The Mixtum and its Elements

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 Introduction 


At the end of the Essay on Crystals and the Substance-Accident Metaphysics we wrote the following :



By means of the knowledge of crystals it probably is possible to solve (or bringing closer to a solution) the problem of  the way of being (actual or virtual) of the constituents in a uniform whole (a uniform thing, a first substance). This problem unfolds as follows :
When the constituents of a uniform thing are  actually  present (in that thing), then this one thing would not be one thing, but many things. A uniform thing is a being, generated by a dynamical system according to the (one) Dynamical Law. So it must be ONE thing. A possible solution of this problem could be, to consider the constituents as only existing  virtually  in that uniform thing (when we decompose this thing, then the constituents become actual (and cease to be constituents)). This solution may not be the correct one. It must therefore be investigated. We can easily imagine (do we?) that a ONE Dynamical Law can generate a compound of  actually  existing constituents (parts). The ONE-ness of the thing is then to be found at the genotypical level : the ONE Dynamical Law, and not at the phenotypical level. We shall elaborate on this interesting problem in the Essay on  The mixtum and its Elements .



So here we are.

The problem concerns  composed  beings (things). We shall denote such a being with the term  MIXTUM  (plural : mixta). The items, out of which such a composed being is (conceptually) built, we shall call the  ELEMENTS  (but also  constituents, or  components ).

A mixtum can be of several sorts :


When, in what follows, we speak about a  mixtum  we shall let the term refer, not to an aggregate, but to one of the other mixta mentioned. So a MIXTUM is a composed being, composed out of elements on the basis of intrinsic factors, resulting in a thing with a  specific  NATURE.

We have to investigate the relation between the mixtum and its elements and their way of being (i.e. their ontological status).


 The Ontological Status of the Elements of a Mixtum 


"The Elements of a Mixtum " here means especially : The Elements IN a Mixtum.

A mixtum (in the sense of not being an aggregate) has a certain UNITY. Where do we find this unity? We seem to find it in the ONE Dynamical Law of the dynamical system that gererated that mixtum. But the ONE-ness of that Dynamical Law (i.e. the fact that we have to do with numerically ONE Dynamical Law) does not, by itself,  guarantee  the unity of such a mixtum, because a ONE dynamical law  can , and sometimes does, generate NOT a unity, but an incoherent configuration of elements, as we can observe in  chaotic  dynamical systems. These systems are able to disorganize the elements : proceeding from an ordered initial state such a system (and by implication the Dynamical Law) can generate a disordered state.

So a resulting coherence or one-ness is generated only in special cases. In such a case the unity only follows, not from the one-ness of the Dynamical Law, but from the special characteristics of that particular law which has operated, and has created the uniformity of its product. In contradistinction to the property of that dynamical law of ' being ONE in number ', that other aspect of ONE-ness of that dynamical law -- a one-ness that is responsible for the one-ness of the (generated) mixtum -- is totally  implicit  in that law. As such it is not observable, and, in a way, not present (in that law). It is present though in the mixtum (in the considered case).

When such a one-ness of that mixtum -- not only numerical one-ness, therefore it is better called  unity  -- is indeed (actually) present in that mixtum, how must we interpret this unity? 

It seems that this can only be done by interpreting the elements of the mixtum not as a distribution of  things  in the mixtum, but as a distribution of  properties. Properties of what? Properties of the mixtum. Some of these can be interpreted as  conserved  properties of the elements of the mixtum, others as new properties of the mixtum. The " conserved properties of the elements " are in fact properties of the mixtum (like the new properties are properties of the mixtum). They are identical with the corresponding properties of the elements because there exists a ' genetic ' kinship or affinity between the elements on the one hand and the mixtum on the other. In this way the elements exist only  virtually  in the mixtum. When the mixtum decomposes those elements become actual again (as they were, before they were taken up into the mixture -- before they became elements).

If we do not interpret the unity in this way, then we must allow that the elements do exist  actually  in the mixtum. In that case the elements are  things. But then there is no unity anymore, because now the mixtum IS many things, and so is an aggregate.

Of course all kinds of elements are often clearly visible in a mixtum as its parts and thus as things. In such cases we must interpret the status of those elements (parts) as still existing virtually, it is true, but very close to actuality : little is needed to make them actual.
 
We can summarize those ideas --which partly go back to P. HOENEN, 1947,  Philosophie der Anorganische Natuur, written in Dutch -- by stating that a mixtum is  one in Substance  and many in  its accidents  (properties), and such a mixtum is a  heterogeneous continuum. This heterogenity -- this ' many in its accidents ' -- can include a  per accidens  heterogenity as well as a  per se  heterogenity, i.e. specific heterogenity. A  per accidens  heterogenity is caused by external factors, and belongs only to the individual in question. The  per se  heterogenity is caused by the retention of some properties of some (or all) elements, or by the newly generated properties of the mixtum.
 

This theory could be correct, but is not free from all kinds of difficulties. To evade it one could suppose -- or conclude from its difficulties -- that all the mixta mentioned in the list above, with the probable exception of atoms, are, like the first item in that list, NOT strict unities. The unity of mixta must then be interpreted as being  gradual  and never absolute (meaning that absolute unities do not exist among those mixta).

But then they are not distinguishing themselves from aggregates (mixtures) anymore, and obviously they do. For example there IS a difference between a mixture of Sulfur and Iron on the one hand and the chemical compound Sulferic-Iron (FeS) on the other. This compound emerges when the mixture of Sulfur and Iron is heated. Another difference is that chemical compounds show definite proportions of the constituents. On the molecular level Sulfuric Iron is always composed of one Sulfur atom and one Iron atom. Another proportion either is not possible at all, or results in another compound with other properties. Aggregates (mixtures) generally are not constrained by proportions, so for example the well known mixture air. Also individual organisms do not seem to be just aggregates of chemicals, but seem to be unities, with STRONGLY INTEGRATED parts.

So it seems worthwile to investigate the above mentioned interpretation, which says that the parts are not a distribution of things in and over the mixtum, but a distribution of properties (of the mixtum) in and over the mixtum.


With all this in mind we shall first examine  chemical compounds  and  crystals, and later on (in another Essay) the organisms.


 The Molecules of Chemical Compounds as Mixta 


The atoms in a molecule are bonded to each other. They are bonded in an intense fashion as we can learn from the Theory of Orbitals. We will give a succinct exposition of this Theory in the Essay on The Chemical Bond.

The intensity of the chemical bond clearly shows that a molecule is a unified mixtum, not an aggregate, and persuades us to interpret it as a real Totality, a unified being with a specific Identity or Essence. If this is correct then the elements of the molecule only virtually exist in the molecule, or, with other words the atoms are virtual, not actual. This virtuality is a special kind of  potentiality : it means not a potentiality for becoming anything whatsoever, but a ' near ' potency, to some specific being, in our case a near potency to an atom of a determined species. Only as a  remote  potency, that which possesses it, is in potency to anything. So we can discriminate between a direct ('near') potency, and sucessively more remote potencies. This is just an expression of the fact that every generation (every 'production-process') of (i.e. towards) something, can only proceed along certain lines, i.e. only via intermediates. So, generally, the process reaches this something only through some intermediate products (stadia).


 Further elaboration of the general theory concerning the status of elements in a composed being, with an application for molecules and crystals 


When a  Composed Being  (= a being resulting from other beings that are going to compose this being) appears (= comes into existence) from whatever process, a composing process, (then we must say that) its properties originate from the lower level. This lower level (' bottom ') comprises the things which are coming together while situated in a certain environment.

So all composing processes are ' bottom-up '. This must be the case, because, where else does the composed thing come from?

WHEN the properties of the composed thing are :



THEN such a composed thing will be just an  aggregate. In this case it is not a unity, not a new substance. The coming-together of the (initially free) components is not a  specific  process. It does not demand specific proportions of the components. The coming-together is in this case a process dictated by general attraction forces only, and often moreover by external factors. The ' interaction ' of the components in the process of coming-together is nothing but a  relocation  of the initially free components towards a non-specific non-predetermined configuration. Many configurations are in principle admitted. If not, then this is caused by  extrinsic  factors, for instance the actual number of components that happen to be present, or it is caused by  external  factors (which are by consequence also extrinsic), or both. The result of all this is just an aggregate, not a new being.


In the above list the last item deserves a little  more elaboration : Properties of the composed thing that cannot, even in principle, occur in the components themselves, because they do not make sense of being a property of any such component. For example the  refraction-index  of a liquid : one molecule, or one atom, cannot have a refraction-index. Other examples are the  revolution-period  of a planet, the  constant pressure  of a gas at a constant temperature and volume ( also temperature  itself cannot be applied to one molecule, because it is a statistical property, but temperature is not a constant for whatever entity, it can vary as a result of energy-influx and so is not specific for any such entity. ). Yet another example of such a propery is the blue-ness of the sky.

When such properties can nevertheless in principle be deduced from the multitudiness of the relevant constituents (components), then they can be called  aggregation resultants. They are not properties of every, or some constituents, but properties of constituentS (properties of ALL -- in contradistintion with EVERY -- constituents, or of some constituents-taken-together). Such aggregation-resultants are in fact not GENERATED by a dynamical process; they passively result (not by just addition) from a  multitude  of constituents, thus resulting from  multitudiness  only.

In all the cases of addition-properties and of aggregate-resultants, it is still possible to speak of properties of the components (instead of properties of the composed thing), expressing the fact that the item in question is just an aggregate.



BUT WHEN SOME PROPERTIES OF THE COMPOSED THING are (1) not (identical with) the properties of some components, and (2) are also not addition-resultants of properties of some or all components, and (3) are also not aggregation-resultants, and so do not comply with the type of properties of the above list, THEN these properties can only be interpreted as properties of the composed thing, i.e. they must be interpreted as the properties of the composed thing ONLY. They cannot be called properties of the components (not of any, not of every, not of all). So a  new  thing has come into existence, being the subject of its properties. The multitude of components has become the unity of the new thing, of the new being. And now, by consequence, also all the other (types of) properties (mentioned in the above list) must be interpreted as properties of that new thing.


This being will of course have many properties in common with its components. These properties obviously come " from the bottom ". But the truly new properties also must in some way come from the bottom : they are, it is true, totally absent in the components, and they are also absent from the multitudiness of the components, but they are nevertheless GENERATED by the interactons of the initially free components. In dynamical system theory such properties are called ' emergent properties '.


In the formation of molecules from atoms (i.e. the composition of molecules from atoms) the periphery (insofar as one can make use of such a -- local -- term) of the atoms is changed. But according to the theory of the Chemical Bond (See the Essay on The Chemical Bond) this change is NOT a mechanical change. It is not a change in configuration by local displacements of particles. So in the chemical bond (especially the covalent bond) we have to do with a change in  abstract  configurations (The ionic bond is much simpler than the covalent bond, but nevertheless occurs at the level of electrons, and at this level the transitions are not of a pure mechanical nature anymore).

So a molecule is -- with respect to its, initially free, components -- a new being, a new Totality. The same applies to crystals, because they can be interpreted as giant molecules (with a periodic structure). See for crystals the Essay on Crystals and the Substance-Accident Metaphysics.

Not only crystals show a definite structural pattern, but also molecules : the atoms (or should we say the properties of the mixtum (= composed thing) corresponding to atoms?) are arranged in definite patterns, they form a  structure. In proteins we even see secundary and tertiary structures : The peptide chain folds itself in a special way.
From a purely mechanically atomistic viewpoint the formation of such structures is not easy to explain, i.e. (hard to) explain in terms of attraction forces and equilibria only. So, especially such molecules (proteins) reveal themselves as specifically new beings with respect to their initially free components. And this will (with a little less convincing force) also apply to all other molecules.

So molecules and crystals are  Totalities. All the properties are  their  properties, they are not the properties of the components, because the components are not there anymore, only the new being is there.

When we, in spite of this, do want to speak about components (which is meaningful in certain contexts) then we must interpret them as VIRTUAL entities.

Of course, speaking about virtual entities could be in it self problematic. But this problem seems to disappear when we realize that we are in fact always speaking about the molecule (or the crystal). And everything in a molecule (and a crystal) is actual : The molecule (and the crystal) itself is actual, and so are the properties of the molecule (and the crystal).

The atom surely is a Totality, it is not an aggregate of components. These components are fully integrated in the atom.

So the following (types of) Totalities have been found : 




The remaining large group of  Composed Things  (not considering Stars and the like) are  Organisms. They are neither crystals nor molecules nor atoms (although they do show some analogies with crystals), but they seem to be real unities. Like crystals, molecules, etc. they do not possess some centrally located item which directs their behavior. Their Essence is dispersed all over that particular being.

We shall treat of organisms in another Essay (consisting of four Parts, See HERE ).


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