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• The treatment of the 'what is it' (quid est) of beings that have a cause which is different from that being itself -- the cause of a thing  A  is itself a thing, but different from  A -- and that means that it is about  properties,  which themselves are  per se  determinations (of something). This was treated in Aristotle's  Posteriora Analytica  as -- what we now would call -- epistemology. The Posteriora Analytica is, however, not wholly epistemology (in the modern sense of the term), but contains the  metaphysical  starting points for any natural science. We will concentrate on these metaphysical aspects, which here means that we concentrate on the ontological status of  accidents  ( per se  and  per accidens  determinations, or [equivalently] manifestations, of Substance ( = Primary instance of Being, presenting itself as either primary or secondary instance of Entity). The  per se  accidents are the most important. The relation of these latter to Substance, with respect to cognition and with respect to Being, will be thematically [that is, not historically] investigated. Thereby we will heavily rely, not only on Aristotle himself, but also of his supreme commentator, St Thomas Aquinas, and on the findings in relevant modern literature concerning the Substance-Accident Metaphysics as well as relevant results obtained by Natural Science.

• The science of Wisdom-proper  considers the 'what is it' (quid est) of beings that have a cause that is, in a way, identical to that being itself. That means the science of wisdom proper is about  Substance  (and its instances), and about that to which Substance ultimately refers, namely first to the (substantial) form, then to the Separate Entities. All this is, for the first time (in history) treated in Aristotle's  Primary Philosophy,  laid down in his  Metaphysics  (fourteen books). All this will be thematically investigated. And also here we will heavily rely, not only on Aristotle himself, but also on the relevant results as they have been found by St Thomas Aquinas, and on the findings in modern literature concerning Substance (especially OWENS's The Doctrine of Being in the Aristotelian METAPHYSICS, 1951, 1978, as well as relevant results obtained by Natural Science.

If, however, we come across (in classical texts) things like a stone, a piece of wood, and the like, presented as an example of a being, then we must realize that these are not genuine beings, not true Totalities, but merely aggregates. Wood, to be sure, originates from an organism (which is a Totality, a genuine being), but is no longer that organism, but a remaining part thereof, which has no dynamical law of its own, and thus has no Essence of its own. It consists of atoms and molecules, which each for themselves are genuine beings, but are not related anymore to the organism. Wood is an aggregate of atoms and molecules, where at most some remnants of some order remain, which once belonged to the integral ordering of such atoms and molecules resulting in an organism. And because of the fact that a piece of wood is an aggregate, many of its determinations are  per accidens ,  and this is much less the case where we have to do with genuine Totalities.
As regards the  Predicaments  (the system of Aristotelian Categories), in classical metaphysics COLOR, for instance red (often white has been used there as an example), is considered to be a quality (that is, belonging to the category of Quality). Although the discussion about the complete reduction (or its denial) of quality to quantity is still not fully settled, I assume that in every such a reduction some residue of genuine quality remains (because in a purely quantitative world no observation or measurement would be possible). So whether COLOR is or is not a genuine quality will not be discussed here, at least not extensively so. We consider -- in all tranquillity of mind -- COLOR as if it were a quality, and use COLOR, for example Red, White, etc., as an example of quality. After all, in most cases the discussion is about the relationship of (a given) quality (as such) with the Totality (the individual intrinsic being), and with the Essence (of the Totality), or, still more generally, about the determination (accident) as such and its relationship with the Totality and Essence. All this, of course, is meant to be within a metaphysical (that is here, an ontological) context of exposition.

In order to ease reading of what follows, we will, where possible, use the old (that is, classical) terminology, including Latin terms (because many ancient texts are involved). We will not very often use the term "dynamical law", but instead of it the theoretically equivalent term "Essence" (Essentia). Also we keep on using the term "accidens" (accident), precisely where classical metaphysics did use it, despite the fact that, in virtue of our view (as presented in this website) of a being as an intrinsic Totality (as contrasted with an aggregate), many cases of 'accidents' do have a more or less  per se  nature. Indeed many 'accidents' are  per se  determinations also according to classical metaphysics (calling them propria). In such cases the term "accident" only indicates the fact of the ontological dependence of that what it signifies (dependence on the matter-form composite as a substrate or carrier), and distinguishes it from Substance, which is ontologically independent as to any substrate.
By doing all this, we can give our metaphysical text a more familiar face (to those who are well-acquainted with classical texts on the subject).

The content of the ensuing metaphysical text will not be in every respect compatible with the metaphysics as it was conceived of by Aristotle himself, because the present text is for an important part based on the expositions of St Thomas Aquinas.
I do not try to eliminate these incompatibilities (between Greek and Medieval metaphysics), because I fear, if I would do so, that many valuable ideas will get lost. After all, we will never solve the main metaphysical problems completely. These ideas will surely help to proceed further.

We will now actually do Substance-Accident metaphysics, but only as far as  determinations  (of substances) are concerned. And although Substance will be considered too, it becomes a main theme not until the second series of documents, the series namely where the focus will be on Greek metaphysics, as it has come down to us from Aristotle.

1. The way of asking (via quaestionis).
2. The way of predication (via praedicationis).
3. The way of the definition (via diffinitionis) ( NOTE 2 ).
   

a.  The way of asking (via quaestionis).

Here it is being investigated what conditions must be met for something to be questionable in order for it to be asked :  What is it? There must be some kind of duality in the thing, or with respect to the thing, in order that the answer to the question "what is A" not just reads "A is A". This duality could for example consist of A and the cause of A, or, of A and the substrate or carrier of A (if such a carrier is present, for instance when speaking about a determination ( NOTE 3 ).
We will find out what types of questions can be asked in connection with that what is it question, for instance questions that should precede it. Further we will find out whether and to what extent there is a difference in asking for the what of derminations and the what of its ontological carrier or substrate, the 'thing'. Because a determination as such is not independent, it always refers to its carrier, and it is there where we must look for the true determination. Therefore the questionability of Substance will be investigated (substance, however, only manifests itself by its properties).

b.  The way of predication (via praedicationis).

Here we investigate to what extent  predication  can yield knowledge. Attention is payed to the distinction between our way of knowing (logic) and the way of being (ontology). We look carefully into how things and determinations are actually denominated, and should be denominated, and precisely to what the terms of the predication (subject and predicate) refer, and in what way they so refer (modus praedicandi en modus significandi), and whether, and to what extent, there is correspondence with the way of being (modus essendi).

c.  The way of the definition (via diffinitionis).

Asking for the  what is it  (quid est) ends up in knowing 'per viam diffinitionis'. Here we investigate what the pretense to knowledge of the  definition  is, or can be.
A definition is the predicate of a 'per se' predication of a determination or intelligible content (for example  rational animal,  which is a definition of the term "man".  This definition [rational animal] is  per se  predicated of "man" in the  per se  predication
"man is a rational animal". Here, "man" signifies the species, "animal" the genus, and "rational" the specific difference).
A distinction is made between several types of definitions. Further it is investigated in what way determinations and in what way their carrier or substrate (substance) can be defined, and whether definitions can be objective.
We shall also enquire as to what the location of the definitions is in the  proof  (deductive demonstration).
The definability of substance (not qua substance, but of whatever (given) substance) is investigated.
Here it is always about the definition of a term, which itself refers to individual beings (s.l.).
As a result of the (degree of) definability of 'things' (in fact, as has been said, of the general terms referring to these things) it is investigated to what extent things with a definite intelligible content form discrete or continuous series in Reality.

In this brief introduction it already is clear that we -- as we already did in First Part of Website -- are looking for Totalities (individual intrinsic real beings) and their Determinations, classically expressed, (looking for) Substance and its Accidents. In Fourth Part of Website we also investigated Substance and Accidents, but there we centered our discussion around  crystals  as an example of inorganic Totalities. We looked to properties of crystals such as intrinsic shape, symmetry and promorph, and have set crystallization in the context of thermodynamics.
So now we will again investigate the ontological status and structure of the Totality (and its Determinations), but now again (as we did in Classical Series of documents in First Part of Website) in a more classically philosophical setting, but with the results of Fourth Part of Website in mind.
In connection with items like the  definition  of whatever given substance (in the metaphysical sense), or the characterization of  per se  and  per accidens  determinations (properties and states), we will involve our findings about the  d y n a m i c a l  l a w  as the Essence of a Totality,  and apply all of it not only to the constitution of man (the classical example), but also to the structure and generation of other beings like crystals, especially branched snow crystals. We must elaborate the understanding of the  dynamical law  still more anyway. This we will do along the lines of an example of a very simple dynamical law. We then show how we come to know the dynamic behavior of the system governed by this law, by solving the (linear) equation which is the (mathematical) formulation of this dynamical law ( NOTE 4 ).
Apart from all this, an ongoing discussion will take place with Nominalism as regards Substance and Accident. This discussion is, however, very limited, and will leave many questions unanswered. The same holds for the possibility of integration of general results of natural science (such as thermodynamics) in this Substance-Accident metaphysics. And precisely because of the existence in the Substance-Accident metaphysics of all these unanswered questions and unsolved problems, Substance-Accident Metaphysics can be legitimately considered to represent a genuine  science.

Contents.

1.   Presenting the four fundamental questions, Quia, Propter quid, Si est, and Quid est.
2.   Deductive demonstration (Proof) (syllogism of the first figure).
3.   Reduction of Quid est to Propter quid with respect to properties ( NOTE 5 ).
4.   Order (sequentiality) of the Questions (quaestiones) with respect to properties.
5.   Order (sequentiality) of the Questions (quaestiones) with respect to substance.
6.   Catallel transformation of Quid est with respect to substance.
      f₁.   An analysis of Essence as forma totius.
7.   Si est
                   Quid est
    Quia est
8.   Natura- and Creatura consideration.
9.   The place of the quaestiones in the deductive demonstration (proof).

Wonder (about something) is a privative state in our understanding, our knowing. It is not simply a nesciens ( NOTE 6 ), but an ignorantia ( NOTE 7 ), and this latter we want to evict, because "all man, as a result of his nature, aspire to know", and it is by knowing (things) that we evict ignorantia.
But there are a number of different  w a y s  that lead to this knowing, of which there is one with which all this begins :  The 'way' of asking. Asking leads to knowing.
With respect to scientific knowing ( NOTE 8 ), all the questions can be deduced to four fundamental questions. Thus, Aristotle, in the first Chapter of his Posteriora Analytica II, expounds :

1. The question concerning a fact, a state of affairs. The question whether something, with respect to something else, is, or is not the case. Said differently, whether a given property (necessarily) belongs to a given subject.
   It is the question quia ( est ). It is the question "is  S  P ?" (or, "is  S  not  P ?").

2. When we know that indeed  S P  (S is P), we ask why this is so. It is to ask for the cause or reason why a given property (necessarily) belongs to a given subject.
   It is the question propter quid.

   In addition to these composed questions we can also ask simple (that is, non-composed) questions :

3. Does  S  exist? It concerns the existence of the subject.
   It is the question si est (or, an est ).

   As soon as we know that  S  is (that S exists), we will ask :

4. What is  S ?  This is the question that asks for the Whatness or Essence of the subject.
   It is the question quid est.

All these questions and their answers stand in a certain relationship to deductive demonstration (proof), i.e. the syllogism (that is one of the possible formal figures of demonstration).
Let's dwell for a moment upon the syllogism :
Suppose -- as an example -- that certain chemical configurations, belonging to the phenotypical expression of the Essence of a class of material bodies, in whatever way cause a 'cellular' character or texture in these bodies, as a result of which these material bodies manifest themselves as individual cells or as multicellular bodies, and suppose that in particular living matter (in contrast to inorganic matter) necessarily possesses this property, and that, in addition to it, we know that animals consist of living matter, then we can set up the following syllogism :

Maior (1st premise) :  All animals are cellular
Minor (2nd premise) :  Sponges are animals
------------------------------------------------
Conclusio (conclusion) :  Sponges are cellular

The validity of this demonstration is immediately clear when we consider the range of signification of the terms, that is, if we consider the terms as indicating collections or classes of things (s.l.). Then we can represent the syllogism by means of a Venn-diagram :

Here "animals" is the middle term and represents (a part of) the definition of the subject (of the conclusion) and is reason or cause of that what is posed in the conclusion.
"Cellular" is the extreme superior term (maius).
"Sponges" is the extreme inferior term (minus).
The conclusion is (deductively) demonstrable because the range or extension of the superior and inferior term is such that a middle term can be inserted between them.
It is for the same reason that a strict proof of the necessary attribution of a  definiens  (definition) to the  definiendum  (that what is to be defined) is impossible because both extensions are equal so that nothing (that is, no middle term) can be placed between them.
The example presented above was a syllogism of the first figure of which the conclusion is universal and affirmative :

where M is middle term, P is predicate of conclusion, and S the subject of the conclusion. So far, for the time being, about the syllogism.

Aristotle shows in the second chapter of the IInd book of the Posteriora Analytica (and St Thomas in loco ( NOTE 11 )) that the 'what is it' question is the same as the 'why' question. However, this is valid (in the Posteriora Analytica as epistemology) only for those things (s.l.) that have a cause which is different from that thing itself, and that means that the reduction is only possible in the case of properties, because for these their cause indeed lies outside themselves, in contrast to substances ( NOTE 12 ).
When we ask :  'what is A?' we do not have an answer when we reply :  'A is A' (indeed, it is metaphysics which nevertheless tries to answer such a question (also) with respect to substances. However, in the present discussion [that is, in the context of the Posterior Analytics] it is not about metaphysics in the strict sense [that we speak], but physics in the broad sense). We also do not get an anwer when we reply :  'A is B', because A is not B, but A is A. But if we, in addition to relations of identity and non-identity, take into account other relations, for example 'A has B', or  ' B is the cause of A', then it is perhaps possible to obtain an answer to the question 'what is it?' which gives more information than 'A is A'. It is clear that especially the second possibility of the two just mentioned can supply an answer to the question 'what is it?' ( NOTE 13 ). Indeed, an anwer could read :  'A is what it is in virtue of B'. So the question 'what is A?' is asking for something (different) on which A is based, which here is B. In this way the what-question is a question asking for the cause.
So we see that for such a reduction to be possible a duality (a catallellism) is needed, and such a duality of essence ( = [loosely] whatness) and cause is only to be found in properties. If we then speak about the reduction of quid est to propter quid, then we, for the time being (that is, as long as we stay within the domain of epistemology), mean exclusively the quid est of  a given  property  ( The treatment of the quid est of a given  substance  does not belong to the epistemology of the Posteriora Analytica).

First of all we must know the meaning of the term that signifies the given property. We ask :  quid est quod dicitur ( NOTE 14 ) (the answer is a nominal definition).
Next we can ask ourselves whether this term indeed has a significatum ( NOTE 15 ), i.e. whether the property is on the subject (the subject is presupposed to exist).
This is the question quia est.
Next we can ask what it is that 'est' ( NOTE 16 ), and this is, as we have demonstrated, the same as asking why it is as it is, that is, why this given property is on the subject ('rests' on the subject).
This is the question propter quid ( NOTE 17 ).
The answer is then at the same time the answer to the what-question, quid est ( NOTE 18 ) regarding the property :
It is the quod quid est ( NOTE 19 ) of the property.

With the simple (i.e. not-composed) questions as regards the  s u b j e c t  things are different.
First of all we must again have at our disposal a definition quid nominis ( = nominal definition) as answer to the question quid est quod dicitur (see NOTE 14), in order to be able to ask ourselves next whether the term actually has a significatum in re ( NOTE 20 ). This is the question  si est.  This cannot be (deductively) demonstrated, but only possibly be observed. After we know that the given substance ( = the subject of the property or properties) exists, we can ask what it is (essentially) :  quid est substantia, that is, we ask for the Essence of the given substance (we could also say that we ask for the substance (itself) of a thing). Because the cause of the Essence is here identical with that Essence, we cannot in a catallel way ask for the cause (that is, we cannot ask in such a way as to involve a duality of the thing and its cause, which here is the duality consisting of the Essence and its cause) (See Aristotle, II Posteriora Analytica, Chapter 10) ( NOTE 21 ). We cannot ask this in terms of some duality, because the Essence does not (within the context of science) have a dual nature. Within the context of science (as contrasted with that of metaphysics) we cannot, as regards substance, say what A is in terms of B (the cause).
The Essence should be intuitively and inductively grasped, as Aristotle describes in Chapter 19 of the IInd book of the Posterior Analytics ( NOTE 22 ).

AERTSEN, J.A., in his Natura en Creatura, 1982, p.22, now discusses the problem as regards the quid est of  s u b s t a n c e s,  following the discussion of St Thomas in In VII Metaph. lectio 17 (that is in his commentary on the Metaphysics of Aristotle) concerning a catallel transformation.
When we, despite what has been said above, nevertheless perform this transformation, then the composition (compositio), resulting from this transformation, out of these 'alleles' is of a totally different nature than is the compositio of a subject and a (necessary) property. The problem of the what-question with respect to substance (concerning what a given substance is) is, because it is a metaphysical problem (and not a problem of natural science), dealt with in Aristotle's Metaphysics, especially in Book VII, and also by St Thomas in loco, and by AERTSEN, p.30-33.
The question quid est with respect to (any given) substance, now, in this metaphysical treatment, also becomes a question as to the cause, and this cause is the forma-in-materia [causes of  it  in turn are the efficient and final causes, which are both extrinsic causes. But for the philosopher it is the intrinsic causes that should be looked for, causes that constitute things from within (AERTSEN, p.31), and this "intrinsic" first of all refers to substance, secondly to some state of affairs, that is, to a substance-accident composite (compositum) (substance-determination composite) which forms a unity secundum quid ( NOTE 23 )].
Well, St Thomas takes the Essence of a given substance (or takes a given substance) as forma totius (form of the whole), that is, forma and materia, but without matter-as-individualizing (materia signata). This forma totius is itself catallel (i.e. dual in character), but is still as such identical with its cause, as a result of which we still cannot ask the why-question. It is clear that the question as to the Essence (of a given substance) (thus what some given thing is) cannot be the business of discursive demonstrating science. It (that is, the whatness) cannot be demonstrated from (that is, 'out of') something else. The only form of being catallel which is left is that of the  individual suppositum ( NOTE 24 )  and  the Essence residing in it ( NOTE 25 ).
AERTSEN, p.32, quotes St Thomas (In VII Metaph. lectio 17, nr. 1667) :

Et similiter cum quaerimus quid est homo, idem est ac si quaereretur propter quid hoc, scilicet Socrates, est homo? quia scilicet inest ei quidditas hominis. ( NOTE 26 ).

Where "Socrates" should mean :  Socrates-as-pointed to with the finger.
So in this way the question is transformed in a catallel way (Socrates as individual suppositum  and  whatness of man as forma totius), as a result of which it will now read (AERTSEN, p.23) :  "why is this, namely Socrates, a human being?".  Something is asked about a thing that is pointed to with the finger, and the conclusion of a syllogism would then read :  "ergo, this, Socrates, is a human being".  And this is said to be possible because a distinction is made between first and second substance. That such a view of an Essence residing in a thing (that is, the distinction between first and second substance) is not undisputed, we will expound later.
The question "what is man?" now reads, after catallel transformation :  "What in Socrates is the cause that he is what he is?" But then we already ask things about particular cases :  We ask for the (intrinsic) cause of contingent supposita (that is, unique things) ( NOTE 27 ).
Human(ity) is the cause of Socrates, and no science asks for the cause of contingent supposita (see NOTE 24). The question is thus not quid est Socrates (transformed into propter quid), but quid est homo ( NOTE 28 ) (See, for example, St Thomas' De ente et essentia Cap.4 (Leonina edition) from line 97). And this, i.e. 'homo' is equivalent to 'Socrates-for-example'. The latter is not contigent anymore, because we have precisely given up Socrates. Let us dwell a little on this point :

In  Socrates-for-example  (like in  homo ) the particular is not considered, but the aspect of  being individual  is ,  and acordingly Socrates-for-example stands for the individual Essence. By cutting off the designated matter (matter-under-designated dimensions) we cut off the particular (the aspect of being a here-and-now individual, the semaphoront), but not the individual.
If we ask about just Socrates, we ask about a contingent case, we ask about the particular (i.e. just this individual, pointed to with the finger). But if we ask about Socrates-for-example we ask about a non-contigent case, although still individual. See the documents  The principle of individuation  (non-classical series of documents) and  What is an individuum? Part I  (classical series of documents) in First Part of Website .

So we still cannot ask for the cause of the Essence :  That is to say that with respect to this, the question "what is it?" cannot be transformed into something catallel in order to form a why-question, because we gave up the individual suppositum (Socrates) and turned to Socrates-for-example (or, equivalently, to homo) and are thus left with the Essence alone.
It is, however, arguable that even the forma totius -- as Essence, or substance, which is the 'primary instance' of the categorial (for St Thomas) equivocal Being (the secondary instances are the accidents) -- itself in turn refers to an even more fundamental primary instance, namely the substantial form (forma partis), and this form we can now take as the intrinsic cause of the Essence (forma totius) :
The substantial form is the ultimate inner cause of the Essence, as a result of which the question concerning this Essence (as what-question) can now be transformed into something catallel :  Within Aristotle's Primary Philosophy (his metaphysics) we have ended up at the most fundamental. We can now say :  The Essence (forma totius = materia non signata + forma) -- that is, a given Essence, is that what it is, in virtue of the form (that is, the substantial form).

REMARK :
At issue here is not what Essence as Essence is, but what a given Essence is. For example, quid est homo? (what is man?), and not :  quid est essentia?.

We now can -- in our modern view -- take the  forma totius  as being the dynamical law as the latter is interpreted toward physical matter (that is, the dynamical law interpreted in terms of physical matter).
The  forma partis  (substantial form) then is the 'pure' dynamical law, thus the  dynamical-law-as-not-interpreted-toward-physical-matter.  We can think of this 'pure' dynamical law as in its purely mathematical form (its mathematical formulation, its formal, intelligible, content).
The  materia signata (designated matter) is the principle of individuation ( NOTE 29 ).
Science can only work with dynamical laws that are interpreted toward physical reality (that is, with physically interpreted mathematical formulas). The purely formal state of such a law, i.e. its purely mathematical structure, cannot, within (natural) science, be understood ontologically (that is with respect to ways of Being), that is to say, such a mathematical structure cannot from within itself be understood. In mathematics such a structure can only logically be understood.
Let us give a simple example of this just  'logically understanding ' (as distinguished from ontologically understanding) :

Suppose we have a dynamical law that reads :

X_n+1 = BX_n   (See, for example, BRIGGS, J.P. & PEAT, F.D.Turbulent Mirror, 1990)

Applied as a law governing (for example) the dynamics of the population size in a dynamical system of individuals of an animal population that reproduces annually in one or another geographical region, the just given expression means :

The population size in the next year is equal to B ( = a constant which is connected with the fertility of the animal species considered here) multiplied by the population size of the present year.

When we now want to know the change of the population size as a function of time, then all we have to do is to mathematically solve the dynamical law (and this is just a logical operation, which is totally unrelated to the things [here, animal populations] with which we were dealing).
The solution of the dynamical law reads :

X_n = Bⁿ

( The population size at year  n  is B to the power of  n )

This can easily be verified logically, namely as follows :
When  X_n = Bⁿ  applies, then also  X_n+1 = Bⁿ⁺¹ ,  but because Bⁿ⁺¹ is equal to BBⁿ (just like 2³⁺¹ is equal to 2⁴ ),  we can write :

X_n+1 = BBⁿ .

When we now enter the value for X_n+1 -- which is BBⁿ --, and the value for X_n -- which is Bⁿ -- into the dynamical law  ( X_n+1 = BX_n ),  we get :  BBⁿ = BBⁿ ,  and because the equation  X_n+1 = BX_n  is (as we saw), upon entering X_n = Bⁿ ,  transformed into a numerical equality ( BBⁿ = BBⁿ ),  X_n = Bⁿ  is the solution of the dynamical law X_n+1 = BX_n .

This solution directly shows that X is a function of  n,  and thus varies with  n,  and that the population growth (increase of the size of the population) is exponential.
In the year  n  the population size is Bⁿ ,  in the year  n+1  the population size is Bⁿ⁺¹ ,  etc. So every year the population size is multiplied by  B  ( NOTE 30 ).  This is here, in the expression of the dynamical law itself also (already) evident, but in the case of more complicated laws (especially in the case of non-linear laws, laws, that is, where X_n is raised to the power of two (or higher)) this (simplicity) is not the case anymore ( NOTE 31 ).
The purely logical understanding thus has led to further insight. The path from  X_n+1 = BX_n  to  X_n = Bⁿ  is purely logical.
And only an interpretation of the formulations toward the real world will lead to still further insight.
We can still further elaborate on the discovered solution  X_n = Bⁿ .
When we place, in front of B, an arbitrary factor, say,  a,  we get  X_n = aBⁿ ,  and this turns out to be also a solution of the same dynamical law  X_n+1 = BX_n .  For if  X_n = aBⁿ  applies, then also  X_n+1 = aBⁿ⁺¹ .  From this in turn follows :
X_n+1  :  X_n = aBⁿ⁺¹  :  aBⁿ = Bⁿ⁺¹  :  Bⁿ = B^n+1-n = B¹ = B.
So  X_n+1  :  X_n = B, and from this follows  X_n+1 = BX_n ,  and this is the dynamical law again.
Said in a slightly different way :  If we enter the value of  X_n  as it is according to the solution, namely  aBⁿ ,  and (if we also enter) the value of  X_n+1  as it is according to that same solution, namely  aBⁿ⁺¹ ,  into  the dynamical law (X_n+1 = BX_n), then we get :
aBⁿ⁺¹ = BaBⁿ ,  which is equivalent to :
aBⁿ⁺¹ = aBBⁿ ,  which in turn is equivalent to :
aBⁿ⁺¹ = aBⁿ⁺¹ .
So the alledged solution  X_n = aBⁿ  has turned the dynamical law into an equality, and thus it is a genuine solution of this dynamical law.
And because we can give  a  any value whatsoever, the dynamical law thus has infinitely many solutions.
In the solution  X_n = Bⁿ  (found earlier)  a  was equal to 1.  When we, for this solution, assess what  X₀  is, that is, what the size of the population was in the year 0  (n = 0), then we get  X₀ = B⁰ = 1 ( NOTE 32 ).
If we compute  X₀  for the solution  X_n = aBⁿ ,  then we get  X₀ = aB⁰ = a.
From this we see, that the factor  a  in the expression  X_n = aBⁿ  is the INITIAL CONDITION (initial value, starting value). This initial value thus is the population size with which 'we begin' (from which [value] on we start our 'observation' of the system and its behavior). Very instructive is the fact that we do not find again the starting value  X₀ = a  in the dynamical law  X_n+1 = BX_n .

From this it is clear that the starting value is  e x t r i n s i c  with respect to the dynamical law.

The just given example of a dynamical law did not refer to a Totality-generating dynamical system, but a system of population dynamics. But this is, in the present context (which is about the mathematical [logical] aspect in natural laws), of no importance.

The dynamical law  X_n+1 = BX_n  is a mathematical description of an exponential process, and, in the present case, it describes (it) as  a  genus.  When we enter a certain value for B, we obtain  a  species  of this law, for example  X_n+1 = 32X_n .
As soon as one takes  X_n+1 = 32X_n  as a real dynamical law, one does this because one has found processes in the real world which turn out (concluded from observation) to proceed according to that law ( NOTE 33 ).
The answer to the question why these processes proceed according to, say,  X_n+1 = 32X_n ,  can be found by the discovery of external causes (efficient causes) and other external factors (for instance an unlimited food supply, unlimited living space, and the like [which can be experimentally imposed on the system in order to unearth the intrinsic mechanisms of the system] ).  This belongs to the task of natural science.
The  metaphysical  consideration limits itself to the  internal  causes (and then, moreover, only with respect to essences, and that means here :  to dynamical laws that generate a Totality, that is, a complete genuine being ( NOTE 34 )).

The law  X_n+1 = 32X_n  represents all processes that proceed according to this law. Each single process, that proceeds according to this law, then is an  individual case .  The law  X_n+1 = 32X_n  embodies -- also when it is interpreted physically, whereby thus  X  represents population size and  n  time -- not yet an individual case.
Suppose that the law  X_n+1 = 32X_n  does not represent a population dynamics, but a Totality-generating dynamical system. Then we can say that
X_n+1 = 32X_n -interpreted-toward-the-reality-involved  (that is, this law mapped onto the relevant segment of Reality)  is the  forma totius  of the corresponding Totality species.
The purely mathematical form (thus without physical interpretation) could then be taken as the  forma partis  (that is, as the substantial form). And so, now the Essence of the (given) Totality is expressed as a duality, namely as the interpreted expression  X_n+1 = 32X_n  on the one hand, and the non-interpreted expression  X_n+1 = 32X_n  on the other.
And now we have accordingly succeeded to demonstrate the catallel nature of the Essence.
The Essence (forma totius) consists of :

1. The dynamical law as physically, but still generally so, interpreted  minus  the (uninterpreted) dynamical law. This is the materia non signata.

2. The formal dynamical law, that is, exclusively its mathematical 'formulation' (i.e. as it is 'formulated' by Nature). This is the forma partis.

As has been said, the dynamical law  X_n+1 = BX_n  is the  generic  essence of the Totality that is generated by the dynamical system that proceeds according to  a  species  of this law, for instance the law   X_n+1 = 32X_n .
How does individuation take place in the case of a Totality generated by the dynamical law   X_n+1 = 32X_n ?
The formal expression  X_n+1 = 32X_n  is the substantial form of the Totality. It is the forma partis of the forma totius. The forma totius is prime matter under unterminated dimensions plus forma partis. This composite is the individuated subject, that is, one or another historical individual of the Totality species  (a "historical individual" is the total set of system stages, reckoned from the moment when the Totality was formed, that is, the total set of Totality stages.).  When now a particular INITIAL CONDITION is added (we can say, "added", because, as we saw above, the particular initial condition is extrinsic with respect to the dynamical law) we obtain a here-and-now individual (semaphoront) of that Totality species, that is to say, the initial condition is a particular (i.e. totally determined as to here-and-now) state or stage of the dynamical system. The next state can now in turn be seen as the initial condition of the system, etc. (every system state can be considered as the initial condition of the system, because it then is the state from which on we decide to follow the system's course). Here we clearly see that an initial condition ('starting state') is extrinsic to the dynamical law.
The 'addition' of the particular (that is, fully determined) initial condition means that a particular  s o l u t i o n  of the dynamical law (X_n+1 = 32X_n) has been chosen, say the solution
X_n = 100 .32ⁿ   (B = 32).
From this it follows that the initial condition  X₀ = 100.32⁰ = 100.  The latter is, of course, just a numerical initial condition. Physically interpreted it stands for 100 system elements which will interact with each other according to the dynamical law  X_n+1 = 32X_n . And because each system element is a real here-and-now being (a substance or an aggregate of substances) the unterminated dimensions of prime matter-under-unterminated-dimensions (matter as not designated, materia non signata) -- which dimensions are potentially determined in this or that direction -- have been actualized (by the individuated subject), resulting in prime matter-under-terminated-dimensions, that is, matter as designated (materia signata). The result is some particular Totality state or stage in a particular place and at a particular point in time.

In the NATURA consideration, that is, within Greek philosophy, especially that of Aristotle, and followed by St Thomas, the quo est ( NOTE 38 ) referred to the quod quid erat esse ( NOTE 39 ),  but in the CREATURA consideration, that prevailed in the Middle Ages, especially as a result of the influence of Cristianity, but also that of Neoplatonism, the quo est began to refer to the  e s s e  ( NOTE 40 ),  that is to say, to the causa essendi ( NOTE 41 ),  and the form is, as it were, shifted back (or forward for that matter) a little bit, resulting in the fact that even separate forms, if existing, obtain a catallel structure, namely  esse + forma (existence + form), and in this way becoming questionable (that is, they then allow to be asked questions about them). For, because according to St Thomas, the emanation ( NOTE 42 ) does not proceed in steps, but directly from God, the Angels (i.e. the separate forms) are, just like the sensible things, creatures, that is to say that they must be such as to 'once' be 'composed' (by God), and also be corruptible, and thus be catallel as to their ontological structure.
This composition is the  Existence-Essence constitution, at which St Thomas is forced to alter his (natura) thinking (signalled by AERTSEN, p.47).
In the NATURA consideration the questions si est  ( = an est)  and  quid est could not be considered apart from each other because the answer to quid est directly represents the cause ( = forma partis) of the Being of (the given) Substance, with which the question si est not only had been just affirmed (because it had to be already), but also so affirmed as a result of being based on something.
In the CREATURA consideration, on the other hand, these questions suddenly become different
(this already in the early treatise  De Ente et Essentia [About Being and Essence], Cap. IV, from line 99 :

possum enim intelligere quid est homo vel fenix et tamen ignorare an esse habeat in rerum natura ( NOTE 43 )).

Different (are the new meanings of the questions), because for Aristotle (See II Posteriora Analytica, Cap. 8,93a20  and  St Thomas, In II Post. An. lectio 8) a what-question without knowledge of the si est was at most just a quid est quod dicitur (what does the term conventionally mean?), while now, in the CREATURA consideration the what-question can be asked and answered in total independency of the si est question.
Rightly, AERTSEN detects an ambiguity in the business of asking. Perhaps somewhere a convergence will take place.

Before we turn to a discussion of the  v i a  p r a e d i c a t i o n i s ,  where especially the ens multipliciter dicitur ( NOTE 44 ), that is, the (aristotelian) Categories, are being discussed, and after that the definition, as the  v i a  d i f f i n i t i o n i s,  and because the definition belongs to the principles of demonstration,  it is, according to us, necessary to expound the relation of the above discussed Questions to the deductive demonstration, in order to not to lose track of the connection.
Scientific knowing concerns a (deductive) demonstration of the necessary attribution of a property to a subject. This discursive science is, however, based on metaphysical principles, because the demonstration must proceed from principles of demonstration, as Aristotle shows at the beginning of the Posteriora Analytica.
These principles of deductive demonstration comprise :

• An ontological hypothesis, namely that the subject  is  (that is, the existence of the subject [of the propery] is presupposed).
  This corresponds to the an est ( = si est).

• A definition, namely the definition of the subject (what the subject essentially is).
  This corresponds to the quid est.

• An inductive demonstration, namely that the property is on the subject (i.e. the actual existence of the property on the subject).
  This corresponds to the quia est.

• A deductive (discursive) demonstration, namely  why  the property is on the subject. The cause is here indicated in the middle term ( NOTE 45 ).
  This corresponds to the propter quid ( = in virtue of what), and this directly provides the answer to the question :  What is the property (quid est [accidens] ),  that is, not an indirect, but a direct description of it, and that is the definitio quid rei ( NOTE 46 ) of it ( NOTE 47 ).
  Before anything is posed or demonstrated at all, we ask quid est quod dicitur of which the answer is the definitio quid nominis ( NOTE 48 ).

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