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Basic Features of the Inorganic World as the natural context of Organisms and Organic Evolution. (Sequel-5) (Conclusion)

Part XVf (of Sixth Part of Website)

Also here, in what follows, knowledge of the Aristotelian-Thomistic Metaphysics is presupposed. It can be found all over in  First Part of Website (Back to Homepage),  especially as to the notion of  Substance (in the metaphysical sense). And also presupposed is knowledge of the theory of the subdivision of Reality into the Explicate and Implicate Orders, a theory so far developed in our noëtic theory of organic evolution, especially as it has been expounded in the two-document  Theoretic Intermezzo  after Part VIII of present Part of Website.

In the present document we will further discuss the nature of  "inorganic substance" (atoms, molecules, and crystals), based on the interpretation of the results of atomic theory, largely as expounded by HOENEN, 1947. [ The nature of organic substance (the organism), its unimolecular nature, was succinctly dealt with in the previous document.]

Inorganic Substance
(Sequel and Conclusion)

The internal structure of crystals


So the kinetic molecular theory [previous document] has demonstrated that gasses and liquids (which, according to the continuum-law of Van der Waals, originate from gasses) consist of actual molecules, i.e. of individual particles. The gas or liquid  as a whole  is not a continuum. Whether the atoms in the molecule itself are also actual individual particles, and whether the molecule is, or is not, a continuum, cannot -- as we saw -- be decided by the results of molecular theory.
What to say about crystals? Also as to them it was assumed by many, already for more than half a century, that they, like liquids and gasses, have a discontinuous structure. [We have extensively dealt with the structure and status of crystals already in First Part of Website, Second Part of Website and Fourth Part of Website ]
And this not solely as a result of the general presupposition of the classical mechanicistic view of Nature, for the properties of crystals had led to a wonderful systematics, and even a successful explanation of and derivation from this systematics has been developed, - certainly being one of the finest theories of physics. Well, this theory assumed the constitution of crystalline matter to be out of individual particles, such that these particles were arranged in space according to certain definite schemes, according to a definite structure. From this supposition one was able, with the help of some specifying hypotheses, to completely derive the structure of naturally occurring crystal-forms. So we again have a typical theory of classical physics. The fundamental assumption that matter, also crystalline matter, consists of individual particles, is further specified by auxiliary hypotheses, and the resulting specified hypothesis then leads to the wonderful results in the crystallography of the 19th century.
What are they, these particles? One still could erect several hypotheses :  There were scientists who thought they needed complexes of molecules, special crystal-molecules. Others theorized that they were the (gas) molecules themselves. Others went still further and assumed that these individual particles were chemical atoms. In a crystal, which is a chemical compound, the atoms of the elements would then be present individually, i.e. actually. If the latter opinion were correct, our problem would be solved :  the chemical compound would then be nothing else than an aggregate of atoms [that is, even when the atoms in the molecule are chemically bonded with one another, the molecule would still be a mere aggregate when these (bonded) atoms exist -- as corpuscules -- actually in that molecule.]. But among these data, obtained in the 19th century, there was something else, forcing to accept the latter opinion in preference to the first. At the beginning of the 20th century (1912) other sorts of experiments were done, apparently confirming that latter opinion (actual atoms in the crystal) :  It was the investigation of crystals by means of X-rays.
Let us consider all these data on crystals more closely.

Properties of crystals.

When looked at, crystals may be homogeneous, and even under the microscope showing no sign of heterogeneity, which nevertheless must be present, evident from what follows. If we only consider observable fragments, they, if taken from different parts of the crystal, do not show any difference in properties. But crystals are not  isotropous, i.e. if we consider properties which depend on direction, such as propagation of light and heat, fissility, speed of growth, etc., then these generally are different in different directions, while parallel directions have the same properties, the crystal is  anisotropous.
These resemblances and differences in properties are not coincidental as is the case in amorphous materials if there are diffenences at all, but they comply to very definite laws characteristic of the species. What is especially important :  these laws describe different degrees of symmetry in different species of crystalline material. The chief elements of this symmetry, co-determining an intrinsic structure -- the external shape of the crystal is just a consequence of it -- are :  centers, planes, and symmetry axes, being combined in different ways. However, not all forms of symmetrical structure which are a priori possible in extensa [i.e. in spatially extended things] are realized in the world of crystals. After all, there would then be infinitely many of them [if only we considered the possible "foldnesses" of rotation axes, 1-fold, 2-fold, 3-fold, 4-fold, 5-fold, etc.]. The number is even rather limited. The symmetric forms found in the crystal world can be reduced to seven Systems (or six, insofar as one considers the hexagonal and trigonal as two different Systems or as belonging to one and the same System), and in these Systems one finds a total of 32 Classes of symmetry forms. One example of this limitation of symmetry in crystals :  A body has an "axis of symmetry" if, upon rotation by some angle, being a fraction of 3600, it completely matches the initial condition, i.e. it precisely covers its initial state as to shape and structure, further meaning that every point replaces another point having in the body the same properties. The axis is a 2-fold one if this only happens after having rotated the body about that axis by 1800. Generally it is n-fold if the match is realized after every 360/n-degree rotation. In abstracto the magnitude of  n  is undetermined, i.e. axes of every foldness are possible. For the axis of a homogeneous cylinder, for example,  n  is infinitely large. This body matches itself after any arbitrary rotation about this axis. But now, see :  In the world of crystals only 1-fold, 2-fold, 3-fold, 4-fold, and 6-fold axes do actually occur, whereas 5-fold symmetry axes, so frequent in the organic world (starfishes, many flowers), are totally absent in the world of true crystals. Also all axes higher than 6-fold do not occur there. This is just one example of the limitation in the symmetry of crystals. And these limitations are such that only the above mentioned Crystal Systems and Classes result.

Theory of the limitation of symmetry.

One has succeeded to set up a theory accounting for this limitation up into details. See here its chief lines :  One supposes that the crystal is in its smallest parts or particles -- which, as has been said, escape even microscopic observation -- not homogeneous, but heterogeneous. As a result of the apparent homogeneity, however, particles with the same properties must follow upon one another periodically, separated from each other by small areas which, again periodically, have other (but among themselves the same) properties. In different directions these areas, separating the first mentioned particles [from one another], generally will have different sizes. Indeed, in different directions the crystal has different properties. We now take an arbitrary point P in one of these particles and connect it by a line with the corresponding (the "homologous") point in the nearest particle (when there are more than one of such points, then with one of them). Let the distance be  a.  If we extend this line, we will (by reason of the periodic heterogeneity, expressing itself as homogeneity in observation) meet at every distance  a  new homologous points. At distances smaller than  a  no homologous points will be found. If we now draw a line from the point P in some other direction to the homologous point that is after the first the nearest point, then also this line is the carrier of a series of homologous points lying at equal distances from one another, generally differing from  a,  being larger. These two lines then determine a plane, and it is easy to demonstrate that all points homologous with P are vertices of a  network  of parallellograms that can be constructed in this plane and tiling it completely. If we now draw from P a third line, not lying in this plane, to the homologous point that now is nearest, then in the same way we arrive at this overall result :  All points homologous with P of the crystal are vertices of parallellopipeda [regular or skew "shoe boxes"], together forming the whole crystal. So one must assume  in  the crystal, if it is heterogeneous in the above described way, a network- or lattice structure. But this net is now a  space net,  a space lattice. One also calls it a "point-system". We shall call it a "reticular structure"
From the supposition of such a reticular structure in crystals the classical crystallographic theory of the 19th century was erected. One supposes, namely, that the nodes of such a net are occupied by the centers of either (complex) molecules, or of individual atoms of the elements (in which one can think of one point-system slided into another). Then one asks the question :  What symmetry elements and combinations of them can still be realized in such a [reticular] system? The answer must be given by a mathematical analysis. And this answer is very remarkable :  The symmetry forms that can occur in a body with reticular structure are precisely those which experience had discovered in the world of crystals. Mathematical analysis, departing from the above described supposition -- supplemented by special physical hypotheses accounting for special cases -- finds back the seven (or six) Systems and the 32 Classes of symmetric forms. Thus, as to the above mentioned particular :  In a reticular structure only 1-, 2-, 3-, 4-, and 6-fold rotation axes -- symmetry axes -- are possible.  A  5-fold rotation axis is impossible, just as those higher than 6-fold. And this is just a single particular out of many, in which the derivation of possible symmetry matches the data of crystallographic experience. One must admit that the theory of reticular structure earned its fame.
So in this way, as was said, classical physics has, in the spirit of the mechanical view of Nature, set up its crystallographic theory. Thus one introduced as hypothesis that a crystal is discontinuous, consisting of particles at a distance from one another, such that the centers of molecules or of atoms are positioned at the nodes of the reticular structure. And from this, one then derives the possible crystal forms. So the theory has the typical structure of a classical explicative theory :  The fundamental assumption of discontinuity, typical of the mechanical view of Nature, is specified by the hypothesis of the reticular structure with its particulars. Then the general scheme of the theory is this :  If crystals consist of atoms, or at least of molecules, arranged, according to the given description, into one (or more than one) point-system, then in the world of crystals, -- out of the endlessly many a priori possible crystal forms, i.e. forms that are possible in a truly homogeneous or in an other-than-reticularly heterogeneous material, -- only these determined symmetry forms, belonging to these seven Systems and 32 Classes, can be realized. And this conclusion is then wonderfully confirmed by the rich crystallographic experience. One can hardly overestimate this theory.

New confirmation of the theory.

Nevertheless, towards the end of the 19th century, this theory shared the same fate as all explicative theories :  As a result of the attacks of energetism and of the omnipresent scepsis it was not accepted or at least doubted, certainly so outside the arena of the crystallographers. But, like in the beginning of the 20th century the kinetic molecular theory found its definitive confirmation, so also this crystallographic theory. It happened in 1912 on the initiative of Von Laue, who reasoned as follows :  If crystals indeed have the structure as described by the theory of point-systems, then they must exert the same influence on waves with very small wave-lengths as do the long since known gratings of Rowland on light-waves. By these gratings, provided that the openings are sufficiently small and sufficiently densely packed, the light-waves are diffracted such that, as a result of interference, we get the well-known grating spectra. Now such a grating is, in the classical crystallographic theory, formed by the crystals. With two differences. The gratings of Rowland were linear, they consisted of a series of parallel stripes. Also two-dimensional gratings were constructed, carrying a series of tranversal stripes, resulting in more complex interference phenomena. Crystals would then be 3-dimensional gratings, hardening only the mathematical treatment. Another difference was more important. While too bigg openings of a grating have no effect, too small don't either. And if crystals are gratings, then (this teaches us a simple calculation from the number of atoms in a given crystal slide) the openings are too small to obtain in light waves the diffraction phenomena of gratings. But Von Laue suspected that X-rays will have small enough a wavelength to betray the grating nature of crystals. This supposition was confirmed. Crystals do indeed produce the diffraction phenomena in X-rays, expected by Von Laue. Such experiments were carried out along another method by W.H. and W.L. Bragg, and again along another method by Debije and Scherrer. The results not only generally confirm the theory, but also allow to measure the distances of the diffraction centers [from one another] - of the atomic centra -- in different net planes of the crystals. At the same time they give a determination of the wavelenght of the X-rays, which subsequently was wonderfully confirmed by the results of the latest atomic theory. For us especially important is this :  The particles, occupying the nodes of the network turned out to be not molecules, but the atoms of the chemical elements.
Again we can summarize the elements of the crystallographic theory in a succinct scheme :  Suppose that crystals are point-systems, and that the points are occupied by the centra of the constituent atoms, then, with the help of X-rays, we must expect these and those (precisely determinable) interference phenomena. And experiments confirm this expectation.
Not surpringly that these results were welcomed with great approval. For our problem [the metaphysical status of the atoms in the crystal, virtual or actual] the great progress that was achieved, as compared to the older crystallographic theory, was this :  First of all, these methods make us know the distances and other particulars of the internal structure of crystals. But most important of all :  The old theory could still do with complex  molecules -- and in that case there was no evidence whatsoever of the actuality of atoms [in such molecules]. To this problem it had about the same attitude as had the kinetic molecular theory -- whereas the new theory accepts the actuality of atoms in the crystal, and this seems to be confirmed by experiments. And so Prof. Jaeger (1920) says :  " These atoms preserve, therefore, apparently their individuality as constituents of such crystalline substances".

Applying the principle of elimination.

If this opinion is correct, then the problem of the chemical compound is solved, then indeed a compound in a crystalline condition consists of actual atoms, then the compound is merely an aggregate, not a totality. Yet, also here we must carefully distinguish and enquire whether there are superfluous elements. If  all  elements of the theory are necessary elements, then the just given conclusion is correct. But if the element, supposing the actuality of atoms -- this element is explicitly mentioned -- turns out to be superfluous, then that conclusion is false.
To investigate this, we, again, are going to set up, in addition to the classical theory, another theory in which precisely this element is replaced by another. That the hypothesis of the reticular structure is not superfluous will be clear. With it stands or falls the entire derivation of the results. If we suppose that the crystal is homogeneous all the way up until its smallest particles, or possesses a heterogeneity other than a reticular one, then all results of the deduction go to ruin. This, however, turns out not to be the case if we drop the supposition of discontinuity [i.e. metaphysically conceived, - the crystal consisting of actual parts or particles]. Suppose, namely, that a crystal is  continuous, optically [i.e. with respect to visible light], it is true, homogeneous, but  heterogeneous in qualities as to its smallest parts [volumes or areas]. The possibility at all of a heterogeneous continuum has already been demonstrated earlier. [Here the assumed continuity must be a "continuity-of-being", i.e. it must comprise one single being, and only one single being, not an aggregate of them. And if there exist local differences in that one single being, then these differences cannot reflect different independent parts or particles of that being, they cannot be qualities of such parts or particles, - they must be qualities of that single one being itself. Only in such a way a "heterogeneous continuum" can be conceived.]. Suppose that this heterogeneity in the crystalline material is  periodic.  In such a way :  parts with entirely the same qualities are separated (and at the same time connected with one another) by parts that among one another again have the same properties, different from the properties of the first group. To mention a particular property, being certainly important here :  The first group of parts may have great density [of each part], the second a low density [resulting in a alternation of densities in the crystal along a certain direction] (nothing opposes to even suppose that the density of the parts of the second group is zero, but nothing forces us to do so). If we draw a line through the center of one of the first parts to the center of another (for instance again the one that is closest), the density along this line will change :  The density maxima may -- and here we introduce the hypothesis which is the foundation of the reticular structure -- lie at equal distances along the line. Along another line through the first point the distance of density maxima may generally be different [than along the first line]. It is clear that also a continuum [metaphysically conceived, thus as one ens] may possess a lattice structure according to the density of its smallest parts. Within the confines of each (equal) density-peak along such a line, the density, i.e. experiencing it in going up to the maximum and leaving it again, may increase and decrease gradually, but it may also do this in a  stepwise  fashion. In the first case we have a reticular heterogeneity that we may call a "gradually working-itself-out heterogeneity" [see HERE], in the second case we have an "abruptly working-itself-out heterogeneity" [see HERE]. Both [including all generalized forms of heterogeneity] can exist in a continuum as we saw earlier. [The latter few sentences of mine differently and better express what is going on here than do those of HOENEN]. So, then we have in this continuum an intrinsic reticular structure, which is sufficient to allow for the classical derivation of possible crystal symmetry. Where the classical theory assumes discontinuity in crystalline matter with separated [corpuscular] molecules and atoms, we introduce a continuous crystal with heterogeneity (which even need not be discontinuous or abrupt), and see :  the derivation with its results remains unchanged. It is entirely clear that the classical assumption of actual particles is a superfluous element of the crystallographic theory.
Considering the X-ray analysis of crystals :  Let us suppose that locations of greater density stronger influence diffraction than do those with lower density. Thus the Bragg's supposed that heavier atoms have a stronger influence on diffraction than do lighter atoms, chlorine more than sodium, while the in-between sections [separating atoms in a crystal] have none. This hypothesis we transfer onto our continuum for which it can equally apply. Then the continuous crystal with its reticular density-structure forms a perfect space grating for X-rays. And then the continuous crystal will produce perfectly the same interference pattern as the classical one of Von Laue. Also in these results the assumption of separated [corpuscular] actual atoms in the crystal turns out to be an entirely superfluous element in the crystallographic theory.
But then also follows from the principle of elimination, that again the classic hypothesis of actual molecules and actual atoms in the crystal cannot obtain any confirmation from the wonderful results of the theory. Again, that hypothesis is, with respect to obtaining the results, totally irrelevant. [As to distribution of qualities over the crystal or of particles over the crystal, the crystallographic theory does not decide.]

Philosophical analysis of the crystallographic theory.

All this does not of course eliminate the further development of atomic theory made possible by the necessary and remaining elements of the crystallographic theory. First of all we have there the confirmation of the existence of minima and the magnitude of atomic weights that these [remaining] elements [of the theory] brought with them. Further, we have the acquisition that it is now certain that crystals, notwithstanding superficial appearance, are not homogeneous up to and into their smallest parts, but that they carry an internal periodic heterogeneity, at least as to density, and precisely the [sort of] heterogeneity [in density] as demanded by the reticular structure. And this periodic heterogeneity is  specific, it is permanent, it is characteristic of each crystal species, it connects with the properties of the elements out of which the crystal is made up, and with which [properties] the crystal stands in genetic conection. This is the further specification added by the crystallographic theory to every general theory of matter [democritean mechanicism, or aristotelian holistic, qualitative, naturalism]. And this specification is necessary because of the results that it gives. We should now demand of the general theory [of matter] that it allows to be specified in this fashion. So we must still find out whether and how this can [or cannot] be done, also in details, in the two systems [mechanicism and aristotelianism] we investigate. In the specification, necessary in Dalton's theory, it turned out to us that the original theory of Democritus had to be corrected in an essential way, although, as a result of this, not yet rendering every kind of atomism impossible. Above we saw that three problems still ask our attention :  The problem of the unity of the chemical compound, the problem of the difference in properties between compound and elements, and that of their similarity.

A.  Discontinuity-hypothesis.
Let us first consider the atomistic solution of the problem of the chemical compound. The last problem [similarity of properties between compound and elements] is solved there automatically. It is the essential thesis of atomism that the atoms remain what they are. So if we find similarity of properties between compound and elements, then in atomism this does not ask for an explanation. On the other hand, the second question of how to explain the difference in properties between compound and elements was to atomism a frightening problem indeed :  so different these properties appeared to be at first sight. We just heard Ostwald declare, precisely because of this reason, precisely because no properties were conserved, and all seemed to be new, that the assumption of the continued existence of the elements in the compound was an absurdity, not far removed from "reinen Nonsens".
This problem is here going to lose much of its worrisomeness :  For the way in which different densities of parts in the crystal correspond to the differences in atomic weight of the elements, proves that there do exist properties of elements that are at least more or less conserved in the compound, it points to some sort of preservation of the elements.
Things are different in the problem of  unity  [of the molecule]. To atomism its solution has become more difficult. Stronger requirements must be satisfied. After all, atomism, in virtue of its very essence, can only consider  accidental  unity, and such unity permanently results from forces (in the technical-physical sense) applied by actual atoms to one another [To clarify the concept of "accidental unity" versus "per se unity or substantial unity", it is instructive to refer to "accidental change" versus "substantial change". Accidental change is a change of a given Substance (in the metaphysical sense), but a change which does not affect precisely that in that Substance what determines what that Substance intrinsically is. This in contrast to "substantial change" which results in the transformation of the Substance such that the intrinsic "whatness" is replaced by another (or by several others, as is, for instance, the case when an organism dies and disintegrates.]. While in the initial development of atomic theory -- stoechiometry and kinetic molecular theory -- things were still chiefly about the stability of the molecule itself as a whole, and about the different valences [determining the stoechiometric proportions in the molecule], here, in developed atomism, more is demanded of these forces :  The atoms, each for themselves, must have precisely such forces -- and as passivity this corresponds to motion and equilibrium only -- that the reticular symmetry of the different crystal Classes must result from them [The particular lattice type, taken up by a given crystalline substance, should represent a minimum of free energy of the resulting crystal. So a configuration of atoms will spontaneously result such that these forces cancell one another as much as possible.]. The solution of this problem has undoubtedly become more difficult [for atomism]. [Introducing the thermodynamic picture just mentioned may, as it seems, render the problem (of intrinsic unity of the molecule or crystal) not so difficult for atomism after all. However it may be that the actually observed unity of chemical compounds is still greater than that expected in compounds insofar as they are exclusively the product of a mere energetically more favorable rearrangement of actual atoms.]

B.  Continuity-hypothesis.
A solution of the problem of crystals as chemical compounds [and of all chemical compounds for that matter] in the aristotelian sense is another matter. Here the unity of the compound, we've seen it, does not bring with it a new problem. Already the first principles of the aristotelian theory are ordered to account for that newly generated unity. New properties -- the third problem -- for Aristotle, in contrast to atomism, only bring with them the demand to look for an effective cause, an agent. And if it turns out that the degree of being new is not so great after all, then surely this eases the task of the aristotelicus. Conservation of properties of elements  in general  is not only legitimate in the theory of Aristotle, but even to be expected. Precise observation should only decide upon the degree and way of this conservation. Since we now have a specification of this "way" thanks to the crystallographic experience, only the question remains whether this way of conservation, finding an expression in the reticular structure [densities correspond with atomic weights], can be explained [in line with the aristotelian view].
Earlier we already have derived as specification of the aristotelian principles of Prime Matter and Substantial Form :  the "principle of the heterogeneous virtual conservation of properties of elements", or the "principle of heterogeneity". This has teached us that in the aristotelian theory it is possible, and after the discovery of the relationship between elements and compounds, even to be expected, that a mixtum will be heterogeneous such that one part of it will have properties being totally or partly equal to the properties of one component, while other parts of the mixtum relate in the same way to other components. And much earlier we had found yet another specification of Aristotle's general theory, that of natural minima, which, as has turned out, already largely comprised Dalton's theory.
[As to the just mentioned "virtual conservation of properties" (of elements in the mixtum, i.e. in the chemical compound), we should add that here this "virtuality" does not (or ought not) refer to "conservation", because here the conservation is real, actual :  Not the elements themselves, it is true, but certain properties of them are  actually  conserved in the compound, but, although they were properties of the "constituent" particles when they were still free, they now are not properties of these particles anymore because the latter have ceased to be particles, they have become  virtual  particles, because they are now virtually-corpuscular constituents of the compound, indeed, virtually-corpuscular, but still actual constituents of the compound. Therefore their properties are now properties of the compound. So here "virtual" refers to the particle-, the corpuscular-aspect of sites (parts) of the compound expressing its heterogeneity.]

Principle of specific heterogeneity according to virtual conservation of atomic properties.

These two specifications must now be united. We heard from Toledo how aristotelian medievals correctly imagined the generation of a mixtum [a chemical compound] :  The elements become divided into their minima, these come to lie adjacent to one another, then the minima of the one element interact with those of the other, and they therby change one another's qualities. The resulting properties will be  specific  to the compound then generated. We already saw during the derivation of the principle of heterogeneity that then the following can be expected :  The change of properties of the elements [as a result of their interaction] will not result in a homogeneous property of the product, but in a specifically heterogeneous state of it, precisely expressed in the principle of heterogeneity [This heterogeneity of the product, the molecule or crystal, will be expressed by a spatial distribution of different properties over the individual molecule.]. Well then, according to the conception of the generation of a mixtum, as Toledo has described it, the result will be :  Minima of the mixtum are generated, each one of them  complying with the principle of heterogeneity. And in this way :  The properties of the periphery of the atoms will have changed [as a result of the interaction of these atoms], while those of the more central parts of these atoms, and still more propbable those of their nucleus, will have less, or possibly not at all, changed. And this heterogeneous complex then is, as expressed by the medievals, the "proper", i.e. specific, "disposition" of the minimum of the compound (mixtum). So the principle of heterogeneity must apply to the minima of the compound, the molecule. And this not only as to density, but also as to other properties. To which ones, detailed observation must decide upon, where there is a substantial chance that the properties of the nucleus of the atoms are completely conserved in the molecule [Although one would conclude from this that then also the nucleus itself will be conserved, this is not necessary, if we assume -- with HOENEN -- that these conserved properties have now become properties of the mixtum.]. So we find a further  elaboration of the principle of heterogeneity.  While this principle generally is about the "heterogeneous virtual conservation of properties of the  elements",  now we discover the heterogeneous virtual conservation of particular  atomic  properties. And so we arrive at the concept of  "virtual atoms" in the [metaphysically] continuous molecule of the mixtum. [Here we see that also HOENEN understands "virtual" to refer, not to "conservation", but to the  atoms  themselves (insofar as atoms, i.e. as individual particles)]. This molecule will have a heterogeneous structure resulting from virtual atoms. If, in the chemical reaction, not merely a single molecule is generated, but a macroscopic mass of a chemical compound such as a crystal [where this mass thus has crystallized], then it must, also when it is [metaphysically] continuous, carry a  periodic  heterogeneity  with virtual atoms. So this is to be expected according to the theory of the medievals [i.e. expected to be at least possible]. How, precisely, this "periodic" is structured, observation must decide upon. Well, in crystals experience teaches us -- as is evident from the necessary elements encountered in the crystallographic theory, and this is again a theory indicating  nearest  causes of phenomena -- the following :  The periodic heterogeneous structure is in crystals a reticular symmetric one [and thus not crystals having, for instance, a periodically banded structure]. And so we see that also this further specification of atomic theory perfectly fits into the Aristotelian principles.

Also the results of this theory -- the crystallographic theory -- still do not solve our problem [concerning the nature of unity of a chemical compound, i.e. of its minima :  reductionistic (mechanicism) or holistic (aristotelianism) ].  Both systems of thought which we investigated (Mechanicism-atomism, Aristotelianism) are able to account for the structure of crystals :  The atomistic view, if it can find the forces resulting in the structure to find its equilibrium. The demands of the nature of these forces have become heavier though [because  specific  structures are generated, not merely stable (but random) aggregates. Specific structures such as the arms of a snow-crystal, and, generally, hopper structures in crystals.]. One also sees how application of mathematical methods [in crystals diffraction measurements, and their symmetry being described by Group Theory], of measurements,  to  "extensive qualities" leave the qualitative nature intact, and giving beautiful results.

Chemical and stereochemical structural theory


An analogous development of classical atomic theory, simultaneous with the older, but preceding the recent crystallographic theory, we find in the structural theories of chemistry. A development we admire. Towards the end of the 19th century, also this theory shared the fate of all explicative theories. Indeed, positivism and sceptical tendencies had convinced a "chemist respecting himself" not to believe anymore in the existence of atoms, and surely not [to believe] in the reality of the fine structural formulas, indicating for every atom its place so precisely in the molecule. Of course, as a means of classification of chemical compounds, as "working hypothesis" for finding new compounds and methods of preparation of them, the structural theory was highly esteemed. But one didn't dare to attribute to it any reality value, at least so in many circles being influenced by energetic and sceptical tendencies. Where, in passing, we want to confess :  We don't understand how a theory can be a pure "working hypothesis", i.e. a hypothesis with which one can work, can classify (if this doesn't mean simple arbitrary indexing), can derive real phenomena, but which doesn't contain any element revealing to us a reality, a true cause of these real phenomena. We've never met an epistemological account constructing the possibility of such a "pure working hypothesis". We even are of the opinion that such a concept is absurd. Fortunately, these matters are now history. Now one, generally, we believe, surely attributes reality value to structural chemistry. Debije even constructed a method -- again with X-ray analysis, as in crystallography -- making it possible to measure the distance of the atomic centers in the gas molecule.

General features of the theory.

For us it is sufficient to consider just the main features of the theory. From the data of the theory of Dalton, combined with the "rule of Avogadro" (supplemented, if needed, with the data of the theory of diluted solutions and the like), one can determine the "empirical formulae" of the molecules of chemical compounds. These only indicate of what atoms of the elements and how much of each a molecule consists. They do not tell us according to what scheme these atoms are connected to one another. But in so doing, one meets with "isomers", i.e. compounds which molecules consist of the same atoms and in the same numbers. The properties of isomers may differ greatly. The fact of the existence of isomers has forced one to further work out the empirical formulae up to the construction of "structural formulae", now also indicating the precise pattern according to which the atoms are connected with one another. And then isomers must have a different structure, a different scheme of connected atoms. It is of course an ideal to find rules to set up such a scheme, resulting in the fact that according to these rules precisely so many structural formulae are possible as there exist isomers with a given empirical formula, no more and no less, and then attribute to each isomer its own structural formula. One knows that this has wonderfully succeeded. Even delicate nuances in isomery can be expressed in stereochemical formulae.
The result was even more striking than we said. There not only is this correspondence between the structural formulae so derived and the reality that the number of isomerous compounds is always equal to the number of, according to the rules, possible structural formulae, but also properties of the compounds can be read off from the structural formulae by who has learnt to read them. There are, first of all, the chemical properties, consisting in the way in which the compound reacts with other substances. In virtue of this, it is at the same time indicated in what way the chemical compound genetically connects with other compounds or elements. Genetic connection -- we saw it earlier -- points to a natural connection, a connection according to "nature", i.e. according to the nature of the substances involved. A connection from which thus follows that there must exist a certain correspondence or similarity in properties between the genetically connected molecules. And indeed it is experimentally established that  with  certain atomic groupings, "functions", being the same in different molecules, do correspond certain properties. These properties cannot, like the structure itself, be derived from the general rules to determine structures (valence rules and the like), but, once the structure of a series of compounds is determined, then observation shows that regularly these properties belong to certain atomic groupings. An thus they are a confirmation of the reality value of the structures and the correctness of the rules having led to the setting up of these formulae. In all this, we must realize that this theory orders a vast amount of facts, involving hundreds of thousands of compounds, a theory that unifies these chemical compounds in one coherent system finding its explanation in these structures, an explanation in the above described sense, i.e. finding in these structures a corresponding mapping. He or she who is more or less familiar with the science of chemical and stereochemical structures must admire its greatness.
See here, then, how all this can be summarized -- one does't do this in an explicit way, but always has it in mind -- in a typically explicative theory in the classical sense.
Suppose, then, that the molecules of the compounds are formed of atoms, continuing to exist actually in the molecule. This again is the fundamental thesis of all classical theory. This is then specified by hypothetical rules according to which chemistry sets up its structural formulae. And then we automatically arrive at the remarkable results discussed :  We always find in Nature precisely so many isomers as we can derive structural formulae from a given empirical formula [Recall that an "empirical formula" just gives the species of atoms and their number in a given molecule.]. These structural formulae well express the mutual genetic connection. A number of real properties of the compounds correspond to atomic groupings in these formulas. And these conclusions are indeed verified in hundreds and hundreds of cases. Finally, the X-ray analysis of Debije makes possible the measurement of atomic centers in the molecule. These conclusions then confirm the correctness of the assumption [actual atoms in the molecule]. And thus we have, apparently, a proof of the actual continuous existence of atoms in the molecule, solving, as it seems, the problem of the chemical compound in the atomistic sense.

Applying the principle of elimination.

We must, however, still investigate whether also to this particular development of atomic theory the principle of elimination of superfluous elements must be applied. Here our analysis can be short, because this case is entirely analogous to that of the crystallographic theories. As to the X-ray analysis of Debije this is immediately clear. But also as to the general structural theory it is easily evident. In addition to the classical hypothesis of the actual atoms we again place another :  Let the molecule not be an aggregate, but a continuum [again in the metaphysical sense]. Not a homogeneous continuum :  that wouldn't have a structure as expressed in the formulae. And this structure evidently is necessary [in order to explain isomers]. So suppose that it is a heterogeneous continuum, this time not, as in crystals, with a periodic, reticular, structure, but with one that corresponds to the properties of the [constituent] atoms, which, as in crystals, are virtually conserved in the continuous molecule. Where then, classical theory in its structural formulae assumes an actual atom, for example a carbon atom, there we think of a part of the continuum having properties recalling those of the element Carbon. In what degee cannot decided upon a priori, and it will certainly not be in the same degree in all cases. Again, observation will establish things. And the same will hold for the other atoms of classical theory. We can express all this in a short statement :  Where classical theory does place an actual atom, we think of a virtual one, where in different cases different degrees of virtuality, i.e. of conservation of atomic properties, may occur [this degree of conservation of atomic properties is the degree of virtuality of atoms in the molecules.]. Above we have derived the concept of "virtual atom". And we now can take over the formulae of the classical theory unchanged. Only whereas one interprets these formulae "classically", i.e. as representing aggregates of actual atoms, we interpret them [i.e. these formulae] as representing totalities, continua, in which these same atoms are only virtually present. It is clear that all conclusions of the classical theory remain unchanged in our theory :  the number of possible isomers, the genetic connection, the correspondence of certain properties to certain groupings of virtual atoms. From which necessarily follows that the hypothesis of the actuality of the atoms [in the molecule] is again a completely superfluous element of the classical theory, and thus not obtaining any confirmation from the true success of the structural theory. Again, what is excluded is only a hypothesis assuming a homogeneity of the molecule of the chemical compound, or assuming another heterogeneity than what is demanded by the principle of heterogeneity as it was worked out above for virtual atoms.

[Atoms in a molecule are held together, first of all by chemical bonds, the most important of which is the covalent bond (some covalent bonds may be a hybrid between ionic and covalent bonding). In addition to such bonds, there may be other 'bonds', forces, that play a role in the molecule adopting its final structure and shape of lowest energy state, such as Van der Waals forces and especially hydrogen bonds (both electrostatic in nature). The Van der Waals forces are simply the fine tuning as far as the chemist trying to determine molecular structures is concerned. Also a covalent bond may "oscillate" between single and double bond as in the benzene-ring and in the peptide bond (the latter chemically linking amino-acids into a chain, forming the "body" of a protein).
All these intra-molecular bondings and forces can be described in terms of corpuscular actual atoms being held together by these bonds and forces in a given molecule, whereas HOENEN describes all this in terms of virtual atoms in the (actual) molecule (he does this in order to preserve the intrinsic unity of a molecule, the molecule as one single "ens"). Description in terms of virtual atoms in a molecule implies that all conserved properties of these atoms are now properties, not of the atoms, but of the molecule. And also the fact that one atom attracts another (in the molecule), for instance in the case of a hydrogen bond somewhere within the molecule (or between molecules in a crystal, like the water molecules in ice), adds up to the set of conserved qualities of that atom. Such an attracting (or repulsive) force, itself being an intensive property (quality), has its proper extensive effect of holding atoms in a molecule at a certain distance from each other, i.e. holding virtual atoms at a distance from each other. These virtual atoms are small but definite regions in the metaphysically continuous molecule, small regions in which a number of qualities (properties) are concentrated. Together these qualities of such a region form a coherent pattern in such a way that the region shows an "inside" and an "outside" and thus clearly qualitatively and spatially distinguishing itself from its surroundings which also inhere qualities. Such qualitative regions in a molecule -- its virtual atoms -- are spaced from one another as a result of the extensive (in contrast to intensive) effects of certain intensive qualities (forces), and so resulting in the molecule's structure.
So in this view a "Substance in the metaphysical sense", i.e. a true Substance, here exemplified by a molecule of a chemical compound, but now generalized, is an overall spatial pattern of small sub-patterns of qualities. And the overall pattern, representing the given Substance, at the same time represents the place, the location, in the aether of a given individual Substance, i.e. the place where that Substance has penetrated the aether. Between non-contiguous Substances we then have non-penetrated aether. And since we may consider the aether itself to be a(n imponderable) Substance with its own possible qualitative determinations such as electromagnetic radiation and gravitational fields, we may maintain that all there is in the physical (and organic) world (the Explicate Order) are ultimately true Substances and nothing else. Indeed, every aggregate is ultimately an aggregate of true Substances. These true Substances are :  free atoms (or ions), free molecules, and organisms.
And it is interesting to know that there is much to say for the thesis that every individual organism is in fact one single giant molecule, embedded in an aquous serum-like support-medium (this is the Unimol view of organisms, and links them with molecules). This organismic molecule must be protein-like, and thus having secondary, tertiary, etc. structures :  It must be folded and folded again, twisted and twisted again, and above all, it must be mat-like, an open molecular structure, everywhere in contact with the serum-like support medium. Most of the bonds in this living molecule are expected to be covalent (i.e. not ionic, and thus not solely consisting of electrostatic attraction, but with commonly shared electrons). And it is especially these (covalent) bonds that turn a molecule into an "atom with many nuclei screened off from the outside world by a cloud of electrons". But certainly also other bonds do play a role in shaping that molecule, especially the so-called "hydrogen bonds". These are in fact formed by the electrostatic attraction between a covalently bonded hydrogen atom and another atom such as oxygen or nitrogen. So, in water, H2O, at subzero temperatures, its molecules are bonded to each other by hydrogen bonds :  each one of its oxygen atoms, while covalently bonded to two hydrogen atoms, is, in addition, connected, by a hydrogen bond to a hydrogen atom of another water molecule, and in this way one "giant water molecule" is formed, an ice crystal (So hydrogen bonds can make large "super molecules"). Inside the living giant molecule hydrogen bonds are expected to be common and help provide it with a very precise three-dimensional structure, the same for all molecules, i.e. all organic individuals, of the same compound, the same organismic species.
When all this is correct, then (1) the theory of virtual atoms in molecules and crystals, (2) the developed view of a true Substance, (3) the theory of the aether as a universal medium of localization of ponderable Substances, and (4) the Unimol view of organisms,  may lend support to the idea that the Explicate Order is the "display window" of a universal "World Cellular Automaton". The "cells" of this window may then be the "quality-points" together forming the discrete network of explicate reality at its most deepest level (this theory of "discrete reality" will be expounded later on in a separate document). Each such a quality-point contains a set of primitive qualities, together, as a result of the mixing-up of many such points, forming patches of "secondary qualities", i.e. our known types of qualities. And it is eventually these qualities that are going to make up the above mentioned patterns and sub-patterns resulting in Substances. The macroscopic, i.e. high-level, phenomena of change and motion are ultimately based on the mentioned hyper-microscopic lowest-level qualitative points that, as cells (of the universal cellular automaton), change their qualitative content as dictated by the rules of the World Cellular Automaton, rules residing in the Implicate Order.

We now continue again with HOENEN's text about virtual atoms in molecules . . . ]

Problem of compatibility of this specification with the fundamental theses [of atomism and of aristotelianism].

Also here our discussion can be short, the results are totally analogous to those of the analysis of the crystallographic theory.
The task of the atomistic explanation of the chemical compound on the one hand has become easier, for it turns out that more properties of the atoms are conserved in the molecule [as concluded from X-ray analysis], more properties than initially was thought. The aspect of being new (of the compound as compared to its elements), the change of properties, is, therefore, not so dramatic as one initially held it to be. If one accepts an amended atomism which, in accordance with modern science and against the classically mechanicistic view of Nature, also admits of intrinsic qualitative [HOENEN adds: accidental] changes, then possibly the changes in properties [in the resulting molecule], which undoubtedly are there, may be explained as accidental changes [In this atomism, the atoms are then Substances having qualities (inhering in these Substances (that's why HOENEN calls them "accidents")), which (Substances, atoms), - upon entering, i.e. going to make up, the crystal or molecule, and then forming an aggregate of Substances, - change, i.e. some qualities of these Substances, these atoms, are replaced by other qualities.]. On the other hand, the problem of the  u n i t y  of the molecule becomes more difficult [for atomism]. The atoms must possess precisely such forces (in the physical-technical sense) that the variety of structures can be calculated as to be each of them a resulting equilibrium [or better: lowest energy state], not necessarily static but rather dynamic. And the probability that this [calculation] eventually will be accomplished becomes, as a result of involving the mentioned forces, smaller [But, as far as I know, nevertheless already accomplished in a number of cases with X-ray analysis combined with quantum theory. However, causal determination of protein-folding, and thus of the shape and internal details of certain (large) protein molecules, still doesn't fare so well by these methods.].
Also the position of the aristotelian, viewing the mixtum as a new substance [because he allows for substantial change], and the molecule as a [metaphysical] continuum, doesn't need new elucidation. Above, we could, from aristotelian principles, work out the "principle of heterogeneity" such that the thesis of the virtual conservation of individual atomic properties, except those of the atom's periphery, resulted from it, and from which in turn was derived the concept of  "virtual atoms". In investigating the structural theory we had nothing else to do than to apply the concept of virtual atoms, to be able to immediately conclude that the hypothesis of the actuality of atoms [in the molecule] in the classical theory was a superfluous element [The phenomena with which the chemical structural theory deals are equally well explained whether one takes the atoms in the molecule to be actual or virtual. The "atoms" in the structural formula of a chemical compound may equally well represent true particles or, with the same right, "quality spots". So with all this, it is not yet decided upon whether atoms exist in the molecule actually or virtually.].

Additive and constitutive properties

[Under this heading it will be investigated -- by studying the relationship between properties of atoms and molecules -- what, precisely, may be the criterium deciding whether the molecule is a mere aggregate of atoms or a strict unity such that the atoms in the molecule exist only virtually, meaning that they are then nothing more than "quality spots" in the metaphysically continuous molecule, i.e. qualities (quality sets) of the very molecule itself.]

Additive properties.

Connected with the chemical structural theory is a dispute having taken place a few years ago [the 1930's, 1940's] between philosophers and also sometimes some physicists concerning our problem. The significance was disputed of the data known as additive properties.
A "constant of a molecule" (or a gram-molecule, i.e. an amount of the substance in grams equal to its molecular weight), is called an additive property if it can be calculated by adding up the relevant constants of the constituent atoms (resp. gram-atoms), in which, of course, the constant of each atom of that particular kind is multiplied by the number indicating the number of atoms of that kind in the molecule. An example is the mass, of which we already have spoken. Here, in the mentioned dispute, it was about other properties. We mention the most important two :  The so-called molecular volume (i.e. the volume of a gram-molecule at the boiling point of the liquid compound (the gas-volume surely is not an additive property, it is independent of the number of atoms present in the molecule), and the so-called molecular refraction, calculated from the refractive index, mostly after the formula of Lorenz and Lorentz.
The mentioned dispute boils down to this :  From additivity it follows that the atomic properties are conserved in the molecule. Thus [one concludes] the atoms themselves continue to exist in the molecule. The opposing party, on the other hand, held that additivity often is not, and rarely or never perfectly, realized. And thus [one concludes] the elements do not actually exist in the compound. The first party departed from a wrong principle, namely that conservation of properties -- even not of all relevant properties -- is a proof of the actuality of the atoms in a compound. Above we have seen that this is false. Also virtual continued existence on its own already demands a certain conservation of properties, and we even saw that some -- not those of the periphery of the atom -- may even be perfectly conserved. But also the arguments of the opposing party were not particularly strong. So we will not follow all these arguments and mention this dispute only because of two reasons :  First, the considered properties, just like that, cannot lead to any result. Second, further analysis will teach us what properties are indeed suitable to be investigated for the solution of our problem.

Way of determining these atomic constants.

We said that consideration of these additive properties just like that cannot solve our problem. As to mass, we already saw it in considering the law of Lavoisier.
Let us take the "atomic volumes", from the summation of which would result the molecular volume. In what way the atomic volume is determined?  H. Kopp investigated the molecular volumes of a series of compounds (fatty acids), of which always the next [compound] contains one CH2 group more than the previous compound. This causes each time an increase of the molecular volume by precisely 22 cm3. Then he could split up this amount with the help of analogous comparisons such that half of it came to be on account of the (gram-)atom carbon (C), and the other half on account of the two (gram-)atoms hydrogen (H). In this way he also determined the "atomic volume" of other elements. An when he then took a new compound, he indeed often (soon we will encounter deviations) was able to calculate the molecular volume as the sum of the atomic volumes of the composing elements.
But does this demonstrate the conservation of an atomic property? By far not. One didn't compare a property of a free atom with that property which it has when bonded in the molecule [only then we can see whether it is conserved]. Compared was :  the property, (rightly) attributed to the atom, but not to a single free atom, but to an atom as it is present in the one and in the other [kind of] molecule. If this property is indeed the same, if additivity has indeed been found, then, evidently, at most follows -- we say "at most", i.e. even if it is supposed that one or another property of a free atom could  not  be perfectly equal to that of a virtual atom, if we, therefore, argue along the (false) principle of those [scholars] who were speaking -- that the atom in the one molecule is present in the same way as it is in the other, so that if it is actual in the one molecule, then also in the other. But if it is virtual in the one, then also in the other. Nothing more. [meaning that actuality or virtuality is not decided by this additivity.]. But this we already knew for a long time, thence that we said that the investigation into atomic properties, having been determined only in this way, as such never brings a solution to our problem. As to another objection, we will return later, and then it will also be clear to us what atomic properties can successfully be investigated in order to reach our goal.
In exactly the same way, now -- for the first time by Landolt -- the molecular refraction was divided into atomic refractions, and then from the latter, by simple addition, was calculated the total constant of the new compound. Often with success. Insofar as now this property turned out to be additive, the conclusion cannot be different from that of the above case [that is, only atoms  in  the molecule are considered, so that it cannot be decided upon whether there is addition of atoms (with their properties), or only of properties (now of the compound), rendering the atoms themselves not to be a subject anymore of those properties, and thus rendering the atoms to be only virtually present in the molecule.]. But molecular refraction turns out to be far from additive, it even deviates (as a result of "constitutive influences") so much from additivity -- as, for that matter, also the, less investigated, molecular volume -- that these  deviations  are used in structural chemistry to determine structures.

Constitutive influences.

The deviations from additivity are attributed to so-called constitutive influences, i.e. to influences from the structure of the molecule, from the way in which atoms are connected, from the action of neighboring atoms. The deviation may be rather big. Thus, Kopp found already in oxygen, being "keton-like" (i.e. with a double bond) bonded, an atomic volume of 12.2, whereas the value for the same atom in a hydroxyl group, -OH (as in alcohols) is only 7.8.  So constitutive influences are at work here.
Something similar holds for chemical properties. If a group CH2 occurs in a structural formula between two keton-functions, it differs much from a same group (CH2) being placed between two other CH2 groeps. The hydrogen is bonded much more "loosely" [to the carbon], meaning that the chemical properties of that carbon atom have become different under the influence of the two neighboring groups.
In this way one better understands additivity where it occurs. It will be found precisely there where a same atom occurs in molecules having an equal structure in the vicinity of that atom. Also there constitutive influences will be present, but as a result of the equality of the structure they will be same in that series of chemical compounds, thence the additivity of the property. And thus the truth of our thesis becomes even more evident, namely that in this method are only compared properties of the atom  in  the one and  in  the other molecule. And also is evident the truth of our conclusion that this additivity all by itself can never lead to a solution of our problem. And here it even is still about properties that can  sensibly  be attributed to a single free atom at all :  the volume (albeit so that it is unknown for a single free atom and probably strongly subjected to changes induced from without) and the chemical properties.

Constitutive properties.

These conclusions, namely, become even more urgent when other properties are considered which do  not make any sense at all  of being a property of a single atom or molecule [In such cases one cannot speak of additivity anymore and thus also not of conservation of atomic properties.]. So it is in the above mentioned molecular refraction or atomic refraction. In constituting this constant one uses the refractive index of the material under investigation. Well, for a single atom or molecule it simply doesn't make sense to speak of a refractive index. This concept is only applicable when considering a system of atoms or molecules. So a refractive index, and thus a constant such as the molecular or atomic refraction, is something which, in the system characterized by it, results as a novum, as  something new  from the collective action and the mutual interaction of the composing particles [And here only as : "the-being-many" of these particles. Only as a result of this "being many", and exclusively as a result of it, something like a refractive index originates, and consequently an atomic or molecular refraction.]. New,  even according to concept.  And then we no longer have to do with constitutive  influences  on a given property, but have to do with something that can only be generated by a structured multitude, then we have to do with a  constitutive property.
This also holds for a property like the color of chemical compounds, thus in fact their absorption spectrum. To speak of the "color" of a single molecule or atom, let alone of a single electron, hardly makes any sense or no sense at all. It does make sense to speak of a color which -- as part of an absorption spectrum -- results from a determined constellation of these components, that is, as something new. In classical theory [as contrasted with quantum theory] color -- absorption bands of small wavelength [color, of course, results from those wavelengths that are not absorbed but reflected or transmitted] -- was attributed to electrons "vibrating" about an equilibrium state with a period corresponding to the period of those light-rays that are absorbed. For infrared it wasn't electrons but mass particles that were "vibrating". Now while it is true that classical theory with its "vibrations" has been abandoned, this particular thought was correct and remains valid :  A property like color only makes sense if there is cooperation of the components, components that each for themselves do not and cannot have "color", because this concept doesn't make sense in these individual components. Thus it is so with the refractive index of a material, with the constant pressure of a gas at constant temperature, and with other gas properties, and so it is with the constant planetary revolution [A planet moves around its star, not because each of its particles does so, but the planet itself so moves, and therefore all its particles do so move. Such a particle all by itself would not go around that star, if at all, along the same orbit as the planet does, so this particular motion around the star along that particular orbit is an activity of the whole planet and only of the whole planet.], so it is with the motion of the hands of a clock, and so the tone of an organ pipe. All of them are constitutive properties, properties that only  result  from collaboration of a multitude of components of which no one individually can have such a property. This then is a true constitutive property of the  whole  against its  parts.
[Going back to "color" again, we know that a single molecule (i.e. each single molecule of some bulk material) does reflect (or transmit) precisely those parts of white light that correspond to certain wavelengths. And because wavelength corresponds to (perceived) color, an individual molecule does have a color. Whether this is correct or not, it doesn't affect HOENEN's explanation as to what precisely are "constitutive properties". A constitutive property of some object is not present at the level of its components.]

Aggregation resultants and totality resultants.

Such a property necessarily is something new relative to the properties of the components. Investigation of these new properties may result in the solution of our problem. After all, when the properties of the components on which their mutual interaction is based, are given, one will be able to calculate (unless mathematical difficulties prevent such a calculation)  which  new, truly constitutive properties follow from their combination. Thus, the revolution of a planet can be calculated from Newton's law, thus the pressure and other properties of a gas from the kinetic gas theory. From the results of this theory we above concluded that a gas is an aggregate [but certainly not in the way atomists thought that molecules were aggregates of atoms], that there is discontinuity between its molecules. Are the calculated properties indeed those actually possessed by the combination, then it is proved that the combination is a genuine  aggregate  of these components. [Although the line-spectrum of hydrogen is, according to HOENEN, a totality resultant, it can nevertheless be calculated (also according to HOENEN) from the properties of the components, proton and electron, of the hydrogen atom. But this calculation must employ quantum conditions, rendering the hydrogen atom to be a non-mechanical system, and thus a totality, despite its computability.]. Does, on the other hand, the combination not have these properties, but instead of them other properties, then it is proved that it is  not  an aggregate, that the resulting property originates from a higher unity than that of an aggregate, i.e. originates from a single Substance [in the metaphysical sense], from a single  totality.  Then we have, accordingly, a new property in a twofold sense :  First (as above) in the sense that the property was not present in the individual components, and that it could not be there (unless as an effect in the cause [by this HOENEN might mean something like :  "unless as enfolded in the dynamical law producing the substance from initial conditions".], and second, in the more decisive sense, that this property is in addition a different one, different from the one that would result from a combination of the same components, which is a true aggregate. [Additive properties, but also aggregation resultants, are not actively generated by a dynamical system, but result only passively from the multitude of constituents.]. A new property in the first sense we will call an  aggregation resultant,  while a property which is new also in the second sense will be called a  totality resultant.
Examples of [constititive] properties of a system [of components] [properties] that are aggregation resultants, we had found earlier :  the tone of an organ pipe, the revolution of a planet [Orbit and period of revolution of a planet can, after the fact, be seen as a summation of the motion of the composing particles and is thus an aggregation resultant.], the pressure of a gas, the blue color of the sky. Also the refractive index of a liquid must be one of them.
[The next sentence of HOENEN's to come was meant to give an example of yet another constitutive property, but now one of which it is, at the present point in the discussion, not yet decided whether it is an aggregation resultant or a totality resultant :  The color of a chemical compound. But because this example is, according to me, not very instructive, I have chosen another one, another constititive property, which also HOENEN will use later on (namely the line-spectrum of hydrogen)].
The line-spectrum of the hydrogen atom also is a new property. The above developed consideration about true constitutive properties can be applied also to it. With this and the like properties the problem is :  Are they aggregation resultants or totality resultants. If the first is proved, then the compound is an aggregate. If the second is proved, that is :  if they differ from aggregation resultants, then the compound is a totality, a new Substance [in the metaphysical sense].
So here we have discovered a true criterium of totality. [i.e. a means to distinguish totality resultants from aggregation resultants, and thus to distinguish totalities from aggregates. And, at the present stage of the argument, it is not yet shown that true totality resultants do exist at all.].
In our discussion we have often said that atomism, if the compound [chemical or otherwise] is a true aggregate, must explain the stability of that compound as an equilibrium resulting from the forces applied to one another by the components [The aggregation must, in order to have that stability, find its lowest-energy configuration]. Here we see that this is a special case of a more general demand :  Atomism must be able to derive the new properties of the compound as aggregation resultants, they may not be totality resultants.
In addition to the problem of unity [of the compound] there was the problem of novelty of properties. Here the means to solve these problems [unity, novelty] turn out more or less to coincide, which is not surprising, because they are aspects of the same problem, that of the chemical compound, the unity resulting from the specifically many. [Indeed, if the properties of a mixtum are true totality resultants, then they come from one single totality, one new Substance.]

False method of solution.

One should not think that the decision has already been made in the rules, according to which one, in organic chemistry, lets correspond certain atomic groups in the structural formulae with certain properties of the materials. One could, already in the 19th century, especially regarding the color -- and thus the absorption spectrum -- couple certain coloric properties to certain structural elements. But with these constitutive properties matters are the same as in the additive properties discussed above [One considers the groups always as existing  in  a molecule, instead of considering the 'free' groups. The results apply to virtual as well as to actual groups.]. These constitutive properties are properties that, evident from observation, go in a number of [different] molecules together with the same structural elements [i.e. correspond to these structural elements] and are equally influenced by neighboring elements, from which at most may be derived the following conclusion :  If the constitutive properties in the one compound are aggregation resultants, then also in these other compounds. If they are in the one compound totality resultants, then also in the other, which one may safely assume by reason of the complete analogy of these compounds anyway. [And the issue here is still whether a given constitutive property is an aggregation resultant or a totality resultant.]
In classically-viewed structural theory the new, constitutive, properties necessarily had to be aggregation resultants, with which it was thus demanded to detect properties of the individual atoms -- if need be introduce them hypothetically -- such that from the stable aggregate of these atoms, as a molecule resulting from these properties, the new property can be calculated. This -- in order to be in line with the classical ideas -- should not hold for just one particular case, but for all relevant cases. An attempt to accomplish this should seem to be hopeless, and this certainly contributed to doubt the reality value of atomic theory despite the wonderful results of the structural theory of chemistry in general. The probability to obtain result indeed was rather too small. Under this sceptical or desperate mood there would have been no necessity that the structural theory itself would suffer and even doubted, if one would have been provided with the elaboration of the peripatetic theory, leading to virtual atoms bringing with them the possibility of constitutive properties that are not aggregation resultants, but totality resultants.

True method.

The investigation into the constitutive properties [ constitutive, because the additive is about atoms or atomic groups that are already taken up into the molecule, i.e. present in it virtually or actually], be they aggregation resultants or totality resultants, must bring the decision. And it came when one first learned to investigate simpler cases. For this, one then has to know the properties of the individual components, the free atoms or their parts, and from them try to derive the new constitutive properties of their compounds. First of all, this solution was found in the chemical atoms themselves, after having found out that these were not genuine elements, not true "atom", but composed and divisible systems. So then, to the problem of the chemical compound, discussed until now, another problem is added, that of the composed chemical atom. The solution [totality or aggregate] doesn't need to be the same :  It may be that the molecule of the chemical compound is an aggregate, and the composed atom not. Before we consider the recent development of atomic theory [here the structure of the atom], we first must review what has been treated so far, because this contains all what was known in the 19th century in classical theory, and could be used to solve a problem which -- after sceptical and energetic tendencies had vanished -- was taken as to be definitively solved in an atomistic sense. In natural science a possible aristotelian solution was certainly not considered, one even had no inkling of it.

Retrospect and outlook

[Here, as has been said, an overview will be given of that what has been treated so far. The very possibility (not yet the actual existence) of the chemical compound as a true totality (metaphysical continuum) has now been established, and also its criterium. And only after this overview, in the next main Section The modern theory of the atom and its consequences), the solution of the question whether there exists (also) in the inorganic world true Substances in the metaphysical sense will be formulated. It will be found out there that for atoms, as well as for molecules, the necessary introduction of quantum conditions into the description of them will hold the solution :  every free atom, and every molecule is a totality, a true Substance in the metaphysical sense, because these quantum conditions render them to be non-mechanical composites. In molecules the constituent atoms will be there in the form of qualities of the molecule, meaning that these atoms in the molecules are not self-contained beings anymore but grade -- with their electron clouds -- into their molecular environment, i.e. grade into the other atomic constituents of the molecule.]


In bird's eye view we have seen the wonderful results having been reached in nineteen century atomic theory. As to its classical interpretation it has originated from the atomism of Democritus, and it consists of a series of still further developed specifications of this philosophy. These specifications embody theories that in each case give nearest causes of newly discovered phenomena and laws. In this lies the explanation of the success of this atomic theory. Indeed, in virtue of its specifications it can deduce a vast number of known facts from its premises, and predict others, and thus explain these facts :  After all, they derive from the causes assumed by the theory.
It is true that the original philosophy of Democritus had to undergo many and drastic changes. One had to accept the equality of the atoms of the same chemical element, by which an essential principle of Democritus, demanding all possible sizes and shapes of atoms, had to be abandoned. Further, the forces, expressed in the chemical compound, cannot in any way be just the collision forces of strict mechanicism. And one had to accept a continuum as carrier of electromagnetic and gravitational fields [i.e. one had to abandon the notion of empty space as the medium of atoms, assumed by Democritus.].  Finally, [atoms as] purely geometric elements are not sufficient, qualitative ones had to be accepted.
Yet in classical theory one element of atomism (apparently) remained unaffected, namely the supposition that the atoms are always actual, that the chemical compound is an aggregate, not a totality. And thence classical theory is atomistic, thence its successes were seen as a victory of atomism.
We have successively investigated the whole theory in all its parts including its atomistic principle. And the result was that all the specifications -- expressions of nearest causes of the phenomena from which [causes] the latter originate -- had to be acknowledged as necessary and thus had to be accepted. But only that one principle, the atomistic principle, rendering every chemical compound to be a mere aggregate and excluding it being a totality, turned out again and again to be superfluous in all cases. In this investigation we did not focus on the metaphysical origin of this principle, only on this one question :  what elements of classical theory are necessary to derive the results, what elements are superfluous. A purely logical criterium. And in this investigation the democritean element [actual atoms in molecules] turned out to be completely superfluous.
Our method was this one :  Everything classical theory explains could also be explained in a system viewing chemical compounds as continua, in the gasses and liquids the individual molecules, in the world of crystals even whole crystals. But these continua cannot physically be indefinitely divisible, but only up to a certain limit, the minima, being among themselves the same for the same material [It is in fact these minima which are continua, together often constituting an aggregate, either of free atoms, or of free molecules.]. These minima must have a heterogeneous structure and surely a very determined one :  There must be heterogeneity according to properties in molecules corresponding to the chemical elements, specifically to the individual minima of them, in line with the demands of the [chemical] structural theories. And because this continuum theory [holding any molecule (or any free atom) to be a continuum in the metaphysical sense, i.e. holding any molecule to be a single fully-fledged "ens"] explains everything that is also explained by classical atomic theory, it is clear that the latter's atomistic demand of actual atoms (in the molecule), introducing discontinuity  within  the molecule, is a superfluous element in classical theory, which [element] thus, according to the principle of elimination, cannot obtain any confirmation whatsoever from the wonderful results having all over been accomplished by classical atomic theory.
But this purely logical analysis is still not sufficient. A metaphysics has to be found such that its general principles allow themselves to be specified such that  these  continua become legitimate and intelligible.
We have found this metaphysics in the Aristotelian principles of prime matter and substantial form, giving, as general principles, precisely the conditions to be satisfied by substances (in the chemical sense), in order that from several individuals [entia, beings] may originate one single continuum [one ens, one being], and vice versa, and especially, in order that from a body (or from more than one) a  specifically  different body (or more than one) may originate. In this theory,  generally,  a chemical compound may be a totality, having originated from different elements. But do these principles allow to be specified such that precisely  those  continua are possible that above have been found to be necessary in an atomic theory taking chemical compounds to be totalities?
Indeed, so we've found, the metaphysical principles of Aristotle allow them to be so specified. We even didn't have to do anything else than to take up again the specifications already applied in Antiquity and Middle Ages -- after they were for a long time partly of even totally neglected -- to unite them, to develop them, and to test them against the rich results of modern theoretically elaborated observation. The possibility of these specifications can be derived in abstracto from the general principles. Their factualness was evident -- already in Antiquity and Middle Ages -- from experience and is confirmed by the new mathematical methods [But these actual specifications for the time being only demonstrate the possibility, within classical atomic theory, of molecules to be true Substances.]. We, namely, found the possibility of a potentiality [prime matter] which only allows itself to be realized in grades and steps, so that it cannot directly be actualized to all substantial forms to which it is in potency, but only as mediated by other actualizations. For prime matter this is then confirmed experimentally, because it is first of all in potency to the elements and only then to chemical compounds, simple and more complex compounds. These chemical compounds thus show  genetic  connection, not directly with all but only with certain determined elements. They also show mutual genetic connection, linked to the first. All this is expressed in the principle of  virtual conservation of the elements in the compounds.  This conservation is nothing else than similarity according to [their] "nature" as principle of activity and passivity. Genetic connection is just an expression, a sign, of that connection-according-to-"nature". But with this kinship (not in the usual chemical sense of the word, but rather in the biological sense) according to "nature", necessarily must go a similarity of properties between the compound and its elements, and mutually between compounds containing the same elements. From kinship by nature thus flows genetic connection as well as similarity of properties. So these correspond to each other. And thus all this is expressed by the principle of virtual conservation of  properties  of elements [the conservation is virtual because now these properties have become properties of the compound.]. These principles were known already in the Middle Ages.
Earlier we found a second specification which we clearly recognize as to be possible in aristotelian metaphysics, and actually realized :  the possibility of heterogeneous, and indeed in different ways heterogeneous, continua.
Connecting both specifications, we found the  principle of heterogeneous virtual conservation of component properties in the compound  [Again, in "virtual conservation of component properties", "virtual" refers to "of component properties" which properties have now become properties of the compound.], a principle that lets itself to be intensified as the equal  principle of the heterogeneous conservation of element properties in the mixtum,  which in this way becomes a principle of  specific  heterogeneity. This was, as to its first part, already worked out in the Middle Ages, where only poor experience didn't find it to be realized in inorganic mixta.
A third specification was the by Aristotle already worked out  principle of limited physical divisibility of [material] continua,  from which did follow the theory of natural minima, equal minima for the same species [of material], and thus the principle of Dalton. Finally, we found the principle described by Toledo, which together with that of Dalton makes possible a derivation of the stoechiometric laws. The same principle of Toledo combined with the already derived principle of specific heterogeneity in element properties led to the  principle of specific heterogeneity as to virtual conservation of  atomic  properties, at least of nuclear properties [or, for heavier elements, properties of nucleus and its immediate vicinity].
An with this, aristotelian philosophy, as specified by these principles, has at its disposal continua that completely satisfy the demands of the crystallographic and chemical structural theories. It has at its disposal, as we can now succinctly say, virtual atoms [because it has at its disposal molecules as (metaphysical) continua.].
Logical analysis told us, following the principle of elimination, that such continua completely satisfy all demands of modern experience with its, described in physical theories, nearest causes of phenomena. Elaboration of Aristotle's metaphysical principles tells us that these continua are indeed possible. This elaboration organically connects nearest causes with the first deepest intrinsic causes of bodies, the material and the formal. An aristotelian view of these theories surely is totally equivalent to the classical view.  All,  that has been explained in natural science, in classical atomic theory, up to the discovery of the composition and structure of the atoms themselves -- the investigation of which would lead to the bankruptcy of the mechanical view of Nature -- all  this finds an at least just as perfect intelligibility in the aristotelian continua with aristotelian minima as virtual atoms. All that. From which it is immediately clear that one was wrong when one was, by reason of the achieved results, of the opinion that the problem of the chemical compound was definitively solved along democritean-atomistic lines. Still more does follow from it :  For if further development of atomic theory refutes the mechanical view of Nature, then only this view of Nature falls, and not any element whatsoever of classical theory, which theory did indicate a true nearest cause of the phenomena, is dragged along with this fall. For by our results it is perfectly clear that precisely those mechanical elements of classical theory, now [these elements] turning out to be false, are superfluous elements. Precisely as we found in qualities. The theory, insofar as it had explicative value -- and that was very high indeed -- was independent of those superfluous elements, and thus will not be abandoned with them. So there remain :  The atoms and molecules and the gas theory and the structure of molecules and crystals. All these bodies built up from virtual atoms, according to the structures [patterns] discovered by natural science. Also here, the collapse of the mechanical view of Nature does not bring with it ruins of physical theories.

After the analysis of atomic theory explaining the stoechiometric laws, we have noted that one, also in education, also in elementary teaching, should not proceed as if Daltons's theory contained a proof of the actuality of atoms in the compound and thus the proof of atomistic atomic theory. Even if, based on later data, actuality would follow, the stoechiometric laws do not contain a trace of evidence for it. The same we now must hold of the entire atomic theory insofar as it is developed up to the discovery of the structure of atoms, insofar, that is, it describes the structure of molecules and crystals. Also even here there is no trace of evidence of an atomistic atomic theory. So also for this theory the logical "Sauberkeit" of scientific reasoning demands that the successes of the theory may not be put forward as evidence of the actuality of atoms [in the molecule], demands that the aristotelian continua with their virtual atoms must get their place in the whole discussion. The more so, when it has later [in quantum theory] turned out that the mechanical view of Nature must be abandoned.
Of course, by all this the level of science will not be downgraded to the level it had at the time of Aristotle or in the Middle Ages. Also here one should discriminate. Aristotle has general, metaphysical, principles of natural philosophy. He had first specifications of those principles. He also had -- that, after all, is the task of natural philosophy -- explanations intending to penetrate into the last specific details, the "species specialissima". These last explanations have now turned out to be full of error, what is of no surprise when taking into account the still poor condition of experience and the lack of mathematical methods. But let us not forget, this was in no less a degree the case in Democritus -- as far as we know details --, it was the same in Descartes, it was the same in atomists and cartesians, even still far into the eighteenth century. Their explantions in detail are not better than those of Aristotle or of the scholastics. To call, by reason of the errors of aristotelici, their system of thought to be a failure and to reject their principles as a foundation for modern specifications, scientifically is in fact funny. In  every  system the particular explanations of the ancients have to be replaced by specifications demanded by modern experience, and then see whether the fundamental principles allow them to be so specified. And then, in the end, it turns out that only Aristotle's principles survive this ordeal. Whereby we yet have discovered the remarkable fact that the first three general specifications of atomic theory, demanded by modern experience, were already found in the Middle Ages by the scholastics as elaboration of aristotelian principles. We didn't do anything else than simply to take up again these principles, to combine them and work them out still further.

Proceeding further.

Our long analysis of atomic theory now also has the advantage that the method to further work out our program to come to a solution of the problem of the inorganic mixtum, has been automatically set up. We have succeeded to develop a decisive criterium. In every composite [free atom, free molecule, crystal] there are truly new, purely constitutive, properties. The question now has become :  Are they aggregation resultants or totality resultants? If the properties -- or a sufficient set of properties -- of individual components are known, and the purely mathematical difficulties not too big, the decision can be made [for each case]. At the same time our attention was already focussed on one particular truly constitutive property very well suited to apply that criterium :  The spectrum, the emission as well as the absorption spectrum of composites [free atoms, molecules, crystals]. Moreover it is fortunate for us that science has automatically come to investigate meticulously precisely this so exactly measurable and familiar a constitutive property, and that it has attempted to derive it as an aggregation resultant. Not because it, 20st century natural science, had in mind the two possible solutions of our problem [aggregates-totalities, reductionism-holism] -- the aristotelian one was rather, and its specifications entirely unknown --, but because the development of science automatically demanded to derive this constitutive property [the spectrum] of the composite [compound] from the properties of the components, and then, naturally, see it as an aggregation resultant. It thus did nothing else than simply apply the criterium we had discovered [And this is not coincidental. Reductionism is, by definition, explanation (also when the explanation is not yet complete).].
And only when then automatically turned out that the spectrum is  not  an aggregation resultant, ideas did come up viewing the composite as a totality again, albeit of course that one didn't know that one, in so doing, introduced aristotelian ideas. Albeit that one didn't know -- precisely because the aristotelian theory was unknown -- how to explain this totality. But it is nevertheless remarkable that one, only as a result of the natural development of physics, came to think of the aristotelian totality-idea. Therefore it is certainly worth the trouble to present some utterances from pure physics.
So M. Planck (1929) declaired :

"Eins steht fest :  Der Rahmen der bisherigen Physik musz erweitert werden, damit die neuendeckten Tatsachen darin Platz finden, und wenn ich mich nicht irre, wird diese Erweiterung in der Richtung liegen, dasz hinfort ein Satz fallen musz, den man bisher stets stillschweigend als selbstverständlich allen physikalischen Betrachtungen zugrunde legte. Das ist der Satz, dasz alle physikalischen Vorgänge sich darstellen lassen als eine Aneinanderreihung von einzelnen lokalen Vorgängen. Die physikalische Welt ist nicht einfach eine Summe von räumlich und zeitlich nebeneinander gelagerten Einzelwelten, und manche Erscheinungen entziehen sich dem Verständnis, wenn man ein physikalisches Gebilde nicht als ein Ganzes betrachtet".

Translation :

"One thing, it is true, is certain :  The framework of current physics must be broadened, in order that the newly discovered facts can have a place in it, and if I am not mistaken, this broadening must extend along that direction where from now on a thesis must fall, a thesis that one, up to now, always had taken tacitly as self-evidenty underlying all physical considerations. That is the thesis that all physical events can be taken to be a concatenation of single local events. The physical world is not simply a sum of spatially and temporally positioned individual worlds next to one another, and many phenomena are unintelligible if one does not consider a physical construct [entity, body, pattern] to be a whole".

[For indeed, all there is in [explicate] reality, at least all existing material things, are Substances in the metaphysical sense, and thus are wholes. Even aggregates ultimately are aggregates of Substances, wholes.]

Here it is very aptly described that it was precisely the mechanical view of Nature that tacitly was presupposed to be self-evident, and which then automatically is eliminated from physics as a result of the assumption of the compound to be a "Ganzes".
A same meaning [philosophical impact] of the new theories [quantum physics] was given by H. Weyl (1928) :

"In prägnanter Fassung gilt in der Quantentheorie der heute von Vitalisten und 'Gestalttheoretikern' zu einem philosophischen Glaubensbekenntnis erhobene Satz, dasz "das Ganze mehr is als die Summe seiner Teile".

Translation :

"In a terse sense in quantum theory is taken up the thesis, today elevated up into a philosphical confession of faith by vitalists and 'gestalt theorists', that "the whole is more than the sum of its parts"."

But this thesis is not simply from new philosophers, it is the ancient aristotelian thesis of the possibility of a totality, of a new Substance originating from (an)other(s). And there it is not an article of faith, but indeed becomes intellible from the principles of the theory [i.e. holism is implied, and therefore intellibible, in Aristotle's metaphysics]. But in order to realize that this applies to mixta [chemical compounds], precisely according to the demands of modern physics, one has to specify the aristotelian principles, as we have done in our long analysis of atomic theory and what went before.
A same voice we could also hear in Holland, where Prof. A.D. Fokker compares the chemical atom with an  organism.  He says (1928) :

"In dat grootere individu [het atoom] zijn de individualiteiten der opbouwende deelen opgeheven geworden. Het atoom is een organisme geworden, dat zijn deelen beheerschend, hun eigenschappen heeft veranderd. Het electron als zodanig verliest zijn eigen bestaan, wanneer het zich in het atoom voegt. Het heeft geen afzonderlijke beweging meer, noch een afzonderlijke omloopsfrequentie. Zijn beteekenis gaat op in, en wordt beheerscht door de beteekenis van het geheel. De elementen, die in dit geheel gesynthetiseerd zijn, zijn geen onveranderlijke starre identiteiten. Hierin ligt een tegenstelling tot klassieke opvattingen van vroeger."

Translation :

"In that overall individual [the atom] the individualities of the components are cancelled. The atom has become an organism, which, while dominating its parts, has changed their properties. The electron as such loses its own existence, as soon as it incorporates itself into the atom. It has no individual motion anymore, nor an individual period of revolution. Its meaning merges into, and is dominated by, the meaning of the whole. The elements making up this whole, are not unchangeable rigid identities. In this we have a contrast to classical views of the past."

[It is clear that this same vision can be applied to molecules with respect to their constituent atoms.]

Where the scene is so well prepared, the rest of our enquiry can be shorter. First we consider the constitution of those new composites which are the chemical atoms themselves :  There we find the first definitive results. And from these results then automatically we find our way back to the chemical compounds.

The modern theory of the atom and its consequences


So the crisis of the mechanical view of Nature has broken out at the time when one, after the discovery of the composition of the chemical atoms, was looking for a structure that could account for the properties of atoms [We here are considering free atoms.]. When here facts and results became known that had no place anymore in the mechanical view of Nature, one still did not immediately clearly realize the failure of that view -- although one saw the overwhelming difficulties -- and it still took several years, namely until these attempts could not proceed along that same [mechanicistic] line anymore, before one definitively realized the bankruptcy.
It may suffice here to consider the first, still relatively simple, cases -- the hydrogen atom in its first analysis and what immediately connects with it -- because we have arrived, from our analysis of the elements of atomic theory and of the specifiability of the principles of atomism and of naturalism [the latter is the aristotelian view, involving "natures"], at a sharp criterium making a swift solution possible. For we find in those first cases already a composite of which the properties -- especially the spectrum -- are known. It originated from components of which the properties are also well known, also when they [the components] separately exist and are so observed. So we have a case in which the calculation of the properties of the composite, truly new and genuinely constitutive properties, is possible and demanded. We now know how to sharply discriminate whether a constitutive property is an aggregation resultant or a totality resultant. If it isn't the first, then it necessarily is the second. In the first case the composite is an aggregate, in the second a totality, a new Substance. In the first case it is to be viewed atomistically-mechanically [reductionistically], in the second case it is to be viewed holistically, i.e. in an aristotelian way, that is, according to naturalism. This was the criterium that we had found after our analysis of atomic theory and of the possible specifications of both systems of thought, the atomistic and the aristotelian. Therefore, our enquiry may finally give a result.

The atom of Rutherford.

After many attempts to find a structure of the chemical atoms, Rutherford has finally succeeded to give the general structure, afterwards specified by others. We here shall not dwell upon all the experimental data upon which the theory rests, but only present the general results.
The atom then consists of a twofold area :  the nucleus, in which almost all mass of the atom is concentrated, and the surroundings of the nucleus. So also here, in the atom, we find heterogeneity. First with respect to mass -- to this possibility we already pointed where we tried to determine the concept of "mass", and further when considering the structure of crystals -- but there is also another heterogeneity. First of all in the nucleus itself, the structure of which is still [1947] less well known. Then in the vicinity of the nucleus, as will be evident in due course.
The nucleus is the carrier of a positive electrical charge. And this nuclear charge shows a peculiar regularity. Since the experiments of Moseley it is established that one can order the chemical elements according to their specific X-ray spectra in an ascending series of ordinal numbers from 1 to 92, and further, when more elements exist. In this series hydrogen occupies the first entry, then follow helium, etc., until we arrive at uranium, having number 92. The meaning of these numbers is also clear :  they express the positive electrical charge of the nuclei :  Thus the nucleus of hydrogen carries a single positive elementary charge, that of helium two ... that of uranium 92.
Now, in the complete atom of every element there always are just as many electrons -- elementary negative charges -- as is the ordinal number of the atom. Thus, in hydrogen 1 electron ... in uranium 92. As a result, the atom electrically is overall neutral. These electrons are then regularly distributed in the nucleus' surroundings. In these surroundings one has learned to distinguish different concentrical areas, shells, indicated by the letters K (nearest to the nucleus), L, M, N, O, P, Q.  One distributes the electrons (insofar available) of the atom, in its "normal" condition [ground state], over these shells according to determined rules, and could in this way extend the old "periodic system". This is, in general lines, the (heterogeneous) structure of the vicinity of the atom's nucleus.

The hydrogen atom of Bohr.

The theory of Rutherford must, in its general lines, be accepted as expressing the real structure of atoms. They indeed must consist of the above described nucleus and its vicinity in which, in one or another way, the electrons, for each element in a number determined by the element's ordinal number, are taken up. But the theory has its great difficulties especially seen within atomism.
Let us consider the simplest case :  The hydrogen atom, of which the nucleus is a single [positively charged] proton, to which, in the nuclear vicinity, is connected one [negatively charged] electron. This electron cannot be stationary. It would [when stationary], as a result of attraction by the positive nuclear charge, crash onto the nucleus [meaning that as such the hydrogen atom would not be stable]. So the hydrogen atom's electron will be in motion, and then, thanks to its tangential velocity, be prevented from crashing onto the nucleus, like the moon doesn't fall on the Earth. So in general one may compare the atom of Rutherford with a planetary system :  The sun is the nucleus, the planets the electrons. But what would be the fate of the hydrogen atom if it really had this structure? According to the theory of Maxwell the electron must, in its motion along a curved trajectory [here resulting in a periodic motion], emit electromagnetic radiation [such as light, or X-rays]. The system [or at least the electron] will lose energy [here :  as a result of the emission, the electron will lose more and more of its kinetic energy]. Therefore the electron will approach the nucleus and finally crash onto it. [more precisely, things are as follows :  If an electrically charged particle is in periodic motion, then it will emit electromagnetic energy and so decrease its own store of energy.]. That is the big difference with a planetary system in which gravitation [instead of electrical charge] is the attracting force, and a "mass" the attracted. Such a [gravitational] system does not, with this motion, emit energy. So in place of the stable hydrogen atom we get, according to the theory of Rutherford, an aggregate having an ephemeral existence and, moreover, emitting an entirely different kind (namely continuously changeable) of light, different from that as is evident from the line-spectrum of hydrogen.
That was the reason of the tremendous correction :  In this [particular kind of] system [of nucleus and electron, making up the hydrogen atom], or [said better] in the electron as it is  in  the hydrogen atom, the theory of Maxwell [predicting electromagnetic radiation from a periodically moving electrically charged particle] cannot rule things [i.e. the correction is such that it is admitted, and even demanded, that Maxwell's theory does not hold in the case of the hydrogen atom (and to all other atoms for that matter)]. We call the correction tremendous, because outside the atomic domain nobody will dare to put aside this theory. With this correction, i.e. the correction of having the electron, while moving along its trajectory, not radiate energy, the stability of the atom is saved, like the stability of a corresponding planetary system. But then we don't have radiation at all. So instead of a wrong spectrum, we now have no spectrum at all!
Here, now, the theory of Bohr intervenes. To the classical hypothesis attributing to the hydrogen atom the described structure, and [to] the hypothesis putting the theory of Maxwell out of action [in the hydrogen atom], he adds two more hypotheses which he had set up according to the quantum theory of Planck. Let us consider the simplest form of Bohr's theory in which still circular orbits of the electron are considered. From the data -- the magnitude of the elementary electrical charges, and the mass of the electron -- can easily be calculated what speed the electron has when the radius of the trajectory has the value  r.  The energy of the system in this state is then, as the sum of the kinetic and potential energy of the electron, also very simply expressible as a function of charges and radius. After the classical laws, lying at the foundation of this calculation, the radius may have all possible continuously changeable values, and then the energy correspondingly may vary in a continuous fashion. Now Bohr introduces his first hypothesis :  He limits this freedom after the model of quantum theory. So he supposes that this conclusion from the classical laws is also forbidden and selects from the continuous series of values of  r  a small number of them :  There will be a smallest value  r1,  and larger values can only be realized by discrete jumps. These jumps he fixed by the hypothesis that the angular momentum (multiplied by a constant factor) can only be an integer multiple of the constant  h  of Planck. From this it then follows that also the energy of the system is not continuous, but changes by jumps. It also becomes quantized and the different "energy levels" can now easily be calculated and expressed as function of mass of the electron, of the elementary charges, of the constant  h  of Planck. And of course the integer  n,  now indicating the consecutive energy levels.  We note that the radii of the trajectories have vanished from this result.
As second specification now the hypothesis is introduced saying that this system only then emits light [electromagnetic radiation] if the electron -- by whatever reason -- jumps [within the atom] from a higher energy level to a lower one. The released energy can easily be calculated from the difference between the two energy levels. [If a photon, a "light-particle", having the right amount of energy, i.e. the right frequency, interacts with the hydrogen atom, its electron will be boosted up to a higher energy level, discretely separated from the initial energy level of the electron, and the photon is thus absorbed. But sooner or later the electron will eventually "fall back" to its lower energy level, thereby emitting a photon of the corresponding energy (frequency).]. All jumps are possible from a level  m  to a level  n  if  n  is lower [in the case of emission] [These energy levels forming a discrete and well-defined series as an intrinsic property of the kind of atom in question.]. With this, the theory of Planck is again applied, because this corresponding amount of energy is equated to the frequency of the emitted [or absorbed] light multiplied with the constant  h  of Planck. To every jump from one energy level to the next lower [or higher] thus corresponds a determined color of the emitted [or absorbed] light. [All possible variants of this electronic energy state are generally present in a volume of hydrogen gas, and this then determines its typical spectrum.]
The result is of astonishing beauty. The formula of Bohr accurately predicts not only the part of the spectrum forming the Balmer series, but also the ultraviolet and the infrared series of Lyman resp. of Paschen.

Applying the principle of elimination.

Again we here have to do with the typical structure of an explicative physical theory :  A more general hypothesis -- here that of Rutherford which itself is a further determination of the atom as a composite -- is further specified by the hypotheses of Bohr and is thus capable to derive an experimentally discovered property, the spectrum of hydrogen. As in analogous cases, so also here we have the task to investigate the theory as to the influence of its elements on the results. That there must be right elements is guaranteed by its wonderful results. But, on the other hand, the outrageousness of some of the suppositions -- the exclusion of the theory of Maxwell, [the exclusion of] the calculation of the trajectories from Coulomb's law and mechanics, followed by the denial of continuity consequent to it -- points to the fact that there is at least a chance that there are superfluous elements hidden in Bohr's theory of the atom. Quantization must surely be applied, for without it the whole derivation vanishes. But in what way quantization must intervene? We already noted that in the formulae, indicating the energy levels, the radii of the electronic orbits, and thus also these orbits themselves, have vanished. And  exclusively from the energy levels  the energy, available to be emitted, is calculated. What frequency the emitted radiation will have is again derived from applying Planck's formula. This element of the quantum theory is necessary to obtain the results. Further :  If the energy of the atom must be subjected to quantum conditions in the described way, and only can have the discontinuous values expressed in the energy levels, then also this element will not be superfluous. And these energy terms must contain the factor  (me4) / h2  occurring in the formulae of Bohr. This factor has the "dimension" of an energy, contains constants of the atom, namely the mass  m  of the electron and the elementary charges (+e and -e) of nucleus and electron, and also the constant  h  of Planck, bringing with it the influence of the quantum conditions.
But, that this energy should necessarily be the kinetic and potential energy of the atom taken as the Rutherfordian planetary system is superfluous. Every other form of energy might do as well, provided it admits the discontinuous energy levels of the quantum conditions. One can apply to a still undetermined form of energy the quantum conditions of Bohr in the form of a hypothesis like Bohr himself did to the trajectories or their radii. Just as well, or, rather in the end, better. Thus, the classical element, the mechanical, the proper atomistic, finding its expression in the view of an atom as a planetary system, again turned out to be a superfluous element.
An then we can add :  If the atom does indeed contain energy levels [discontinuous existential conditions for an electron having a certain determined amount of energy], which energy levels do not, however, come from  motion  of electrons about a nucleus, then automatically is removed the first objection referring already to the atom of Rutherford, namely that the theory of Maxwell would be invalid for these electronic motions. If this motion doesn't exist here, but only something analogous to it, i.e. something only bringing with it equal energy [but now not involving motion], then there is no question of the demands of Maxwell's theory, [then it has no relevance to the behavior of the electron, beause now there are no moving electrical charges anymore].
Moreover :  The demand of quantum conditions in trajectories being calculated [not from Bohrs view of the atom, but] from Coulomb forces, would not only be strange, but contradicts the way in which the trajectories result, for then the possibility of a  continuous  series of trajectories would follow.

The hydrogen atom, a totality.

From this analysis it is evident that the mechanical elements in the theory of Rutherford-Bohr are certainly superfluous. Even more follows from it :  They are false [because true local motion of the electron had to be excluded, and thus the atom's alleged mechanical nature.].
For here we have the case to which we've looked forward so much, the case of a composite, consisting of two components, of which the properties are well known. Well known generally, because the laws are known, electrical and mechanical laws, from which the possible motions of the components can be calculated. But also known in details. Charge and mass of the components have been exactly measured. The fact that these particles, separate and individual, do satisfy these laws, has moreover been established experimentally :  so a swarm of individual electrons in cathode rays, so even a single individual electron, which (fixed on a drop of oil) was observed by Millikan for hours, so a series of individual protons in the mass spectrograph of Aston. So we here indeed have a case in which we can decide whether an aggregate of these components has the stability of the experimentally known hydrogen atom, and whether the constitutive property (the spectrum) that should result from their mutual interaction in an aggregate, is indeed an aggregation resultant. We can now find the solution of the two problems that had remained to be investigated.
And then the calculation tells us that (1) the  aggregate  of these two components [the proton and the electron, together constituting the hydrogen atom] does  not  possess the stability of the hydrogen atom, that (2) the  aggregation resultant  from these two components cannot be the hydrogen spectrum.
So the hydrogen atom will not be an aggregate of these components, but a totality, a true Substance (in the metaphysical sense).
In a mass [i.e. a volume of hydrogen gas] giving the hydrogen spectrum, surely individual electrons and protons can occur, and this is even probable. In this gas, therefore, may also occur the spectrum that must form as an  aggregation resultant  of these [potential] components. And this may well account for the continuous part of the hydrogen spectrum. But with the more urgency the conclusion presents itself :  The so familiar  line-spectrum  of hydrogen is a  totality resultant.  The same, an aggregation resultant  alongside  a totality resultant, we will once again encounter in the X-ray spectrum.
The quantum conditions of Bohr cannot be applied to an aggregate of proton and electron. Then [if it was an aggregate] indeed, in the calculation of the energy it is supposed that Coulomb's law and the mechanical laws do apply, and at the same time this is denied by the quantum conditions. If one takes seriously these quantum conditions, and not merely as a trick to picture something else in parts, then there is contradiction [between applying quantum conditions and applying Coulomb's law and the mechanical laws].

[Quantum conditions must (as it has turned out) be applied to characterize an atom, and therefore it cannot be an aggregate, it is a totality, a new Substance (in the case of hydrogen, new with respect to a free proton (a potential hydrogen nucleus) and a free electron). So it is now certain that we have a new intrinsic unity, the atom, and the aristotelian-thomistic metaphysics now demands that such a unity must be a metaphysical continuum, a single "ens" (= a single being), implying that its constituents are virtually existing in it, otherwise there would be not one, but several "entia" (beings). The constituents have now turned into properties of the atom.
But if we, alternatively, hold all this to be a specification of some other metaphysics (not the mechanical one again), then it is conceivable that this strict demand that that unity must be a (metaphysical) continuum may be mitigated. There may be more types of intrinsic unity, not so tight, it is true, as a continuum, but unities nevertheless. And such types of unities may be "dynamical systems" with several hierarchically ordered structural levels. Such a dynamical system is a successive series of dynamical system-states, each representing the one "Substance". But every such state is the result of the mutual interaction and rearrangement (dictated by the system's dynamical law) of ultimately self-contained unities. These initial unities and (subsequently) the resulting unities congregate into the current system-state, which is therefore, in spite of having intrinsic causes, an aggregate. Therefore, any such system-state cannot be a true Substance if a Substance is to be a single ens, in spite of the fact that we may interpret the relevant "dynamical law" as to be the one single "essence" of any such system-state (like we did so interpret a metaphysical Substance in First Part of website).
So we must stick to the demand that a true Substance is a metaphysical continuum (in the sense that it is one single ens). But because in such a continuum there exist still "distances", distances that spatially separate regions of different qualities of that Substance, the demand of unity may have to be even stricter :  The different qualities may be connected with each other non-locally. However, this is, according to our general theory of Reality, exclusively the case in the Implicate Order. In the Explicate Order, with which this series of documents exclusively deals, elementary qualities of a given Substance are spatially separated from one another.
So, all in all, we here stick to the view that a true Substance is a single ens, is a metaphysical continuum. And, as we have seen, the hydrogen atom (and thus all other atomic species) fully satisfies this view.

Quantum conditions in a totality.
But if the atom is a totality, then the quantum conditions as to the energy are very comprehensible indeed. Of course they cannot be derived a priori, surely not the  specific  quantum conditions. But the generic is intelligible. The atom as totality surely is that what we earlier, when investigating the philosophical background of quantum theory, called an elementary agent. There we found :  A true continuous change, thus a change that intrinsically is one, is not only the  attainment  of a goal (peras), but a  striving  for it as goal (telos). This striving is passive in the change itself, active in the agent, aiming at this  telos.  Aiming without knowledge of course, but following its "nature", which is "ordered to it". If then an agent is an elementary agent -- and this will be an atom -- then it is to be expected that its actions are also  specifically  determined, that these actions have a telos (one or many) proper to the species and that the agent's activity is, "according to its nature", ordered to it. The quantum conditions of the energy express nothing else. And so it happened that a scholar like Sommerfeld, busy with a continuation of Bohr's theory, in the formulae of Bohr met with the expression of the long forgotten  causa finalis,  the cause according to goal. What precisely the  specific  quantum conditions are, can of course not, as we already said, be found a priori, just as little what the essence is of this form of energy. But surely it cannot be that of a planetary system. But when experiments demand the quantum conditions of Bohr -- and still more elaborated ones -- , they can, without troubles, be taken up as specification of the general theory, because this theory asks for something like that [This general theory, the aristotelian metaphysics, demands a causa finalis in all processes.]. We again have an example of the general truth :  The general principles are not sufficient to  derive  the specific, but they must be capable of  taking up the specific, demanded by experience, and be capable of letting themselves to be so specified.

Physical and Organismic Image of the Atom.

We now have established that the atom, of which there are about a hundred different species, is a true Substance, a single intrinsic being. And yet we must realize that most atoms have a strong tendency to chemically connect with other atoms to from new Substances, molecules. And molecules have -- in addition to conserved properties of the constituent atoms, now turned into qualities of the molecule -- new properties, structures and shapes. And in turn these molecules may produce larger molecules, either as a result of polymerization ("metamerization") or as a result of chemically connecting with other molecules. And so large molecules did originate, such as the "biomolecules" (nucleic acids, proteins), possessing special structures and shapes to execute specific functions in, and for the sake of, still larger wholes, organisms. And, according to the Unimol view of organisms, it may be that these larger wholes themselves are single, giant, living molecules, each such molecule being embedded in some aquous serum-like medium as its immediate existential condition. And of course we know that such molecules -- organisms -- show a bewildering manifold of new properties.
And it is indeed the very  a t o m  (especially those belonging to the chemical elements Carbon (C), Hydrogen (H), Oxygen (O), and Nitrogen (N), the so-called oganogeneous elements) from which "all has started". In the ascent from atom to organism new properties successively came into being. Although we know the atom almost exclusively from spectroscopy, i.e. although we only have a physical image of the atom, we can be sure that the mentioned new properties, especially the organismic ones, are truly new, i.e. are not present in the atom, meaning that the atom is not some "preformed" organism. Nevertheless these properties must be  p o t e n t i a l l y  present in the atom. So there must be much more in the atom than is revealed by physics.
Such considerations can be found for example in the earlier mentioned work of Oskar Müller, 1959, namely in chapter III,
"Ein-molekülares Leben" discussing the Unimol view of organisms. And in order to more or less complete our exposition of the atom (as it freely exists and as it virtually exists in molecules) it may be instructive to present some of his thoughts [often paraphrased by me].

The physical atom is practically just a re-synthesis from spectral analyses (and thus corresponding to a spectroscopic image of the atom) in the framwork of preconceived philosophical and chemical representations. Here we may recall that the introduction of the scales, balance [measuring weight] into chemical research -- taken by us just as self-evident and as "epoch-making" -- has directed chemistry into a definite trajectory, which, we must say, was already "portended" and unavoidable as a result of the philosophical corpuscular image of atoms. If we, just hypothetically, imagine a different path of chemical knowledge having started from mass-free purely qualitative essences, and a path in which scales haven't played any role at all, then it could have been that we, instead of organic structural formulae merely had curve ribbons of rotational-vibrational spectra, and others. We then probably would not speak of valence-deformational vibration, oscillative vibrations, topple vibrations, and rotational vibrations, and also not of trajectories and transitions. The characteristic intensities, maxima, minima, local aggregations, etc. we would probably have provided with ground numerals or letters and in this way obtained a system that could express and visualize all chemical differences precisely as well as we do it today with structural formulae and their rules of formation.

It is an "Unding", a bad idea, to want to derive, - from the reduced physical image of the atom, reduced to be useful to a special domain of investigation, - organic subsequent phenomena, belonging to a domain not covered by that reduced physical image. This, one can -- if one believes to base things in that way -- only accomplish when departing from an organismic image of the atom. And when this has been done (recognizable by its attained capacity to explain), one may try to connect the physical and organismic image of the atom, and thus arrive at a general image of the atom.

When we would accept the philosophical demand that living objects are made up of similar, analogous, building blocks, then the difficult task arises to transform the philosophical verbal finding into a scientificallly founded real finding. To understand biologically organismically, cannot mean to view the atoms as sub-organisms, but to evaluate the rich knowledge extracted from organisms as to its usefulness and transferabilty, and with it to better understand atoms, better as can be done when neglecting the additional organic consideration.

The atom is the integral sum of  all  its potencies, which -- as a smaller or larger part of the whole -- must logically derive from the consequent phenomena already known to us [i.e. from molecules and organisms] [And, of course these latter phenomena must actually derive from these potencies.]. Only these potencies in their totality and in the observable phenomena corresponding with them [as their actualizations] result in a complete image of the atom, and all questions about the observable world may refer to precisely this atom. With this, it becomes clear that the true image of the atom almost entirely consists of "premonitions", and that our present image of the atom is only a physical shell, and we "from within" only know ourselves as certain consequences and effects.

The striving to reduce all natural events to a "mechanics" of atoms (just merely as an image, for in the atomic dimensions there isn't any mechanics anymore) is the only possibility. But one should not try to derive the complex organismic happening from those few atomic properties that were necessary to explain the simplest chemical compounds, and which properties could moreover also have actually been found but being insufficient to also comprise the organismic. So we must assume additional atomic potencies [cognitively] derived from organismic existence.

The organismic structural principle doubtlessly continues beyond the microscopic and submicroscopic, and we can be convinced that it doesn't end with macromolecules (in the classical chemical sense), but that it continues all the way down into the atomic domain, where one may expect a quasi-organic structure. Better is of course the reverse way of expressing things, namely that atomic "structure" - although not being geometrically sensible anymore -- continues high up into the macro-organismic domain, there assuming forms and functions that are, it is true, founded in the atom, but which the atom lacks in precisely these forms.

To detach consciousness as central and seemingly immaterial phenomenon of Life from the atomic constitutional, and then take it, for example, energetically, is of no advantage, and after consulting quantum theory also not stimulating, because then one adds to one unsolved problem at least two to three more of them.

There is no contradiction in deriving consciousnes and all spiritual possibilities from laws and properties of atomic substance. But one should not, or only for a small part, derive them from those physical laws and properties constituting our physical image of the atom. For this, the extended biological image of the atom is needed, which, for the time being, is still no more than a wish-construction, but in the course of time will reveal a growing content. Both -- physical and biological image of the atom -- are of course not independent images side by side of each other -- that would imply dualism -- but only aspects of the same whole. This conviction does not contain something phantastic [something just made up], while every other conviction calls for phantasy in a degree not permissible in science.

If one wants, one may of course say :  The incomplete atomic theory (image of the atom) is to blame for false or absent statements about the ultimate psycho-physical events and relationships. Certainly, the very existenc of Life demonstrates that not only the ancient mechanical image of the atom, but also the modern substantially amended electronic-quantumtheoretic image of the atom is still incomplete.

The little known depths of organismic life directly go back to the totally unknown, and also at most indirectly ever clarifiable, depths of the atoms. It should be noted :  The atoms are, it is true, cognitive-methodically, representatives of the observable world, as its building blocks we have "found" them, but qua systemic thought [i.e. as to their essence] they are representatives of a metaphysical groundwork, and they, at first sight, look to us so colorless, and openly imperfect, because from there [i.e. from this metaphysical groundwork] they bring with them so little that is observable. Subsequent different thinking and knowing perhaps will see them [the atoms] as possessing a multitude of properties, that may be compared with that of their [the atoms'] subsequent products, namely the living organisms.

Earlier, following HOENEN, we stated that atoms are elementary agents. They cause and are embedded in fields. About the latter Oskar Müller says :

The field theory of atoms leads, at least pictorially, to a dematerializing of the world's building material. This, however, is connected with the fact that our everyday concept of matter is formed by the bulk effect of the many atoms and only there.
There where the field has taken up such a structure that every mutual penetration halts or only in a minimal degree is possible under high resistance, lies the external boundary of that what we call "tangible" matter. If then at the same time there is also a complete (as in metals) or partly (as in crystals) non-transparency of light, then one has -- supplementing the impenetrable tangible -- the prototype of compact matter. Mathematical-analytically always as substance remain :  the field sources. Atoms can of course not possess direct properties which we know as sensible and interaction effects. There do remain only a few sensible properties which, so to say, must be mathematical at the same time (weight and charge). The rest consists of purely mathematical properties. So atoms are only carriers of phenomena in a very limited degree, they are rather sources of potentialities and direct, or more often, indirect sources of properties.
The crossing of the lower boundary of bulk leads one into a new domain that may be compared with a phase-transition (crystal-sublimation -water vapor), where also the optical sensible discontinuity is "total". The dematerialization only applies to the single atom [if seen as a field], for when it appears in masses it doesn't render the field matterless.

[Returning to HOENEN's exposition again . . .]

Other composita.

At the conclusion that the hydrogen atom -- and so all the other atoms -- doesn't find any explanation in the mechanical view of Nature, but is a totality, the physicists, in establishing things of this atom, had not yet arrived, in spite of the fact that the then collected data turn out to already be decisive. And if hydrogen is a totality, the same follows, already by reason of the strict analogy, for the atoms of all the other chemical elements. For all atoms of elements that have a characteristic X-ray spectrum [in hydrogen it is the optical spectrum that demonstrated its totality-nature.] -- and these are all elements except the lightest ones -- an X-ray spectrum having its explanation running perfectly parallel with that of Bohr for hydrogen, also this spectrum all by itself points to the totality-nature of these atoms. We will return to it for a while in due course. Nevertheless, classical-mechanical views were still around. Only when the helium atom (He) and the hydrogen molecule (H2) were examined also by quantum theory, the crisis of the mechanical view of Nature was definitively acknowledged. As to the helium atom, one even cannot construct a planetary system anymore and subject it to quantum conditions, in order to derive the spectrum. And this not as a result of the difficulties of the "three-body problem". In the hydrogen molecule, resulting from two hydrogen atoms [engaged in covalent chemical bonding], apart from a few [properties], no account could be given for its properties [without introducing quantum conditions], or, rather, again a composite resulted with different properties than those of the experimentally known hydrogen molecule. [In the hydrogen atom its only electron resides in a spherical orbital ('electron cloud'). This orbital is only completely occupied when two electrons reside in it. So in the formation of the hydrogen molecule the two orbitals of the two hydrogen atoms are going to overlap, now forming one complete orbital commonly possessed by both hydrogen atoms, and having two electrons. So with the hydrogen molecule we in fact have to do with a double-nuclear atom, i.e. two hydrogen nuclei shrouded in a single commonly possessed electron cloud, electron orbital. And of course this orbital is defined by quantum conditions, rendering the hydrogen molecule to be a totality, a new Substance, new with respect to the originally free hydrogen atoms being themselves also totalities.]
Also here, in the case of the helium atom, and in that of the hydrogen molecule, the composite cannot be an aggregate, it is a totality, a single ens.

As to the hydrogen molecule -- and corresponding gas molecules -- we can see a demonstration of its totality-properties also in the "molecular heat" of the gas. It boils down to the following. Statistical mechanics tells us how to calculate the molecular heat. The result is that for each "degree of freedom" of the particles making up the gas, about a calorie is needed per mole, as contribution to the molecular heat. In one-atom gases one rightly supposes that these particles behave like material points and thus, in 3-dimensional space, possess only three degrees of freedom. Collisions generally will not cause rotations. The calculated heat, at constant volume, thus has a value of three calories. And this is confirmed by observation. In two-atom gasses, such as hydrogen (H2), the shape of the molecule will not be like a sphere anymore but like a dumb-bell. And here will, as a result of collisions, often take place rotations about two axes, adding two more degrees of freedom. So the molecular heat will be 5 calories, again confirmed by observation. But this should have been different if the molecule were an aggregate. Indeed, then the two atoms would, as a result of the forces applied to each other, stick together and held in some equilibrium. Not in a static, but in a dynamic equilibrium. About the equilibrium state they may vibrate and these are kicked off by collisions. So indeed there is (at least) still one more degree of freedom in such a molecule, in addition to the five already accounted for. But then the molecular heat would be (at least) six calories, and this contradicts experience at normal temperatures.

[In oxygen, also a two-atomic gas (O2), but with the oxygen atoms bonded to each other, not by a single, but by a double bond, the molecules may rotate (the speed of which can only vary discontinuously according to precise quantum conditions) as a result of the impact of a photon (a "particle" of electromagnetic radiation such as light) with the right energy, but [these molecules] also may vibrate as a result of the double bond being contracted or stretched, also as a result of impact of a photon of the right energy. And also this vibration follows definite quantum conditions. This provides the extra degree of freedom about which HOENEN was speaking, if this vibration were actually possible. And according to HOENEN it is only possible when the molecule is an aggregate, because such vibration means a certain motion of the constituent atoms with respect to each other and thus a certain degree of mutual independence. In HOENEN's case the input of energy was realized by collisions between the gas molecules, while in the other case, reported by BALL, 1994, this input took place by photons interacting with the molecule. But these two cases are, with respect to molecular heat, not equivalent. In the case of photons, resonance does play a part, while in mechanical collisions it doesn't. This is beause the interaction of a molecule with a photon is electrical in origin :  it is an interaction between the electrical component of the photon's oscillating electromagnetic field and the molecule's electron cloud. To absorb or emit a photon of a given frequency, the molecule must itself generate an electric field that oscillates at that frequency. Rotational motion will do this if the molecule possesses some imbalance in its distribution of electric charge - if, crudely speaking, the molecule has an excess of negative charge at one end and of positive charge at the other. In the hydrogen chloride molecule (HCl) [a molecule in which the two atoms, hydrogen and chlorine are bonded by a purely ionic chemical bond], for instance, the electron cloud is pulled towards the chlorine atom, creating an excess of negative charge there and a corresponding positively charged region around the hydrogen. A molecule with this kind of asymmetric distribution is said to possess an electric dipole moment. The molecule's rotation causes the direction of the electric field to alternate, allowing it to interact with the oscillating electric field of a photon [this is the so-called resonance] and permitting absorption of the photon's energy. Molecules that have no electric dipole moment, such as oxygen (O2) and nitrogen (N2) [and certainly also hydrogen], cannot undergo rotational transitions [from one energy level to another]. All this will undoubtedly be of influence on the molecular heat of such gasses.
But if energy input by photons into gas molecules (and thus the interaction of light -- generally of electromagnetic radiation -- with gasses) is not considered, but only imput of energy as a result of collisions between gas molecules, as it is in HOENEN's discussion of molecular heat in gasses, then the demand of resonance is not needed :  rotation of such a molecule as a result of collision is perfectly possible, and, at least when the molecule is a mere aggregate of two still independently actually existing atoms, also vibration [is possible as a result of collision]. Collisions between molecules are the result of local motions of the gas molecules. The permitted energy rungs here are, however, very closely spaced, implying that we may see these local motions (translational motions) as effectively to be "continuous". But they need to transfer energy to the molecule that is enough to kick off a rotation of a certain quantum-mechanically determined speed as well as to kick off a vibration of a certain quantum-mechanically determined frequency. In this way we should see HOENEN's discussion of molecular weight in gas molecules. And it is clear that the supposed vibration of a two-atom gas molecule is the kind of motion supposed to be possible in an aggregate but not in a totality. In the latter case [the molecule being a totality] the vibration of the molecule ( = the stretching and contracting of the chemical bond between the constituent atoms) must be the oscillating "motion", the alternation of place, not of corpuscular atoms, but of a set of qualities of and inside the molecule. And indeed, it is questionable whether a mere mechanical collision [and they  are  mechanical] can cause such a "vibration" of qualities at all. We think it can't. And thus the 5 calories actually measured in two-atom gases, instead of six, points to these molecules to be true totalities.

While the kinetic molecular theory was confirmed by these results of statisical mechanics [i.e. demonstrated that gasses consist of individual particles], the atomistic view of molecules as aggregates appears to find in it its refutation.
Nevertheless, in this a solution can be found. If one supposes that also these vibrations are subjected to quantum conditions, it becomes explainable that their influence at normal temperatures cannot be detected anymore  [Here it cannot be meant that the very frequency of the vibration is subjected to quantum conditions, because that only implies that the discontinuous changes in frequency cannot as such be detected at the macroscopic scale, meaning that there such changes are in effect continuous. The subjection to quantum conditions, as mentioned here by HOENEN, apparently, refers to the vibration itself as a discontinuous phenomenon as such not effective at the macroscopic scale.].  Then consonance with experience is attained again, but by calling for a hypothesis that in the hydrogen atom has demonstrated its totality-nature. These "vibrations" are not genuine vibrations anymore, as it should be in an aggregate. Also in this the totality-nature of the hydrogen molecule is expressed.
Also as to more complex molecules one obtains the same result. From the absorption spectrum. Also this was in classical theory ascribed to "vibrations" -- when the molecule is an aggregate it must be so -- ,  for the visible part of the spectrum to vibrations of electrons, for infrared especially to vibrations of atoms. What can be explained of this spectrum again demands, just like the hydrogen atom, introduction of quantum conditions. From the spectrum as aggregation-resultant, colors would result here, colors corresponding to vibrations of which the amplitude [and thus the intensity] may vary continuously. Also here experience demands, contradicting this conclusion, quantum conditions. And again, this spectrum only makes sense when the molecule is taken to be a totality.

If all this is true for the chemical molecule, it must also be true for the crystal. And even for the whole crystal [because one may view a crystal as to be one giant molecule.]. Let us consider a crystal of a given chemical compound. Then, X-ray analysis demands that the nodes of the crystal's reticular structure are occupied by the centers of the chemical atoms. Now, in classical theory, there were, as we saw earlier, two concurrent hypotheses. They had in common to assume discontinuity in the crystal. But the one hypothesis puts into the nodes the centers of complex molecules, "crystal molecules", whereby, of course, each individual molecule  could  be conceived as a continuum, albeit that classical theory didn't do that. According to the other hypothesis the nodes were occupied by the centers of the atoms, whereby different point-lattices could be slid through one another. In this hypothesis there can be no question of continuity of molecules. But we also saw that a theory, viewing whole crystals as continua, but then as heterogeneous continua (of virtual atoms, not virtual molecules) with a reticular structure, just as well can account for the properties of crystals as the classical theories could.
X-ray analysis now has definitively refuted the first classical hypothesis. So only remain :  the second classical hypothesis and the continuum hypothesis according to which the whole crystal is a totality. Now, in virtue of the result that the molecule of the chemical compound [in a non-crystalline state] is already shown to be a totality [as a result of the necessary introduction of quantum conditions in the formation of (at least) the covalent chemical bond], it is excluded that the atoms of that same compound, as soon as it is a crystal, would form a mere aggregate, what in the second classical hypothesis is an essential element [centra of the reticular net occupied by [corpuscular] atoms]. So this second classical hypothesis too is excluded, excluded in virtue of the earlier result, and modern atomic theory leads to the result that also the crystal, as a whole, is a totality [Earlier, in  Fourth Part of Website,  when studying snow crystals, we already found, on morphological grounds, that crystals are totalities, true Substances.]. The similarity [of the crystal] with the individual chemical molecule is expressed by Jaeger, 1920 (although we do not know whether he had in mind our concept of totality) in the following words :

" The notion of "crystal-molecule" as a structural unit [i.e. in the crystal] has, therefore, lost its significance ... the whole crystal ... behaves as one gigantic crystalmolecule."

We above said that X-ray analysis has definitively eliminated the hypothesis of crystal-molecules [not the crystal as one single molecule, but the crystal consisting of individual whole molecules], of which the crystal is supposed to be made up. This will not be countered by anyone in the case of a crystal as that of table salt (sodium chloride), in which molecules of NaCl cannot be detected in any way, and also no complexes of it. Each sodium atom, Na [in fact each sodium ion, Na+ ], is directly surrounded by six atoms of chlorine (Cl) [in fact ions of chlorine, Cl - ], and vice versa. Each atom [ion] namely is the center of an octahedron of which the six corners are occupied by the other sort of atom [ion] [these ions are held together by attracting electrostatic forces, meaning that the chemical bonding type is ionic]. Nevertheless, in other crystals some researchers assume atomic groupings [instead of single atoms at the nodes of the reticular net], groupings that are supposed to be autonomous chemical molecules. Jaeger objects to this. Also in these cases from our reasoning follows that these molecules themselves are continua [i.e. totalities]. And that they connect to each other also in a continuous way seems certain to us. In these crystals it may be true that there is a preformation of molecules such that it is already determined in the structure which [of the] virtual atoms will, at the phase-transition, form the chemical molecule, but this is not an objection against our conclusion. One should then also have to speak of virtual molecules [in the crystal]. [i.e. the atomic groupings in such a crystal are virtual molecules, and they form a disposition to become actual molecules when the crystal melts. The virtual molecules are, first, also themselves continua, and they connect continuously with the other virtual molecules [in the crystal] and with the possibly existing virtual atoms in the crystal.]


And thus the result of our investigation is :  The modern data point to the fact that all these composites, that were left to be investigated, after it was established that gasses and liquids -- which according to the equation of Van der Waals can transform into gasses -- are aggregates,  that, namely, all these composites :  [free] atomic nuclei, [free] chemical atoms, the molecules of chemical compounds, even whole crystals, are not aggregates, but totalities, i.e. true Substances in the metaphysical sense.

[ ... ]

Again, conservation of atomic properties


Having discussed the structure of the chemical atoms, consisting of nucleus and nuclear vicinity [atomic nucleus and electron cloud], both with heterogeneous structure, we still can analyze two considerations from which one has concluded that the chemical molecule is an aggregate, not a totality. It again concerns the conservation of properties [in the molecule]. And this at the same time provides the opportunity to further determine earlier results.
Earlier, we spoke of additive properties, which, together with an atom [of a determined species], seem to go over, as it were, from one molecule into another. Most of these properties were either purely constitutive, or certainly strongly subjected to constitutive influences, so that additivity, and with it "conservation" of the property is only the case if the structure in the compared molecules is about the same. These properties (such as, for instance, the atomic volume) are, if they stand under constitutive influences, hardly traceable in free atoms. When they are genuine constitutive properties they even do not make sense in free independent atoms.
There are, however, properties that certainly can be ascribed in a strict sense to individual atoms, and that are also conserved. That is, properties that not merely with the atom seem to go over from one molecule to another, but that are actually possessed by the free atom bringing them with it unchanged when it connects with other atoms into a molecule.  In  and  of  the free atom these are, as will turn out, genuine constitutive properties originating from the heterogeneous structure of the atom, itself resulting from its components. But they are nevertheless properties of that free atom itself. We mention :  (1) the specific X-ray spectrum of the chemical elements, and (2) the properties revealing themselves as nuclear properties in radioactive chemical elements.
One has -- not long ago -- put forward the conservation of these properties  [ X-ray spectrum, radioactivity] as decisive proof of the thesis that the chemical atoms continue to exist actually in the molecule of the chemical compound, implying that the molecule is not a totality. As starting-point of this reasoning one took the pseudo-principle :  If a property of a component is conserved in a composite, then this always is evidence of the fact that that component itself is actually present. Now we above saw that the development of the aristotelian principles also for a totality -- in which thus the components do not continue to exist actually, but only virtually -- demands a conservation of component-properties. To conclude just like that from the observed conservation of properties :  "therefore the components, the atoms, actually exist in the molecule", is thus evidently not permissible. It results from a misunderstanding of the aristotelian principles. One should investigate each case separately.

The specific X-ray spectrum.

The chemical elements, or compounds, being struck by cathode-rays -- electrons with high speed -- emit X-rays.
First we consider, in this respect, chemical elements.
This radiation is partly continuous, and this is the so-called "Bremsspektrum", caused by the sudden slowing down (brake) of the electrons. As to another, best studied, part it is a special line-spectrum, characteristic of the chemical atoms, and relatively simple. The origin of this spectrum is well known. It can be calculated in the way as Bohr did for the hydrogen atom :  By taking into account the "falling" of electrons, [residing] in the vicinity of the nucleus, from a higher energy level, upto which they had been boosted by the impact of the cathode rays, down to a lower energy level. The resulting characteristic radiation is, however, only exclusively X-radiation, thus radiation of very high frequency, if the falling-back electrons do belong to the deeper shells of the nuclear vicinity, the shells K, L, M, N, O (especially the first three), of heavier elements. The characteristic spectrum is known of all elements, from carbon to uranium. In lighter elements, and in the peripheral shells of heavier ones, the frequency [of the emitted radiation] is not high enough. The spectrum becomes the usual, optical, spectrum.
In passing, we here note :  The "Bremsspektrum" and the characteristic element-spectra occur together. The first directly originates from the colliding electrons of the cathode rays and is an aggregation-resultant (the aggregate is the system of the atom with the electrons of the cathode rays). The characteristic spectrum, originating at the same time and same place, cannot be an aggregation-resultant [because it is discontinuous and thus demanding quantum conditions, resulting in the fact that this spectrum does not express mechanical relations.]. Also here is demonstrated the totality-nature of the atom [now thus with X-rays] with respect to its components.
From the described facts is clear :  Both spectra, the optical and X- characteristic element-spectrum (lower and higher frequency), are genuine constitutive properties of the atom. The optical spectrum originates from the periphery of the electron cloud, the X-ray spectrum from the shells immediating enveloping the nucleus, provided the atom not being too light to give high-frequency radiation. Both spectra, as purely constitutive properties, are totality-resultants of the atom. Aggregation-resultants would be something else entirely. But both spectra are true properties of the  separate  atoms.
If one now investigates the spectra of chemical compounds, the following has turned out :  The light-spectra do not pass over into the molecule, while the X-ray spectra do. In this we may remark concerning the optical spectrum :  Investigation of a given compound often will discover the spectra of the elements as well, because, as a result of the creation of the spectrum, part of the compound is split into free atoms. Concerning the X-ray spectrum we note :  For many chemical elements one has not succeeded to observe the characteristic radiation, because the objects must be investigated in their solid state [so for nitrogen, for example, this is a serious problem]. In such cases one obtains the characteristic spectrum of an element, by omitting those of the other elements from the total result. Yet the method is secure, because one has general formulas to calculate the spectra, in which [formulas] for every element one has to substitute only its ordinal number -- the value of the nuclear charge. This was the great discovery of Moseley.
And see now, in what way one had attempted to support the actuality of atoms in the molecule :

First, the characteristic X-ray spectrum [emanating from the inner domain of the atom] of a chemical compound is just the sum of those of its elements.
Second, the high-frequency spectrum is thus certainly a true additive property. This property of the atoms is really conserved in the molecule.
Third, thus the atoms themselves remain actually present in the molecule.

And thus that third conclusion -- not the first and second, referring to nuclei and the atoms themselves -- would refute our analysis, that had resulted in holding the molecules of chemical compounds to be totalities, and a fortiori our analysis of crystals.
Yet it turns out that upon further analysis this is not the case. The first thing, but not the most important one, that we note is this :  In the "proof" it is supposed that the chemical compound, being bombarded by cathode rays -- a relatively tremendous agens -- remains intact under this impact penetrating down into the closest nuclear vicinity. But, we note :  Will the irradiated molecules not directly become disintegrated and the [now free] atoms boosted into their excited state, in which the inner electrons are lifted up from their shells and emitting characteristic X-rays when falling back? To us it is pretty sure that it must so happen. But then it is not the compound anymore that emits the characteristic spectrum, but its products of disintegration, the free atoms. And thus the "proof" collapses.
Yet this consideration doesn't appear to us the most important one to which further analysis of the facts brings us. More important is this :  Also when the molecule is an aristotelian totality, and albeit that the whole remains intact under the impact of the agent creating the X-rays, then we must, according to the specified aristotelian principles, expect that the characteristic element-spectra are conserved in the spectrum of the compound, which [spectrum of the compound] can only be the sum of them.
See here why.  Recall the principle of Toledo describing the origin of the minimum of the compound from the minima of the elements. These minima interact with each other, change one anothers properties, until a structure results from this change, a structure characteristic of the compound, the proper "disposition" of the compound. Already earlier we considered :  It is not necessary that this change penetrates all the way down into the center of the individual minima. It is very well possible, but unprovable a priori, that it is only more or less peripherically taking place. More developed experienc will decide upon it. Well, this experience exists in the modern results of chemistry.
The mutual interaction of Toledo's minima, in the end resulting in the chemical compound, expresses itself in what one calls chemical properties, or with a vague word :  affinity. Now, from the latest results it is established that these chemical properties, actively and passively, result from the electronic structure of the  outermost  shell of the atom [The shells of an atom contain so-called "orbitals", which are, or may be, electron "clouds" (in fact regions in which one or two -- not more -- electrons may reside somewhere in it). The electrons of the orbitals of the outermost shell participate in chemical bonding. Some orbitals of deeper shells may stick out through the outermost shell, and also the electrons of these orbitals may participate in chemical bonding.], and it is established that the mutual interaction is limited to that peripherical structure of the atom. Concerning the "proper disposition", as it was called in the Middle Ages, the heterogeneous structure, after modern terminology, of a minimum of a compound that is about to be generated, we can say :  Changed with respect to the individual atoms is that part that corresponds to this periphery. Stayed the same are the central parts of the atom :  the nucleus and (in heavier atoms) the shells of the immediate vicinity of it. So this now follows, as further specification of Toledo's principle, according to the modern results of chemistry.
But from this will follow for the chemical compound :  The optical spectrum, originating in the periphery of the atoms, a periphery now having a differen structure, will differ from that of the elements. [Today we may, perhaps, say :  The optical spectrum, originating in the periphery of the molecule (referring, in the case of the covalent bond, to the shared orbitals and their electrons).]. The X-ray spectrum, on the other hand, originating from deeper shells, remaining, in chemical bonding, the same in the molecule, will not differ from that of the elements, will be purely additive, also when the compound happens not to disintegrate by the agent creating the X-rays.  See :  What we find for an aristotelian view of the molecule as a totality, after further specification of the principle of Toledo by means of modern discoveries about the causes of the generation of the compound, is this :  The optical spectrum of the elements will no longer be there, but the high-frequency spectrum must pass over unchanged from the elements into the compound. That this change is actually fulfilled is, of course, not a proof of the totality-nature of the chemical compound, but it can't by far not be a proof against it (as was supposed). In fact we again have to do with an application of our principle of elimination. The fact that molecules are totalities was found in other data :  There are indeed genuine constitutive properties that are totality-resultants. The X-ray spectrum is not such a resultant of the molecule [it doesn't result from the molecule as totality], but it is one of the atom.


The second result of modern experience, in which one believed to see a proof of the actual continued existence of the chemical atoms in the molecule, comes from the phenomenon of radioactivity. The speed by which a radioactive element is spontaneously disintegrated, or, the other way around, its "average length of life" or also its "half-life" -- to be measured by the change in intensity of radiation of a given material -- turns out to be a constant for each radioactive element. Now experience tells us that this constant is perfectly the same whether one investigates the free element or that element in its compounds. So it is a[n atomic] property that is perfectly conserved in the compound. And then, in analogous fashion as above, one again concludes :  Then the atom is actually present in the compound. And if this holds, so one proceeds, for atoms of radioactive elements [free or in compounds], then it also must hold for all [also non-radioactive] chemical compounds because of the analogous construction out of elements. The "proof" comes from scientific circles -- Th. Svedberg came up with it -- and it had much impact, even in scholastic philosophers.
See here the essential lines from Svedberg's (1915) reasoning :

" Doit-on ou doit on pas reconnaitre aux atomes chimiques une existence individuelle?"

Translation :

"Should, or shouldn't one recognize in chemical atoms an individual existence?"

The problem is acutely stated, for it is about an "existence individuelle", i.e. an actual existence  in  the molecule of the compound.
The existence of actual molecules was already established :

"On a établi d'une facon incontestable l'existence des molécules ... mais il ne résulte pas immédiatement de ces faits qu'il existe des atomes, c'est-à-dire des moellons formant les molécules, que celles-ci ont une structure." [Svedberg, 1915]

Translation :

"One has established in an incontestable way the existence of molecules ... but it doesn't immediately result from these facts that atoms do exist, that is to say the elements making up the molecules, whether they [the molecules] possess a structure".

Svedberg has rightly seen that the demonstrations of the discontinuity between molecules in gasses and liquids are still not demonstrations of discontinuity in the molecules themselves, which was, as we saw earlier, not understood by so many. It is only peculiar that he equates discontinuity, and thus actuality of the parts, with "structure". A heterogeneity, and thus structure in qualities alone, he doesn't seem to know. And then his proof comes that radium chloride "has a structure", i.e. that the atom radium, and thus [also] the atom chlorine, exist in it unchanged and actually :

" Il n'est pas difficile que les molécules du chlorine de radium possèdent une structure. Nous savons d'une part que tout changement éprouvé par la molécule du radium est lié au dégagement de quantités énormes d'energie, et d'autre part, que, qualitativement et quantitativement, ce dégagement s'effectue dans le chlorure de radium exactement comme dans le radium pur. Par conséquent la molécule de radium doit etre contenue telle quelle dans le chlorure". [Svedberg, 1915]

Translation (as good as it goes) :

" It isn't difficult to demonstrate that the molecules of radium chloride possess a structure. On the one hand we know that all change suffered by the molecule [atom] of radium is conneted with the release of enormous quantities of energy, and on the other hand we know that, qualitatively and quantitatively, this release is effected in radium chloride in exactly the same way as in pure radium. Consequently, in the molecule the radium is, just like chlorine, conserved".

And so in other compounds in virtue of the strict analogy. Svedberg demonstrates this analogy only by a thought-experiment, but it is there all the same.
Is this proof valid? We already saw that a general reasoning from conservation of a property, just like that, is worthless. And here, upon further analysis, that proof remains worthless. Surely, the radioactive constant is a true atomic property -- albeit only a statistical one, but this statistics must be a consequence of a specific structure of the atom -- surely this property is found again in the molecule of radium chloride unchanged. But this again is what one must expect also in an aristotelian view of the molecule as a totality, even more so than in the above case of the specific X-ray spectrum [because here, in radioactivity, it is about a change in the very nucleus of the atom.].
Now our analysis can be short indeed. Above, we found, as a last specification of Toledo's principle, that in the molecule, also when it is an aristotelian totality, must be conserved :  the properties of the nucleus and closest nuclear vicinity. The X-ray spectrum is a property of the latter and therefore must be conserved. Well, the radioactive properties are purely nuclear properties. And thus even more, these properties and the structures from which they result [these structures have now become qualitative patterns] must be conserved in the molecule also when it is a totality. To a connoisseur of the aristotelian philosophy and of its specifications, the proof of Svedberg is entirely worthless. And thus again our conclusion is :  From this conservation does not  follow  that the molecule is a totality, but, because we know from elsewhere that this is the case, it cannot form any objection at all. We again have an application of the principle of elimination.


One now sees the always proceeding specification of aristotelian principles. First we found, from the fact of the existence of mixta and elements, that prime matter is a potency, bringing with it a stepwise actualization. Genetic connection could be further worked out into the demand of the virtual conservation of element-properties. This allows for the possibility of a corresponding heterogeneity, as it is already seen in elementary observation in organic mixta. After the introduction of the aristotelian theory of minima this specification transforms into the possibility of a corresponding heterogeneity in the structure of the molecules themselves and consequently into that of a corresponding periodic heterogeneity in crystals. And both latter heterogeneities are specific. The heterogeneity is easily derived from the principle of Toledo and it entirely complies to the demands of crystallography and of chemical structural theory. The same principle may be further worked out with the help of observational data, indicating the seat of chemical affinity, and then gives the more detailed structure of the molecules, in which, namely, the structure of the nucleus and  closest  nuclear vicinity of the atoms -- as "proper disposition" in St Thomas words -- must be conserved, while the change, having resulted from the effective causes of the compound, only takes place in the peripheral structure of the atoms. These effective causes are then the various elements themselves with cooperation of the aether [because in chemical bonding electric fields are involved, and these are qualities of the aether.].
And in order to further work out these specifications we had to do nothing else than to take up again the specifications -- three in number -- of Antiquity and Middle Ages, to connect them with each other, and, by means of the latest observational results, also here loyal to the aristotelian principles, to further work them out.
And the result was that we found :  A number of true totalities, which only and completely comply with the demands of modern science. And these results are not affected by the crisis of the mechanistic view of Nature. On the contrary, they are sanctioned by this crisis. Therefore, modern science is Aristotelian-Thomistic. Therefore  all  valuable elements of the classical theories are conserved. Only the mechanistic element has vanished from it, and that turns out to be already superfluous upon close scrutinity with the aid of the so simple principle of elimination of superfluous elements.

* * *

With all this (present and the previous six documents), written down in the year 2010, we have come to an end of presenting the view of HOENEN (1947) concerning the ontological status of space, time, motion, qualities, atoms, molecules, and crystals. The argument of HOENEN that these items can legitimately be considered along Aristotelian-Thomistic lines, is, according to us, very sound indeed. Of course the expositions about atoms and molecules (i.e. atomic and chemical theory) should be held against more recent developments ( I myself consulted some literature from the 1980's and 1990's). But because the expositions of HOENEN are pretty much general, it can be expected that they will keep their validity in many years to come.
We now have arrived to a clear understanding of metaphysical Substance, and where it can be found in inorganic Nature. Of course organisms are the primary instance of Substance, having a true self, and true intrinsic unity. But it is interesting to have come to know that also molecules, crystals, and atoms are true Substances.
The  next document  is, in a way, connected with the last two (documents) on inorganic Substance :  All molecules are Substances, even the largest and most complex of all, the organims. Indeed, in this next document we will, largely following, Oskar Müller, 1959/1960, investigate the view that every individual organism is one single chemical molecule, one living molecule. But in contrast to inorganic molecules (including those of free proteins) the living molecule is embedded in an aquous serum-like medium which is its closest existential condition. In contrast to inorganic molecules, the organismic molecule must maintain itself  a c t i v e l y  and it does so by taking in energy and matter from its outermost environment and exporting matter and entropy out into it. In all this, the mentioned aquous serum-like medium mediates things. This theory of the one-molecule nature of organisms will be referred to as "Unimol".
So indeed, connecting with the previous two documents, we will delve deeper into the various types of chemical bonding. Further, we will see how much Unimol may contribute to the understanding of organismic unity, i.e. the organism as a true Substance. And it perfectly connects with the established virtual existence of atoms in the molecule, guaranteeing its intrinsic and total unity.

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To continue click HERE  for studying the Unimol View of organisms, rendering the latter to be homogeneously classified with all other molecular Substances, Part XVg.

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