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Aristotelian Metaphysics
Theory of Natures

Ontology of the individual thing

Part I

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This document (Part I) introduces the systematic and thematical exposition of Aristotelian metaphysics as a theory of natures, or the ontology of the individual thing.


Metaphysics and Natural Sciences.

Natural Science investigates and tries to explain natural phenomena. It does this by observation, experiment and the formation of theories (models). But it can do this only on the basis of certain fundamental (and non-provable) presuppositions.
For instance, the inductive method (establishing of matters in individual cases, and then generalizing the results), as the all pervading general method of natural science, presupposes that things (in the broadest sense) of the same intrinsic nature necessarily behave according to that intrinsic nature under all circumstances. For example :  a  glowing piece of wood will continue to glow in a container filled with air, will flare up in a container filled with oxygen, will go out in a container filled with carbon dioxide, and also in a container filled with nitrogen. Such a presupposition is absolutely necessary for natural science to be possible at all. It cannot be questioned within natural science itself. It belongs to the province of natural philosophy.

All this is already discussed and expounded in First Part of Website in the document The Species-Individuum Structure in the Critical Series of documents.

Implicitly departing from such presuppositions, natural science proceeds to investigate natural and observable phenomena. It attemps to reveal the near causes of these phenomena, by creating theoretical models, which then must be tested empirically (that is, by observation or experiment).
A reductionistic assertion of many scientists is that natural science is ultimately concerned with finding first (that is, most fundamental) -- but still in principle observable -- causes (observable often only by macroscopic effects), by saying that some subsciences are more fundamental than others, so that ultimately all phenomena can be reduced to one small set of "first" and simple phenomena.
Other scientists, however, assert that reality has many levels, that are equally fundamental. They say that many complex phenomena cannot be reduced to simpler phenomena. Such complex phenomena involve intrinsic natures in their own right (in addition to natures of simple things), which cannot be reduced to simpler natures.

Explicitly departing from the necessary presuppositions of natural science, a philosophical theory can be set up, that is maximally general, and that is such that the theories of natural science (those that are fairly certain) can be seen as specifications of the (general) philosophical theory. This general philosophical theory or metaphysics is (or should be) philosophical and metaphysical (and therefore, ontological) by virtue of three reasons :

There are still several such philosophical theories possible as candidates, for example mechanicism, atomism, etc. Here we will investigate the Aristotelian metaphysics.
In First and Fourth Part of Website we have found out that this metaphysics, together with many useful elements from Thomism, is the best to meet the above requirements. However, we have found out that it must be supplemented by the theory of the Implicate Order.
The Aristotelian metaphysics is about individual things and their natures (accidental as well as per se). It does not contradict the general tenets of the ontological theory of Layers, as expounded in Fourth Part of Website (especially Parts I, II and III), because the latter theory has only a different angle of view.
The Aristotelian metaphysics discovers structures of reference expressed by  pros hen  equivocals. For example :

Being has an equivocal nature (and is therefore expressed by equivocal terms). Its primary instance is Entity (better known as Substance), that is, that what falls under the first Category (of Aristotle), while its secondary instances are those beings that fall under the remaining categories (like quantity, quality, and the like).

Entity, in its turn, also has an equivocal nature. Its primary instance is the Form (known as Substantial Form), while its secondary instances are prime matter, and the (ontological) composite of prime matter and substantial form.

So the substantial Form of material things is the first instance of Entity.
But the Aristotelian metaphysics contains indications that this first instance is perhaps not the very first instance of Entity :  Maybe the substantial Form points to a still earlier (that is more fundamental) form, that is a form, not only considered without its matter, but a form actually separated from matter. Such "separate entities" could represent the entities as they are supposed to reside in the Implicate Order.
Later we will investigate this interesting suggestion.

We will investigate the Aristotelian metaphysics only in  a  thematic  way. This means that we do not pursue it as it is actually held by Aristotle. We use valuable elements of that metaphysics in order to arrive at a metaphysics that can also in modern times be accepted as a general metaphysical theory that allows itself to be specified into a number of fundamental results of natural science. So we are not obliged to stick to Aristotle's views. We can drop things from it, and add things to it, as we please, that is, as we deem necessary in order to obtain an acceptable metaphysics. This we had already done all along in the whole website. So again, our exposition of the Aristotelian metaphysics is not in any way an historical account. By the term "Aristotelian metaphysics" we consequently mean a metaphysics inspired by that of Aristotle (and supplemented with additional ideas of myself and of other authors).

The Aristotelian metaphysics deals with Being only insofar as it is Being -- Being qua Being. Here "Being" does not signify "Existence".  In "Being", (intelligible) c o n t e n t  is necessarily involved. The possession of content is a condition for something to exist. And if we are speaking of Being, of content, of whatness, of knowability, etc., we have, first of all, in mind an individual material thing (this in contrast to the theory of ontological Layers, that is, category Layers). All is seen from the 'viewpoint' of this individual thing. All is with respect to this individual thing. This individual material thing is first of all composed of two 'elements', viz.,  p r i m e  m a t t e r  and  s u b s t a n t i a l  f o r m,  resulting in the (matter-form) "composite", without these elements themselves being material things, that is, they are not elements in the usual sense (like the atoms that are going to make up a molecule). These elements make something into a material thing, that is, they are among the necessary conditions that something is to be a material thing at all. The composite, thus consisting of prime matter and substantial form, is the individual  s u b s t a n c e  (in the metaphysical sense of the term). This substance an instance of  E n t i t y.  But this substance is as such not observable, and so is as such not yet a sensible thing. For this we need properties. They make the thing -- the being -- observable. Such properties are also beings, but in a secondary sense. So, for instance, the  s i z e  of the thing. It belongs to the (aristotelian) category of  q u a n  t i t y.  Further, say, the  d e n s i t y  of the thing. It belongs to the category of  q u a l i t y.  Insofar as such properties originate directly from the substance, they are properties in the true sense. They are called  p r o p r i a  (that is, intrinsic determinations). These belong  per se  (that is, intrinsically) to the thing and thus to the substance. For example, from the essence of a crystal necessarily arise its intrinsic shape, its intrinsic point symmetry and its promorph (as is extensively discussed in Fourth Part of Website ).  While substance is the first instance of Being in material things, these properties are secondary instances of Being.
But there are also 'properties' of the thing which are not properties in the strict sense, but just accidental determinations of the thing, originated by extrinsic causes. We can also call them  "s t a t e s"  of the thing. A man can be tanned by the sun. But being tanned does not necessarily follow from his being a man. The being-tanned is a per accidens determination, per accidens with respect to being a man :  this particular man just happens to be tanned, just happens to be in a tanned state. Another example is the actual shape adopted by a branched snow-crystal. Its star-shaped form is the result of external conditions, such as high humidity (causing rapid growth) and a temperature of around 150C.  Its intrinsic shape, on the other hand, is that of a hexagonal prism, which emerges when the ice crystal is allowed to grow slowly (low humidity) allowing in turn that the water molecules built up the crystal in a systematic and orderly way, a way, totally determined by the crystal's essence (which itself is the crystal's space group P63/m 2/m 2/c  plus  its chemical composition, H2O ).
When such properties and accidental determinations (states) are maximally generalized, we arrive at a number of highest genera, like quantity, quality, etc. And the highest genus of those things of which these properties and accidental determinations are properties and accidental determinations, is substance.
Well, substance and the highest genera of properties and states are the Aristotelian Categories. The whole set of categories first of all consists of two groups :  Substance and Accidents (where the first group has only one member). Substance is ontologically independent (that is, it does not need a carrier), while the Accidents are not. They must be carried by a substance (of which they are properties or accidental determinations). In this case substance is a substrate, a necessary substrate of the accidents, a substrate for accidental forms (just like prime matter is a substrate for the substantial form).
And it is only the coming together of all these 'elements', viz., prime matter, substantial form, properties, and accidental determinations, that a thing is at last constituted, i.e. that a thing is ontologically constituted (not generated) out of ontological elements.
All the types of beings, viz., substance, accidents, form, matter, potential being, actual being, separate forms (that is, forms actually separated from matter), are investigated in terms of their ontological  priorities  with respect to one another.
See, if necessary, the document  Substance and Accident  in the first Series of documents in First Part of Website , and also the document  The Distinction between Substance, Essence, genuine Property and State  in the "Critical Series" of Documents in that same Part of Website.
In fact, when proceeding with the present and subsequent documents, we presuppose a knowledge of the reader of that what has been laid down in First Part of Website.

General Lay-out of the investigation.

First we will keep things very general. We investigate Being only insofar as it is Being, and all its direct consequences. Substance -- the first aristotelian category, will be studied as an instance of Entity, which itself is the first instance of Being in the material order.
At a later stage, though, we will proceed in a less general way, and will occupy ourselves with the observable manifestation of that instance of Entity, as we have this manifestation in accidental categories, that is, the properties and states of substances, especially those under the heading of Quantity and Quality. And this automatically brings metaphysics in contact with Natural Science, because the latter is primarily concerned with sensible being. We investigate whether indeed this metaphysics lets itself specify into those theories of natural science that are more or less well-established.
But, as has been said, we first of all keep things very general, namely by studying just Being qua Being.
Being has  a  pros hen  structure, and such a structure is expressed by  pros hen  equivocals, under which one is primary (All this will be further explained below).
Entity (substance) is the primary instance of Being in the material order. But Entity itself also has  a  pros hen  structure. Its first instance is form (substantial form). And it seems that this form is in fact not the very first instance after all, but still a secondary instance of Entity. The ultimate instance, the true first instance, of Entity seems to be  absolutely separate Entity,  that is, form separate from matter, and that means not only separate from matter in notion, but separate from matter in reality. It further means that this form is not just separated from matter (in notion, or in reality), but truly separate :  It has nothing to do with matter, and was never connected with it.
This course, starting with the primary Being of sensible things, Entity, and ending up in the highest Being of all, Separate Entity, will be followed and investigated. And we attempt to find out whether the domain of Separate Entity is identical to at least some form of Implicate Order. For all this we heavily rely on the long and detailed exposition of the doctrine of Being as it is found in Aristotle's books on metaphysics carried out by J. OWENS in his above mentioned book. We will follow OWENS's exposition in a thematic way, that is, what we're going to present is not an historical account, we feel free to add, omit or change things on the way.
When investigating Being, Aristotle departs from individual sensible beings, that is, from individual observable things. These things have a certain nature, and everything is investigated as to how it relates and refers to that nature, that is, whether a given something belongs to, or flows from, that nature  per se,  or only  per accidens,  etc.  His main example (serving to elucidate his general exposition) is man (human beings), that is, man is, logically a species, physically manifested by individuals that share a common nature. Ontologically an individual human being is a substance (in the metaphysical sense). He has an intrinsic essence or specific nature. He has intrinsic properties (intrinsic, and thus  per se  with respect to his specific nature) and can find himself in several states (which are extrinsic or accidental determinations, that is, extrinsic or  per accidens  with respect to his specific nature). From his essence or specific nature the intrinsic properties necessarily flow and render this nature observable.
In itself this is an appropriate way to exemplify things. But it has a disadvantage :  A human being is an organism. And, while in Aristotle's days human beings were -- as to their properties and states -- better known than inorganic bodies, the situation has changed since. Today we still do little understand organisms as to what they are, let alone man, one of the highest evolved species of organism. On the other hand, our insight and knowledge of inorganic bodies, such as chemical compounds and crystals, has increased dramatically since the days of Aristotle. We know the internal structure of crystals and molecules, and also their genesis. And because crystals appear in macroscopic individuals, having definite shapes and symmetries, crystals seem to be perfect candidates for serving as concrete examples during the exposition of the metaphysics of Being. In fact, that's why we have devoted so much attention to them in earlier documents (First, Second and Fourth Parts of Website).
So we propose that in addition to using man as an exomple, we also use the crystal in that way. And because snow crystals are especially instructive for our purposes we will focus mainly on them, when presenting an inorganic example. Snow crystals are extensively studied in Fourth Part of Website ,  so in the reader we presuppose a knowledge of them. Indeed, in the case of a human being it is hard to point to his nature or essence (is it the genes, or is it also located elsewhere in his body, for instance in his brain?). Man has been evolved from other creatures, during evolution, which could eliminate a clear distinction of his nature and that of his predecessors. Things are much clearer in the case of crystals. At least we can say the following of them :

In the document Crystals and Metaphysics (First Series of Documents) in First Part of Website we have established that the essence or specific nature of a crystal manifests itself as its :

Space Group + Chemical Composition

The Space Group, which indicates the crystal's total symmetry (point symmetry as well as translational symmetry), already accounts for the given thermodynamic conditions under which the given crystal is stable (Under other such conditions other crystal forms of the same chemical substance are stable). It also accounts for the point symmetry of the chemical motifs as they are 'placed' in the crystal lattice (which is some 3-dimensional network of points) resulting in a final (and total) symmetry (expressed by the Space Group) of the crystal, and in its point symmetry, that is, its translation-free symmetry (this latter symmetry is directly, and macroscopically, visible when the crystal was allowed to develop in a uniform medium). This crystallographic point symmetry does not need to be the same as the point symmetry of its intrinsic shape. Often this (crystallographic) point symmetry is lower than the (morphological) symmetry of the crystal's intrinsic shape.
The Chemical Composition, on the other hand, accounts for the actual structure and morphology of the chemical motifs  ( The same point symmetry of a motif still allows for several different morphologies of these motifs).
So  Space Group  plus  Chemical Composition  represent the crystal's essence or specific nature (as it is manifested in the observable world).
More indirect  per se  properties of a crystal are its intrinsic shape and its promorph (which, in addition to symmetry, indicates the number and spatial arrangement of antimers [counterparts] ).

When we have a given growing crystal, and when conditions become non-uniform, but remaining such that that same crystal form (expressed by its Space Group) is still stable, and thus does not transform into another crystal form (of the same chemical substance), the external shape of the crystal is going to deviate from its intrinsic shape (which is what results from uniform growing conditions), resulting in some distorted shape (while the internal structure is undisturbed). Of course the crystal can adopt many such distorted shapes, and all these shapes are extrinsic shapes, not flowing solely from the crystal's essence or specific nature. They originate from irregularities in the growing environment, and indeed reflect these irregularities. Such a distorted shape also does not reflect the crystal's internal symmetry anymore, although this symmetry is still there. So here we have a good example of a  per accidens  determination of a substance (in the metaphysical sense).
The star-shaped form of a branched snow-crystal is another example of a  per accidens  determination :  The crystal does not find itself under conditions where it can grow 'all by it self ', that is, grow on its own terms, by systematically adding elements in the proper order. No, it finds itself under conditions (high humidity levels) that urge a fast energy discharge, and that means fast growth. Now the crystal's growth is not orderly anymore, that is, the crystal is not allowed anymore to grow layer by layer (that is, finishing one layer over its full extension, and only then starting the next layer), but must 'concentrate' instead on letting material preferentially deposit onto sites of the crystal surface that stick out best into the growing medium, resulting in the formation of branches and side-branches. So this branched shape is a truly accidental determination of the crystal (while the latter's internal structure and symmetry remains the same [apart from some defects which are more or less unavoidable when growth is fast] ),  that is, accidental with respect to its essence or specific nature. And this is evident from the fact that there is an almost unlimited variety to be found in the shapes of branched snow-crystals. On the other hand, the  intrinsic  shape of a snow crystal (ice crystal) is just a hexagonal prism (without branches).
Further there are all kinds of interesting crystallographical and physical phenomena to be found in all crystals, such as twinning and metamorphosis, that are useful for exemplifying and expounding  specific nature, intrinsic properties, individuality, etc.
Another feature of crystals, that makes them very suitable to exemplify the mentioned metaphysical notions, is the analogy they show with organisms, as explained in Fourth Part of Website .
So we see that a crystal indeed is very instructive and useful to elucidate (and test) all kinds of metaphysical notions. It will, acordingly, accompany our expositions to come.

Let us reproduce some photographs of snow crystals from Fourth Part of Website :

(From Part XXIX Sequel-32, After LIBBRECHT)

(From Part XXIX Sequel-33, After LIBBRECHT)

(From Part XXIX Sequel-33, After LIBBRECHT)

(From Part XXIX Sequel-32, After LIBBRECHT)

Figure above :  Snow crystals displaying the intrinsic shape of H2O crystals. (From Part XXIX Sequel-6, After BENTLEY & HUMPHREYS)

(From Part XXIX Sequel-4, After BENTLEY & HUMPHREYS)

Figure above :  Distorted actual shape.  An asymmetrically grown snow crystal.

Figure above :  Antarctic Snowflakes.
These diamond-dust snow crystals fell at the South Pole. They grew slowly in the dry Antarctic air, thus becoming nearly perfect hexagonal prisms -- the intrinsic shape of H2O crystals. Most are only about 0.2 mm (0.008 inches) in size. Cirrus clouds are made of similar or even smaller ice crystals. (After LIBBRECHT)

So we see in snow crystals, that the actual shapes, taken up by them, are highly diverse indeed, while their intrinsic shape is just a hexagonal prism. However, apart from defects, the internal structure and symmetry, as well as their crystallographic point symmetry and indeed their promorph, remain the same in all natural snow-crystals.

The dependence of the actual shape of snow crystals upon temperature and humidity is given in the Nakaya morphology diagram (already discussed in Fourth Part of Website). Click HERE to see that diagram (click on the image to see it in full size).

Before we start with a systematic (but thematic!) exposition of Aristotelian metaphysics or ontology, let us first summarize (serving as a preview) (1) the Aristotelian vocabulary of Being, (2) the expressly stated doctrines, and (3) the Aristotelian separate Entities.

The Aristotelian Vocabulary of Being.

Expressly stated doctrines (in the Metaphysics [books] of Aristotle).

' Being ' in the Metaphysics is "expressed in many ways" according to the  pros hen  manner. Its nature is the nature of its primary instance, Entity. But Entity has also primary and secondary instances. The primary instance of Entity in sensible things is the  f o r m.  The absolutely separate form (not the separated form) -- separate from matter -- is also referred to as the primary Entity.
On the other hand, the science of separate Entity is the primary philosophy, and deals universally with all Beings. It is the science of the first causes of things, the science of Being qua Being, the science of Entities, the science of the causes of observable divine things (which are the celestial bodies).
Efficient, final, and material causes have in various ways been reduced to the formal cause  ( In fact, these four causes also relate to each other in a  pros hen  manner). The form has appeared as the ultimate basis of all universal and scientific knowledge, just as it has emerged as the ultimate foundation of Being.

The Separate Entities.

In the extant texts of Aristotle's Metaphysics no doctrine of Separate Entity (as the ultimate primary Entity) is given. But we can find enough hints pointing to such a doctrine. And indeed, in other writings Aristotle does mention and characterize them.
Being is a structure of reference, a  pros hen  structure. And the ultimate reference is to absolutely separate Entity, that is form that is in no way the form of a matter.
The metaphysical treatises state that all corruptible things imitate the incorruptible, and that all sensible things, both corruptible and incorruptible (the celestial bodies), depend upon separate Entity as upon their final cause. These statements are not developed any further in the Metaphysics. But in (Aristotle's) De Anima it is stated that the goal sought by all things, and the purpose of all natural actions, is the 'eternal and the divine'. The two terms seem employed synonymously and explicatively (OWENS, p.461). They designate very aptly the separate Entities, which are unchangeable and divine in the highest degree, and are the causes of what is visible in the divine (that is, [also] the causes of the heavenly bodies). Ultimately it must be their divinity and their eternity that is shared by sensible things. Sensible things cannot attain this divinity and eternity in the corruptible singular. They attain it only in the perpetual species. It is the species [not as logical intention though] that is divine and eternal. The singular thing does not matter in itself. It is only on account of the species. Its every act naturally strives to perpetuate its species. That is the goal of itself and of all its activity. It is divine, as best it may be, by being perpetual in its kind.
Permanence, accordingly, but permanence in and through activity, is what imparts the divine to sensible things. This seems to describe the Aristotelian notion of Entity as formal cause. It is form as act. If such is the case, Entity is derived to sensible things because their form is able to share in a greater or lesser degree in the permanence of the divine (OWENS, p.461).
In  De Caelo  Aristotle says that all other Beings derive their Being and life from the divine  duration :

It is clear then that there is neither place, nor void, nor time, outside the heaven [ that is, beyond the sublunar world and celestial spheres, and thus beyond the material world ]. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it. Nor is there any change in any of the things which lie beyond the outermost motion. They continue through their entire duration unalterable and unmodified, living the best and most self-sufficient of lives. As a matter of fact, this word 'duration' possessed a divine significance for the ancients, for the fulfilment which includes the period of life of any creature outside of which no natural development can fall, has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment which includes all time and infinity, is 'duration' -- a name based upon the fact that it  is always  -- duration immortal and divine. From it derive the being and life which other things, some more or less articulately but others feebly, enjoy.
[De Caelo, I  9,279a 17-30, Oxford translation]

The sensible thing, in striving after the permanence of separate Entity, imitates and expresses the permanence, the Being of the separate Entities themselves. When sensible things are called Being, it is not their own nature, but the nature of the separate Entities, that is primarily designated, just as the health in the body is expressed when a medicine is called healthy. Sensible things are Being only insofar as they imitate Being through their continuous activity. Separate  f o r m  is  Being  and is  universal  to all Beings [but not generically universal]. It is the  cause  of Being, it is the Entity to all, by way of final causality. Because it is the highest type of reality it is the most universal. Yet like any form, it is  actually  individual, and not abstract. It is form in the sense of act.
As a science of  pros hen  equivocals, the primary Wisdom contemplates  f o r m  without matter -- which is the nature of the separate Entities -- that is, form in itself, and (also contemplates form) as it is expressed in every other instance of Being.

The Implicate Order and the separate Entities.

The "imitation through activity" may perhaps be thematically interpreted as  simulation,  or explication (unfolding). That is, the domain of the separate Entities could perhaps be equated with the Implicate Order (after having made some appropriate changes of its concept). The noëtic processes in the Implicate Order are expressed, explicated or simulated by the Explicate Order. All observable processes are expressions of what happens in the Implicate Order :  Holistic Simplification (taking noëtically place) in the Implicate Order expresses itself, or is simulated, in the Explicate Order by Reductionistic Complexification (where the apparent NOVUM is in fact not a NOVUM, in virtue of the Holistic Simplification).

The   p e r   a c c i d e n s   and  the   p e r   s e.

Aristotelian metaphysics considers  n a t u r e s  of all kinds. For example the "nature of man", that is the intrinsic constitution of any individual of the species  man.  It is the dynamical law as it inheres in the elements of the dynamical system that can generate an individual of the species man. It is the substantial form of man. But there are also "natures" of a totally different type, for instance  blackness  (as the color of the skin). This latter nature is also a form, but not a substantial form. It is a determination of a substance (in the metaphysical sense).
Other examples of natures are :  the "nature of a crystal of  Ice I(h)"  (that is the variety of ice-crystal that develops under normal circumstances as they naturally prevail at the earth's surface and atmosphere). This nature is the dynamical law (crystallization law) inherently residing in a supercooled H2O melt or in below-zero supersaturated [with respect to water vapor] air or any other mixture of gases containing water vapor. It is the substantial form of the ice I(h) crystal. It is directly expressed by the Space Group  plus  chemical composition, that is :  P63/m 2/m 2/c  (space group)  plus  H2O molecules  (chemical composition).  And, again, a totally different "nature" is, for example, the crystal's  ditrigonal outline  :  that is, normally (which means crystallization under uniform conditions) the outline or shape of the (resulting) ice I(h) crystal, as looked down along its c-axis, is that of a regular hexagon (six equal sides, six 1200 angles) (This is the intrinsic shape of such a crystal, in the sense that the ability of the crystal to manifest itself as a regular hexagon totally flows from the nature of such a crystal). But under certain conditions different from uniform conditions the shape or outline of the (resulting) crystal (again as seen when looking down along the c-axis) is ditrigonal, that is a hexagon still possessing 1200 angles, but with three equal sides, alternating with three other equal sides different from the former. This  ditrigonal outline  is a form (in the metafysical sense), but it is not a substantial form. It is a determination of a substance (in the metaphysical sense)  ( Here we assume, for the sake of giving an elucidating example, that indeed the ditrigonal shape of an ice crystal is caused by external conditions deviating from uniform conditions, letting -- alternately -- three prism faces grow faster than the three other prism faces. Instead of a ditrigonal shape, we could have taken - as an example -- a still more asymmetric shape, but this latter is harder to designate in the form of a short convenient expression.).
Well, Aristotelian metaphysics distinguishes such natures, and when it is speaking about them  as natures  it considers them as points of reference, that is, points with repect to which something else is evaluated :  Given some nature, and at the same time considering something else, this something else either necessarily flows from that given nature or not. We then respectively say that that something else is either  per se  with respect to that nature, or  per accidens  with respect to that nature. But when it is  per se  with respect to that nature, it can be  per accidens  with respect to some other nature. And when it is  per accidens with respect to the first mentioned nature, it can be  per se  with respect to some other nature.
Let's give some concrete examples with respect to the above exemplified natures.
The "blackness", as we see it in the skin of some human beings, does not necessarily frow from the "nature of man", it is  per accidens  (or, equivalently, extrinsic) with respect to that nature, it is an accidental determination. On the other hand, "being able to learn chess" necessarily flows from that nature, it is an essential determination.
Further we can say, that "causing a body to absorb incident heat radiation" necessarily follows from the nature (of) "blackness" (or, better expressed :  follows from blackness which is the nature of black). So "causing a body to absorb incident heat radiation" is a  per se  feature of blackness.
And again, the "ditrigonal shape or outline" does not (according to our example) necessarily flow from the nature of an Ice I(h) crystal, so it is  per accidens  with respect to that nature, it is an accidental determination. On the other hand, the ability of the crystal to manifest itself as a regular hexagon is intrinsic to that nature, it is an essential determination.
In a regular hexagon the three lines each connecting two opposite corners meet in one point. In the ditrigon the corresponding three lines do not meet in one point anymore. And this latter feature necessarily flows from the nature of the ditrigon, and thus is a  per se  feature of it.
On the basis of these  per se  and  per accidens  features and determinations there are corresponding  per se  and  per accidens  predications, as soon as we assert such features or determinations to be features or determinations of something.

The relativity of the  p e r   a c c i d e n s  and the  p e r   s e.
The  per accidens  and the  per se  of something are always the  per accidens  and the  per se  with respect to something else, that is to a nature of some kind.
Above we considered "man" to be a species, not only in a biological but also in a metaphysical sense. By all authors, writing on the subject, this is done so. But, as we've argued in First Part of Website, this may be incorrect :  What we normally call an individual human being in fact represents a species. In the overwhelming majority such an individual human being is the one and only member of the species he represents. Only in the case of monovular twins we have before us more than one individual of a same species. Apart from such identical twins, each human being genetically differs from any other human being. And if it is correct that the dynamical law, that inheres in the elements that together constitute a dynamical system that generates a human being, resides in and around the genome [= the genetic constitution] of the (already generated) human body, and if it is moreover correct that this dynamical law is the ESSENCE or NATURE of that human being (as argued in First Part of Website), then, apart from identical twins, each individual human being represents a different species (in the metaphysical sense), a species that happens to have (for one reason or another) only one member. Only in the case of identical twins we are happy to see more than one member of one and the same species. And the human race as a whole then represents a genus (instead of a species) in the metaphysical sense.
But although this is probably correct, it makes "man" an awkward example, because of the fact that almost all species have only one member, and where there are more, then in most cases we still have only two such members. So we have little to show if we are speaking about variability between individuals of a same species, to exemplify accidental determinations, and distinguish them from essential determinations.
So in order not to lose having at our disposal "man" as a convenient example of the  per se  and the  per accidens,  of  the  individual,  the  nature,  etc., as it is used throughout the relevant literature (and especially by Aristotle himself), we decide to stick to this usual and wide-spread way of metaphysically interpreting "man", namely as representing one species only. In its function as an instructive and indeed repeatedly used example, this is, according to me, legitimate as long as it (only) serves to explain the  per se  and the  per accidens  and related features. If we use "man" as a species again (that is, the conventional interpretation) instead of a genus -- which latter is, as said, probably correct -- meaning that we return to 'normal practise', then we consider a "nature" that is shared by billions of individuals, instead of a nature that is shared by at most two or three individuals only. This means that the "nature" of the conventional interpretation is impoverished with respect to content as we compare it with the "nature" as it shows up in the alternative interpretation (each human individual representing one particular species, except in the case of identical twins) :  Of all the many features that we find in a given human individual, many will belong to just "individual features", i.e. to features (determinations) that are only  per accidens  with respect to the common nature that is (in the conventional interpretation) shared by all these billions of human individuals (of the past, present, and future), while in the alternative interpretation, most of these features will be essential determinations, directly flowing from the "nature" that is now only shared among at most two or three individuals. So if we consider a "nature" higher up the level of generality, then with respect to it more features of individuals will have the status of  per accidens  than with respect to the corresponding nature lower down that level of generality. Let's give an example.
A vertebrate animal as such, that is an animal only insofar as it is a vertebrate, has less intrinsic properties than, say, a mammal :  while a mammal has, for example, hairs, constituting its external cover, a vertebrate-as-such does not have them (that is, is not hairy), because the nature of a vertebrate-as-such does not already determine whether the external cover should consist of hairs, scales, feathers or whatever. And the same goes for many other features such as the possession of lungs. Likewise a cow has horns, while the nature of mammal-as-such does not determine whether such an animal should have horns or not.
So in order to explain the  per se  and the  per accidens  we must have in mind their relativity. It does not matter what the degree of generality is of the nature with respect to which we assess whether something is  per accidens  or  per se,  as long as we precisely specify that nature.

There is yet another phenomenon with respect to the  per se  and  per accidens  that deserves attention here :
If a thing is called by the name "Socrates", then the fact that Socrates is a human being is  per accidens  with respect to Socrates. This is, because the name Socrates lends itself equally well to be assigned to something else, for instance to some given individual rat  ( as was indeed done in the novel "Willard " ).  It lies not in the nature of the name "Socrates" to be assigned to some given human being. In the streets of Athens there was a Socrates, and that happened to be a human being.

The doctrine of the   p r o s   h e n   equivocals.

Above we already succinctly explained what  pros hen  equivocals are. But we did this by speaking about  concepts.  This, however is not entirely correct, but we did it anyway because modern thought is so obsessively concerned with concepts. But Primary Philosophy, that is, Aristotelian metaphysics, is definitely not about concepts, but about  things,  beings, and in particular about  individual  things, where "things" are taken in as broad a sense as possible, that is a sense that contrasts them with mere concepts.
And accordingly, equivocity is about  things  (which can be matter-form composites, forms, natures, qualities, quantities, causes, etc.). A group of equivocals is a group of things (that are related to one another in some way).
Because this doctrine is highly important by playing a crucial role in Aristotelian metaphysics we will expound it in considerable detail.

Let us first speak about  equivocals in general  (there are several types of equivocals).
In the opening lines of the Categories Aristotle defines the equivocals :

Things are called equivocal whose name alone is common [that is, things that are designated by the same name], the definition as denoted by the name being in each case different. For example, a man and a painting are both called a  zoön.  With these the name is common, while the definition as denoted by the name is in each case different. For if one should explain what is the nature of  zoön  in the one and the other case, he would give the proper definition of each.
Equivocals, accordingly, are things which have one name in common, but different definitions insofar as they are denoted by that name  ( This latter clause is added because in the case of  pros hen  equivocals (which is equivocity by reference to one thing or nature, the primary instance) the secondary instances also have their own definitions :  a certain type of knife is 'medical' (referring to medical practise) but also has a definition of its own.
Univocals, on the other hand, are things of which both name and corresponding definition are common. Zoön -- now meaning only 'animal' -- has the same definition as found in man and ox.

Today 'synonym' and 'homonym' which are more or less related to 'univocal' and 'equivocal' designate  terms.  Only  words  are now called synonyms and homonyms, at least in the primary sense of the designation. With Aristotle, on the contrary, these are all defined as  things.  In equivocity, therefore, the  things  are equivocal, the  name  is  identical,  and the definitions (as referred to by the name) are  different.  But we can still say that a  word  is used 'equivocally'. But it is  things  that are formally defined as equivocal.

The types of Equivocals.
There are three types of equivocals : Things that are equivocal by chance are accidentally denoted by the same name, but their definitions are totally different, having nothing in common. For instance, the name "date" can mean either the fruit of some species of palm tree, or a chosen day of a particular month of a particular year. Such equivocals can be disregarded in the present study.
Things that are equivocal by reference represent our  pros hen  equivocity. Things that are equivocal in this sense also have the same name but different definitions, but here the definitions are not totally different, they have common elements.
Things that are equivocal by analogy (in the sense of Aristotelian metaphysics) also are things having the same names, but the definitions involve a proportion, as in those things designated by the word "good" :  As sight is good in the body, so is the mind in the soul.
Now we are ready to speak in more detail about  pros hen  equivocity (and -- later -- about equivocity by analogy).

The pros hen equivocals.
These are by far the most important equivocals. Many special metaphysical doctrines depend on it.
The Greek "pros hen" means 'toward one', in the sense of  "a group of things, all referring to one thing".  The  pros hen  is a relation involving two terms only, namely the relation of a secondary instance to the primary (while equivocity by analogy involves four terms [standing in a relation of equality of proportions :  A : B = C : D ] ).
The  pros hen  equivocity -- like all equivocities, except equivocity by chance -- does not come from the name or concept, but from the things involved :  By virtue of the nature of the given things (or just by virtue of those natures themselves) equivocity is possible in one context, or not possible in another, that is, by virtue of the very things under consideration they can be signified by one and the same name in one context, or must be signified by different names in another.
The  pros hen  equivocity, that is, the equivocity by reference, is explained by Aristotle in the Metaphysics. Speaking of Being, he says :

It seems to be expressed in the way just mentioned, like the 'medical' and 'healthy'. For each of these also we express in various senses. Everything is expressed in this way by some kind of reference, in the one case to medical science, in the other to health, in others to something else, but each group in reference to one identical thing. For a treatise and a knife are called 'medical' because the former proceeds from medical science, while the latter is useful to it. And things are called 'healthy' in a similar manner :  one thing because it is a sign of health, the other because productive of it. The same way holds also in the other cases.
Various things are 'healty' or 'medical' through reference to something one. This is 'health' in the former case, and 'medical science' in the latter. 'Health' is a form or nature which is found only in the disposition of the bodily organism. The form 'health' is not present in the color (as a sign of health) or in the medicine (as productive of health). Nor is the habit 'medical science' located in the treatise ( which is a mere product of medical science) or in the knife (an instrument of [the practise of] medical science). These secondary instances -- the color and the medicine, the treatise and the knife -- all have their own proper forms. But they are of such a nature as to have some reference to health in the one case and to medical science in the other.
The nature expressed in each case -- this knife is (a) medical (one), this treatise is (a) medical (one) -- namely  medical,  is found in only one of the instances, namely 'medical science', the primary instance, because a knife is in itself not medical, neither is a treatise in itself medical, but medical science is. All the secondary instances have different natures, but with a reference to the nature of the primary instance. Even a medical knife (as distinguished from just a knife) is not medical in itself, because such a knife (considered as the given metal thing) can also be a cleaver (that is, a tool for the butcher). Medical science, on the other hand, is medical tout court :  the thing 'medical science' can only be medical science.

Realistic theory of knowledge in Aristotelian metaphysics.
Again we must stress that terms and concepts play only a subordinated role in Aristotelian metaphysics, which treat of things (where "things" are contrasted with terms or concepts, which are merely signs [natural or conventional]. " Things" can then be, observable objects, but also natures [but not 'natures' of terms or concepts], forms, qualities, quantities, causes, etc.). The explanation of cognition (theory of knowledge) that is adhered to by Aristotelian metaphysics requires this procedure (terms and concepts playing a subordinated role). The knower and the known are identical in the act of cognition. The mind becomes the thing known. It knows itself and its thinking process only concomitantly. The thing known therefore is not the end stage of a process in which some imperceptible alteration of its nature may have occurred, which means that one is not coming to know the thing by first getting to know some corresponding state-of-mind (which position holds the danger of an infinite regress), but that one comes to know the thing immediately. There is no internal or real relation set up in the thing itself (the thing is not transformed into a concept). The only real relation or change is in the knowing subject, when something else is known. The thing itself is not affected by any (cognitional) process. It has not turned into a concept. The concept -- which as such is only known after conscious reflection -- is the means by which the thing becomes known. It is not the (changed) thing itself. See the document Realistic View of Knowledge in the first Series of documents in First Part of Website to learn more about this explanation of cognition.
Accordingly, the  thing  is, for Aristotelian metaphysics, known prior to the (knowledge of the) concept or word. It does not have to be approached consciously and explicitly through term and concept. The procedure of a science -- like the Aristotelian metaphysics -- which studies things can disregard terms and concepts, even while necessarily making use of them. There is a science that deals with words -- Grammar. There is another, Logic (not yet as such classified by Aristotle himself), which deals with concepts. Further, there is a science that deals, among other things, with the (neurological) origin of concepts (not their logical connections) --Psychology. The Aristotelian Natural Philosophy and the Primary Philosopy, on the other hand, deal with things, movable and separate respectively. Things are directly known and studied. While concepts (natural signs) are necessary (but implicit) means of cognition of things, concepts and words (conventional signs) are further necessary to group together these things and to express them to one's self and to one's hearers.
The "obscurities in the nature of the concepts" is accordingly a misleading formulation of a real Aristotelian problem (OWENS, p.130). The true difficulties -- and Aristotle is keenly aware of them -- lie in the equivocals. These are primarily things. Things are in some ways the same, in some ways different. If a different term were used every time the definition differed, all danger of confusion would vanish. So too would be lost in the expression the unity and interrelations that groups of things have among themselves. The term would be made technically precise and definite. But it would thereby shut out of its air-tight compartment much of the indefinable richness contained in the things. To Aristotle, as to Plato, things appear from their very nature both same and different. Aristotle refuses to employ a different word for each concept and definition, predetermining each term to a definite technical meaning. He uses rather a method of speaking that will allow the sameness of things to remain manifest, while being careful to attend to their differences. Things are that way. Aristotelian metaphysics tries to regard them as such (OWENS, p.131).

Let us say a little more about cognition as it is outlined by the realistic theory of knowledge, and as such reflecting a theory of knowledge as it is actually present in Aristotelian metaphysics. For this we use some expositions given by J. WILD, Introduction to realistic philosophy, 1948.
When explicitly stated and critically refined, knowledge is science. If we assert that knowledge is a purely physical process, then natural science (physics, chemistry) must, at least in principle, be able to reveal what knowledge as knowledge is and how it is generally acquired. But what about natural science itself, which is a kind of knowledge? Can natural science physically (or chemically) investigate itself? Certainly not. It can, of course inform us about the cooperation of external and internal senses, which are physically centered in the brain. Hence it is not surprising that brain lesions and other injuries to the central nervous system, interfere with these processes. The realistic view of knowledge does not require us to deny any fact that is known to science. But in addition to these particular physical facts, discoverable by the special techniques of natural science, it must also recognize the amazing fact of science itself (WILD, p.447).
We must acknowledge a formal object of the senses, as well as a different formal object of reason. WILD, pp.458, writes [comments of mine between square brackets] :

[...] my senses may make me aware of this individual, human being now in the room. They do not make me conscious of his humanity [that is, of his intrinsic specific nature], his height, his weight, his pale complexion, the color of his hair, the sound of his voice, but [my senses make me conscious] of all these different formal natures confused together in this material individual. The senses do not falsify reality. They apprehend their proper objects as they really are in the individual thing, i.e. as concreted together with what is formally distinct from them. But they do not apprehend them as they are in themselves, man as such, the color yellow, and so on, apart from everything formally irrelevant to them.
Sense does not give us a false view of reality but a confused and fluid, material view, rather than a distinct and stable, formal view [any individual thing that is observed -- by the senses -- is always in the process of change]. This we achieve by reason alone, which can separate each nature from everything with which it is confused and apprehend man as such, extension as such, color as such, and so on, each alone as it is in itself. The extra-mental nature, when thus abstractly considered by a mental act, is called "the absolute nature". When we raise the philosophical questions :  What is this thing you are talking about? What is man? What is color? What is the precise definition of any entity? we are seeking for the absolute nature of the thing.
This absolute nature is not a universal. [...]
The first act of understanding is to bring such a [...] nature before the mind, to make it intellectually, non-physically present. This absolute nature is not an individual [in the text of WILD there is abusively printed " a universal"], certainly not a construction. It exists, amalgamated with many other forms in the extra-mental individual, which may be grasped in this confusion by sense. It is not a universal either, for it has not yet been compared with other individuals of which it may be predicated.
It is an absolute nature or neutral entity which is neither individual nor universal.
According to Aristotle's Primary Philosophy such a nature, when it is the nature of some given substance (that is, an ontologically independent being), is a primary instance of 'a this', while the ontological compound of matter, form and accidents is a secondary instance (of 'a this'), which we can call 'an individual' or 'singular'. An accident (property or state) can then be assessed as being 'a this' (primary or secondary) per accidens, because it enjoys being 'a this' only (and totally) in virtue of (that of) the (substantial) form, or of (that of) the matter-form composite, instead of (being 'a this') entirely in virtue of itself. ]
The ultimate, simple units of discourse, or Categories [...] are such neutral entities. When I think of quality or quantity or man as such, this is not an individual object, for I have abstracted from all individual determinations  [ According to the Primary Philosophy this is not even necessary, because they are already each of them 'a this' (per se or per accidens) and thus not individual]. Neither is it universal, for I am not thinking of this nature as related to the individuals from which it has been abstracted
This is fully in accord with the Aristotelian Primary Philosophy, which says that a universal can never be Entity, whether first or secondary instancies of it. It is also in accord with the Aristotelian assession of (at least) the substantial form as being neither a universal nor an individual, but a (in this respect) neutral entity.].
What then is the universal, and how does it arise?
It is not a separate thing existing by itself, as both extreme realists and idealists suppose. It is  a  relation.  The foundation of this relation is the absolute nature, or category. Once the mind has brought any form into such a state of solitude [i.e. having it abstracted from all that which does not properly belong to it], it can be compared with the concrete individuals from which it has been separated by the mind. When, as the result of such a comparison, the absolute nature is seen to be present in these individuals as well as in an indefinite number of other possible individuals, it is then a universal concept, identically related to any number of singular instances. This universal relation exists only in the mind, for the abstract consideration of an absolute nature and the comparison of it with a multitude of subordinates, are mental acts which occur nowhere else.
This distinction between the abstract nature, or category (not yet a universal), and the mental relation of universality, enables us to avoid any idealistic mentalizing of extra-mental nature. When I predicate man of Socrates, Plato, and an indefinite "class" of men, I do this by setting up a relation of universality in my mind. But what I predicate of Socrates and so on is not this mental relation but the absolute nature man which is perfectly capable of existing outside the mind with further individual determinations. The absolute nature is thus the link which exists both outside the mind materially, and inside the mind immaterially.
Once isolated in this way it [that is the absolute nature, whether it is substantial form or one of the accidental forms] may be mentally related by the relation of identical predication to the material things in five different ways, the five kinds of universal relation, [namely] as their genus, difference, species (genus and difference together), necessary accident [i.e. ontologically dependent being that necessarily flows from ontologically independent being (substance), and so representing a genuine property or proprium], or contingent accident [i.e. ontologically dependent being not necessarily flowing from ontologically independent being (substance) ].  These five universal relations or different ways of predication, or  p r e d i c a b l e s,  exist only in the mind. What is related by these relations, [namely] the absolute natures or  c a t e g o r i e s,  and the individual entities, exist outside the mind in rerum natura. The critical part of this logical procedure is the bringing of the absolute nature into a noetic presence before the mind. [...]
It is an immaterial process of assimilation which, like all processes, involves that which is acted upon (the [so-called] possible intellect) and that which acts upon it (the active intellect [or reason] ).  The primary, efficient cause of the process is the active reason. The instrumental efficient cause is the imagination, which actively provides a concrete object to be rendered intelligible. The extrinsic, formal cause of understanding is the form of some external thing existing in matter. The intrinsic, analogous, formal cause is this same form existing in abstraction from matter in the possible intellect.
So, according to the realistic theory of knowledge, as expounded by WILD in the above quotation, a given absolute nature (as a member of the vast collection of natures that are classified according to te system of Aristotelian Categories, which [categories] are these natures, expressed maximally generally), is outside the knower (in the extra-mental world) as well as inside the knower (but here in its pure [but not yet universal] form), and this makes the thing directly known. The universal appears 'later', namely when this absolute nature is (by a process of comparison) found again in a great many individual extra-mental things, and then predicated of these things. So if we consider one nature at a time, the  c o n c e p t,  mentally signifying this nature (and with it the thing possessing that nature), is not prior to, but comes after the thing. The Aristotelian concepts, then, should not be considered as self-contained intelligible units. The metaphysical concepts are the signs of equivocal things, and must mirror the equivocity (whether it be  pros hen  equivocity or equivocity by analogy [to be expounded below] ).  If they are considered as self-contained intelligibles, each complete and secluded in itself, they will correspond precisely to only one instance of the things they denote. When such a self-contained intelligible is applied to another of the instances, it will naturally exhibit wavering, inconsistency, and even contradiction. The definitions of equivocal things are admittedly different. If a word or concept is first precisely defined, it will be restricted to one or the other of these definitions. Little wonder then that vacillation or contradiction is seen when the word or concept is applied to the things whose definitions are different. The different definitions must be definitions of the different things, where each definition records a shared content, shared by individual things, forming a group of univocal things. So these definitions should not be definitions of concepts or words, but of things. And if we have a group, not of univocal things, but of equivocal things, then these things have different definitions (but each definition referring to a subgroup of univocal things), but are denoted by the same concept (natural sign) and the same word (conventional sign). Aristotle's procedure is to let the things (that is, extra-mental entities whatsoever) speak for themselves. He waits for them to reveal their own inner nature. They show themselves to be the same in some ways, to be different in others. Concepts and words simply follow and reflect as best they can the nature of the things themselves. This procedure -- as OWENS (p.131) points out -- evidently has the nature of a contemplation of things, rather than that of constructing a 'system' of philosphy. It is not a process of 'making our ideas clear', or of bringing order by means of ideas into a chaotic sense-manifold. Nor is it a method of trying to 'understand the universe by our ideas'. It is rather an effort to penetrate further into things in their own non-human reality. Such a procedure is possible only where no preconceived notion of Being shuts out the 'intentional' or 'self-transcendent' nature of the knowing subject, as that nature is understood both by common sense views and by the philosophical development given it in pre-Cartesian thinkers (OWENS, p.131) ( 'Self-transcendency' is the label for the realistic theory of knowledge in idealistic language).
I hope I have sufficiently explained the proper way of using words, concepts, definitions, etc. in Aristotelian metaphysics.

Equivocity by  analogy

We have discussed equivocity by chance, and equivocity by reference. Now we will speak of the third type of equivocity, equivocity by analogy. The general conclusions, reached above, about the proper use of words , concepts, definitions, etc., of course also hold for these equivocals.
An analogy is an equality of two ratios, such as

A' : B' = A" : B"

Here A' and B' are proportional to A" and B", that is to say,  A' relates to B' as does A" to B". In this way A' is more or less akin to A" in a certain respect, while B' is in the same way more or less akin to B".  The doublet  A' and A"  has about the same function as the doublet  B' and B" .  But because  in (many) other respects  A' can in principle be way out different from A",  and B' way out different from B", the group {A', A", B', B"} so formed by the analogy is not a generic group, it is wider. Things that differ in genus can be one by analogy (where "differ in genus" almost always should mean "differ in (Aristotelian) category").
An example could be the following assertion :

Classical Greek is to modern Greek as Latin is to Italian.

While in  pros hen  equivocity only two terms are involved (secondary instances -- primary instance), in equivocity by analogy four terms are involved.
In the Primary Philosophy much use has been made of equivocity by analogy. In this philosophy one can thus reason from  A" and B"  to   A' and B', or vice versa. Let's give an example.
While clay is the matter of the pot, the latter is its form when the pot is actually formed from te clay on the potter's wheel. Before the making of the pot the clay possessed some other form. The transition took place upon a substrate that itself remained what it was -- the clay. So we can say that when a lump of clay is transformed into a pot, the matter (the clay) remained what it was, while the form (the initial shape of the clay) was replaced by another form (another shape of the clay, the final shape).
Now, by analogy, we can imagine what the ingredients are in the case of a maximally radical change. In such a change all content is replaced by another. But in order for it to still representing a genuine change we still must have a substrate which remains what it was during and after the change. This ultimate, content-deprived substrate (which as such is not observable) must have the same relationship to the content that it carries (and which content is interchanged during the radical transformation), as the clay, the (physical) matter, had to its shape or form that it carries (and which shape or form is interchanged during the (less radical) transformation). And therefore we are justified to call the ultimate substrate : "matter", and the content that it carries : "form". But to still distinguish them from 'ordinary' matter (such as clay, copper, etc.) and from ordinary form (such as shape), we call the ultimate substrate "prime matter" and the content it carries "substantial form".
In this way we have a group of four 'things', prime matter, substantial form, physical matter, ordinary form, that are akin to each other by the analogy :

prime matter : substantial form  =  physical matter : ordinary form

That is, they are equivocals by analogy.

So in Aristotelian metaphysics equivocity by analogy differs from equivocity by reference (pros hen). Therefore, to call the  pros hen  type 'analogous' is not Aristotelian usage, though common in later Scholastic works.

This concludes our exposition of Aristotelian equivocals. We will meet them often in the sequel.

Universality and Individuality, the FORM as 'a this'.

The most difficult problem in Aristotelian metaphysics is the relationship between Form, Universal and Individual. Of course it is in the realm of sensible material things where this problem arises, so the ensuing discussion takes place in the context of material beings. In the documents to come, we will gradually approach a solution to this problem (as it is given by OWENS, p.381--399). However (because we expound Aristotelian metaphysics in a thematical way instead of historically interpreting Aristotle's writings) it is instructive to present the solution beforehand. Of course many details will then be still obscure, but they will be dealt with in the ensuing documents.

The status of the substantial form in material beings.
On account of the  pros hen  nature of Being, the Primary Philosophy can permit itself to deal with only one type of Entity, the form, and yet thereby deal universally with all types of Entity and Being. The substantial form of a material intrinsic being is connected with the prime matter, as the act of the latter. In this sense the form is neither separated not separate. But it can be separate in notion. This does not mean 'separable by thought' (which it also is), but 'separate in intelligible content'. The intelligibility of such a form is in no way dependent on its substrate, as on the contrary that of an accident (property or state) is. This form is an intelligible content in itself. The matter that makes its substrate, adds no intelligibility to it whatsoever. So in this sense such a form is 'separate'. The accidents that follow upon it are not required for its intelligibility. In itself it is a complete intelligible unit, and so separate in knowable content from all else that depends upon it in the sensible thing.
Does 'separate in notion' connote universality?
The form, which is separate in notion (as contrasted with absolutely separate, that is, a self-subsistent, form), is the primary Entity of the sensible thing. But no universal can be Entity (because nothing in extra-mental reality exists in a universal fashion, while Entity is an instance of Being in extra-mental reality). 'Separate in notion' therefore should not mean universality. So when we say that the form, which is Entity, is separate in notion (which it is), we know that this 'separate in notion' cannot mean that the form is a universal.
But what is separate from matter cannot be singular. And because the form is separate from matter, albeit only in notion, it cannot be singular. Said differently :  Because the form, as it is in itself, is separate from matter (this is what 'separate in notion' means) it cannot be singular as it is in itself. The singular always contains matter, and for that reason is indefinable. But the form is separate from matter, at least in notion, and is definable. It cannot be singular.
The form, apparently, can be neither universal nor singular.
What is it then?
In Aristotelian metaphysics the form is called  ' a this '.  And 'a this' is an Aristotelian equivocal, applying to the matter as potency, to the matter-form composite in virtue of the form, and to the form as such. The form can be considered the primary instance of 'thisness' -- just as it was the primary instance of Entity -- within the composite.
In Aristotelian metaphysics only singular things exist in the sensible world, and only universals are knowable (and they do not exist in this world). This is a dilemma, because how then can we know (which we do, albeit only incompletely) the sensible world? Does the peculiar character of the form hold the solution?
Wherever this precision of thought may lead us, it at least is clear-cut in its basic divisions. The form is an Entity and 'a this', without being of itself either singular or actually universal (it is potentially universal). Because it is not singular, it can be knowable and can be the principle of knowability for the singular thing. Knowledge of the form will be knowledge of the singular individual, because the form is identified  per se  with that singular thing as its act, and the form contains all the knowability found in the singular. At the same time the form can be Entity, because it is not actually universal.
How is such a form to be conceived?
It must be understood as something 'separate in notion' but not 'separate without qualification'. It is to be conceived as a physical constituent (for example as the dynamical crystallization law inherent in a supercooled volume of liquid water, which (law) starts to operate when proper crystallization nuclei are present, and which law then results in an ice crystal, which is a (new) substance in the metaphysical sense. This dynamical law then is the substantial form of this substance.) of a sensible thing (the ice crystal of our example), and not able to be found without its sensible matter (the dynamical law inheres the matter of the supercooled melt as well as that of the resulting crystal), except in thought. It is the actual and formal principle and (intrinsic formal) cause of a singular thing, without being of itself a singular. As the act of sensible matter, the form is the cause of Being to the sensible Entity, which is singular. In the passive mind, the same form is without its physical matter. It is the act of that passive mind. In the  l o g i c a l  o r d e r  it is actually universal (while in the entitative order it is only potentially universal), it is the act of intelligible matter and forms the logos or definition of the sensible thing, and as such can be applied universally to all the individuals that are the same in form. Speaking about individuals, how should we assess the "individual", the individuum? In Aristotelian philosophy the term is applied equally to the undivided singular and the undivided species. It can mean either undivided in number or undivided in form. To restrict the term to its English signification of a 'singular', and to use it to translate the Aristotelian 'a this', is to miss the two-fold sense of 'thisness'. Or if the distinction is made, the non-singular sense of 'a this' is relegated to the order of universality. Yet Aristotelian metaphysics requires that the form of sensible things, taken in itself, be neither singular nor universal, although it is the cause of Being and the foundation of universality. When the form is -- in cognition -- applied universally to all the individuals that are the same in form, we get the species. In the actual cognition of a thing the form is known as it is in the one singular, but after the actual cognition has passed it can still be used to know all other such singulars universally. The singular and the universal, accordingly, are to be explained in terms of form, and not vice versa. All three are given as facts, with form prior in knowability. If the problem is posed in two terms only, singularity and universality, it becomes utterly insoluble. If the premises are 'only the singular exists, only the universal is known', how can the Aristotelian notion of  e i d o s,  which is both physical form [in the sense of the dynamical law of that dynamical system that has generated the given Being] and logical species, ever be grasped? It would then have to be fixed as either singular or universal, or else merely catalogued as a hopeless union of the two contradictory alternatives (OWENS, p.393). The form must be kept as prior to, and act of, both composite Entity (singular) and logical universal (that is, the form, as it resides in the sensible thing, and appears in the passive intellect, is potentially a universal). The singular and the logical universal have to be explained in terms of  f o r m  (as the primary instance of Entity), which is neither singular, nor universal. This form is the  what-IS-Being,  eternal (as expressed by the "IS"), unchangeable, ungenerated. As prior to the composite it is prior to the changeable singular, and so prior to time, for time follows upon change. For that reason the form is timeless, and can be rightly called the  what-IS-Being.  It always and necessarily is the Being of the thing. From it everything else in the thing derives Being. The sensible (matter-form) composite can be understood either singularly or universally. As singular it is Entity. As universal it is not Entity.
All this also decides the problem of the principle of individuation.
Because in the Aristotelian metaphysics the substantial form is in itself not universal, there is no need to posit a principle of individuation, in order to render the composite individual. The composite is already an instance of 'a this'. (From a slightly [or maybe not so slightly] different perspective one can assume that a principle of individuation is needed to account for the individuality of material beings :  See the document  Principle of Individuation  in the first Series of documents in First Part of Website ).
The (matter-form) composite, as singular, is 'a this' (second instance). The form, as separate (in notion) from matter and composite, is likewise 'a this' (first instance).
'A this' cannot be a universal or a quality, it is something determined, and belonging to the first (Aristotelian) category (while quality belongs to the third), either as singular (it then is the composite), or as a form considered without matter (it then is its primary instance).
The form is the cause of Being, and the principle according to which things different in number are one in species. The form should therefore explain Being. It should be the cause sought by the science of Beings according as they are Beings. It should be the basis of universality in that science. Yet the form in itself is not a universal. It is 'a this', without being a singular. It is the actual expression of the singular composite (that is, it is the act of the singular composite), and so enters into a  per se  unity with the individual thing. In this way the most fundamental aspect of the problem -- the relationships between individual, singular, form and universal -- is solved. The relation of form and individual thing has been made clear. If the English word "individual" may be used to render both senses of 'a this' (which senses are :  (1) secondary instance :  singular composite,  (2) primary instance :  [substantial] form),  it will allow the solution to be stated in a more modern fashion :
The Aristotelian form is individual in itself, and is the cause of the individuality in the singular thing of which it is the act. In this two-fold way form and individual coincide. Form and singular thing are respectively the primary and secondary senses of 'a this' (OWENS, p.398/9). See also next scheme :

In the next section we will investigate how the above results influence the nature and interpretation of the Species-Individuum Structure (SIS) as a structure that pervades all material reality.

The  Species-Individuum Structure  of material Beings.

This structure was studied in the document  The Species-Individuum Structure  in the Critical Series of documents in First Part of Website .
One of the presuppositions of natural science is that any form, be it a nature, quality, quantity, but also every specific event, can in principle be repeated over several distinct cases, in time as well as in space.
So we see that material reality -- which is studied with respect to its nearest causes by natural science -- is pervaded with two fundamental aspects :  individuality  and  specifity,  that is to say :  any given specific content can in principle occur in more than one cases. We have, after Van MELSEN, A., Natuurfilosfie (natural philosophy), 1955, called it the  Species-Individuum Structure of material reality.
It is clear that this structure is in some way strongly akin to the  Matter-Form Structure  in Aristotelian metaphysics (where "matter" is either prime matter, carrying the substantial form, or the matter-form composite, carrying the accidents).
We must therefore investigate the precise relationship between these two structures.

But before we do so, we must once again consider the above mentioned 'thisness' of form, that is to say, while above we had more or less followed the arguments of Aristotle as expounded and interpreted by OWENS, we now will seek a thematic justification of the results.

First we speak about the difference between "individual" and "individuum" (that is, 'an individual').
Any given aggregate, for example a solution of salt in a volume of water, but also a granite pebble (consisting of mineral grains), is individual, but it is not an individual, that is, it is not an individuum. It is a collection of individuals (molecules or mineral grains) which did not come together according to a definite repeatable pattern, that is, they did not come together according to some intrinsic law. The individuality of the aggregate is the case in virtue of the fact that the aggregate ultimately consists of true individuals (molecules, crystals). So an aggregate is individual only  per accidens.
In the following we will speak only of something being  individual,  or of  individuality.
Any existing material thing is individual. Such a thing is either a genuine substance (in the metaphysical sense) or an aggregate of such substances, so we can confine our discussion to substances, that is, to any given substance (because, as has been said, an aggregate is individual wholly in virtue of its constituent substances [in the metaphysical sense] ).  Such a given substance is, for instance, a given crystal. It is metaphysically composed of prime matter-informed-by-a-substantial-form,  necessary 'accidents' (properties) and contingent accidents (states), and is, as has been said, individual (in the present case it is also an individuum). It is embedded in an environment and subject to environmental conditions. The accidents are ontologically dependent beings which manifest the  prime matter - substantial form  composite (matter-form composite for short), that is to say, they render this composite observable. But because the necessary accidents are directly implied by the matter-form composite, and the contigent accidents follow from the interaction of the composite with the environment (where the composite always reacts according to its nature), the individuality of the thing flows from the matter-form composite, that is to say, already the matter-form composite is individual.
But where, in the matter-form composite, does the individuality come from? Does it come from the (prime) matter, the (substantial) form, or does it come only from the composite (that is, not until the composite has been formed)?

Individuality means :  in se  undividedness (where "in se" means :  "in itself") and even per se  (that is, in virtue of itself)  indivisibility,  and  separateness (dividedness) from other(ness).
Or perhaps better :  In se  undivided and indivisible content, separate from other content,
where  "separate from other content"  is two-fold :  (1) separateness and (2) repetition, or, respectively,  (1) separate from different content and (2) separate from identical content.

So when investigating individuality and its necessary conditions we must consider  in se  undividedness and indivisibility, and separateness from other(ness)  (both senses of"otherness" as just described).
Prime matter cannot be individual (and then passing it over to the composite), because prime matter has by definition no content. It can (therefore) not form boundaries in either space or time. So it cannot, all by itself, bring forth separateness, neither qua content, nor spatially or temporally (because spatial or temporal separateness must involve in-between contents).
Form, as it is in itself, that is the form separate in notion, as well as matter (in the metaphysical sense) is undivided in itself (but, matter is divisible, while form is not). And when the form turns out also to be separate from other(ness), it would be truly individual. Let's inquire into that.
A given form is separate from another form, if the latter differs from the former according to content. And two equal forms (equal with respect to content) can coexist --  and thus be separate (otherwise they would be one form) in space and time, meaning that the form can be repeated, either in space or in time --   o n l y  when they are separated by a third form that is different from them with respect to content.
So here we have the beginnings of the ability, possessed by the form, of repetition and separateness :

Repetition of form A in space. Repetition implies separation. Separation in space is accomplished by the insertion of form B spatially between A and A, where form B serves as a spatial boundary between A and A.

Repetition of form A in time. Repetition implies separation. Separation in time is accomplished by the insertion of form B temporally between A and A, where form B serves as a temporal boundary between A and A.

But it is also clear that for all this  a  substrate  is needed. This is because we must be able to say that, in the case of spatial repetition and separateness, the substrate is here actualized by form A, and there actualized by form B, and (farther) there actualized by form A.
In the case of temporal repetition and separateness we must say that the substrate is now actualized by form A, then actualized by form B, and (further) then, finally, actualized by form A again.
And this substrate is either prime matter (when the forms are substantial forms), or the matter-form composite (when the forms are accidental forms [properties, states] ).
Here we have dealt with the possibility for some form to be repeated, that is being separate from identical content. But the conclusion equally well applies to the possibility of separate from different content, because that is already implied :  The substrate is here actualized by form A, and there actualized by form B. And also :  The substrate is now actualized by form A, then actualized by form B.
So to fulfil the condition for the possibility of separateness and repetition (and thus of separatenes from other(ness)), the form needs a substrate. This substrate is, as has been said, either prime matter (when the form is substantial), or the matter-form composite (when the form is accidental [a property or a state] ).
In itself the form is undivided and undivisible -- first condition (met) for individuality.
The possibility of repetition of one given form (separate from identical content [by insertion of a different content) and the difference in content of the given form  with respect to another form (separate from different content), together constitute the  separate from other(ness)  -- second condition (met) for individuality. This second condition needs matter to be present as a substrate of the form.
So indeed a form, any (type of) form, can be individual, but not wholly in virtue of itself, it needs matter. So when 'a form is (said to be) individual' it is already a matter-form composite, and the individuality of the latter implies separateness from other(ness), which in turn means that the composite is singular. And this aspect of being singular comes necessarily from matter. So when something is singular it contains matter, ultimately prime matter.
But for the composite to be indivisible-and-undivided-in-itself, that is, in itself to be undivided and indivisible content, does not require matter. It can not come from matter, because matter as such is divisible. When a composite is divisible, it is so in virtue of the matter. Its content is not divisible. The form alone suffices for indivisibility and undividedness. The form is  in se  and  per se  (in itself and by itself) undivided and indivisible content. And to be undivided-in-itself (not necessarily also to be indivisible) is to be  'a this'.  So the composite is 'a this'. And especially the form is 'a this', and only 'a this'. Its  in se  undividedness is expressed in the strongest way.
The two aspects of individuality -- in se undividedness,  separate from other(ness) -- precisely correspond to 'a this' and being singular. The aspect (of individuality) representing a stronger instance of undividedness, namely indivisibility (of content), is compatible with being 'a this', but does not contribute any further for something to be 'a this'.
The matter of a composite is 'a this' only in virtue of the form, so also the composite itself. So the 'a this' of the matter of the composite, and the 'a this' of the composite itself, are secondary instances of 'a this', while the 'a this' of the form is the primary instance. This form is the substantial form.
The same applies for any accidental form, but here only  per accidens.
Prime matter cannot, all by itself, be 'a this', because it is totally indeterminate. It is not undivided content. Only as actualized by the form is it 'a this', but then it is the composite. And only the composite is truly individual, because it is at the same time singular (in virtue of the separateness made possible by the matter as substrate), and 'a this' (in virtue of the  in se  undividedness of the form).
Individuation thus needs matter and form.
Although  form-separate-in-notion, that is the form as an intelligible unit of content, is already 'a this', it is not yet individual. For this it needs matter, it must be actualized matter.
So matter is the  p r i n c i p l e  o f  i n d i v i d u a t i o n  after all.
And indeed, because all things, and that is all matter-form composites, are individual, the form, as it resides in such a composite, but considered in itself, cannot be a universal, which means it cannot actually be a universal (it is only potentially a universal). But at the same time it cannot be individual either, because it as such lacks matter, and thus lacks singularity, and so lacks -- as it is in itself -- separateness from other(ness), which is a necessary condition for something to be individual. So the form is neutral in this respect, it is just 'a this'.

Above we spoke about  undividednessindivisibility  and  sepateness from other(ness)  as the conditions to be met for something to be individual. Let us consider the condition of  indivisibility  in more detail, because we could ask whether this condition is really necessary for something to be individual, and if so, we should ask in what respect it is to be indivisible?.

The expression :

something is individual "

is equivalent to the expression:

some specific intelligible content is individual "

and any specific intelligible content is not divisible, because it is immaterial.

This argument would be true, if (1) indeed in this context the only alternative for "something" is :  "some specific intelligible content", and (2) if it were true that a specific intelligible content can be truly individual. Above we saw that this is not the case just like that. Let's dig deeper into this question.
Although an existing material aggregate (i.e. a [material] unity per accidens) is individual, it is not of itself individual, because it has no self. The aggregate is nothing more than its elements. Their aggregation has external causes, and thus the aggregate has external causes. So the individuality of the aggregate is not its own, but comes from the individuality of its elements, which ultimately are  per se units, possessing individuality all by themselves. Each one of these elements is truly individual, and carries a specific intelligible content of which it can be asked whether it is individual too. So the individuality of an aggregate can be reduced to that of its (ultimate) elements, and the per accidens intelligible content of the aggregate can be reduced to the per se intelligible content of its ultimate elements, and questioned as to its individuality. But, to be more precise, such a content or form can be called "individual" only in the sense of "individualized", and it is individualized in virtue of its being associated with a substrate that carries it. And such a substrate is matter. But then it is the composite -- not the form -- that is individual. The form is not individual by itself, but only as the act of matter.
Indeed, as explained above, it is only the composite of substrate and specific intelligible content that is truly individual.
Is such an individual composite then not only undivided but, moreover, also indivisible?
A prime matter-substantial form composite is a structure. Normally a structure is a certain definite configuration of parts, like, for example, a given machine. A machine is composed of parts, which each for themselves exist independently, and lie outside each other. But because the cause of the machine -- as structure -- is extrinsic (it is designed and made by humans), it is not a true substance (in the metaphysical sense), not an intrinsic structure. So it is an aggregate, albeit of a special kind. It is divisible -- it can be disassembled into its constituent parts. As (specific) machine, however, it is not divisible, because the result of such a division, that is the disassembled machine, is not that (specific) machine anymore. And this indivisibility is to be expected, because the specific machine is in fact the intelligible content of the aggregate that is called a machine.
A true substance, on the other hand, is, first of all a prime matter-substantial form structure, that is a structure consisting of a configuration of matter and form. But as structure it is of an entirely different type than the structure of a given machine. Both matter and form are not parts lying outside each other :  Prime matter cannot exist without some substantial form by which it is actualized, and a substantial form cannot exist without prime matter as its substrate. So a matter-form composite is as matter-form structure inherently indivisible, that is, indivisible as to matter and form as its parts. But it is also indivisible qua intelligible content, because this content is the one substantial form which cannot be divided into 'parts'.
But a prime matter-substantial form composite is itself in turn a substrate -- thus a matter, a substrate namely, for the whole set of determinations (accidents) that make it manifest and observable. It cannot exist without determinations. Indeed, part of the determinations (properties) necessarily flow directly from the prime matter-substantial form composite, while the other determinations (states) flow from it in virtue of its interaction with the prevailing environment, an interaction wholly according to its nature. All this results in an observable structure of the fully-fledged substance (in the metaphysical sense). But, like the prime matter-substantial form composite, its parts are not entities that exist ontologically independently. They are just determinations. The structure of the fully-fledged substance is not a configuration of material parts, each ontologically independent, but of qualities, quantities and relations. It generally is a heterogeneous continuum  (discussed and explained in Part XXIX Sequel-33 of  Fourth Part of Website ). And such a continuum, like any other (type of) continuum, is, although undivided in itself, nevertheless divisible.
What is not divisible, however, is the intelligible content of the substance, like 'machine' was in the case of human artifacts, because it is immaterial. That is, although the fully-fledged substance can be conceptually divided into, say, its several different determinations, all the determinations can be reduced to the prime matter-substantial form composite (and ultimately to the substantial form), and this is, as established earlier, intrinsically indivisible qua intelligible content. So in this sense, and only in this sense, the substance is by itself indivisible. The  divisibility  of the prime matter-substantial form composite and of the fully-fledged substance, stems not from the composite as such, or from the fully-fledged substance as such, but from its matter.

So the conditions for something to be  per se  individual are :

A form, as it is in itself, does not meet these conditions, because it is not without exception separate from other(ness). Complete separateness of a form includes separateness, not only from a different form but also from the same form, i.e. it includes the ability of repetition. And because certainly for this latter ability a substrate for the form is needed, the form does not possess this ability all by itself. The form is not individual, but, because it cannot be a universal either, it must be neutral in this respect. And because a form is undivided in itself it is 'a this', which we can now characterize as neutral with respect to individuality--universality.

Let us now apply these findings to crystals.
Any given crystal is  per se  individual. It is also a true individuum, because it is a true substance (in the metaphysical sense), an intrinsic unity, an intrinsic being.
Let's consider an ice crystal.
Such a crystal is first of all a prime matter-substantial form composite. The substantial form is the relevant dynamical law (specific crystallization law). Because the substantial form of our crystal inheres in matter, the dynamical law inheres in the water molecules making up a volume of supercooled liquid water, and later making up the ice crystal. The specific crystallization law is separate in notion, that is its intelligible content is apart from prime matter. As such this law, that is the substantial from, is, as is clear from the above discussion, not only  in se  undivided, but also, as intelligible content,  per se  indivisible. It is, however, not  separate from other(ness),  because for that it needs matter. So the crystallization law is not individual. But because it is  in se  undivided, and moreover residing in an individual substance (the given ice crystal) and thus not being a universal, it is 'a this'.
What about the indivisibility of the crystal?
The substantial form (crystallization law) immediately expresses itself as :  Space Group plus chemical composition. Both are properties, in the sense of necessary accidents (propria). They represent the crystallization law. A crystal can be cleaved. Each piece of cleavage still has the internal symmetry as described by the Space Group of the original crystal. Also the chemical composition is the same in those pieces as it was in the original crystal. So, in contrast to a molecule, a crystal can be divided, without loosing its identity or nature, thanks to its periodic structure. What cannot be divided, however, is the crystal's specific intelligible content (crystallization law), even as it is expressed by its  Space Group plus its chemical composition. And, in addition to this, the crystal's intrinsic shape cannot be divided, because it is an intelligible content too. And if we transform this latter intelligible content, which is an intrinsic intelligible content, intrinsic with respect to te crystal's nature or essence, into the actual intrinsic shape of the crystal, that is the intrinsic shape as actually realized, then the crystal is indivisible, despite its periodic structure. This is because also the actually realized intrinsic shape is a specific intelligible content.

But is  indivisibility of intelligible content  a  necessary  condition for something to be truely individual, or is it either always implied or not necessary at all? Let's look into this question.
If we look -- to take an example -- at a quartzite rock or pebble, where we have in mind that variety of quartzite consisting entirely and exclusively of the mineral quartz  ( SiO2 ),  which is present in the form of very small deformed crystals, that is :  quartzite is a microcrystalline aggregate of quartz. All the quartz crystals are tightly packed together, that is they are interlocked and fused together, but not according to some specific ordering or specific pattern.
We can say, therefore, that the quartzite pebble is  in se  undivided, and of course it is separated from other(ness). Is it divisible? Yes it is divisible :  We can divide it macroscopically without destroying its actual intrinsic shape, because it has no intrinsic shape. Its shape is always extrinsic. The fragments, resulting from such a division, are still each of them (volumes of) quartzite (like the cleavage pieces [or whatever macroscopical fragments] of a crystal are specifically still that crystal [fragments of ice crystals are still ice crystals] ).  So the divisibility of quartzite is more complete than that of a crystal. We can also say that a crystal is  indivisible,  because is not divisible in all respects -- it is not divisible as to its actualized intrinsic shape, while a quartzite pebble is  divisible, because it is divisible in all respects. And this could mean that also its specific intelligible content is divisible. But we know that such a content is not divisible. So we can conclude that in the case of a quarzite pebble there is no genuine specific intrinsic intelligible content to be found. The 'specific intelligible content' could be divided simply by the fact that it was not such a content at all. The individuality of the quartzite pebble is totally derived from that of its constituent quartz crystals. And only the latter possess true individuality :  They are  in se  undivided, they are (in all respects) indivisible (including their actual intrinsic shape), and separate from other(ness).

It is important to note that the difference qua individuals (the difference of, say, two identical drops of water) is not a difference in either position or place. Of course it is true that with this individual difference also a difference in place, position or time is given -- by which we can at all distinguish between individuals that are identical in all other respects --, but these differences are not the cause, but the effect of the difference qua individuals. For if we would interchange the places of those individuals, the latter would not be interchanged. After all, both individuals possess, in virtue of the fact that they are specifically identical, the same capacity to take each other's place, without them ceasing to be two individuals.

Having considered concrete examples concerning  the Singular, the Individual, Individuality, the Form as 'a this' or neutral entity, and  the Universal,  we are now ready to discuss the  Species-Individuum Structure,  that pervades all of material reality.

The Species-Individuum Structure.
In the document  The Species-Individuum Structure  in the Critical Series of documents in First Part of Website  we discussed this structure as being a fundamental presupposition of natural science, that is, of its main method, the inductive method (which consists in generalization on the basis of singular findings). It is presupposed that a given intelligible content of a material entity can, in principle, be exactly repeated in nature or in experiment. Based on this possibility we can formulate natural laws. We also discussed the possibility that any such given intelligible content of something does not (and never) repeat itself exactly, but can repeat itself in an approximate way. When this is so, then natural science, and its inductive method, is still possible when the range of variation (which must be random) easily falls within the range of exactitude of observation and measurement. Also we discussed the possibility that the Species-Individuum Structure is not an ontological structure at all, but just a cognitive structure.
Because (1) the Species-Individuum Structure is so pervasive (either in its exact form, or in its approximate form), (2) it provides much justification for Aristotelian metaphysics (because it assumes natures), and (3) it deepens our insight in  individuality,  form,  the universal,  etc.,  it is paramount to address the above questions, and thus to dig deeper into the essence of the Species-Individuum Structure. And the best way to do this is by paraphrasing the text of its discoverer, A. van MELSEN, in his book Natuurfilosofie (natural philosophy, in Dutch), 1955, pp.14. We will do that in due course.
Even if we limit ourselves to material things, natural science cannot cover it all, which here means, not because of the fact that there is such a bewildering multitude of things and processes, but in principle. This is so, because natural science is necessarily based on certain presuppositions, that is fundamental presuppositions which are such that without them natural science is not even possible in principle, and which cannot therefore be discussed or questioned by natural science itself, that is by natural science as empirical science (which means that it starts from observation and experiments, and verifies its theories again by observation and experiment). Therefore there must be another science -- not an empirical science -- that must be able to deal with these fundamental presuppositions. And this science is natural philosophy.
Van MELSEN is very clear and instructive on these points, and we cannot do better than to present his views in the form of a rough translation, including unannounced amendments and supplementary remarks, of long portions of his text, pp. 14.


Natural science is based on presuppositions
It is without doubt that, notwithstanding the enormous development of natural science since the 17th century and its wonderful achievements, we can still speak of a certain factual insufficiency of natural science. After all, every solution of old problems raises new questions. The unveiling of the secret of the actually occurring chemical compounds puts new facts before science, namely those of atomic structures, in turn demanding an explanation. So it seems that the horizon of the task, which natural science has set for itself, recedes further backwards after every success. It turns out that natural science will never be able to reach some definite end point, it always is just under way.
But what interests us at the moment is neither this  de facto  insufficiency of natural science to solve all problems within its domain, nor the fact that it is always under way. All this has to do with an insufficiency of natural science within its own domain.
We are focussing instead on a different sort of insufficiency, namely on an  in principle  impossibility to even only bring up, or enter upon, certain problems as regards the material world (which world is nevertheless the proper domain of natural science). So as regards such problems natural science can only have, or start from, unquestioned  presuppositions.  What are these problems? To answer this question a short analysis of the most fundamental and general of methods of natural science is necessary, namely the inductive method.

The presuppositions of the inductive method.
The inductive method pervades all of natural science. It consists in generalizing certain individual findings.
The application of the inductive method supposes something, to which we normally pay little attention, but which is of decisive significance for this method.

The inductive method, namely, presupposes that the behavior of the various material phenomena is controlled by their  n a t u r e,  that is, that this behavior is in principle the same under different circumstances, meaning that  A  always gives behavior  A'  under circumstance  B,  always gives behavior  A"  under circumstance  C,  always gives behavior  A'''  under circumstance  D,  and so on.

If this were not so, then it would be impossible to conclude something as regards the phenomenon in question by means of varied experiments in which the visible behavior is different.
If we -- to take a school example -- want to know something about the specific factor in the air, which is responsible for combustion, then we will do experiments under varied circumstances. We will, for example, take several smouldering chips of wood, and see what happens when we place them respectively in air, in pure oxygen, in pure nitrogen, and in pure carbon dioxide. The result turns out to be that the chip of wood keeps smouldering in air, flares up in oxygen, and go out in both last cases. The conclusion is evident. It is the oxygen that is responsible for combustion. But it is not this chemical aspect of the conclusion that interests us at the moment. There is something else, that is much more important, namely that the chemist can draw his conclusion only under the tacit supposition that wood behaves, under all circumstances, according to its nature. Each of the four chips of wood does represent the same wood-nature, despite the fact that they are four different individual chips of wood. The fact that these individual chips of wood behave differently under the circumstances of the experiment, doesn't alter the fundamental datum that ultimately a same way of reacting according to the one wood-nature lies at the base of these different behaviors. If we would doubt it, the whole conclusion would lack any base. In that case, namely, the different behavior of the four chips of wood then could be ascribed to their different individualities. There would be no binding factor making the four experiments with the four chips of wood to refer to the same wood.
One could, however, object that while it is of course true that in the above series of experiments one must assume that all chips of wood, used in the experiments, indeed possess the same wood-nature, but that this is not at all a presupposition that lies outside the domain of natural science, as suggested. On the contrary, so one could argue, for the experimenter it cannot be enough to suppose that he is dealing with four chips of wood of the same sort. He must be certain that this is the case. If needed he should obtain this certainty by means of experiment.
The answer to this objection is very simple :  It without doubt belongs to the task of the experimenter to obtain that certainty, but it will turn out that he can get this certainty only on the basis of the presupposition with which we are presently dealing.

The necessity of the presupposition.
Let us inquire into the means that are to the experimenter's disposal in order to be sure that the different 'chips of wood' are all wood. We then immediately see that these means include induction, because every experimental means necessarily includes induction. Every experimental means supposes the correctness and probative value of the method of induction, and therefore also (the correctness of) the fundamental presupposition of all induction, namely that entities of the same nature behave according to that nature under all circumstances.
Let us elucidate this a little more. All means that are to the chemist's disposal, when he wants to check whether the involved chips of wood are indeed the same wood, ultimately boil down to investigate whether the 'chips' do have certain relevant properties, that is properties characteristic of wood, in common. But by doing this the chemist supposes that the different chips will indeed always and under all circumstances behave according to these properties. If this were not tacitly assumed, then there would be no reason whatsoever to believe that the properties that are found to be present in the test chips will also appear later during the experiments, that is, be present in those chips (or those parts of the same chips) that are going to be used in the experiments.
Indeed we can go further. It is evident that without the presupposition with which we are presently occupied, the scientist is even not able to use his scientific knowledge. For let us suppose for a while that our chemist is a very critical scientist, not being convinced by the wood-like features that are externally displayed by the chips, and being prepared to conduct a chemical analysis  ( For the time being, we set aside that he is compelled to use parts of the chip, which cannot be used for the later experiment anymore. Indeed, they are consumed by the analysis, and he must again assume that these parts that were used in the analysis are representative of the chip as a whole). What will such a chemical analysis teach the experimenter?
The result will finally boil down to the fact that the chemist obtains chemical substances (condtituents of wood) having certain properties. From these he concludes as to the presence of certain chemical elements in those substances. For this the chemist makes use of tables of atomic weights and certain reaction equations. In this way he uses the atomic weight of Carbon and the molecular weight of carbon dioxide. Now it is important to realize that nowhere in his tables and reaction equations is spoken about the individual carbon with which he deals at the moment. All tables and equations speak of Carbon just like that, that is, of just "Carbon". All his data are expressed in general statements :  Carbon is characterized by this and that properties, carbon dioxide by this and that, etc. Everywhere it concerns carbon as carbon, nowhere does it concern those particular individual carbon atoms, that are present in his chips of wood that he is now investigating. Rightly the chemist is convinced that all that is indicated as characteristic for Carbon, refers to all individual cases where carbon is present. But -- and this is paramount :  this conviction rests on a very determined presupposition, that accompanies his entire investigation, namely the presupposition that all carbon behaves in the same way.
The result of our philosophical analysis can thus be formulated :  Without doubt it is the task of the chemist as chemist to enquire in concreto whether certain given individual things (in our example "chips of wood") belong to the same species (that is, whether these chips really are chips of wood ).  However, his method of inquiry necessarily presupposes, albeit implicitly, that in the world there are things of the same nature and that such things ultimately react in the same way in virtue of that nature.
[Here we touch upon the nature of causality. Further, we can, on the basis of  same nature-same behavior  set up natural laws].
Only in virtue of this presupposition it is legitimate to judge that certain different individual things or events are representative of the same purpose. They represent the same specific nature, although they differ as individual (that is, qua individuum). Indeed, the carbon of which one at the time had determined the atomic weight is not the same individual carbon that played a role in the experiment of our chemist.
Our presupposition can therefore be expressed in yet another way :
Natural Science supposes that individual things and events can be classified according to certain species.
Or shorter and more terse :
The material world (which is the subject of natural science) has a Species-Individuum Structure.
Every single material thing or every single material event at the same time represents a species
[Such a species or nature does not necessarily to be non-reducible, that is, many of them will be reducible to more fundamental natures, as is, for instance, the case in aggregates :  the nature of a given aggregate is reducible to that of its (ultimate) elements. That such a fundamental and ultimate nature is already found in the atom, the molecule, the crystal, and the organism, is a tenet of Aristotelian metaphysics, and cannot be decided by our finding that the material world is completely pervaded by a Species-Individuum Structure, where the species aspect of this structure can refer either to the substantial form, or to some accident (specific property, or specific state), or to a type of event].
Only on the basis of this presupposition the inductive method makes sense. So our supposition cannot be proved or questioned within natural science. It is a supposition that is, so to speak, incarnated in the fundamental methods of natural science, and which we can justifiably call a  presupposition,  because it precedes every scientific investigation.

Natural Science itself cannot bring its presuppositions up for discussion.
Just the fact that a presupposition is incarnated in the fundamental methods of natural science, makes its questioning within natural science impossible. After all, every discussion within natural science must make use of the methods of natural science, and it is precisely these methods that include the presupposition.
Many a scientist, who has followed the above analysis of the implications of the inductive methods, will, however, be inclined to say :  let it be true that natural science cannot prove its presuppositions or bring them up for discussion,  but is this necessary? Is just the success of the inductive method not sufficient to justify any presupposition? What else is needed? Indeed there is some truth in this line of thought, but one should realize that with this  in fact a justification of the inductive method is presented which lies outside the domain of natural science, for the argument presupposes that success is proof of the correctness or truth, and whatever may be the value of this statement, one thing is clear, and that is that there cannot be presented a scientific proof (a proof by and within natural science) of it. On the contrary, every scientific proof presupposes the truth of this statement. After all, a hypothesis is considered to be true or correct, if it succeeds in predicting certain phenomena. With this the hypothesis is deemed to be proven. Success, therefore, is precisely the reason why we attribute to a scientific proof probative value, and the presupposition that lies at its foundation must originate from something else rather than from natural science itself. Success demands, in order to be success, that things and events conform to the Species-Individuum Structure, because the latter structure implies the possibility to predict, and when such prediction comes true, we have success. So success presupposes the Species-Individuum Structure (SIS) rather than the other way around :
Presupposition of SIS ==> Possibility of prediction ==> (possibility of) Success.
There is yet another agument for that matter from which it is evident that the reason why natural science presupposes the Species-Individuum Structure (SIS) cannot ultimately lie in a possible success of natural science. Indeed, natural science doesn't have any choice with respect to the presupposition of the SIS. It must accept this presupposition. If it doesn't do this it cannot carry through any classification or induction. By the same reason it would not be possible to draw up any regularity, natural rule or law. Without this presupposition there would be just a vast quantity disparate experiences, whithout any connection. Every particular experience would have a content that would be totally separate from that of any other experience.
Therefore our conclusion must be that the presupposition of the SIS must originate in some  pre-scientific knowledge, a knowledge that is already at man's disposal before he can even begin with natural science. This origin is not hard to find :  that the material world possesses a SIS is already teached by the most general daily experience. So it is that the presuppositions of natural science are nothing else than the presence, within science, of certain basic data, derived from the daily, pre-scientific familiarity with the material world. Thanks to this familiarity and to that what is experienced in it natural science is only possible.

The difference between fundamental and other presuppositions.
In order to avoid a certain misunderstanding concerning the nature of the presupposition with which we are presently dealing, it is instructive to point out that we are speaking about a presupposition of natural science as such. Not at issue are presuppositions that only refer to one or another special scientific theory. So in biology, for example, it is presupposed that the general physical and chemical laws also hold for living beings. Biology does not study these physical and chemical laws, it only applies them. In the same way in all areas of natural science it is supposed that the law of energy conservation holds. When such a supposition turns out to be wrong -- as sometimes happens -- then the only effect is that the law in question is changed. There is no way that natural science as such is being questioned. As regards the presuppositions we are talking about, on the other hand, natural science as such is at issue. If the presupposition of the Species-Individuum Structure would turn out to be wrong, every possibility of scientific work and endeavor will come to a halt, because then the basis of the very scientific method is removed. Therefore natural science does not have any means at its disposal to verify this kind of presuppositions. For at the moment the scientist would begin to question such a presupposition, and in order to verify it would discard all methods based on it, then every method of natural science would have to be discarded, the theoretical as well as the experimental. Within natural science not any possibility of enquiry would be left.

Conclusion of the above discussions.
So the fundamental presuppositions of natural science (where the SIS is one of them) confront us with a very interesting problem concerning the structure of the material world, which (problem) totally lies outside the domain of natural science, that is beyond the range of scientific possibilities of enquiry. This, by the way, does not mean that natural science neglects this structure. Indeed, natural science constantly presupposes this structure when using certain fundamental methods of enquiry. But natural science is not able to explicitly involve this basic structure of the material world in its discussions. It is this fact that justifies us to speak of a certain insufficiency of natural science.


( Van MELSEN, pp.21 )

Scientific and pre-scientific knowledge.
From the fact, that certain problems concerning the material world fall outside the range of natural science, does not, of course, mean that they fall out of the domain of human knowledge all together. Indeed, natural science takes its presuppositions, from which we read off those problems, from pre-scientific experience. Therefore this experience must have a certain grip on the presuppositions of natural science. The question to which we must now turn our attention is whether study of such presuppositions can result in a systematic body of knowledge about certain aspects of the material world, a body of knowledge different from that of natural science.
Pre-scientific knowledge generally is knowledge as is present in daily experience. Natural science always departs from such knowledge, that is from experience of daily-life phenomena, such as the freezing or evaporation of water, the combustion of wood, the rusting of iron. It doesn't deny them, but purifies their daily-life descriptions and classifications from all kinds of accidental or even misleading elements. As natural science progresses this purification process is intensified. When purified and definite conceps of phenomena and variables are finally obtained the seach for near causes can be improved. So natural science transforms pre-scientific experience into the more refined scientific experience.
But now we can ask :  Does all pre-scientific knowledge in every respect relate to scientific knowledge as primitive knowledge to the more refined and mature knowledge (which latter is developed primitive knowledge)? This is the decisive problem with respect to the very possibility of an autonomous metaphysics of the material world. Is the answer to the question yes, then there is no other way to nature than through natural science.

Primary and primitive pre-scientific knowledge.
Natural science develops initial knowledge, and thus, in its investigations, transforms primitive pre-scientific knowledge into evermore refined scientific knowledge, but, as we have seen, it must, just for the sake of these investigations, take up certain aspects of the pre-scientific experience without critique. One of the data that are, as it were, in this way forced upon natural science is the Species-Individuum Structure of the material world.
This fundamental fact compels us to make a distinction in the body of pre-scientific experience. We will distinguish between primitive and primary aspects. The primitive aspects therefore are those that are not only open to scientific enquiry, but also need this enquiry, in order to develop. On the other hand, the primary aspects are those that must simply be accepted by natural science if it wants to be natural science at all.
The primary pre-scientific experience is that part of experience that refers to a fundamental pattern of the material world, while the primitive knowledge fills this pattern with a definite specific content (and this primitive knowledge develops further and further). Both aspects of experience always are present together. They are not separate areas of experience as we do see it for instance in the experience of a sailor and of a clerk. The result of this going together is that the data of all experiences possess the same fundamental pattern, the same structure, irrespective of their specific content. And it is the specific content that is primitive, that must be developed further. That, for example, the phenomenon of combustion, already known in every-day experience, is not a unique event, but a phenomenon that takes place many times, is taken for granted also by natural science. That is not what it investigates. Its enquiry is aimed at the specific content, saying what combustion in fact really is. It investigates what is essential to combustion and what not. And thanks to the enquiry as to what combustion really is, that is as to the specific content of combustion, it has developed a concept of combustion which is much better suited to order the combustion phenomena than the pre-scientific concept is. The presence of flames, for instance, which is an essential part of the pre-scientific concept, is no longer essential to the chemical concept of combustion. Why not? What has motivated the chemist to not including the aspect of flames -- which is after all such an evident datum in the original experience -- in his definition of combustion? It is because the chemist has discovered that the property of "the bonding with oxygen" is much better suited for a systematic description of the phenomenon than the appearance of flames. And such a refined concept can still be relatively primitive :  the concept of combustion as "the bonding with oxygen" looks, in a broader context than just elementary chemistry, still rather primitive (it can be further developed along the lines of energy transport and conversion involving electrons).
Although one must justify the mistrust of the scientist as regards the pre-scientific experience, that doesn't alter the fact that when this attitude refers to all aspects of this experience, it cannot in this form be justified. It cannot, in the name of natural science itself. This is because in all cases there is at least one exception to be allowed with respect to these pre-scientific experiences, namely for that part of it that enters into natural science as its fundamental presuppositions.

The object of the metaphysics of the material world.
The formal object (or subject as it was expressed in earlier times) of the  metaphysics of the material world  [which, in the present website, refers to inorganic as well as organic beings, including human beings]  can, on the basis of the above discussion, be determined as follows :
The metaphysics of the material world -- which includes ontology, the study of ways of Being -- studies that fundamental structure of material reality which makes material reality to be precisely  material reality,  and in virtue of which material reality can be the object of scientific enquiry.
Materially its object coincides with that of the collective of all natural sciences (physics, chemistry, biology, etc.), but formally it differs from it because the metaphysics of the material world occupies itself exclusively with those aspects of the material world which are already presupposed before any scientific enquiry has taken place, that is, presupposed by the fundamental method (induction) of natural science, and thus as such fall outside the formal object of natural science.
So both natural science and the metaphysics of the material world have their point of departure in the daily experience and familiarity with the material phenomena, but each of them studies a different aspect. Metaphysics studies the primary aspect of what is given in daily experience, while natural science concentrates its attention to the more detailed content of that same daily experience. And this content has a primitive character as we saw above.

Mutual independence of metaphysics and natural science.
The sharp formal distinction that exists between metaphysics (of even already the material world) and natural science results in the fact that the respective ways of viewing things of both sciences ultimately have little to do with each other. The specific results of natural science do not contribute to the solution of the proper formulation of the metaphysical problem.
[We must realize, however, that even already in the context of just investigating the material world -- thus apart from the connection that exists between natural science and metaphysics-as-a-philosophical-background-of-natural-science -- there is no complete independence of metaphysics from natural science. That is, while legitimately claiming the Species-Individuum Structure of material reality, a claim that cannot be refuted by natural science, metaphysics has other claims that could be refuted by certain particular results of natural science. Aristotelian metaphysics, for instance, claims that reality cannot totally and exhaustively be reduced to certain basic entities below the level of the (chemical) atoms. It claims that the atom cannot be totally reduced to its constituents (so-called elementary particles, or wave packets for that matter). It further claims that the molecule cannot be so reduced to its constituent atoms, the crystal not to its constituents, and, finally, that the organism cannot be wholly reduced to its chemical constituents and chemical processes. In other words, Aristotelian metaphysics claims that atoms, molecules, crystals, and organisms are genuine substances in the metaphysical sense, that is they are non-reducible heterogeneous continua. In First, Second, and present Part of Website we have spent a great deal of effort to investigate these claims along philosophical lines but also along the lines of the results of natural science (concerning the nature of the chemical bond and chemical compound, the nature of crystals, and the nature of organisms, that is whether these natures are reducible or non-reducible natures). Much additional enquiry along the lines of natural science is needed to finally settle this problem.
The Species-Individuum Structure applies to every intelligible content whatsoever that is part of the material world (and can consequently be repeated), which means that it also applies to reducible intelligible contents such as the 'nature' of a given aggregate. So the SIS does not discriminate between aggregates and intrinsic wholes, and cannot therefore have any bearing on the truth of the above claims about the wholeness of atoms, molecules, crystals and organisms.
At least we can say that the specific results of natural science do not contribute to the solution of the proper formulation of certain general tenets of metaphysics, because these results are obtained by methods that already presuppose the point of departure of metaphysics. That's why these results do not throw any  new  light on that point of departure. They leave this point wholly what it is.
On the other hand, the results of metaphysics, especially concerning the basic structure of material reality, that is, its Species-Individuum Structure, are of no benefit for natural science. This is because this science has already from the very beginning taken account of the basic structure (SIS) of material reality, because it always works with methods that already presuppose this structure. Reflection on this basic structure, taking place in metaphysics, has no influence on the results of natural science as to their specific value.
However, metaphysics could be significant for the view onto natural science as a whole. Indeed, a certain interpretation or view of the concept of natural law, for instance, does not touch upon the specific content of Newton's law or Dalton's law, but it does touch upon all natural laws as natural laws.
Indeed we can view metaphysics -- metaphysics of the material world -- as a philosophical background or interpretation of the results of natural science. Or, more precisely :  The metaphysics of the natural world should be such that the results of natural science are  specifications  of this (more general) metaphysics. We claim that this background is  ontological,  that is, not just epistemological in its nature. That is to say, that this metaphysical background does not exclusively express our (human) way of acquiring knowledge. Specifically it means that we claim that the Species-Individuum Structure (SIS) is an  ontological  structure. It does describe a fundamental structure of material reality, a structure independently existing extra-mentally, and upon which our ways of expression are naturally based. That we indeed claim that it is ontological is based on (1) our acceptance of  a  realistic theory of knowledge  and (2) (based) on the  application  of our theoretical understanding of material reality (laid down in the form of scientific concepts and natural laws) in all kinds of practical contexts.

Justification of the realistic theory of knowledge.
The great danger, threatening every philosophical reflection, is a certain laziness, typical of man, as a result of which one does not penetrate into the very thing that is at issue in a philosophical reflection. The proper dimension of the philosophical problem is not reached.
This is especially the case in evaluating philosophical realism. In discussing the problem of realism one does not discuss cases such as the fact that we see the sun as a disc, while she isn't a disc, or the datum known from physiology that certain artificial nervous stimuli evoke sensations of things that aren't there, from which it is then concluded that our senses are not reliable, and that it testifies to naïve realism to attribute to things the properties that we observe. Of course all of these are important problems, but they do not touch upon the proper epistemological problem (the proper problem of how we gain knowledge and whether this knowledge is, in principle reliable and objective or not). Indeed, a little thought about the mentioned examples teaches us that every adjustment of the so-called misleading sense data is introduced in virtue of that same sensible experience, because it is also sensible experiences that force us to decide that the sun is not a disc, or that something is observed that isn't there. Whatever is at stake, it is certainly not the fundamental reliability of the sense organ. For that is presupposed when we make use of scientific data  ( The interpretation of a sense datum is verified or amended by other sense data). We will in no way assert that the mentioned examples have nothing to do with the problem of the fundamental reliability of the sense organ. After all they teach us that the fundamental reliability must be sought in something else than in the spontaneous interpretation of the sense datum. We only assert that someone who has the opinion that the mentioned examples prove that the sense organs are fundamentally unreliable, shows that he hasn't seen the proper philosophical dimension of the problem at issue.
We will, albeit succinctly, try to reach the proper dimension of that what is relevant to the problem of realism. And then we could do no better then reflect upon the following statement :

Every attempt to deny in principle the ability of the human mind to know things as they are in themselves leads to a contradiction.

The main thesis of Kant provides an interesting example of such a contradiction. This well-known thesis reads :

For us true reality (das Ding an sich, the thing as it is in itself) is unknowable by reason of the structure of our mind. As a result of this structure we come to know reality only as it  appears  and not as it is in itself. The manifestation (that is, how reality presents itself to us), namely, is co-determined by the  a priori forms  of reason as well as of the senses.

Well then, this statement contains a contradiction between that what is explicitly said in the statement and that what is obviously its deeper meaning.
Indeed, the  meaning  can not be other than to convey true knowledge about the real state of affairs. The real state of affairs is expected to be as is indicated by the statement. Or, to say it in different words :  The meaning of the statement is to communicate to us the state of affairs as it really is, and not as it appears.  According to Kant we think that we know something about reality, but we are informed that this is mistaken. It only appears to be, but it is not.
All this is presented as positive knowledge, that is, we know something about certain real (not just apparent) relations that obtain between the knowing mind and reality. However, the  content  of the statement denies that we can know what the state of affairs  really  is.
So  content  and manifest  meaning  of the statement engage in a glaring contradiction. If Kant's statement were true, then there would be no reason whatsoever to express it, because the statement would not inform anything to us about the  real  state of affairs, and that is after all the only thing we (an also he) are interested.
The only way to avoid this contradiction is to accept the unknowability of reality as this reality is in itself, only in a limited form (that is, a limited form of such unknowability), and indeed in such a limited form that it in no way affects the fundamental ability of the mind to know things as they are. Having done that, the statement can then refer to certain aspects of human knowledge, but not anymore to human knowledge as such.  But now we have abandoned the non-realisic view, we now think realistically.
The mentioned contradiction can be approached yet from another direction.
If it were true what the statement of Kant (expressing his thesis) says, namely that  " the thing as it is in itself "  is unknowable, how could we possibly know that? How could we know that  " the thing as it is in itself "  is there, and that it is unknowable? It surely cannot be totally unknowable, otherwise it would make no sense to say anything about it. So also here we again stumble across the contradiction between content and meaning of the statement.

The Species-Individuum Structure is an ontological structure.
With the foregoing still not all obstacles on the way to a metaphysics of the material world are cleared. Indeed, although it may be true that ultimately only a realistic view of knowledge can be held in a consequent way, it is not then automatically implied that there is no influence whatsoever of the structure of the human mind on our fundamental views concerning material reality. So it is necessary to convince ourselves, that the general properties that are, according to the primary experience, possessed by material reality are  real  properties of material reality itself, and not of our way of knowing. How it is especially with the Species-Individuum Structure, which is presupposed in natural science, and which has such an important role to play in Aristotelian metaphysics? Would it be possible that this structure wholly comes from our way of knowing, from the structure of our minds? The answer is not so difficult. How important indeed be the role of our way of knowing and expressing things in acquiring knowledge about them, it is not clear how we ever could attain a satisfactory understanding of material reality, if material reality itself did not possess something like a Species-Individuum Structure. And it is fair enough to assert that we do have a fairly satisfactory understanding of material reality, as is demonstrated by many successful predictions.
And when we speak of a "satisfactory understanding", it is good to realize that this not only refers to a "theoretical" understanding of material reality, but also to the practical application of this understanding in the controlling of parts of the material world. Indeed, also this  application  is based on the presupposition of the Species-Individuum Structure. For it is, in this context, not only important that all theories are expressed in general propositions, but also that we do not for a moment hesitate to apply these general theoretic propositions to concrete practical situations. The confidence with which we board a plane is based on the knowledge that the general laws of mechanics, although they were not designed with having in mind exclusively this particular individual air plane, do apply to it nevertheless. And may there be lacking something in this confidence, then it is not based on the fear that something would be wrong with the applicability of the general laws, but it is based on something else, namely the knowledge that there are other general laws, according to which  every  air plane, if something is wrong with it, comes down.
The upshot of all this is that if material reality itself would not possess a Species-Individuum Structure, then we could not apply our knowledge. But obviously we can.
So the Species-Individuum Structure imbues all our contact with material reality, it is always presupposed, and if there does exist indeed some distance between theory and practise, this distance is not created by one or another limited applicability of general laws, but by the fact that every concrete situation is, as it were, the point of intersection of many general laws, while it is not always given to us to precisely know which general laws must be applied in that particular concrete situation.
In the above discussion one must not miss particularly this one point though :  What interests us is in fact never the general proposition or general law as such, but what this 'general' has to say about the concrete reality with which we are dealing. Now every concrete reality (every concrete real thing or event) is always individual. When the chemist formulates the general chemical proposition :  " silver is corroded by sulfur" then he fully realizes that there doen't exist "silver in general". Only concrete more or less pure silver things exist. The general proposition of the chemist is only applicable to reality insofar as those concrete siver things have certain properties in common. Otherwise the general proposition would not make any sense. But it makes sense to express our knowledge in the form of general propositions, because the various individual things and events indeed do behave according to a certain nature which they have in common. Their individuality also includes a common specific nature. By knowing this nature and expressing it in the form of general propositions or statements, we at the same time grasp certain aspects of their individuality.
One often speaks of a trick with respect to the procedure of natural science, which indeed unfolds things into pure cases of repetition in its experiments, in which all that is not repeatable is artificially removed. One can agree with this procedure provided one realizes that this procedure of natural science can yield success only when the structure of reality permits such a procedure. And establishing this is the same as to say that the Species-Individuum Structure in our knowledge corresponds with the Species-Individuum Structure of material reality. Things are concete, they are individual, but at the same time they have, in their individuality, certain specific properties, and this makes it possible to express in general propositions, which say something about that specific aspect, at the same time something about the individual thing.

There seems to be a certain contradiction between the use of the terms "general" and "specific" in the expression :  general propositions, which say something about the specific aspect of things. Indeed , "general" seems to exclude "specific". The contradiction is, however, only apparent. A general proposition as  "silver is corroded by sulfur"  is  general  because it refers to all siver, but it also includes something  specific  because it only says something about  silver.

It may be true that the representation and the concept (and especially the model) which natural science forms for itself of the things as to their specifity, shows signs of the human way of knowing, but this does not affect the fundamental ontological status of the Species-Individuum Structure of material reality. If it were, then those representations and concepts would be devoid of any value.

Philosophy is unavoidable.
P o s i t i v i s m.  --  An epistemological justification of a philosphy, especially a philosophy of Being (including material Being) on a realistic basis (that is according to a realistic view of knowledge) not only must deal with a non-realistic theory of knowledge (such as that of Kant), but also with one that denies the possibility of every philosophy in the traditional sense. This philosophical movement -- it is after all a philosophical movement -- is known as positivism or empiricism. Although there are many variants they all have in common the view that the only way along which man can come to know more about reality than that which is immediately at his disposal, is the way that leads to positive empirical science. Therefore a metaphysics of the material world, as will be and has been expounded on this website, and which is not constructed along the lines of natural science, can have no meaning, or makes no sense, whatsoever.
The expression "can make no sense" must thereby be taken in a very specific technical sense. It means that the statements of such a metaphysics are neither true nor false. They simply do not make any real sense, they are meaningless. The positivist arrives at this for metaphysics destructive conclusion by means of the following argument.
First he applies a principle that can be expressed as follows. In order for a statement to make sense it should be possible to indicate a procedure according to which, albeit only in principle, the truth or falsity of the statement can be assessed. This principle is in itself sound and does not rob metaphysics (or philosophy in general) of any sense or significance. However, the positivist limits the possibilities, which are at man's disposal to determine the truth or falsity of a statement, exclusively to sensible experience (observation and experiment). This means that the content of a statement in order not to be meaningless must be such that it can be directly or indirectly verified by the result of one or another sensible experience. It is this restriction, which is responsible for the opinion that positive empirical science is the only form of science that can teach us something about the real world. It is this restriction of the above mentioned general principle that makes all philosphy in the traditional sense, and thus including the metaphysics of material reality, meaningless. For although also this metaphysics departs from sensible experience, it nevertheless considers only those aspects of it which do not constitute the specific content of a sensible experience. Indeed, the Species-Individuum Structure of material reality never constitutes the specific content of a sensible experience (we cannot 'see' this structure). Therefore the existence or non-existence of this structure can never be demonstrated by positive empirical science. The enquiry of positive empirical science only concerns the specific content, that is to say, that which in one observation possibly differs from that what is given in another observation.

The same contradiction.
There is much that is attractive in this positivistic view. It could be characterized as an attempt to persuade humanity to exclusively limit itself in the activity of science to that what is more or less ad oculos (that is, by seeing it) demonstrable, and so be clear to everybody. All influence of religion, philosophy of (human) life, metaphysics, ontology and what not, which keeps humanity divided, could then be avoided within that what is called science. But, alas, the positivistic view cannot be held in a consistent way without destroying itself. The positivistic view contains a contradiction like the one mentioned above. In the case of positivism it almost assumes a visible form. Time and again positivists write books to demonstrate that philosophy has no meaning. But their own books are philosophical. Therefore their rejection of philosopy is, according to their own principles, meaningless.

Broadening of the positivistic view.
In order to avoid the just mentioned contradiction, positivism attemps to broaden the category of statements or propositions that are considered to be meaningful, such that it allows at least some legitimate space for philosophical propositions. This new brand of positivism then distinguishes between (1) propositions which directly express data of sensible experience, and (2) propositions that say something about the way in which the data of sensible experience are expressed in propositions. Propositions of the first kind belong to the domain of the empirical sciences. The most elementary type of this kind consists in propositions which express a concrete sensible experience, such as "this thing is red", "that thing is warm". Propositions of the second kind belong to logic, provided the term "logic" is taken in a broad sense. This kind of propositions does not, therefore, say anything about the real world, because they exclusively refer to the way man expresses and orders acquired knowledge.
Both kinds of propositions are meaningful, which implies that with respect to both types of propositions is can be decided whether they are true or false. The method of verifcation will, however, be different. When we have to do with empirical propositions (propositions about data of experience), then verification consists in determining whether what is expressed in the proposition corresponds to that what is evident from relevant sensible experience. On the other hand, the truth or falsity of a logical proposition totally depends on the fact whether this proposition is formed according to the rules of logic or to the rules of the language which is used in describing the data of a particular area of experience.
As to the philosophical propositions, for the positivist it is clear and determined beyond doubt that such propositions at best belong to the just described category of logical propositions, because they do evidently not fit in one or another empirical science. Philosophy, therefore, can never refer to reality, but only to the way in which we have knowledge of reality.
This positivistic view of the status of philosophy strongly differs from what we ourselves hold, namely that the task of philosophy lies in the enquiry of those aspects of reality which are, it is true, presupposed in the positive empirical sciences, but not explicitly investigated by them. For such an enquiry carried out by philosphy the opinion of the positivist is still that it is meaningless, because this philosophy pretends to say something about the real world that goes beyond just recording and ordering of the data of sensible experience, implying that no verification in a positivistic sense is possible.
The broadening of the positivistic thesis by which at least some space is created for philosophical (read logical) reflection about the data of sensible experience, does not, however, remove the contradiction signalled above. Indeed, the distinction -- in itself correct -- between logical and empirical propositions can never found the two categories as representing the only two categories of meaningful propositions, because apart from these two categories at least one more category must be admitted, namely those propositions in which it is expounded why the two other categories represent the only types of meaningful propositions. It is simply a fact that a treatise in which the positivistic thesis is expounded, is, in virtue of the intension and development, neither a work of empirical science, nor a purely logical analysis. It is a philosophical determination of one's position with respect to the question of the possibility and legitimacy of obtaining relevant knowledge of the world. And as such this 'philosophical determination of one's position' falls outside that domain of propositions and statements that are acknowledged (by positivism) as meaningful.

An interesting exposure of this contradiction can be found in the 2nd edition of A. J. Ayer's work "Language, Truth and Logic" (1946). In the work itself he adheres to the well-known neo-positivistic doctrine that asserts that there is no room for meaningful propositions outside the categories of logical and empirical propositions, resulting in the non-existence of genuine philosophical propositions. However, in the introduction to the second edition he writes :  "Nevertheless I now think that it is incorrect to say that there are no philosophical propositions. For, whether they are true or false, the propositions that are expressed in such a book as this do fall into a special category. And since they are the sort of propositions that are asserted or denied by philosophers, I do not see why they should not be called philosophical."
( NOTE 1, Van MELSEN, p.44 )

So again we have a contradiction between the meaning and the content of such a treatise. Indeed, the meaning of it is to say something meaningful with respect to philosophy and human knowledge in general. But the content denies it to have any meaning at all, because the treatise is neither made up of propositions expressing sensible experiences, nor of logical propositions. It is made up of propositions that say something about the limits of our knowledge, and that are propositions which are more fundamental than the two categories admitted by positivism.

Conclusion.  --  From all this one can draw only one conclusion, namely that the only way to avoid the contradiction is to honestly admit that meaningful human knowledge about reality cannot be limited to the registration of sensible experience. Evidently there is more present in human experience than those aspects that are expressed and ordered in empirical science. Otherwise it would not at all be possible to ponder about what are genuinely meaningful statements and which are not. And such pondering is itself without doubt meaningful. Therefore we must say that the positivistic attempts to ban all philosophy other than logical and linguistic analysis, are based on too narrow a view of human experience. This experience contains more than what is accessible to a treatment along the lines of empirical science, and this is also implicitly acknowledged by positivism when it develops its own philosophic view with respect to the possibilities of human knowledge. It is then no surprise to find that also those thinkers who generally are attracted to positivism, nevertheless refuse to comply with too rigorous an application of the basic tenets of the system. So positivism has become more of a certain intellectual climate than a rigorous doctrine.
Philosophy is simply unavoidable, because the attempt itself to ban philosophy is already philosophical in nature. So there really is no reason to fear that the outcome of some doctrine about the business of empirical science (that is, some epistemology) would force us to abandon philosophy (and therefore a metaphysics of the material world) on the grounds that all philosophy is meaningless. No epistemology could end up with such a denial of the legitimacy of philosphy without becoming involved in a contradiction.
The conclusion that human knowledge of the real world cannot a priori be limited to positive empirical science is especially important as regards many problems, such as the Species-Individuum Structure, the impossibility to totally reduce all qualities to quantities, and of all the qualitative to the quantitative, etc., that are discussed in Aristotelian metaphysics. Indeed, we have seen that no empirical science can solve such problems, because such a science exclusively concerns the specific content of sense data. The reflection on the general aspects of experience lies outside the range of every positive empirical science. It is true that such a science implicitly presupposes such general and consequently primary data of experience, but they cannot, precisely because of that, become the object of investigation by empirical science. In this way a reflection on natural science and its presuppositions logically leads to a metaphysics of material reality, and based on it, an epistemology.

Philosophy has more than relative value.
It is necessary to discuss yet another attempt to rule out philosophy. Sometimes we hear the assertion that the nature of the philosophical movement to which somebody adheres, depends on his personal temperament or disposition. One philosopher will prefer positivism because it simply is compatible with his personal disposition, he likes its intellectual climate. A different temperament, on the other hand, automatically leads to a more speculative type of philosophy. So if this were true, one's decision and choice with respect to one or another philosophical system is not intellectually motivated, but depended on an extra-scientific personal development of some view concerning reality and life. That's why in a philosophical discussion it would be meaningless to peruade the other as to the incorrectness of his choice of philosophical system. For him the choice is right (if it indeed complies with his personal disposition and character). So philosophical convictions would then only have a relative value, not an absolute value.
However, the same internal contradiction, as the one we have met above, also deprives this statement, concerning the value of philosophy, of its meaning, despite its attractiveness as seen at first sight. The almost hopeless disagreement and confusion in the philosophical theatre -- compared to which the disagreements in natural science go pale -- could persuade us to locate the problem of philosophical disagreement in the relativity of philosophy, based on the personal disposition of the philosophers. But who thinks this over for a while, immediately detects that the same contradiction pops up again. For the question immediately presents itself whether the thesis that someone's philosophical view is determined by his personal disposition, and thus is only relative, is in turn dependent on the personal disposition of the one who expresses that thesis. And according to that very thesis this thesis itself is only relative. Again there is a contradiction between the meaning of the thesis and its content. Evidently the meaning is to indicate a really existing relation between the personal disposition of a given human being and his deepest philosophical conviction, in order to explain in this way why people differ in their deepest convictions. So the meaning of the thesis is to communicate an objective state of affairs. It is, however, in the same way evident that this thesis is only meaningful if it is based on the implicit supposition that man is certainly capable to present and express absolute statements. Indeed, the thesis is, whether it is true or not, about something absolute, something that ultimately judges about the value of all human knowledge, because it says something about the fundamental relation between what  is  and what we  know,  between reality as such and knowledge as such. And it is precisely that with which philosophy is dealing. Therefore a philosophical thesis, that declares all human knowledge to be relative, has itself only relative value. It can never refer to human knowledge as such -- because that is supposed to be absolute by the thesis itself (that is by expressing the thesis, or, said differently, by explicitly communicating the thesis to others). It can only refer to certain areas or to certain aspects of human knowledge.

With respect to personal temperament as determining factor, it must be admitted that in many 'philosophers' their 'decision' as to what philosophical system to adhere, actually is determined by personal disposition or temperament. But such a decision, i.e. a decision based on personal disposition or temperament, is not a necessary decision, but a volontary one. And because philosphy is not a matter of taste, but a way of genuine enquiry, any so-called philosopher whose adherence is determined by personal disposition is not a philosopher at all, but a self-entertainer.

Looking back to the several attempts to deprive human knowledge (and thus with it, philosophy) of certain essential characteristic features, our conclusion must be that right from the beginning human knowledge must be interpreted realistically, that it is not limited to just a registration of sense data, and that it is ultimately (that is in principle, and that is, after the removal of errors) absolute. It is certain that human knowledge is, in more than one of its aspects, affected by various factors, and that human propositions are often based more on appearance than on facts, resulting in the fact that all knowledge possesses more of relative than of absolute value. But all this doesn't alter the fact that fundamentally human knowledge directly refers to reality and that is has an absolute character. Kant may be right when he points out that the nature of our cognitive apparatus makes it for us impossible to know reality as it is in itself, but that can never refer to our knowledge as such, but at most to only certain aspects of it. The positivists and empiricists may legitimately stress the fact that the basis of all human knowledge lies in the sense organ, and although one will not easily underestimate the limitations that are implied by this fact, the fundamental truth that human knowledge can do more than just record and order sense data, can never be affected by it. Finally, psychologists and sociologists may justifiably argue how much our convictions, also our deepest, are influenced by our psychological structure and our social status, but all this does not render human knowledge relative in principle. It just warns us how careful we must be even with respect to our deepest convictions and how precarious philosophy in fact is. But were it true that the ultimate absolute value of human knowledge would be corroded by this, what value could we then attribute to the work of psychologists and sociologists?
So we return to the very first data of pre-scientific knowledge of material reality with the solid conviction, that although the domain of philosophical enquiry is utterly precarious, there can never be definitive and conclusive epistemological reasons for abandoning this enquiry.
A systematically erected metaphysics of material reality (philosophy of nature, including all living beings) has much value for epistemology, because it can broaden the basis on which epistemology is grounded. Indeed, such a metaphysics demonstrates that there is still another side or level in human knowledge than the one that is shown by natural science. A preliminary exploration of the objections sometimes raised by epistemology against the possibility of such a metaphysics, have demonstrated that they are certainly not sufficiently valid to already stigmatize an attempt to such a metaphysics as being in vain.

Quantity, Quality, and Substance  in Aristotelian metaphysics.

The Aristotelian categories, Quantity, Quality and Substance are extensively studied in  First Part of Website .  But now, after what has been learned in  Fourth Part of Website  we can say much more about them. This, however, will be done during our systematic treatment of Aristotelian metaphysics in the documents to come. In the present document we will issue just a few succinct statements in order just to know where we stand when starting the mentioned systematic treatment.

A substance in the metaphysical sense of the term is the primary instance of material Being (secondary instances are the 'accidents' (properties and states)).
Every substance, as a physically complex being, differs from an aggregate, also a physically complex being, in that its cause as to what it specifically is (that is, as to whether it is an ice crystal, a carbond dioxide molecule, a helium atom or a domestic fly (Musca domestica), etc.) is  intrinsic,  while such a cause as to what a given aggregate is, is  extrinsic,  that is, lying outside the aggregate itself. Therefore a given substance is a unity  per se,  while an aggregate is a unity only  per accidens.
A substance, as substance, ontologically consists of prime matter and substantial form. This latter form is the act of the prime matter in the given case. Therefore substance is often called the composite. It is a secondary instance of Entity, while its (substantial) form is the primary instance of Entity.
For a given substance we can identify its substantial form with the dynamical law of that dynamical system that generated that substance. When this dynamical law finds itself as inhering matter, it starts to operate and generates the substance  ( This is fully worked out in  First Part of Website ).
Prime matter is as such pure potentiality and is therefore as such not observable, that is, it cannot be directly detected by the senses. It occurs, however, always as actualized by one or another substantial form. Also this form is not as such observable (Indeed, the dynamical law is as such not observable). Probably as a result of this, the prime matter-substantial form composite is also not directly observable.
From this matter-form composite flow some features which manifest it, that is, features that render it observable. These are the genuine properties (of it), which are features that completely and exclusively flow from the composite, and states (of it), which partially flow from the composite (and partially from the environment).
It is these features that we actually encounter, that is to say, we encounter the composite (the substance s.str.) by way of these features.
While substance is ontologically (at least in the 'downward' direction) independent, these features cannot exist without a substrate of which they are properties or states. In philosophy they are called 'accidents', and as such contrasted with substance. And when we take these features or accidents as maximally general, we arrive at the basic genera of Being, which, together with the category of substance, form the system of Aristotelian Categories.
These features, accidents, whether they are genuine properties or just states, show, among others, quantitative as well as qualitative aspects, or, perhaps better expressed, are quantitative or qualitative (or are of some other nature). So material reality manifests itself by way of, in any case, quantity and quality (which are as such, that is, when taken maximally generally, two of the basic genera of Being, or categories, and -- apart from the category of substance -- by far the most important ones).

The fundamental  quantitative  character of material reality (its things and events) means more than that material reality shows temporal and spatial extension. Quantity penetrates all of material reality in every respect, also those aspects which we usually denote as qualitative. To mention just one example :  a color is not only always the color of a thing-having-itself-extension, in virtue of which also the color has extension, but a color also has  intensity.  Now intensity has its own quantitative character, different from that of pure extension.
Quantity is fundamentally present wherever there are material beings. Indeed, quantity is already implied by the Species-Individuum Structure. The complex concept "many individuals of a same species" implies the concept "number", also called  quantitas discreta,  which is  quantity-partitioned-into-parts .  We could surmise that this discrete quantity presupposes continuous quantity -- quantitas continua -- that is,  quantity-extended-in-amalgamating-parts.  We can also say that continuous quantity can be divided into actual parts, and when this is done we have discrete quantity, or, differently expressed, continuous quantity has potential parts, while discrete quantity has actual parts.

The term "quality" refers to certain sensible perceptions. A quality of something is some intelligible content made visible (directly or indirectly).
The reduction of qualities to quantities can never be complete. For example in natural science differences in color are expressed by differences of the value of certain physical quantities, such as wavelength, frequency and amplitude, but this does not mean that it is about  pure  quantities. Indeed, the quantities that occur in the mathematical formulas, describing the colors and their characteristic features, are not purely mathematical entities. They refer explicitly to certain material dispositions, because together with these quantities are given the ways of observing and measuring them (and this implies the qualitative [see below] ).
Qualities must exist, because in a purely quantitative world observation would be impossible. Indeed, even a simple measurement of length demands that there exists an observable difference between the end points of the object to be measured and the medium in which that object finds itself. So we can say the following :
Empirical science presupposes the existence of a factor in material reality which renders the quantitative relations observable. And it is this factor which we call the qualitative.
Material qualities essentially do have a quantitative pattern (expressed by relations of intensity). This pattern does not comprise the whole quality, but it is an essential aspect of it. Further, all material quantity implies quality, in virtue of its measurability (and that material quantitity is indeed measurable we know).
All the quantitative is filled with the qualitative, and all the qualitative has a quantitative pattern. Therefore the qualitative and the quantitative never exist as juxtaposed parts of material reality. Both parts totaly penetrate each other. And this is the same type of co-existence as we have it between prime matter and substantial form. And this is not a coincidence, because the accident (in our case quantity or quality) is nothing else than a further determination of the substance, that is, of the matter-form composite. It takes part in the manifestation of this composite. Therefore, the 'dis-simplicity' of the substantial order, that is its intrinsic duality -- expressed as matter + form -- is expected to stay its course right up into the accidental order. In the latter order the duality becomes observable or manifest as the distinction between quantity and quality.

A substance manifests itself, first of all, by a specific set of qualities. We can also say that the nature of the substance manifests itself first of all by a specific set of qualities.
Is this set of qualities reducible to a set of simpler qualities in the case of a genuine substance? In the case of an aggregate it certainly is. Large sections of our website have been already devoted to this question, so here we can be succinct. It concerns the vexed problem of the NOVUM, that might appear when elements unite to form one new substance as, for instance, in a chemical reaction, and in contrast to the formation of just a mixture, such as a solution of one ingredient into another, which is just an aggregate.

The mentioned NOVUM must not be equated with the NOVUM that appears when we go from the Inorganic to the Organic Order. This latter NOVUM is a categorical NOVUM, that is, it is a new ontological principle, new, as compared to the set of principles of the inorganic world. And it is not only a new principle, appearing on the scene as soon as we enter (from the inorganic category Layer) into the organic category Layer, but it also modifies all other categories of the Organic Layer. It was treated in Part XXIX Sequel-25 of Fourth Part of Website .
The NOVUM we are presently dealing with is not a categorical NOVUM, that is, not a NOVUM that applies to a whole Layer of Being (for instance the organic, or inorganic Layer). It is a NOVUM only with respect to some new specific physical pattern, a pattern which emerges for instance in the result of a chemical reaction or of a crystallization event. This pattern is not universal for the whole category Layer. It is just some specific pattern emerging from some given reaction, a pattern that cannot totally be reduced to the starting elements of that particular reaction.

When we speak about a given chemical compound in terms of it being a substance in the metaphysical sense, we must not think in terms of some macroscopic quantity or volume of that compound, because such a volume is only an aggregate, namely an aggregate of individual molecules that are specifically identical. It is only the single molecule that is supposed to be a substance in the metaphysical sense of the term.
To understand a complex being means that we can describe such a being in terms of simpler things that we already understand. This means that we -- having understood the complex being -- can reduce the complex being to its elements. And even when these elements themselves are not yet fully understood, we have accomplished at least a beginning of the understanding of the complex being. The thesis that this in principle can be done for all cases of complex beings is called reductionism. Whether this is equal to asserting that for all explanations one can use mechanical models is not easy determine. Indeed, perhaps the only way man can understand complex beings is by way of mechanical models, for it is hard to say whether or not non-mechanical models (not just wave 'mechanics') are really explicative.
On the basis of the known specific directedness of chemical reactions and of the known definite chemical affinities of chemicals, we can generally say that the new qualities of a chemical molecule are already potentially present in the atomic species that (in the form of individuals) make up the molecule. Or, said differently, the new qualities are already potentially present in the relevant individual atoms as they exist freely and for which (atoms) it is not necessary for their specific identity (their whatness) that later they may enter into a process of interaction resulting in the molecule.
If we could indeed fully understand all the qualities of the molecule in terms of such freely existing atoms, and when this applies to all kinds of molecules (and consequently also for all crystals) whatsoever, then reductionism (as a doctrine) would be true at least within the whole domain of chemistry.
We know that modern chemistry has not reached this stage. And we don't know whether it can reach it at all, even in principle. The problem cannot yet bew solved.
But if we assume that a given individual molecule (or a crystal) is one genuine substance or 'mixtum' (after all, the molecule fundamentally differs from just a mixture of the same atoms present in the same number, which [mixture] is an aggregate), then it cannot in turn consist of genuine substances. And while an aggregate, can, for it to be understood, be reduced to its constituents (elements), a substance is expected not to be so reducible, otherwhise it would just be a collection of various substances instead of being one substance. A substance should be a genuine whole, possessing only one substantial form.
If we say that the qualities of the molecule are already potentially present in the atoms as freely existing, then we want to determine this potential existence in concreto, that is, we say that "potentially existing" is still not good enough for understanding. Now we know that in the relation  potency-act  act is prior to potency. In order to understand the potency in a particular case we first must understand its corresponding act. This is, because, in a way, potency IS its act. When we apply this to the attempt to understand a given molecule, we must depart from its actual qualities as given, and see how they are potentially present in the relevant freely existing atoms. The obtained relation between potential qualities in the atoms and actual qualities in the molecules,  that is, the new qualities of the molecule as actualizations of those same qualities as they are present potentially in the relevant freely existing atoms,  represents the chemical kinship between the atoms having these potential qualities and the molecule that is formed by them. But this is not a reduction from molecule to atoms anymore!.  It is, instead, a holistic simplification :  We start with the molecule, subtract its new qualities (while taking into account what this entails), and we're left with the atoms. Said differently, when we want to understand a molecule, we must understand its constituents, including those qualities of them which are only potentially present in them. But this means that we can know these potential qualities only by studying the whole (the molecule) in which these qualities appear actually. The particles or elements (atoms) and their properties to which we want to reduce the molecule (in order to understand it) can only be known fully by departing from the molecule, because the latter shows us whereto the particles are geared with respect to the mentioned potential properties. So in the case of a genuine substance the parts can only be fully known by knowing the whole, and so the substance has ontological priority with respect to its parts (because act is ontologically prior to potency). But this means that the parts are just accidents of the substance. These parts then appear as qualities of the substance, namely those qualities that were 'preserved' during the transition from atoms to molecule. The other qualities of the elements that were only potentially present have been actualized, resulting in the new and actual qualities of the molecule in addition to the 'preserved' qualities. And this is the same as saying that the elements of the mixtum exist (only) virtually in the mixtum, namely as qualities of that mixtum.

This concludes our introduction to the systematic and thematic exposition of Aristotelian metaphysics, which will be carried out in the documents to come.

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