Continuation of the Philosophy Site of Jaap Bax

Second Part of Website

Sequel to the Special Series of Essays

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A Retrospective of the Site, developed this far

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This page (and what follows) is a continuation of the Philosophy Website of Jaap Bax.
All what precedes this page can be found when the "back to homepage" link is used. The adress is :

There one will find out that the theme centers around a Philosophy of Being. It is an attempt to update a philosophy designed by the Greek philosopher Aristoteles in the fourth century before Christ, and developed further by St Thomas Aquinas in the thirteenth century. From that time onwards it underwent hardly any further developement, probably by reason of a shift in interest, undoubtedly in connection with the emerging Natural Science.
Today Natural Science has brought about a large body of knowledge, and one feels the need to look at this knowledge from a broader perspective. Where do we get this broader pespective?
Of course from Philosophy!
But many (utterly) different philosophies circulate already for a long time. Which one of them would be appropriate to provide a framework for the mentioned broader perspective of our knowledge of the world?
Well, first of all that philosophy must be sufficiently general in order to cover all of Reality. Secondly it must be one that stands with both feet on the ground.
In my opinion the above mentioned Aristotelian-Thomistic Philosophy of Being, meets these demands. It is a philosophical theory about BEINGS insofar as they are beings. Its outlook is a moderate holism that not exclusively recognizes the ultimate constituents of the world as genuine beings (while the rest would be just aggregates of them), but also recognizes as such some classes of complex beings, i.e. besides those ultimate elements when freely existing, it also considers many composed beings as genuine beings with an identity of their own.
In the mentioned preceding collection of Essays this Philosophy was extensively presented, in the light of modern insights as well as treated along classical lines.

The first series of this collection, the "Non-classical Series", introduces the reader to this philosophy which is -- as a theory of Being -- a Substance-Accident Metaphysics, i.e. it investigates the Substance-Accident structure of things (beings). It recognizes several 'constituents' which are themselves not (yet) things but cause something to be a being (a thing) at all (They are the intrinsic causes of every genuine being, whether organic or inorganic).
This philosophical theory, originating -- as has been said -- from Aristoteles and St Thomas Aquinas, is, in that first Series of Essays, directly further developed according to modern insights from philosophy, but especially from some relevant results of Natural Science. To be more specific, the ancient philosophy of being is further developed in the light of modern dynamical systems theory.

The second series of the mentioned collection of Essays, the "Classical Series", is more or less classical in character. It deals with that same philosophy of being, but now as it was presented by St Thomas Aquinas. However we have added critical notes where it seemed necessary.
Some important texts of St Thomas are given in English translation. They are investigated and interpreted. Sometimes hints are given to modern solutions to problems inherent in some texts.

The third series, the "Critical Series", investigates whether a (modern updated) Substance-Accident Metaphysics is possible at all, because in Natural Science there are indications that genuine, more or less separately existing, things (beings) do not in fact occur. The world could be one giant dynamical whole occasionally showing local temporary patterns appearing and disappearing again in a holistic dynamical sea of chaos (while the Substance-Accident Metaphysics presupposes the existence of a multitude of individual genuine beings (things)).
Further, the Substance-Accident Metaphysics presupposes the truth of a certain view concerning the nature of knowledge. If this theory of knowledge turns out to be false, then a Substance-Accident Metaphysics becomes obsolete.
And besides all this, the possibility and character of a Substance-Accident Metaphysics depends in a way on one's view about the constitution of Man, i.e. the view concerning the Mind-Body Problem. Does a human being consist of two fundamentally different 'parts', a material part (body) and a more or less independent immaterial part, or is he wholly equivalent in this respect to the rest of Nature?
Still further, Nominalism accuses the Substance-Accident Metaphysics of confusing logical structures with real, i.e. ontological, structures.
All this is investigated in that third Series.

Finally we have a fourth series of Essays, the "Special Series".
While in the preceding three Series our approach was, in a way, 'horizontally', i.e. it covered many problems and many types of objects (to be interpreted as genuine beings), like molecules, crystals, organisms and man, in the fourth series we go 'vertically', i.e. we choose one or more types of objects that represent genuine beings, and investigate them in detail. After having given a detailed account of their structure we will apply our updated Substance-Accident Metaphysics in order to verify it and to exactly assess the type of being of those objects and their properties according to that metaphysics.
Our updated Substance-Accident Metaphysics interprets real genuine beings as products of dynamical systems. The dynamical law of such a system then is assessed as the being's Essence. This Essence causes the visible intrinsic features of such a being.
The first type of objects (real beings) we have chosen to investigate in that respect are CRYSTALS. A detailed account of them is given in terms of their intrinsic symmetry, internal structure and chemical composition.

Well, this then is the global content of the Four Series of Essays at

From the present page onwards ( we will continue this Special Series (THIS CONTINUATION HAS JUST BEGUN TO EMERGE) :
While the last Series of preceding Essays ended with the treatment of the structure of two-dimensional crystals as prelude to an understanding of three-dimensional crystals, the present Series, i.e. the continuation of the Special Series, will treat of the structure and shapes of three-dimensional (single) crystals.
After that we will make an attempt to see such crystals as products of dynamical systems. In this some thermodynamics is involved. When this is done we can properly interpret crystal individuals in the light of our updated Substance-Accident Metaphysics. And with all this our treatment of single crystals will come to a conclusion.

Remark : A reader could wonder why so much attention is devoted to crystals. The latter usually are associated with precious stones like diamond and topaz. But one should realize that almost all individual inorganic beings are crystals. For example every grain of sand, and every snowflake is a crystal, and the whole crust of our planet is, in any case, made up of crystalline material.

Organisms :   Tectology and Promorphology

The next important type of objects to be investigated in more detail are organisms. These are however extremely complicated and not yet fully understood. This is because they are historical beings, owing their structures and functions to a long history of adaptations and transformations. So we will investigate only two aspects of their structure. The first aspect is the structure itself, where we confine ourselves to macroscopic structure, which here means the composition of organic bodies out of macroscopical form units. The study of it is called Tectology by its founder, Ernst Haeckel, who worked in the first half of the nineteenth century. This structure is interpreted as one of the effects of the dynamical law (Essence) of the given organism, and this effect (the mentioned macroscopical structure) in turn determines the second aspect. This second aspect is the global geometry of organic bodies. The latter is pretty much understood, and connects them, in a way, neatly to the aforementioned crystals. This global geometry of organisms describes their stereometric basic form, reflecting the basic symmetries of their shapes in terms of axes and their poles. These basic symmetries are, ultimately, also the effects of the (same) dynamical law (Essence) of the given organism. The science which deals with these symmetries (axes and their poles) is called Promorphology by again its founder Ernst Haeckel.
This Promorphology is relevant and appropriate for objects that show, in contrast with single crystals, parts that are oriented around one or more imaginary axes. This means that those parts have different orientations with respect to each other (while in single crystals the parts do not have different orientations with respect to each other). An instructive example is a starfish. It has five similar parts situated around an imaginary axis. This is a quite different structure from that of a single crystal, which is fully periodic, i.e. it consists of a repetition of a unit in such a way that all units have the same orientation, and those units are repeated in three directions.
In all cases where the parts are organized in a non-periodic way, and thus such that they have different orientations with respect to each other, while at the same time not being just random aggregates of parts, we will speak of a tectological structure of the given object.
Well, Promorphology, i.e. the study of the stereometric basic form of genuine beings, is especially geared to objects having such a tectological structure.
It is clear that all organisms have a tectological structure, so the founder of Promorphology, Haeckel, concentrated fully on them.
There are other objects that have a tectological structure, for instance most human artefacts, but these are not intrinsic beings, their Essence lies outside them, they are just aggregates.
When, however, we consider the structure of molecules, we can conclude that they indeed do have a tectological structure, and are at the same time intrinsic beings, i.e. genuine beings.
And, moreover, there are intermediates between crystals and organisms with respect to possessing a tectological structure :
Many twinned crystals do indeed have a tectological structure, because the members of such twins have different orientations with respect to each other, while at the same time they are connected to each other in a regular fashion, according to one or another twin law, implying that twins are genuine beings. So Promorphology can be applied to them.
After the discussion of the tectology of crystal twins and anticipating their promorphology, we will treat of the tectological structure in organisms and show how a Promorphology can be based on such tectology. This Organic Tectology implies the recognition of an organism as a composed morphological whole :   It is composed in a regular way of subordinated form individuals. We will distinguish six orders of such form individuals, i.e. we will distinguish six different types of morphological individuality. The theme of  i n d i v i d u a l i t y,  so important in the first part of our website, recurs again. In this way organic Tectology is a doctrine of organic macroscopical structure based on the composition of several subordinated form individuals making up the given organism. This composition we will -- as has been said -- interpret as an intrinsic effect of the Essence of the given organism.
And then (i.e. after we have dealt with Tectology) we are finally ready for a full Promorphology of organisms and of crystal twins. In fact I will deal with organic Promorphology right away, and will append the promorphology of twinned crystals as inorganic examples within the treatment of the relevant promorphological categories. In so doing we will determine the ideal stereometric basic form (i.e. the promorphology) of many organisms, and will interpret this feature also as an intrinsic effect of the Essence of the given organism.
So, with respect to organisms (i.e. after the study of crystals), we will study two features, both intrinsic effects of the Essence of a given organism (among a multitude of other intrinsic effects), namely Macroscopical Structure, investigated by Tectology, and Stereometric Basic Form, investigated by Promorphology.
It is clear that in doing all this we keep on having in mind our updated Substance-Accident Metaphysics, as was developed in the first part of our website, but the strong emphasis on the structure of crystals, crystal twins and organisms gives it the face of a NATURAL PHILOSOPHY.

The documents of this "website continuation" concerning three-dimensional crystals, thermodynamics of crystals and twin crystals, are not yet worked out, but will be so worked out soon. The theory of organic Tectology on the other hand, is completed, and is followed by, what could be called an application of it (centering around physiological individuality in organisms). It is followed in turn by the theoretical treatment of the mentioned organic Promorphology, i.e. of the stereometric basic forms of organisms. This treatment is also completed. So the reader of this "website continuation" should start right away with Tectology (starting with the document Introduction to Tectology), then pursue all its documents concerning the morphological individuality in organisms and physiological individuality in organisms, and then begin a study of Promorphology (starting with the document Introduction to Promorphology).

The sciences of organic Tectology and Promorphology are not to be found anywhere in the modern literature as far as my knowledge goes. They were established by HAECKEL in his Generelle Morphologie der Organismen, 1866, but are not worked out further since. This is because of the general lack of interest in very general (macroscopic morphological) theories in Biology, but also because of one's preoccupation with the exciting microscopic aspects in organisms that has been discovered since. Of course Haeckel's theories had to be updated. On this website we made a beginning to do so. The result is two elegant, beautiful and interesting theories with a marked philosophical content.

What follows is a survey of the CONTENTS of the continuation of the website :

Continuation of the Documents on the Theory of Crystals, their total symmetry (described by Group Theory), their internal and external structure and shapes, and an ontological interpretation of several crystallographic phenomena, among which first of all (crystal) twins.
This is followed by a study of two main features in Organisms :   Macroscopic structure as a subordination of organic form individuals (investigated by Tectology), and Stereometric Basic Form (investigated by Promorphology) :

1.  The Total Symmetry of Three-dimensional Crystals. Part I.
1a.  The Total Symmetry of Three-dimensional Crystals. Part II.
      Group Theory
 ( C12   D2  Automorphisms )
1b.  The Total Symmetry of Three-dimensional Crystals. Part III.
      Group Theory
 ( C6   D3   D6  (inner)Automorphisms )
1c.  The Total Symmetry of Three-dimensional Crystals. Part IV.
      Group Theory
 ( C6 C3 C4 C2 C1C7   Automorphism )
1d.  The Total Symmetry of Three-dimensional Crystals. Part V.
      Group Theory
 ( C12  Cosets  Homomorphism )
1e.  The Total Symmetry of Three-dimensional Crystals. Part VI.
      Group Theory
 ( Sequel  C12  Cosets  Homomorphism )
1f.  The Total Symmetry of Three-dimensional Crystals. Part VII.
      Group Theory
 ( Cinfinite   D3  Homomorphism  D6  C2  D2 )
1g.  The Total Symmetry of Three-dimensional Crystals. Part VIII.
      Group Theory
 ( D6  Homomorphy theory  D4  D5  Dinfinite )
1h.  The Total Symmetry of Three-dimensional Crystals. Part IX.
      Group Theory
 ( C4xC3   C6xC2   C2xC2=D2   D3xC2 )
1i.  The Total Symmetry of Three-dimensional Crystals. Part X.
      Group Theory
 ( C4xC2=C4i   C2xC2xC2=D2xC2   Automorphisms )
1j.  The Total Symmetry of Three-dimensional Crystals. Part XI.
      Group Theory
 ( CinfinitexCinfinite    CinfinitexC2    Dinfinite    Cinfinite    Even/odd permutations )
1k.  The Total Symmetry of Three-dimensional Crystals. Part XII.
      Group Theory
 ( Relevance of group theory    Classification of simple groups
Symmetry groups   Indirect product    D4=C2semiC4 )
1m.  The Total Symmetry of Three-dimensional Crystals. Part XIII.
      Group Theory
 ( Sequel to symmetry groups :   A4    S4=O    S4xC2=Oi
A5    A5xC2 )
1n.  The Total Symmetry of Three-dimensional Crystals. Part XIV.
      Group Theory
 ( Cosets.    D6    Q6 )
1o.  The Total Symmetry of Three-dimensional Crystals. Part XV.
      Group Theory
 ( Conjugation   Normal subgroups.     D4    A4
Center    Centralizer )
1p.  The Total Symmetry of Three-dimensional Crystals. Part XVI.
      Group Theory
 ( Homomorphism  Quotient groups  Normal subgroups
D3    D4    A4    Cinfinite    C5    C4 )
1q.  The Total Symmetry of Three-dimensional Crystals. Part XVII.
      Group Theory
 ( Automorphism    D4 )
1r.  The Total Symmetry of Three-dimensional Crystals. Part XVIII.
      Group Theory
 ( Automorphism   D3   C12   C6 x C2   Q4 )
1s.  The Total Symmetry of Three-dimensional Crystals. Part XIX.
      Group Theory
 ( Automorphism   Q4    Q6    S4 )
1t.  The Total Symmetry of Three-dimensional Crystals. Part XX.
      Group Theory
 ( Two-dimensional periodic patterns    P4mm )
1u.  The Total Symmetry of Three-dimensional Crystals. Part XXI.
      Group Theory
 ( Two-dimensional periodic
        patterns    P1   P2   P3   P4 )
1v.  The Total Symmetry of Three-dimensional Crystals. Part XXII.
      Group Theory
 ( Two-dimensional periodic patterns    P6   Pm   Pg   P2mm
        P2gg   P2mg )
1w.  The Total Symmetry of Three-dimensional Crystals.
       Part XXIII.
       Group Theory
 ( Two-dimensional periodic patterns              Cm   C2mm   P4gm   P6mm )
1x.  The Total Symmetry of Three-dimensional Crystals.
       Part XXIV.
       Group Theory
 ( Two-dimensional periodic patterns    P31m   P3m1 )
1aa.  Group Theory :  Sequel to Symmetry of two-dimensional         patterns. (Subpatterns and Subgroups)
2.  The Chemical Lattice Types of Three-dimensional Crystals
2a.  The Shapes of Three-dimensional Crystals
3.  The Thermodynamics of Crystal Growth
4.   Twin Crystals
5.  Introduction to Tectology
5a.  Tectology : Morphological Individuality.
      Cells, Organs, Antimers
5b.  Tectology : Morphological Individuality. Metamers
5c.  Tectology : Morphological Individuality. Persons and Colonies
5d.  Tectology : Physiological Individuality. Cells, Organs,
5e.  Tectology : Physiological Individuality. Metamers, Persons,
6.   Introduction to Promorphology
7.  Anaxonia, Homaxonia, Polyaxonia
8.  Protaxonia : Monaxonia
9.  Stauraxonia homopola
9a.  Homopola sigmostaura
10.  Stauraxonia heteropola : Homostaura isopola
11.  Homostaura anisopola, Heterostaura
12.  Autopola oxystaura, Autopola orthostaura
13.  Allopola
14.  Allopola amphipleura, Allopola zygopleura
15.  Heteropola gyrostaura
16.  Protaxonia spiraxonia
17.  Spiraxonia allogonia
18.  Spiraxonia isogonia, Concluding remarks on Promorphology.
19.  Basic Forms of the six individuality orders.   Cells I
19a.  Basic Forms of the six individuality orders.   Cells II
20.  Basic Forms of the six individuality orders.   Organs.
21.  Basic Forms of the six individuality orders.   Antimers.
22.  Basic Forms of the six individuality orders.   Metamers.
23.  Basic Forms of the six individuality orders.   Persons.
24.  Basic Forms of the six individuality orders.   Colonies.
25.  Promorphology of Crystals.     Preparation I.   P4gm.
26.  Promorphology of Crystals.     Preparation II.   P4gm.
26a.  Promorphology of Crystals.     Preparation III.  P1,  P2,  Pm.
26b.  Promorphology of Crystals.     Preparation IV.  Pg.
26c.  Promorphology of Crystals.     Preparation V.  Cm,  P2gg,         P2mm,  P2mg,  C2mm.
26d.  Promorphology of Crystals.     Preparation VI.   P4gm.
26e.  Promorphology of Crystals.     Preparation VII.   P4mm,  P4,         P3.
26f.  Promorphology of Crystals.     Preparation VIII.   P3m1.
26g.  Promorphology of Crystals.     Preparation IX.   P3m1.
26h.  Promorphology of Crystals.     Preparation X.   P3m1.
26i.  Promorphology of Crystals.     Preparation XI.   P31m.
26j.  Promorphology of Crystals.     Preparation XII.   P31m.
26k.  Promorphology of Crystals.     Preparation XIII.   P31m.
26l.  Promorphology of Crystals.     Preparation XIV.   P31m.
26m.  Promorphology of Crystals.     Preparation XV.   P31m,          P3m1.
26n.  Promorphology of Crystals.     Preparation XVI.   P6,  P6mm.
26o.  Promorphology of Crystals.     Preparation XVII.   P6mm.
26p.  Elimination of glide translations I.
26q.  Elimination of glide translations II.
26r.  Preparation to the Promorphology of 3-D Crystals.
        Part One
26s.  Preparation to the Promorphology of 3-D Crystals.
        Part Two
26t.  Preparation to the Promorphology of 3-D Crystals. Part         Three.
26u.  Preparation to the Promorphology of 3-D Crystals. Part         Four.
26v.  Preparation to the Promorphology of 3-D Crystals. Part         Five.
27.  Promorphology of Crystals I.
28.  Promorphology of Crystals II.
29.  Promorphology of Crystals III.
30.  Promorphological Theses and Tables.
52.   a  HOLISTIC philosophy as an alternative world view
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