions were met), resulting in a particular configuration of those elements.
In organisms on the other hand, energy plays, it is true, a somewhat similar role, but organisms do not represent energy minima with respect to a certain initial collection of system elements.

Organisms

The case of organisms is, consequently, quite different.
This is because also AFTER the Totality has been formed (this point in the -- individual -- history of the relevant dynamical system is hard to determine), chemical and electro-chemical reactions keep going on during the existence of the organic individual. The Totality is highly dynamic and far from thermodynamic equilibrium (in contradistinction to molecules and crystals). Recall that organic Totalities obtain their stability not by residing in one or another energy minimum, but by a constant influx and efflux of matter and energy.
With respect to Organisms it is not directly clear how to determine (indicate) the system elements (i.e. answering the question : " What are the system elements relating to the dynamical system that generated the organism in question?").
Are they the initially freely existing atoms, corresponding with virtual atomic constituents of an organic body, or (are they) some molecules from a specific set of organic molecules?
Are they food particles (going to assimilate to, and making up, the organic body)?
The functioning organism consists of assembling processes, dissociations and reassemblings, in a miraculously organized fashion. Here the Totality is never static, but can only exist as a dynamic entity. And here the (penultimate) constituents are more like processes than things. But those processes must somehow be orchestrated into a unity by some overall dynamical law. This ultimate dynamical law, penultimately located somewhere in and around the DNA, is the Essence of the particular organism.

Remark: Concerning the last sentence, "This [...] dynamical law [...] is the Essence of the particular organism", we must add the follwing : Here "particular" means : "belonging to a certain -- but whatever -- sort". If "particular" would mean : "this individual", then we should interpret the sentence as follows : "This dynamical law is the Essence of the particular organism, but not insofar as it (= the organism) is particular". This is because the (concept of) Essence, as developed here, always relates to a specific Essence. Only when a species contains no more than one individual the sentence can relate to this individual, but still not insofar as it is an individual.

In Organisms atoms and atomic complexes continually enter in and (go) out (of) structural patterns. So there is a dynamic of going in(to) and out (of) virtuality.
Because in the Organism (and generally also in Molecules and Crystals) the atomic species themselves are NEVER transformed into other species (their atomic number = nuclear charge = their specific identity, does not alter), a process only occurring in nuclear reactions and in spontaneous atomic decay -- radioactivity, we must consider the ATOMS as the ultimate constituents of the organism (like we did with respect to molecules and crystals, where it was evident from the outset). The organism is an ongoing atomic dance resulting in disintegration and generation of molecules. Many of these generated molecules are subsequently going to form patterns of a higher order, seen as concentration gradients, concentration patterns and other supra-molecular structures like cells and muscle fibres. Some atoms, often in the form of ions (= electrically charged atoms), remain isolated and, in a way, are freely existing in the organic body.
In what way must we interpret this state of affairs ontologically?
Seen from the bottom up we can say :   Every molecule in the organic body is dictated by its own dynamical law, and so also every larger organic substructure, like organs. But all these lower-order organic laws, and also the ' decisions ' which law(s) -- from the set of all the alternative laws which could in principle operate at the corresponding lower levels -- should start to operate on which occasion, (all these lower-order laws) are orchestrated by the overall high-order dynamical law, guaranteeing the unity of the dynamic organic body, and causing in a way the higher-level functions of the organism. At the lower levels of the organism formation and disintegration of lower units -- for example molecules -- take place.
But seen from the Organism as a whole --- thus seen from the highest level, all the items which (together) make up (in contradistinction to : are going to make up) the organism must be considered as virtual parts. And depending on their degree of integration into the whole, and thus depending on the degree of the loss of their (own) identity, is their degree of virtuality. Strongly integrated parts are highly virtual because their transformation (back) into actual (isolated, freely existing) things demands more ' effort '. Although we can, in a sense, speak about molecules, interacting with each other (as metabolic processes) in(side) the organic body, this way of speaking is metaphysically incorrect, because it destroys the unity of the Totality (which is admittedly presupposed). Those interactions are NOT interactions between molecules, they are not activities of those molecules, but activities of the organism itself (Of course the first (reductionistic) interpretation remains useful in medical and natural science). All these metabolic processes are -- ever changing -- determinations of the ONE organism. These changing determinations are ultimately dictated by the (overall) dynamical law. ( In fact, here, it does not concern the changing of determinations, but the (ever) changing of the organism by means of alternation of determinations of that organism. )

As we just saw, the distinction between a reductionistic (physical) approach and a holistic (metaphysical) approach becomes more prominent in the case of organisms than it is the case in molecules and crystals. In organisms especially, the term "determinations" is metaphysically motivated. Also the conceptual nature of the dynamical system and of the set of ultimate system elements (the relevant atoms) is more prominent than it is in the case of molecules and crystals.

THE DYNAMICAL LAW OF AN ORGANISM IS NOT INHERENT IN THE ORGANISM JUST LIKE THAT, BUT IS TO BE LOCATED ONLY BY REFERRING BACK TO SOME PROPERTIES OF THE INITIALLY FREELY EXISTING ATOMS.

These atoms are going to constitute the organic body, and while doing so they are not specifically changed (they are not, while doing so, changed into other atomic species), but only peripherically, i.e. in their outer electron shells (See the Essay on The Chemical Bond). So the dynamical law is ultimately inherent in the set of all atomic species which enter the structure of the organic Totality. Thereby the number of individuals of each atomic species is not precisely fixed beyond a certain minimum, because different individuals (of the same organic growth stadium) of an organic species turn out to vary in bulk (just like crystals, but unlike molecules). Often a larger supply of food results in a somewhat bigger organic individual. Certain limits to their size are of course set by the dynamical law (generally unlike crystals), especially by the DNA-part of that dynamical law.
To be sure, this dynamical law is (ultimately) residing in the above mentioned set of atomic species, but penultimately it resides in and around the DNA, as has been said. But we must elaborate on this a little further :
The set of all atomic species, and, of each species a not precisely fixed number of atomic individuals, that has -- seen after the fact -- entered into the organism (in the context of a continually going in and going out process) originally contains (implicitly) a multitude of possible dynamical laws. But when those atoms are finally organized in a certain way up into the molecular genetic framework of a certain organism, we can -- again after the fact -- state that a special dynamical law (out of the many, originally possible) has operated and continues to operate, resulting in the further formation and maintenance of the organism. So the above mentioned set of atoms is the ultimate set of system elements, and in this set the dynamical law in question (among others) resides. Penultimately this law -- and now excluding others -- resides in and around the genome (the DNA) of the generated organism.
But the 'construction ' of the organism from the ultimate set of atoms mentioned, must be understood as a conceptual construction, a conceptual generation (of the organism), not as a factual one. This idea of conceptual generation serves to locate the dynamical law.
The dynamical law is (conceptually) found by referring back to some properties of initially freely existing atoms. This implies that there is a definite relationship between determinations and Essence, be it that these determinations are not those of the Totality in question. This relationship is however a very complex one and, as far as my knowledge goes, not clearly understood. The dynamical law cannot be equated with a determination, because it is not contained in one special determination, but is situated over several determinations, i.e. it involves several determinations which are themselves distributed across several system elements. So the ontological status of the dynamical law is different from that of a determination. We have expressed this difference by means of a discrimination between the genotypical and phenotypical domain. See the next Figure.

System Elements and a possible Dynamical Law.
Diagram symbolizing a possible dynamical law (red line) as it derives from certain properties of the system elements. The red line symbolizing this dynamical law should imagined to be interrupted (in the spaces) between the system elements. As one uninterrupted line it symbolizes the one-ness of this dynamical law. Each system element harbors many properties. All system elements participate in the constitution of that dynamical law, but not all properties of the system elements do so participate. Another possible dynamical law should be indicated by a similar line, going through all (or some) system elements, but 'hitting' different regions within each system element. Of course the line representing a dynamical law could intersect some system elements twice or more times, whereby each intersection corresponds to a certain property of the system element involved.

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So we have in fact the following relationship (going from left to right) :

 DETERMINATIONS ESSENCE DETERMINATIONS ( of system elements ) ( Dynamical Law ) ( of generated Totality )

The above scheme reflects a very close connection between determinateness on the one hand, and lawfulness on the other.
When some one thing is determined in some way, be it per se or accidentally, and so possessing a certain feature during all of its existence or just during a certain time interval, the acquiring of such a feature is the result of some local process and is as such repeatable over many instances because a process is a regular event, i.e. an event dictated by a certain local law operating at a certain locality of that particular thing or involving the whole of that thing. As we have already stated, it involves a repeatable interaction of the thing or a part of it with one or another agent, or (other) thing. The ontological status of the resulting determination is assessed with respect to the given thing as being either extrinsic or intrinsic, and with respect to the latter either per se or per accidens.
The relation between the Totality and its determinations on the one hand, and the ultimate system elements on the other, is diagrammed in the following Figure.

Schematic representation of the Totality (as a complete set of determinations) and its ultimate system elements containing the Dynamical Law.

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What has been said about organisms with respect to their Essence (dynamical law), the system elements, the elements of the organic Totality and the Totality's determinations, is of course no more than a preliminary sketch. Much more research, biological and philosophical, is required to settle the issue in a more satisfactory way.
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The Totality itself

In many cases the generated Totality is itself also a dynamical system. But this system does not differ essentially from the system that generated the Totality in the first place. All this we see in the case of organisms, and less so in the case of crystals.
A growing crystal in a solution or in molten material is a dynamical system because the system elements in the solution (or in the molten material) are ordering themselves (into a regular pattern). In the case of a crystal growing in a solution the elements move towards the growing crystal. This movement is caused by the dilution of the solution in the immediate vicinity of the surface of the crystal, and this dilution is itself caused by the apposition (and thus reception) of system elements onto the crystal. Accordingly the dynamical aspect is, in the case of crystallization, not so prominent, but nevertheless present. System elements, once being received IN the crystal, do not really move anymore, but only execute vibrations around their average position. We can further observe an attraction-repulsion balance between the constituents of the crystal. So inside the crystal no generative processes (with respect to the becoming of the crystal) take place anymore. Generally the crystal does not show internal changes (except of course in the case of instabilities). What is taking place inside the crystal is just the maintenance of what has been formed. And because of this we can call such a crystal a more or less static system.
Also in the case of freely existing atoms and molecules the dynamical aspect only relates to vibrations and rotations of their parts around their average position. In some small molecules this dynamical aspect can be relatively significant. Of course the expression " vibrations and rotations of their parts " relates to a physical description. A metaphysical description will express those dynamic phenomena in terms of alternating determinations of the atom or molecule in question.
The case of organisms is, as has been said, different. There, the dynamical nature is, also after their formation (generation), well present. This is because of the OPEN nature of an organic system to the outside world. It is in a state of constant exchange with the environment. And now also inside the organism changes are constantly taking place : Growth (and maintenance) of an organism takes place not only in the form of apposition of physical matter, like in the case of crystals, but (also) by means of intussusception of physical matter (i.e. the insertion of physical matter), made possible by the semi-liquid condition of a large part of the body of organisms. But even in the case of organisms crystallization processes do occur, as is evident in shell-bearing animals like many snails, and also in Foraminiferans, Radiolarians and Diatoms.

Remark: Foraminiferans are unicellular marine animals generating a calcareous shell. Radiolarians are also unicellular marine animals generating skeletons, consisting of different mineral species dependent on the subgroup to which those organisms belong. Diatoms are unicellular vegetable organisms living in fresh or salt water, and generating shells of Silica.

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Conclusion

On the basis of the foregoing discussions we are now able to characterize the Totality (the real being), its Essence and its Determinations.
The Totality is the complete set of all types of determinations. When we use classical terminology we have to state that a (first) Substance is identical to the complete set of all types of accidents. But in Classical Metaphysics this statement would be denied. Classical Metaphysics considers the (first) Substance as ontologically something else than the complete set of all the types of determinations (accidents). The accidents inhere in their Substance. The Substance is the substrate of the accidents and is itself considered as an individual instance of the Essence of the thing (still according to Classical Metaphysics), and this Essence is contrasted with the accidents. But, Classical Metaphysics considers this Essence as an intrinsic cause of the thing, i.e. the Essence causes the appearance of the thing (how it looks like, when we abstract from variable appearances [ NOTE 1 ]). For example Classical Metaphysics considers the Essence of Socrates as follows : (An instance of) humanity, where humanity is the common Essence of all humans. In the case of Socrates we have to do with a particular instance of this Essence. When we were asked to describe this Essence, called " humanity ", then one comes up with a definition of MAN. It goes like this :

Man is a rational animal

Now Classical Metaphysics considers the Essence of a thing as a principle, an intrinsic cause. But " rational animal " is not a principle. It is undoubtedly an effect of a principle. So following the correct way to characterize the Essence AS Essence, one should say that the Essence (insofar as Essence) of a thing is that intrinsic something, that is responsible for the typical structure of the thing, i.e. for how the thing looks like while abstracting from variable appearances, and thus (responible) for how the thing is typically constituted.
In the case of Socrates one should say that the Essence of Socrates (but also of Plato, etc.) is that intrinsic something, let us call it " humanity ", that is responsible for the ability to think rationally (and this implies a specially structured organic body as the ' machinery ' for this ability).
Expressed in the language of this Essay we can state that the Essence must lie in the genotypical domain, and that all the determinations must lie in the phenotypical domain (The latter is the domain of the produced (generated) appearances).
" rational animal " is something which is caused, produced, and so must lie in the phenotypical domain. It then follows that " rational animal " is a determination, and thus NOT an Essence. Within the metaphysics presented on this website the Essence of a thing is the dynamical law governing the dynamical system that generated that thing. And this dynamical law is indeed situated in the genotypical domain, it is generative, not generated, it just inheres in the system elements in an implicit way, and still more implicitly in the elements of the Totality, and so not concretely visible.
When we consider one particular determination of the Totality, then we can say that this determination ("accident" in Classical Metaphysics) inheres in the Totality. That Totality, which is the complete set of all types of determinations, is accordingly the subject of that particular determination, or, maybe we can state that the complete set of all types of determinations MINUS that particular determination is the subject of that particular determination. But see our exposition of the ontological status of the SUBJECT in Part One.

Now it is possible to assess metaphysically all aspects of the Totality, its dynamical law and its determinations, in a more or less final way, using some terminology from Classical Metaphysics :
The Dynamical Law in its fully abstract form -- we could think of a mathematical formulation of it -- is the Substantial Form. This Substantial Form is going to associate itself with matter, and ultimately with physical matter, as soon as we consider the dynamical law in its concrete (but still general, i.e. not individuated) form, because the concrete dynamical law is immanent in the physical matter (namely in the system elements). But, in (conceptually) proceeding this way we do not (yet) include that aspect (i.e. principle) of physical matter which causes individuality (See for individuality the Essay on The Principle of Individuation). We start from matter-as-not-yet-definitely-delimited. How do we conceptually obtain such (common) matter in the first place? We obtain it by means of a conceptual subtraction procedure (the subtracted aspect will later be added back again) : What then remains of the matter, i.e. of the physical matter, namely after not considering, and thus subtracting, that aspect of matter that individuates, is, because of that, no longer physical matter anymore, but is the strictly formal aspect of physical matter, a non-individual matter (the common matter). Said differently, it is (in-)formed matter only, and as such, Form in a broader sense, i.e. actualized matter. Subsequent addition of the individuating aspect of matter renders it physical again.
Let us further summarize things in the following scheme, partly borrowed from St. Thomas Aquinas (some terms were already considered earlier in this Essay [Part One]):

But firstly we will translate some classical Latin terms :

• forma totius = form of the whole, i.e. it represents the whole essence.
• forma partis = form of the part, i.e. it represents a part of the essence
( = substantial form of material beings).
• materia signata = matter as designated.
• materia non signata = matter as not designated.
• forma substantialis = substantial form
(of material or immaterial beings).
• materia prima = prime matter (matter as prime).
The Essence is the forma totius. This forma totius consists of materia non signata + forma partis (= forma substantialis ).
The formal aspect of the dynamical law is (as we just saw) the forma partis.
The materia non signata indicates the immanence of the forma partis in physical matter.
The Essence ( forma totius ) (is itself not, but ) becomes singular (particular, individual) by virtue of the materia signata (i.e. it becomes individual when matter becomes designated matter).
The materia signata is prime matter under terminated dimensions, and guarantees the here-and-now individual (See again the Essay on The Principle of Individuation).
The Essence is the concrete dynamical law.
The forma totius, together with the materia signata , gives an individual matter-form composite.
The forma partis together with the materia non signata + materia signata gives that same matter-form composite.
The forma totius is the non-individuated Essence.
The Essence + materia signata is the individual substance (s. str.).
The Essence generates determinations of the Totality. The individuation conditions must, to be sure, be satisfied, but they do not contribute anything-with-respect-to-content in the process of that generation.
The Essence + determinations + materia signata gives the individual substance (s.l.), and thus the Totality. It is an individual real being, or, in short, the existing individuum .

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Complete concretization of the dynamical law, resulting in its actual operation, demands (i.e. implies) the presence of an initial system state. This initial state is not an addition to the dynamical law (this happens only in the case of computer simulations of dynamical systems), but contains the formal dynamical law, and in a way, IS the concrete and active dynamical law, said differently, that initial state is the concrete dynamical system.

Remark: When the dynamical system is still in its natural initial state, the dynamical law is generally not yet the Essence of one or another Totality, and this remains the case as long as such a Totality is not yet generated by the dynamical system.

Ontologically more precisely formulated, the initial state contains the dynamical law immanently, and because of this the law is now concrete and individual, but as such still only implicitly existing, and (thus) although individual, it is not an individual, not an individuum.
The dynamical law is, as has been emphasized many times, inherent in the system elements. These are the things which, while interacting with each other, embody the dynamical system, and in so doing generate the Totality in the case of a Totality-generating dynamical system. The dynamical law itself is, accordingly, not generated by these elements --- these system elements must be distinguished from the elements of the generated Totality --- but IS already (present) in them. Because the (concrete) dynamical law generates the Totality (from an initial state still lacking the Totality), it also generates the intrinsic determinations of that Totality. These determinations thus are generated by WHAT the Totality essentially IS, said differently, they are generated by the Essence of the Totality.
By generating those determinations the dynamical law, which is now the Essence of the generated Totality, determines itself further, and its concretization implies a space-time position, and only then it can, in the form of a Totality, that is, of a true being, exist in the Real World. This we can also state in another way : With the concretization and individuation of the dynamical law, a Totality is generated. This Totality is the phenotypical expression of that dynamical law and thus of that Totality's Essence, which itself belongs to the genotypical domain (or level) of the Totality. Phenotypical expression is identical with the generation of intrinsic determinations and with it with the generation of the Totality which interacts with the environment.
This Totality is, as has been found out, identical to the complete set of determinations. Implicitly it contains the dynamical law, and it rests on prime matter as its ultimate substrate. But this ultimate substrate is only potentially existing. It is the potency for receiving any content, any form, albeit via certain intermediate forms (this is why processes always proceed along certain definite trajectories).

Remark: When we speak about dynamical systems in relation to the Essence of a uniform thing, we only have in mind Totality-generating dynamical systems. In addition to these, certain dynamical systems do exist which do not generate any Totality. They disorganize a patterned initial condition, or do not organize any disorganized initial state. These systems are not treated of here.

Remark: The classical terms used here, were, as has been stated, borrowed from St. Thomas Aquinas. And, for who wishes to read something of his work, I recommend to read his treatise on Aristotelian metaphysics, called De Ente et Essentia. See for this treatise, in an English translation, the first external link at the end of the homepage.
For another English translation of this same text, together with an excellent and extensive commentary, see BOBIK, J. 1970, Aquinas On Being and Essence, A Translation and Iterpretation , University of Notre Dame Press.
For the Latin text, together with a German translation, see BEERETZ, F., 1983 Thomas von Aquin, De Ente et Essentia, Das Seiende und das Wesen , lateinisch / deutsch, Philipp Reclam Jun. Stuttgart.

Apart from Greek and Medieval writings, and some later texts, little is written on the subject treated of in this Essay, especially on the status of determinations and parts within Totalities. I can recommend a book called Philosophie der Anorganische Natuur, by P. HOENEN, 1947 (written in Dutch). In its sixth chapter it treats of the virtuality or actuality of parts, but only concerning inorganic beings.

This concludes our description of the metaphysical constitution of an individual uniform being, including its determinations and its Essence.

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The Open Dialogue

The problems we have treated of here are not easy to solve completely. They remain somewhat enigmatic. It is even not precisely clear what Metaphysics is all about. Also the precise goals of Natural Science are sometimes obscure. Should a discovery of a final, i.e. ultimate, (mathematical) equation, governing all the workings of the World, be the supreme goal of Science? Should this equation be (mathematically) solvable by the efford of the human mind (i.e. should its solvability be demanded)? What is the (ontological) nature of natural laws anyway?
So, because of the difficulty of the aforegoing problems, concerning the nature of the Totality, together with the somewhat vague nature of metaphysics itself (which should not be a reason to abandon it -- by the way, such reasons would finally be of a metaphysical nature themselves! ), I will not insist on absolute consistency between the various Essays on this website, because the investigation must remain OPEN, i.e. open with respect to alternative solutions, and so open with respect to philosophical dialogue (including the internal dialogue of the philosopher himself).

I already suggested alternative solutions in terms of a physical description of the phenomena of determinations (versus a metaphysical one).
The metaphysics, i.e. the metaphysical approach presented in this Essay -- alongside the physical one -- presupposes, as has been said, the appearance (when we ascend from the atomic scale to higher ones) of genuine and new unities, " Totalities ", having their own specific and individual identities. To account for such a unity, a metaphysical description is given in terms of principles of being, in fact principles of beings. But such a presupposition -- the presupposition of the absolute unity of Totalities above the (level of the) atom -- could (turn out to ) be false. It is not a priori impossible that those supra-atomic Totalities, although not just aggregates, are nevertheless NOT absolute unities : although the dynamical law, generating such a Totality, is ONE, or can be supposed to be ONE -- and thus guaranteeing that the product is not an aggregate -- the resulting Totality need not a priori be ONE itself. The dynamical law could organize a multitude of things (elements of the initial condition) into patterns of elements (themselves either changed in the process, or not), elements, that remain things, also after their being organized into a pattern, organized into a ' Totality '. Such a consideration would accordingly be a fully reductionistic theory.

Remark: An argument that there are nonetheless supra-atomic unities -- absolute unities -- was presented above : The existence of self-conscious beings, like humans. We, humans, seem to experience our absolute unity. But although each one of us could indeed be an absolute unity, the experience itself could be an illusion, certainly a useful illusion for survival, but an illusion nonetheless (An example of an illusion -- here an optical illusion -- is given in the Figure below). So this experience is not a proof of our being an absolute unity.

An optical illusion. The lines are parallell .
(Borrowed from the homepage of Baruch Eden)

The metaphysical approach given in this Essay presents, it is true, also a reductionistic theory, because I considered all generations, i.e. formations (of Totalities), as generations from the ' bottom-up '. The Totalities are in their entirety generated from, and only from, the elements of the dynamical system. But, in contradistinction to the fully reductionistic theory, in that same metaphysical approach such generations are supposed to lead (at least in many cases) to absolute unities, having no parts, but only determinations. So this is, what we could call, a holistic bottom-up theory of beings. Such a theory could, by the way, influence the approach in Biology in a constructive way, by considering an organism as an intrinsic whole, with its own specific and individual identities, clearly distinguished from a man-made machine, which is not an intrinsic unity. The same applies to the new science of Artificial Life (a-life).

As has been said, it seems that a unity is already guaranteed by the ONE dynamical law. If several laws are successively active during the generation of something, and if this succession and the resulting generation is in principle repeatable, then there is in fact only ONE law operating instead of several.
But when in some way it would turn out to be impossible to reasonably suppose a one-law process underlying the generation of each organism (and each crystal for that matter), then a metaphysics of beings, of Totalities -- having their own specific and individual identities -- must be transformed into what I call an " INSOFAR AS " - metaphysics, because then, not only in the phenotypic domain unity comes in several degrees and never in an absolute way (as we have already ascertained in our investigations), but also in the genotypic domain. In this case there are no things whatsoever representing absolute unities, at least not in the Sphere of real beings. Such an insofar as metaphysics then considers things insofar as they are UNIFORM THINGS, unities. (Only) Insofar as a thing is a unity, it will have all the general properties of a hypothetical genuine unity, an 'ideal' being. This genuine, absolutely unified being then figures as the primary instance for all the things that are unities only in a weaker sense. This primary instance should reside in the Sphere of Ideal Beings, while its shadows reside in the Sphere of real beings. But of course it could be that there exists no primary instance at all, and that it is only a figment of our categorizing mind. If it indeed turs out that there really are no beings whatsoever (apart from possibly ultimate ones) representing, severally, a genuine unity, i.e. each having been generated by one definite dynamical law, then we cannot speak of "determinations of something", if we mean by "something" some one thing. Such a 'thing' would always be some more or less arbitrary aggregate, like, say, blood, having red as a possible determination.
All this could imply that everything we observe in the real world, 'substances' as well as 'accidents', are just determinations (attributes) of one Substance only. And this Substance could reside in another domain than its observable attributes do. Of course further philosophical research, sustained by data and theories of Natural Science, is needed in order to approach the true state of things. And not only "further" philosophical research, meaning a continuation of my (way of) investigation, is needed, but also other philosophical research, proceeding in different directions and starting from different assumptions than the ones presented on this website. In this way indeed the dialogue can remain open to all possible directions. And only in the context of such a broad dialogue the present investigation and its results can claim to be a contribution, i.e. a contribution to our culture.

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Trancendentals, and the doctrine of Categories in the sense of Nicolai Hartmann

In Classical Greek and Medieval Metaphysics we encounter the doctrine of the Transcendentals ( Transcendentalia ).
The Transcendentals are determinations that are intrinsically connected with EVERY being whatsoever, and that means also with every Accident. They thus are intrinsic principles that have to be satisfied by anything for it to be a BEING. For example the determination UNITY.
Another doctrine relating to an ontology (= a theory of being) is the Doctrine of Categories (Kategorienlehre) of Nicolai Hartmann who worked in the first half of the twentieth century. This Doctrine of Categories must NOT be confused with the doctrine of categories of Aristotle (which are treated of in the Essay on Substance and Accident). The Categories in the Hartmannian sense are principles of Being, not of beingS. While Aristotle's point of departure is the uniform thing, especially the individual uniform being, Hartmann's point of departure is the whole sphere of Being, which is permeated by general and special principles of Being.
I have found a certain interesting relation between the above mentioned Doctrine of Transcendentals and the Doctrine of Categories of Hartmann.

In the Essay (Critical Series) Historical Individuum, Here-and-now Individuum, first subsection (Individuals and Nominalism) we found out that a certain similarity exists between the Transcendentals (i.e. the terms UNITY, GOOD, BEAUTIFUL, THING, SOMETHING, TRUE and BEING) on the one hand, and the 'accidental' terms QUANTITY and QUALITY (and other such terms) on the other.
These two types of terms can be, in a way, predicated of every real being whatsoever.
They are however not equivalent just like that :
When we attribute a transcendental, say UNITY, to the Substance X, then we can say that X is wholly a unity. This unity involves every (other) determination of X (which are themselves unities, when considered apart). This is so because all determinations of X must be such as to guarantee and comply with X's unity.
When, on the other hand, we attribute an accidental (higher or highest) term, say QUANTITY, to Substance X, we can only do so when we transform the expression "X is (a) Quantity" to "X is quantitatively determined", because X is simply not a quantity throughout, i.e. not a quantity just like that (it is also qualitatively determined, etc). In contrast with X being a unity, i.e. with the application of the term UNITY, X being a quantity does as such not involve all other determinations of X, determinations, which it indeed possesses in addition to quantity. Something being a quantity just like that is expressed when we attribute the term QUANTITY to, say, 1.70 meter length. Indeed 1.70 meter length is a quantity and nothing else.
But in spite of all this, i.e. in spite of this difference, the strong similarity between the two types of terms remains : We can say : Socrates is a unity, and also : Socrates is quantitatively determined. And so with respect to every other real being.

Well, if we do not accept determinations (Accidents) as beings at all, then Quantity can, with the qualifications mentioned, be considered as a transcendental ( NOTE 2 ), but only so, when we confine our considerations to the Real World, and this restriction makes sense, because the Ideal World and its status is more or less speculative (the distinction of a real versus an ideal world is also Hartmann's). Quantity being a transcendental means that EVERY genuine real being is in one way or another quantitatively determined, and whatever is in one way or another quantitatively determined, is a genuine real being. Quantitatively determined thus is ' convertible ' with (real) being. But, being 1.70 meter long is NOT a transcendental, because not EVERY (real) being is 1.70 meter long.
The same goes for Quality. Every real being is qualitatively determined, but not every real being is red.
Quantity and quality thus are genuine principles of (real) Being, or Categories in Hartmann's sense. Within the context of the distinction between genotypic and phenotypic domains, the upper genera Quantity, Quality, etc. are principles of phenotypical expression. They belong to the ontological framework in which the dynamical law is expressed.
Being-one also is a transcendental (always so interpreted in Classical Metaphysics), and thus a principle of being, because every being is ONE. Even an Accident is ONE, and also an ideal being (an inhabitant of the Ideal World).
These Transcendentals or general Hartmannian Categories 'horizontally' penetrate all being (they penetrate the whole Real World).
The Doctrine of Categories of Hartmann poses -- within the Real World -- several different "layers", which contain each for themselves, besides a number of general categories, a set of special categories of their own, because of which every layer differentiates itself from the next lower layer by the appearance of some "categorical novum", i.e. the appearance of one or more new categories, for instance the appearance of special "organic categories" when we ascend from the inorganic layer up into the organic layer. But it has become clear to me that such an ontological 'stratigraphy' is an incorrect assumption. The study of dynamical systems has shown that complexity is not a conserved 'magnitude'. Complexity can be generated and destroyed. The study of dynamical systems shows that it is possible to generate complexity from scratch. So we do not need to postulate a categorical novum, new in the sense of not originating somehow from a lower layer (level). A new property can be generated from the 'bottom up', so from a categorical viewpoint the property is not new, not a novum. To be sure, we can -- in the Real World -- discriminate between layers, levels, but these do not have any ontological significance, they just are structural, or, as in organisms, functional levels, or, just levels of description.
Because of this it is necessary to ascribe to those Hartmannian Categories, which he deemed valid for the lowest ("physical") layer only, a universal, i.e. general, status, resulting in their being valid for EVERY real being, including organic beings. No new Categories appear, when we ascend from the inorganic layer to the organic layer, and also no Categories of the inorganic layer are broken off, i.e. loose their validity.

A Hartmannian Category sometimes has the character of a law. But because not every law possesses a universal validity, i.e. many of them are relevant for a specific domain (of the Real World) only, we can (also) consider the presence of special laws. These are the many laws, found (i. e. formulated) by physicists and chemists, laws that govern certain specific natural processes.

Remark: Such formulated laws often are valid for idealized cases only. Here in this Essay, and throughout this website, we are, however, concerned with the complete laws, i.e. lawswith respect to real cases, whether or not one has already been able to formulate such laws. It always concerns ontological questions, not epistemological ones.

Of course such a special law, dictating a certain (type of) process, does not possess the status of those things signified by a transcendental term. Real dynamical systems belong to such processes. Well, the dynamical laws, of which we spoke already on many occasions, are such laws, each of which governing a certain dynamical system, and when such a system generates a Totality then that dynamical law is the Essence of that Totality. The Essence, of a Totality, then is the Essence of a Totality species, T, and can be interpreted as a special Hartmannian Category. This Essence can in principle govern several individual Totalities, T1, T2, T3, T4, etc.

When we now interpret the Transcendentals of Classical Metaphysics ontologically (that to be possible remains to be seen), and also the significata of all the accidental aristotelian Genera, then it is possible to commit ourselves to the study of the Doctrine of Categories in the sense of Hartmann, with certain amendments, in the form of a doctrine of 'transcendentals' as can be seen in Classical Metaphysics, but now also including the accidental genera (as 'transcendentals').

It is not my intention to do this on this website. It is a suggestion for further research. One of the objectives of such an investigation could be an attempt to integrate several more or less classical philosophical systems, with the help of necessary amendments based on new data and insights.

The most important works of Nicolai Hartmann on the subject of Categories (in his sense) are the follwing :

• HARTMANN, N., 1940, Der Aufbau der realen Welt
• HARTMANN, N., 1950, 1980, Philosophie der Natur
• HARTMANN, N., 1938, Möchlichkeit und Wirklichkeit
• HARTMANN, N., 1935, Zur Grundlegung der Ontologie
They are certainly worth studying. They reveal much insight into the ontological structure of the World, the Real as well as the Ideal World.

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