In all the foregoing documents of this First Part of Website we considered a possible metaphysics (ontology) of intrinsic beings, of which the most clear examples are crystals (as representatives of the inorganic world) and organisms. We found out that an intrinsic being is generated by a dynamical system, and that the dynamical law of the latter can be consisered to be the Essence of that being, i.e. its intrinsic whatness.  What is generated by the dynamical system is that intrinsic being, not its properties :  they are just co-generated, or better, implied.  This is so, because only genuine beings are generated, and properties are not genuine beings. Nevertheless we can loosely call the properties of a generated being (or intrinsic thing) the manifest products of the dynamical law (of the dynamical system that generated that being).

In the documents (essays) that follow -- the Special Series -- we investigate these properies, i.e. the properties as products (better :  implications) of the dynamical law, but, because of that : intrinsic properties. They form the being's ontological periphery, while its Essence is its ontological kernel. Of course there are many properties of intrinsic beings (crystals, organisms). From these we have selected for further ontological study the following :  Symmetry and Promorph .  These are very important aspects of the spatial structure of any given intrinsic being. So it is natural that the following documents extensively consider crystals .  Symmetry is well expressed in them. In the Special Series of the present website (i.e. First Part of Website) we then study the 32 Crystal Classes and geometrically investigate the symmetries involved. But as soon as we want to study the internal symmetries of crystals it becomes very complex and not easy to depict graphically on a two-dimensional drawing pad. So we will concentrate for the time being on the two-dimensional analogues of crystals (also done in First Part of Website), the study of which will already be very instructive to understand their three-dimensional counterparts. Then, in the Second Part of Website, after some general considerations concerning three-dimensional crystals, we will prepare for the study of their three-dimensional structure and symmetry, not by means of graphical representations, but by means of the mathematical theory that describes and elucidates their symmetry :  Group Theory .  In doing so we will concentrate on symmetry groups and give many examples. This culminates in an extensive group theoretical study of two-dimensional periodic patterns, which were studied earlier (First Part of Website) from a geometric-crystallographic point of view. After this we will turn to the internal symmetry of three-dimensional crystals, and describe it group theoretically, while making use of much that we have learned from their two-dimensional counterparts.
Then it will be time to turn to the symmetry of organisms .  If we look to organisms we will see that, unlike in crystals, most of them are -- strictly taken -- totally asymmetric. But on closer inspection most of them do display symmetry nevertheless, but in a more or less hidden fashion. We could say that in organisms, just like in crystals, intrinsic symmetry is generated during individual development, but is often more or less 'overruled' by other processes. So we must somehow extract the intrinsic symmetry that lies beneath the orgamism's asymmetric appearance. Such an extracted symmetry we will call the promorph of the given organismic individual. Most organisms possess such a promorph because they are regularly built up (but, also, again, often partly overruled) out of subordinated individuals. These subordinated individuals together constitute the whole organismic individual as it appears as such to us. Think, for example of a common starfish. It consists of a regular repetition of five similar parts or subordinated individuals. The study of these subordinated individuals, accounting for some general aspects of the organism's morphology, and with it for its intrinsic symmetry, is called Organic Tectology and is considered on the Second Part of Website.  It forms the prelude to the study of symmetry in organisms :  Promorphology ,  also on Second Part of Website.  In Promorphology we extract the intrinsic symmetry of given organisms (or of their parts, i.e. of their subordinated individuals) together with another aspect, closely related to this symmetry, namely the repetition not only of identical parts, but also of just similar parts, where these parts are ordered around an imaginary point, axis or plane within the organism. Such parts are called antimers .  Well, what we do in Promorphology is determining the promorph of a given organismic individual. And we do this in the following way :  The simplest geometric body geometrically expressing the ideal intrinsic symmetry of that given organismic individual, and, also geometrically, expressing the number and arrangements of that individual's antimers, is the promorph or ideal stereometric basic form of that given organismic individual. We will see that the Promorph generally digs a little deeper into the global structure of a given organismic individual then Symmetry alone does.
After having expounded the "Promorphological System of Basic Forms", i.e. systematically presented all the possible types of promorphs, we will apply this Promorphology to crystals as well. This demanded a lot of theorizing, because crystals do not as such possess antimers, which fact tends to forbid considering crystals in a promorphological way. It turned out, however, that crystals have something like a 'hidden' promorphology, and we succeeded to reveal it.

All this is quite a lot about symmetry :  Two-dimensional crystals, Group Theory (as prelude to the study of symmetry in three-dimensional crystals), Group theoretic consideration of two-dimensional periodic patterns (for its own sake, or also as prelude to 3-dimensional crystals, and still in progress), Organic Tectology (subordinated individuals), Organic Promorphology (Stereometric basic forms in organisms), and, finally, Inorganic Promorphology (Stereometric basic forms in crystals).
The reader can find all this, to begin with, in the last series (Special Series) of First Part of Website (present website), and the rest in Second Part of Website.  As such then, the reader studies one of the most important and general properties of intrinsic beings ,  beings, generated by certain dynamical systems, and as such directly implying these properties (which are aspects of the total spatial structure of such a being).

So this whole prospect as outlined above is very special (in contrast to general) indeed, because it elaborates on just a few aspects of spatial structure emerging from one or another dynamical system when this system generates an intrinsic being. It consists of a whole lot of crystallography, biology and mathematics, and the reader might become impatient as to when, if ever, the website continues the more general metaphysical approach of its very beginning (largely, First Part of Website, where philosophical issues like substance, form, matter, substrate, individuality, essence were pursued). So I can well imagine that the reader wishes to see a continuance of  p h i l o s o p h y,  i.e. a further elaboration of the Theory of Being, rather then the extensive treatment of symmetry involving Crystallography, Group Theory, Promorphology, etc.  ( The documents on these subjects, could, however, also be studied for their subject's own sake and intrinsic interest and importance, totally apart from philosophy).

Well, for such a continuance of philosophy (here almost exclusively natural philosophy) the website has much to offer :  The philosophically minded reader could skip the whole Second Part of Website, i.e. skip all the detailed treatments about symmetry and promorph, and directly proceed further with genuine philosophical issues, and choose between three possiblities :

• In Third Part of Website  an alternative ontological theory is offered, which deviates strongly from the philosophical ideas expounded in First Part of Website, but which is nevertheless interesting. It is a theory of radical Wholeness, viz. the Theory of the Implicate Order, first proposed by the physicist DAVID BOHM in 1980. It is a very important, interesting, but speculative theory, and has some similarity with the metaphysics of the greek philosopher PLOTINUS (third century).

• In Fourth Part of Website  the philosophical approach of First Part of Website is more or less continued. However, here, unlike as we did in the First Part, we do not place the individual intrinsic being in the center of consideration anymore, but consider fundamental complexity layers or levels that cut across beings. According to such an approach we see, for example a given property (of a class of things, beings) not only as determining certain things, beings, but see it also as it is in itself, as a particular state (in which something can find itself, without specifying that "something" any further). In this way we classify such a property as a determinant, as opposed to something determined.  Any state of affairs, i.e. any being-thus, has its necessary and sufficient conditions for it to be realized. Such a being-thus PLUS its necessary and sufficient conditions form, what we will call, an If / Then  constant .  And as such it is not (i.e. as such it does not exist) but only applies, and it applies universally and always, as long, and wherever its  If component prevails. The latter is the constant's domain of relevance. In this way Reality consists of two (interpenetrating) ontological domains :  The determining, i.e. all the  If / Then  constants, which we will collectively call NOMOS, and the determined, i.e. all the existing things and properties in the world, which we will collectively call COSMOS. Such  If / Then constants are in fact more or less a reformulation of the "categories" proposed by the philosopher Nicolai HARTMANN (first part of 20th century). In this Fourth Part of Website we, at the same time, propose a Theory of Mathematical Wholeness :  If we descend through the world's complexity levels all the way down, i.e. if we descend from the domains of the psychic to the domain of the organic, and then to the domain of the physical, we seem to find out that (according to cosmological theories) if we descend further into ever smaller magnitudes we end up with something not physical anymore. Indeed, where we end up is -- according to my theory -- the purely mathematical domain of existence. Said the other way around :  The physical is the result of some leaps or jumps of complexification of certain mathematical entities :  these mathematical entities become (not by us, but ontologically) physically interpreted resulting in the physical level of reality. Comparable complexity leaps then lead to the organic layer, and from there to the psychic layer and beyond. But because the ultimate level or layer is -- in this view -- mathematical, all the relations in the material world are ultimately logical, implying that this world is as a whole mind-like.
  All this can be found in Fourth Part of Website, but still in a state of continued construction and development.
  In this Fourth Part of Website, which we can call our General Ontology, we will have to use special examples in order to develop the general theory. And it is in these examples that SYMMETRY and PROMORPH will in most cases reappear because they are straightforward and well-definable properties, as such helping to make the general ontological theory as clear as possible. Maybe the reader, when encountering these examples, whishes to study symmetry and promorph after all, as they are considered mainly in Second Part of Website, because they have aroused his or her interest.
  I can certainly recomment reading the documents of our Fourth Part of Website. The theory proposed there is very encompassing and will certainly stimulate philosophical thought.

• In Fifth Part of Website  we again look into Aristotelian metaphysics, let again ourselves be lead by St Thomas Aquinas, apply our theory of Essence as Dynamical Law, and also apply our new (acquired in Fourth Part of Website) knowledge of crystals, crystallization and thermodynamics, in order to test and further work out this metaphysics. Further we will try to place it into the broader ontological context of the Implicate Order and Holistic Simplification (as this context was discussed in Fourth Part of website).

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