(Takes a few minutes to load the images)

Aristotelian Metaphysics
Theory of Natures

Ontology of the individual thing

Part III

Substance and Accidents ( The Thing and its Determinations)
The Predicables

e-mail : 

Back to Homepage

This document is the continuation of the systematic and thematic exposition of Aristotelian metaphysics as a theory of natures, or the ontology of the individual thing.

Because, when expounding Aristotelian metaphysics, we will, in addition to the example of man, often use inorganic beings, and because, among these latter beings, we consider snow crystals especially instructive, we begin by reproducing (as we did in Part I) a few photographs of them from Fourth Part of Website.  They will serve us well in the ensuing discussion of the "via praedicationis", that is, the discussion about the aristotelian Predicables and Categories (Predicaments).

(From Part XXIX Sequel-32, After BENTLEY)

(From Part XXIX Sequel-32, After BENTLEY)

(From Part XXIX Sequel-32, After LIBBRECHT)

Figure above :  A snow crystal with sectored plates developed on its arms.
(After BENTLEY & HUMPHREYS, Snow Crystals, 1962 (1931).)

Figure above :  A snow crystal with sectored plates developed on its arms.
(After LIBBRECHT, The Snowflake, 2003.)

In the previous document we considered the four Fundamental Questions, revealing metaphysical presuppositions :  Via Quaestionis.  Now we will continue our enquiry into Aristotelian Metaphysics (with the help of St Thomas Aquinas) by investigating predication, leading up to an understanding of the aristotelian Categories :  Via Praedicationis.

Via Praedicationis


  1.   Catallelism and Predication
  2.   The Predicables (Praedicabilia)
  3.   The difference between Praedicabilia (Predicables) and Praedicamenta (Categories)
      and the difference between Predication and Signification.

     c1.  Meaning and Extension.  Distinction among the several Predicables revisited.

     c2.  Again, the distinction between  Difference (differentia [specifica] )  and
           Property (proprium).  Genotype and Phenotype.

  4.   Ens multipliciter dicitur.  The Predicaments or Categories.

     d1.  Substance

     d2.  Substantia dupliciter dicitur :  subiectum et essentia.

     d3.  The accidental Categories.

     d4.  Substantia dupliciter dicitur revisited.

  5.   The Essence
  6.   Idea as Essence.  Platonism
  7.   Predication
  8.   On our way to the Definition

a.  Catallelism and Predication.

Earlier we saw, following AERTSEN (where he is working on an exegesis of Thomistic texts), that by  asking  a way is opened to knowing. This asking is only then possible when that what we want to know is indeed liable to being 'interrogated'. Asking is always with respect to Beings, and if we suppose that knowledge is possible, then such a being must have a catallel nature (that is, a dual nature, or a nature consisting of two 'parts') in order to be liable for being questioned, because the question itself is also catallel, or can, at least, always be transformed into such a (catellel) question, as shown in the VIA QUAESTIONIS (previous document)  (A question only makes sense if there is, apart from something unknown, also something known, because a question must always be a question about  something ,  something that we as such already know).
Our presupposition that says that we can know, leads to the possibility to ask, and this in turn leads to the proposition that that something which we want to know must also be catallel :  It is a so-called 'transcendental' argument which leads to ontological conclusions, as KANT uses them to prove, among other things, that everywhere and always causality is at work. The value of such arguments is difficult to assess :  WILKERSON, T.E., Kant's Critique of Pure Reason, A COMMENTARY FOR STUDENTS,  1976,  discusses them at pp.199.
This catallel nature of question and answer automatically leads us to  predication  which is inseparably connected with it, because it is in fact here where the catallelism resides, and an investigation of it (that is, of predication) will, according to St Thomas, yield insight into the ontological structures of that what is being questioned. The way of predication is directive as to the questioning of Being and for the way of Being of that what is worthy of being questioned (AERTSEN, p.53).
The answer to the question should in the end become a definitio quid rei (a difinition that says what a given thing is), which will further be used as  middle term  in the demonstration of a proprium of a given subject (that is, the demonstration that a certain determination is a  per se  determination with respect to a given subject). Enquiry into the  per se -- per accidens  predication model yields insight with respect to the Essence, of which the definition is the logical counterpart.

In order to be able to evaluate the  via praedicationis  properly as to its alleged ability to provide knowledge, and further because predication plays such an important role in Scholastic writings (which have done a great deal of work to explain and further develop Aristotelian metaphysics), it seems to us not superfluous to systematicaly investigate predication by critically evaluating this scholastic tool.

b.  The Predicables (Praedicabilia).

Those terms which are signs that point to extra-mental things (that is, things that are independent of the thinking about them) were called in the Midle Ages  primae intentiones.  Today they are called terms of the object-language.
Terms that are signs for other terms were called  secundae intentiones.  Today they are called terms of the meta-language.
It is possible to order terms of first intension (primae intentiones) on the basis of their character (which is a logical undertaking), in virtue of which we classify and name the terms, yielding in this way certain secundae intentiones. For example, the term 'animal' (a term of first intention) relates to the term 'rational' (also a term of first intention) as genus to difference. These latter two are secundae intentiones (second intentions).
This ordering can, among other possibilities, take place by means of distinguishing several ways of predication, and it is this logical activity which make us able to distinguish the so-called  predicables.  Predication, namely, can be done in different ways (which will be discussed below). I have, in order to gain better insight, tried to use, in addition to classical examples, also other examples.
But before doing so, I must mention a number of consequences that flow from my view of Essence (as outlined extensively in First Part of Website ).
The Essence of a genuine complete being is, in that view, the dynamical law of the dynamical system which can generate that being (which we also call a Totality) from basic elements. This dynamical law is the genotypical aspect of that being. All  determinations ,  on the other hand, together constitute the phenotypical aspect, the concrete Totality, the relevant concrete being. These determinations can be  per se  with respect to the Essence, or only  per accidens  with respect to it. All these determinations manifest the in itself invisible Essence out into observable Reality. The formal aspect of the dynamical law is the substantial form of the given being.
Let us now apply all this to the predicables.
The  species  (logically) expresses this Essence.
The  genus  (logically) expresses this Essence in an incomplete way.
The  difference  (logically) expresses an essential quality as a further specification of the Essence.
So those entities to which the species, the genus, and the difference refer, belong to the genotypical domain of the Totality.
All other predicables, namely  proprium  and  accidens,  belong, as to what they refer to, to the phenotypical domain of the Totality, because they represent  determinations  generated by the (physically interpreted) dynamical law, that is, by the Essence of the Totality. They are the phenotypical expression of the Essence NOTE 49 ).  Genus, Difference, and Species thus stand (with respect to their supposita NOTE 50 ) in concrete cases) for the dynamical law or parts of it  ( This is worked out more fully below).
However, in far and away most cases the particular dynamical law is not known, and it is because of this that we are forced to work with the phenotypical representatives of dynamical laws.
Apart from signifying the Essence by Genus or Species, indication of the supposita of the predicables by means of phenotypic representatives of them is only necessary, there where a predicable stands for a closer determination NOTE 51 ) of the Essence (that is, an aspect of the Essence), and this is the Difference.  It accordingly will, out of sheer necessity, be expressed in the form of the (as such taken) phenotypic representative of it. With respect to Man we do this by using the term RATIONALE ( = being rational, that is, being able to discursively think), whereby we must realize that  being rational  as such is just a determination (because it is phenotypical). But we let  being rational  nevertheless refer to a part or aspect of the dynamical law (to which the term in fact does not refer, it refers in fact to something phenotypical), which we, as in the case of the dynamical law itself, unfortunately do not know. There where we do not do this (thus there where we pretend to be strict),  being rational  stands just for a (phenotypic) determination, namely a proprium (a  per se  determination). We will say more of this below.

Earlier investigations (performed in What is an Individuum? Part III, in the Classical Series of Documents of First Part of Website )  have shown that  m e t a p h y s i c a l l y  Socrates (or Plato, Peter, etc. for that matter) is not an individual of the species MAN, but of the species SOCRATES.  The species Socrates happens to be represented by only one individual, but this is accidental. If Socrates were a member of a monovular twin, then the species SOCRATES would be represented by two individuals, say, Socrates1 and Socrates2. The same goes for Plato, Peter, etc.
Socrates1 consists of a series of stadia (leading from young to old). Together these stadia form the  historical individual, Socrates1.  Each such a stadium is a here-and-now indivual (semaphoront) of Socrates1.  Also Socreates2 consists of a series of stadia together forming the historical individual Socrates2, and each such a stadium is a here-and-now individual (semaphoront) of Socrates2.
So the difference between Socrates and Plato is not an individual, and thus accidental, difference (a difference between two individuals of the same species), but a  s p e c i f i c  difference, i.e. a difference between two different species. In this way we do not have the special feature  person  as typical for human beings anymore. The clear differences between Socrates, Plato, Peter, etc. are specific differences reflecting correspondingly different dynamical laws (Essences), and are not remarkable anymore, as they should be if Socrates, Plato, Peter, etc. were all just individuals of the  s a m e  species (biologically, they still are, of course). And indeed, the members of the species Socrates, that is the members of the monovular twin, differ only little (as we see in actual monovular twins), as is to be expected from individuals of the same species.
Having said this, we can, in order to conveniently discuss the findings of Classical Metaphysics, still consider human beings -- figuring as examples -- as if they all belong metaphysically to one and the same species, because here we are not discussing Man but are only discussing what we should understand by the Essence, Genus, Difference, Species, Proprium, or Accident of some given intrinsic thing, whether this thing is Socrates, or a salt crystal, the dog Fido or a water molecule.

Genus and Species, for example Animal and Homo, are each for themselves not closer determined and not analysed, and consequently do not pose a problem. I let them directly refer to, respectively, the genus of the relevant dynamical law and that dynamical law itself. Further down I will say more about it.

Next we will investigate the different  ways of predication  and show how this investigation gives the five predicables (praedicabilia).
In the human example we will assume that all humans belong to the same species (HUMAN BEING,  HOMO), and that the genus (that is, the next higher logical level of generality) is ANIMAL.  Further, the difference is (assumed to be) RATIONALE ( = rational, i.e. able to think discursively). (Everywhere 'praedicare' = to predicate).
Sometimes we have, in the examples of the different types of predication (given below), used HAS (instead of  IS ).  In fact we should always predicate with IS (for example "a human being IS rational"), because in the present context it is always about what something IS.
If we predicate with HAS (if this is a genuine predication at all) then two beings (complete or incomplete) are expressed in the proposition, whether the attribute term is concrete as in  "Socrates HAS a nose",  or abstract as in  "Socrates HAS noseness",  or in  "Socrates HAS a length of 1.70 meter".
But in substance-accident metaphysics we always want to express the fact that Socrates (and also Socrates-for-example) is one being. And this can only be done by predication with IS.  And indeed, all 'predications' (propositions) with HAS can be transformed into equivalent predications with IS :

"Socrates HAS a nose" ==> "Socrates IS nosed"
"Socrates HAS noseness" ==> "Socrates IS nosed"
"Socrates HAS a length of 1.70 meter" ==> "Socrates  IS  1.70 meter long"

However, when we would carry out this transformation for all HAS-propositions, many of the resulting IS-predications would look awkward, so we abstain from carrying out such transformations (but know they can be done).

  1. Praedicare in quid  is expression of the Essence and is done with  Genus  or  Species.
    For example the predications :

    The  genus  expresses the Essence in an  incomplete  way (in quid incomplete), it signifies the qualifiable Essence (where the qualification can be done by adding the difference).

    The  species  expresses the Essence in a complete way (in quid complete), it signifies the qualified Essence (but does not mention the qualification explicitly).

  2. Praedicare in quale :  Here a quality (that is, a formal intelligible content) is predicated of a subject. This can be done in three different ways :

    1. Predication of the  s p e c i f i c  d i f f e r e n c e  (differentia specifica) means expressing an essential quality (in quale quid) in order to determine (qualify) the Essence further.
      For example the predications :

      • A human being ( = species)  is  rational  (difference predicated of species) NOTE 52c ).
      • Butane is saturated NOTE 53 )  (difference predicated of species).
      • Oaks are vascular (i.e. they are vascular plants) NOTE 54 )  (difference predicated of species).
      • An Ice crystal ( = species)  is  the  further qualification (involving the chemical compound H2O) of the concrete general crystallization law  (difference predicated of species). NOTE 54a ).

      REMARK : 
      The terms (as in the above examples)  'rational',  'saturated',  'vascular',  and also  'further qualification of the concrete general crystallization law'  are, as first intentions, all belonging in the Predicament of  'Quality',  that is, they signify predicamental accidents. Nevertheless, in the above predicative contexts they belong, now as second intentions, all to the Predicable  ' Difference'.

    2. Predication of  a  n e c e s s a r y  p r o p e r t y  :  that is the quality by which the Essence can be replaced :  the  proprium.
      It signifies not essential, but nevertheless diagnostic features.
      For example the predications :
      • A human being ( = species) has the  ability to laugh (is able to laugh)  (proprium predicated of species) NOTE 54b ).
      • Hover Flies (Syrphidae) possess a vena spuria NOTE 55 )  (proprium predicated of species (broadly the same applies here as what had been said in NOTE 53.  The 'species' is here not in fact a species but a higher genus, and the proprium is consequently not a specific proprium but a generic proprium).
      • Celestial bodies  can undergo an eclips  (proprium predicated of species [in fact of a genus] ).
      • Copper is cupri-colored  (not essential, but nevertheless typical for bulk copper) (proprium predicated of species).
      • Parasitic flies  ( Tachinidae) possess a so-called postscutellum NOTE 56 ) (proprium predicated of species [in fact, of higher genus] ).
      • An Ice crystal ( = species)  is  symmetric according to the space group  P 63 / m  2 / m  2 / c  and has chemical composition :  H2O  (proprium predicated of species).
      • A triangle ( = species) has  three angles that together make up 1800  (proprium predicated of species).

    3. Predication of  a  c o n c o m i t a n t  f e a t u r e,  that is an inessential content :  the  accidens.
      For example the predications :
      • A human being ( = species)  is  white  (that is, a human being is in some cases white [while in other cases he is black] )  (an accidens is predicated of a species).
      • An Alum crystal ( = species)  is  tablet-like formed NOTE 57 )  (an accidens is predicated of a species).
      • A shark ( = species)  is  aggressive NOTE 58 )  (an accidens is predicated of a species [in fact of a higher genus] ).
      • An Ice crystal ( = species)  has  six branches  (See, for example, Figure above ) NOTE 59 )  (accidens predicated of a species).
      • An Ice crystal ( = species)  has  sectored plates  (See, for example, Figure above ) NOTE 60 )  (accidens predicated of a species).
      • A crystal of Chrome Alum ( = species)  is  purple  (accidens predicated of a species) NOTE 60a ).

Praedicare in quid (1), praedicare in quale quid (2a) and predication of a proprium (2b) are three forms of  per se predication :  If of something a species, genus, or difference is predicated we get an ens per se NOTE 61 ), that is, a necessary unity.  For example :  the-human-being-Socrates, the-rational-Socrates. Predication of a proprium, on the other hand, results in a necessary twoness, for example :  Socrates, who can (as can all man and man alone) laugh NOTE 62 ).
In the first two cases of per se predication we get  things.  In the last case (proprium) we get  a  necessary state of affairs  (namely two entities that are coexistent). The 'necessary' in this latter case is weaker.

The accidental predication (2c) does not result in a necessary unity or twoness, so neither a thing nor a necessary state of affairs, but a contingent state of affairs. For example :  Socrates, who happens to be white (Socrates, as an individual of the human species, happens to be white) NOTE 63 ).

All up to now mentioned predications are genuine predications (logically per se predications).
Aristotle, I Posteriora Analytica 83a 14, however, also mentions the so-called quasi predications (logically accidental predications) :
  1. An  accident is predicated of an accident.
    For example :

    The literate is white.

    ( Socrates, as an individual of the species  human being  happening to be literate, happens to be white [not all humans are literate, not all humans are white].  It could still be that all literates are white, but this is not a necessary connection :  all literates then just happen to be white.  In fact also many black people are literate, so in any case literate is a true accident ).

  2. subject  is (as logical predicate) predicated of an  accident  (as logical subject).
    For example :

    The white is wood.

    ( " The white" here means :  " That white [some]thing overthere",  where "that something" must be such that for it to be white is not necessary, implying that here "white" is an accident.  "Wood" is a substrate [it carries white], and normally it is then logically a subject ['this wood is white']. Here, however, it is logically a predicate, while "white" [which normally is a predicate] is logically a subject ).

They are logically accidental predications, because in both cases of such a quasi predication something (the logical predicate) is only concomitantly predicated of an accident, and primarily, it is clear, always (predicated) of that something that is the carrier NOTE 64 ) of that accident (which accident functions as logical subject). Said differently :  In a quasi predication the logical predicate is in fact not predicated of an accident, but of the latter's carrier.

Let me expound this further.
The above predications

The literate is white

The white is wood

are, on the basis of their content accidental predications (in the sense of the last type of genuine predications, discussed above (2c)). This is because not every literate is white, and, respectively, not every white (thing) is wood.
They are, however, quasi predications because of the fact that their subjects (literate, resp. white) should in fact be predicates (Socrates is literate, this wood is white).
The logical subjects (literate, white) of the two quasi predications, clearly connote their own carriers, that's why the terms used (literate, white) are concrete. When their abstract counterparts were used, that is (abstract) terms that only signify a content without connoting the carrier of that content, then our predications would read :

The literateness is white

The whiteness is wood

which is nonsense (because literateness as such is not white, and cannot be white, and whiteness as such is not wood, and cannot be wood).
So the logical subjects must connote the carrier.
When we indicate this connotation more explicitly (then by just using concrete terms), our predications will then look as follows :

" This literate human being is white"

" That white thing there is wooden"

In the last predication we have replaced "wood" by "wooden", because "wood" was meant to signify something like "a concrete piece wood", only implicitly meaning "wooden". We have made that explicit.

Ontological Intermezzo

We spoke about the SUBJECT and about the CARRIER.
Roughly we can say that a subject is the logical counterpart of a carrier, and that a carrier is the ontological counterpart of a subject. A carrier can also be denoted by 'substrate'.
'Subject' figures in logic, while 'carrier' or 'substrate' figures in metaphysics. But often, namely when no confusion is to be expected, the term 'subject' is used where it is supposed to stand for a carrier.
When referring to determinations, the carrier carries the accidents (determinations), and in Classical Metaphysics this carrier is called 'Substance', that is, that what stands under (the accidents). As is evident, it is paramount for obtaining a healthy updated version of the Substance-Accident metaphysics that we must have a correct and detailed understanding of the carrier-as-such, that is, what it precisely means for something to be a carrier or substrate, especially for the case of something to be the carrier of accidents.
We did this in the documents  Revised Ontology of Determinations I  and  A Supplementary approach : Mereotopology of Reality  of the Non-classical Series of Documents in First Part of Website .
Let me reproduce the Section  The Totality and its determinations  from the first mentioned document  ( Revised Ontology of Determinations I ) :

The Totality and its determinations

When we inspect a generated uniform thing, a Totality, we see PARTS and DETERMINATIONS. For example when we look at an organism we see all kinds of anatomical parts like organs and limbs, but we also see determinations like magnitude, figure and color. In the same way, when we look at a crystal we can -- with the use of sophisticated instruments -- infer that they consist of parts, and (without such instruments) we can also observe certain determinations such as luster, color, hardness, magnitude and figure. Everything we see in and on such a thing we can interpret either as a part of that thing or as a determination of that thing. We don't see the Essence. This is of course because the Essence (forma totius) is abiding in the genotypic domain, not in the phenotypic domain. And if we interpret the parts of the thing also as determinations of the thing, then we can say that when we look at the thing we ONLY see determinations of the thing. We also understand that a determination cannot exist by itself, but only by virtue of that something of which it is a determination. In Philosophy it is expressed as follows :   An accident (in the metaphysical sense) cannot exist by itself but only when it is received in a subject. One identifies this subject as the (individualized) essence of the thing. And this subject, because it is not a determination, should have just an implicit existence, and when it is indeed seen as the Essence of the given Totality, and thus its cause, we obtain a second reason for it to have just an implicit existence, because all what is explicitly and actually present in the Totality is caused by the corresponding dynamical system, or in other words, all what is present in the Totality is an effect of the (concrete) dynamical law (= the forma totius ) and so is caused by the Essence. In fact also Classical Substance-Accident Metaphysics did ascribe a causal nature to the Substantial Form, and with it to the forma totius. And the Substantial Form is often identified with the Essence : The Essence, especially the Substantial Form, is the formal principle (while matter is the material principle) of the thing and so the forma totius is also the principle (the Essence) of the thing.
( The forma totius is the formal principle of a material thing, that's why matter -- taken in itself -- is the material principle ).
All those principles are ontological principles.
And an ontological principle (or Hartmannian category as one might say) has an abstract existence and is not as such observable. Only its corresponding concretum (which is the fulfilled principle) exists explicitly and on its own. This is also the case, as we saw earlier, with our dynamical law (of the dynamical system that generated the thing in question), which is also such a principle (namely a nexus category of a certain kind), and, indeed, it is the Essence of the thing. But because the only features we actually see, or can make in some way sensible, are determinations (when we interpret the parts also as determinations) of the thing, and because we also know that a determination (that is, any single determination) in itself (i.e. on its own accord) cannot exist (every type of determination is interweaved with all other types, like quantity implies quality, relation, etc.), we ought to conclude that we would not see anything at all when we look at the thing (the Totality), that is, when we go from one determination of it to the other and ask successively at each determination whether it is visible or not. But because we DO see all kinds of features in and on the thing we must conclude that only a COMPLETE COLLECTION OF ALL THE TYPES OF DETERMINATIONS is able to exist by itself, and be visible, while a single determination or an incomplete collection cannot. When this is correct we could interpret the  collection of all the types of determination  as the SUBJECT of whatever determination belonging to that collection. But this collection is caused, so although it is a subject, it is not the Essence of the thing (because the Essence is not caused, but causes). So that collection is the carrier or substrate of whatever single determination belonging to that collection. This collection can exist by itself only when it is a collection of determinations representing EVERY TYPE of determination associated with and demanded by the Real World (in contradistinction to the Ideal World -- See for these Worlds the Essay on  The Universal  in the Non-classical Series of Documents in First Part of Website ).  This needs one further precision. Because the Essence is immanent in the elements of the dynamical system that has generated the thing (the Totality), it is also immanent in the elements of the Totality, and so immanent in the Totality itself, and thus immanent in the subject.
So the very SUBJECT (that is, carrier or substrate) of every (single) determination (of the Totality) is :   The complete collection of these determinations + the Essence (the Essence being only implicitly present in that subject), + the prime matter (See next Remark), and one may add (to the characterization of the subject) :   minus that (single) determination of which we conceive its substrate. And thus the subject, so conceived, is the carrier of that particular determination.

Remark :   The just mentioned prime matter is -- as pure potentiality for content, and as ultimate substrate -- a principle of the possibility of radical change and (together with dimensive quantity) a principle of individuation. Prime matter, as ultimate substrate, is necessary for the SUBJECT to become itself a substrate (but only a penultimate substrate).

All this, however, needs some further qualification :
Elsewhere, namely in the Essay on Mereotopology in the Non-classical Series of Documents in First Part of Website , we discussed Substance within a more or less formal, mereotopological, approach (based on an article by SMITH, B. 1997). There we spoke about the CARRIER-ONLY, which is supposed to be the SUBJECT of the determinations, and we tried to assess that carrier-only, i.e. we attempted to determine the exact content of the concept CARRIER-ONLY, and obtained a somewhat different result, different from that what is stated above about the SUBJECT :
The carrier-only does not involve entities that are one-sidedly specifically dependent on it. Such entities (Accidents) are conceptually removed (from a full-fledged Mereo-totality - a Substance in the broadest sense, including non-scattered aggregates) resulting in the carrier-only. But we found out that not all such entities can be removed without destroying the specific identity of the Mereo-totality. The only entities that can be so removed are the occurrent entities, i.e. the replaceable determinations (Accidents) like being tanned by the summer sun.
In the present context these removable entities are the extrinsic determinations (time, place, thermodynamic conditions) as well as the intrinsic per accidens determinations  (like being tanned by the summer sun :  "intrinsic" because they are determinations wholly of the Totality or Mereototality,  "per accidens" because they just happen to be on the subject).  The determinations that should remain, i.e. that should not be removed, are completely specified individual determinations that are necessary for the (content of the) Mereo-totality's specific identity, but also every necessary sequence of determinations :   although the particular determinations, composing such a necessary sequence, are replaced by others (successively belonging to such a sequence) they cannot be removed, because the sequence as a whole is, ex hypothesi, necessary in constituting the Mereo-totality's phenotypical specific identity.
For the full-fledged Mereo-totality to actually be able to exist, it must involve a complete set of types of determinations, intrinsic and extrinsic. After removal of the replaceable determinations, but not of those that belong to a necessary sequence, we are left with the CARRIER-ONLY. So this carrier-only is still determined. It is determined by the "ESSENTIAL PARTS" (of the Mereo-totality), and, moreover, these 'parts' represent the only determinations of that carrier-only.
In the discussion above [the first part of the present Intermezzo], on the other hand, we found out that the SUBJECT is subject with respect to one or several determinations for which it is the subject. It was found to be identical to the whole Mereo-totality minus those particular determinations, and so this SUBJECT still contains, in addition to the non-replaceable determinations, some replaceable determinations.
But it is also possible to assess the SUBJECT (the carrier-only) in an absolute way, as we did in the mereotopological discussion :
When we consider all replaceable determinations (Accidents) 'simultaneously' to be involved in a dynamics of replacement, we finally will obtain the (genuine) CARRIER-ONLY (subject) just like that, i.e. in an absolute sense, after we have removed those determinations.
And this genuine carrier-only, the genuine subject in an absolute sense, is - as we found out in the mereotopological discussion - identical to the HISTORICAL individual : The individual, taken in its whole time span of existence, contains, in addition to its essential determinations, other determinations that are not fully specified (because they vary during the individual's existence), and that is equivalent to their being removed. What is left is indeed the carrier-only.

For the important argument (taken from the document on Mereotopology in First Part of Website) revealing not only what is precisely the carrier-only (that is, in the case of a true Totality -- fully-fledged substance, substance in the broader sense -- :  SUBSTANCE (s.str.)), but also (within that carrier-only) the boundary between the genotypic and phenotypic domain of a true Totality,  see this NOTE 64a ).

The complete set of types of determinations, mentioned earlier, is, as we found out in the mereotopological discussion, not the carrier-only (or subject) in an absolute sense, but only in a relative sense, namely with respect to one or another single determination (or a few such determinations), when viewed without these particular determinations. It (i.e. the mentioned set) is just a general precondition for the Mereo-totality to exist.
Determinations are always determinations of something (else). Parts of a subsistent being can also be interpreted as determinations. Everything that (ontologically) comes after the prime matter of such a being can be seen as a determination, including the essential parts. They are determinations of the prime matter. The latter is the ultimate substrate, the ultimate subject. But as such the substrate for any possible content.
End of quotation from First Part of Website.

The next Figure summarizes all the above results about the ontological constitution of a real being :

Figure above :  The ontological constitution of a real being.

END of Ontological Intermezzo

Above we had investigated predication, and the enquiry into the ways of predication yields the following predicables (praedicabilia) : They are the Genus, Species, etc. as such, and, consequently, not one or another genus, species, etc. (in that case they would be first intentions [primae intentiones] ).  They are Genus as Genus, Species as Species, etc., and as such they are second intentions (secundae intentiones), that is, logical entities, that result from (that is, are as such ascertained in) our way of thinking NOTE 65 ).

In order to obtain a better understanding of the Praedicabilia we will, in what follows, try to indicate several distinctions, whereby it automatically becomes evident that this is not so easy as seems at first sight (that is, when we would only consider the human example) :

The distinction between  genus  and  species NOTE 66 ) on the one hand, and  differentia, proprium  and  accidens  on the other, consists in the fact that the first are 'whatnesses', while the last are 'qualities' or 'traits'.

The distinction between the  accidens  on the one hand, and  proprium  and  difference (differentia) on the other, is that one or another accident (signified by the accidens) can at one occasion be present on a given individual subject, at another time not (anymore)  ( This either with respect to time, or to 'space', which latter means qua extension of the qualification (accident) over the (set of) individuals of the species  ( Some individuals have the qualification, others don't).
This is not the case for proprium and differentia.

The distinction between  proprium  and  differentia  is in fact very hard to ascertain. Often it can only be so ascertained in an arbitrary fashion.
If we ask :
"How can a human being be (typically) qualified?"  then we can say either :
"He is capable of laughing",  or (we can say) :
"He is rational".
Which one of these would be the essential quale (differentia) cannot be ascertained just like that. Conventially one says that it is "rational" that is this essential quale, while taking "capable of laughing" to represent the proprium. But this is an arbitrary decision. We will return to this problem later.

The distinction between  proprium  and  accidens  (which both must be in a subject) is that the accidens, with respect to a given subject, can vary (that is, replaced by another) in space or time, while a proprium is always present in the subject :  So it goes for  " The human being laughs"  that "laughs" is an accident (because he does not always laugh), while for  " The human being is capable of laughing"  "capable of laughing" is a proprium (because he carries this capability always with him).
Further, can (and must), together with a given proprium (in its definition), (also) a certain appropriate subject be mentioned, wherby it applies that this appropriate subject belongs to one species or one (higher) genus for which it is a proprium. So when we consider all individual white (physical) bodies, then those bodies that are always white, do not represent a genus or species, and therefore  white  is not a proprium NOTE 67 ).

In Book I of the  Topica  Chapter V, Aristotle defines four praedicabilia :
Definition, Proprium, Genus, and Accidens.
The Definition consists of Genus and Differentia, and can, therefore, in the list be replaced by the Differentia. So we get :
Genus, Difference, Proprium, and Accidens.
The fact that the Species is not mentioned forms a special problem  ( Porphyry [3rd century A.D.] does enter the Species in his Introduction to the Categories ) :  Science is not about particulars (because these are contingent), but about necessities. A species is only predicable of particulars (like Socrates :  "Socrates is a human being") (what is [by definition] subsumed under a species are just individuals), that's why Aristotle does not enter the Species here :  All terms are predicated of the species :  For demonstrative science the Species is the ultimate subject of predication (Indeed, science is about species and higher generalities, it is about iron and about metals, it is about light and sound, it is about the silk worm, butterflies and insects, it is about the mammoth, man and mammals. It is never about the dog Fido or the greek philosopher Socrates, that is, it is never about individuals in the sense of particulars).

All this, however, not in virtue of the terms themselves, but in virtue of these terms as they are (figuring) in a given predicative context (that is, as a result of our way of thinking) :  Because, when predicating the term  'capable to laugh'  of a given species, we mean (by this predication) the attribution of a quale (that is, a formal content) to the subject, which quale is such that it can diagnostically replace the Essence,  we characterize the term  'capable to laugh'  as representing a proprium, that is, as belonging in the Predicable ' Proprium'  (and so in the same way with respect to the other predicables).
So we see that by classifying a term, on the basis of what is meant in a given predication in which it figures, into one of the Predicables, we act according to general metaphysical presuppositions about reality, that is, about the ontological constitution of Being.

In order to understand well what is coming next, it is perhaps useful to give here the Categories (or, equivalently, the Predicaments), which will be treated further below. Together they form the most fundamental  generic diversity  within the domain of Being (s.l.).
Generic diversity originates by that which makes possible different types of predications about the subject -- as it is said by St Thomas in  In Metaph. V, lectio 9, nr. 891/2 :

   What the subject is.
   What the measure of the subject is.
   What the disposition of the subject is.
   To what the subject is related.
   What the subject 'possesses' (has on it).
   When the subject is.
   Where the subject is.
   What the pose of the subject is.
   What the subject does.
   What the subject undergoes.

This results, after maximally generalizing, in the ten highest Genera.
What then is the precise difference between these Categories (Predicaments) and the above considered Predicables?

c.  The difference between praedicabilia and praedicamenta  and the difference between predication and signification.

From what has been written in the Section on Predicables it is clear that the predicables are terms of second intention  ( that is to say, terms such as 'genus', 'species', 'proprium', 'difference', 'definition', 'accidens', and also the term 'predicable' ),  while the predicaments (categories) are terms of first intention
Recall that terms of first intention are signs signifying extra-mental things (A human being [that is, Socrates, or Plato, or Peter, etc.]  IS  an animal [ = collection of all sensitive organisms] ).  Terms of second intention are signs signifying other terms (of first or second intention)  ( The term 'animal' is a genus, that is the term 'animal' is a generic term.  In the proposition "animal is a genus" the term 'animal' refers to a certain type of terms [namely a genus, of which 'animal' is an instance], it [as 2nd intention] does not refer to extra-mental things like sensitive organisms ).
This difference (between predicables and predicaments) gets relief in the following :

The term 'color',  belonging in the accidental predicament 'Quality', and which (term) can be predicated in a per se manner of, for example, 'red[ness]' (i.e. in virtue of the essence of red[ness] ),  is the  genus  of 'red[ness]'.  That is to say, because the predication  " Red[ness] is a color"  is an essential predication (here  predicare in quid  with respect to an auxiliary being [namely red(ness) ] ),  the term 'color' is a genus (it is not a species, because the subject is not individual).  The term 'color' thus belongs in the Predicable 'Genus'. It is established now what kind of term the term 'color' is, namely a genus. And this genus is, as genus, a term of second intention.
As a term of first intention 'color' signifies something in extra-mental reality. It signifies a collection of things which are such that we can legitimately attribute the formal content  color  to it. When we, in steps, generalize 'color' we obtain a sequence of higher and higher genera. And the highest genus in this sequence (red-color- ...) is 'Quality'.  Now we know that 'color' belongs in the Predicament 'Quality' (and because red[ness] is [per se] a color, 'red[ness]' also belongs in this Predicament.
'Red'  as predicated  in  " The sun is red "  is, however, the predicable 'accidens' (because here the term is used in an accidental predication [the sun is not always red] ),  while 'red' is always (also) a predicamental accident (because it is a quality of a given individual being, that is, it belongs in the predicament of Quality, and is as such an ontologically dependent being) NOTE 68 ).  So the various members (red, color) in the same Predicament (Quality) can differ as to in which Predicable (genus, species, difference, etc.) they belong :

Color belongs to the predicable 'Genus'.  Predicative context :  red is a color  (predicare in quid [ = essential predication] with respect to a qualification [as subject] ).
Red belongs to the predicable 'Accidens'.  Predicative context :  the sun is red  (accidental predication).

Capable to laugh  is a quality (i.e. not as term, but in virtue of that in reality to which the term 'capable of laughing' refers). The term signifies something which cannot stand on its own 'feet' (i.e. which is ontologically dependent, it cannot exist all by itself) but must be in a subject (must be carried by a substrate), so this term is a predicamental accident (that is, the term belongs in one of the nine Predicaments that come after the Predicament of 'Substance', in the present case, the Predicament of 'Quality').
But when the term  capable to laugh  is predicated of  human being  (as in :  "a human being ( = species) is capable of laughing") it is the predicable  ' Proprium'.  The term  capable to laugh  is the predicable  ' Proprium'  because it can be predicated  only  as  proprium.
So as a term of first intention  'capable to laugh'  is a (predicamental) Accident, while as a term of second intention it is the Predicable  ' Proprium'.  Also here the difference between predicables and predicaments is evident.

The Predicaments (Aristotelian Categories) refer to the way of  b e i n g.  Therefore they, and the subordinates of each one of them, are, as terms, terms of first intention.
The Predicables refer to the way of  p r e d i c a t i o n.  Therefore they are terms of second intention.

St Thomas states in  In VII Metaphysica  nr. 1331, following the Stagirite ( = Aristotle), that (predicamental) accidents, strictly speaking, do not have a true quod quid est, that is, a definition, because in the definition of a given accident we must always include something extrinsic with respect to it, namely the subject. Insofar as one nevertheless wants to speak of the 'essence' of a predicamental accident (because predicaments are terms of first intention -- predicables do not have an essence), then one can do so only by way of analogy and via an abstract term, for instance the essence of whiteness (and not of white, which is a concrete term).

The predicables classify terms into groups, but, as we've said, only from a predicative context :  The term  'capable to laugh'  is in itself not a proprium, but a predicamental accident. But  'capable to laugh'  insofar as this is said from something in a per se way (per se predication) is a proprium  (And this is directly related to the extension of the terms or concepts [a concept is a natural sign, while a term or word is the corresponding conventional sign] ).
The way of predication (i.e. the different ways in which a predicate can be appropriate for a subject) is here accordingly the criterion for distinguishing the different predicables.
The problem with this, however, is that the 'way of predication' is also called a criterion for distinguishing the different predicaments from each other (Aristoteles, Metaphysica V, 7, and St Thomas In V Metaphysica, lectio 9, nr. 890 :
Unde oportet, quod ens contrahatur ad diversa genera secundum diversum modum praedicandi, qui consequitur diversum modum essendi NOTE 69 ) ).  So the via praedicandi here leads, according to St Thomas, to an understanding of the different ways of being expressed in the Predicaments (Categories).

William of Ockham (14th century) indeed states (according to the interpretation of MOODY, E.A., The Logic of William of Ockham, 1965, p.69, note 1) that the predicaments are not ways of predication, but ways of signification.
The name 'predicaments' suggests that it is about ways of predication, but the way of predication as such does not yield a distinction among the predicaments at all :

Socrates is (a) human being, Socrates is 1.70 meter long, Socrates is pale, Socrates is shoed, Socrates is cutting, etc.

If we look into the  per se / per accidens  character of such predications (and that is only possible after we have considered the signification (meaning)), we can distinguish between the predicables, that is, we can then determine whether a term is a proprium, accidens, genus, etc. is.
So it is the Predicables that are distinguished on the basis of ways of predication (and not the Predicaments). But distinguishing between ways of predication can only take place on the basis of the signification (meaning) of the terms. It is directly on this that the Predicaments are based. So the meaning of the terms determines directly into what Predicament the term belongs, while the predicative context determines to what Predicable the terms belong.

The Predicaments (Categories) are terms, as incomplex signs, for things (that is, to represent things by referring to them). They are not elements of propositions (predications), i.e. no parts of complex signs (propositions). Signification must precede predication, because the truth of propositions depends on the signification (meaning) of the terms. The Predicaments belong in that part of Logic which deals with the 'simplex apprehensio', that is to say, the first act of reason (the apprehension of the concept), and not the second act, the proposition. The Predicaments are ways of description of a given thing in which the degree of interiority of this description varies with the predicaments. Indeed, the description of a thing as  ' having shoes on'  (belonging in the Predicament ' Habitus' )  is very external, while 'being white' (belonging in the Predicament of 'Quality' )  is already more intrinsic, while something like  ' being a human being '  (belonging in the Predicament of  'Substance' )  is the most intrinsic way of description (way of signification).
So in this way we get the Predicaments as highest genera of these way(s) of description of a thing  ( That is to say, by maximally generalizing such descriptions [shoed, white, human being, etc.] we arrive at the ten upper genera, Habitus, Quality, Substance, Quantity, Relation, etc.)  NOTE 70 ).

If we consider a given term in ordere to determine its logical and ontological status, we first look to what this term means, and that is here, to what in extra-mental reality it refers, if it refers to that reality at all, and in so doing :  detached from any possible propositional or predicational context. That is we consider its signification. If this term indeed refers to something in extra-mental reality then it is a term of first intention. Such terms are classified by the system of Predicaments. In fact all terms of first intention can be reduced to ten types, classes or (highest) genera, the ten Predicaments. As to in what Predicament a given term of first intention belongs is determined solely from its signification, that is, from its meaning, apart from any predicational context.
When we now consider the given predication in which the term happens to figure, we determine, again on the basis of the term's signification -- and that is now on the basis as to in what Predicament the term belongs -- the present predicative context of the term, that is the  per se / per accidens  nature of the predication and in what way the term figures in the predication, that is, what status the content to which it refers has :  does this content completely or incompletely express the Essence of an intrinsic being, is it the content (quale) that completes the incompletely expressed Essence, is it the content that can, diagnostically replace the Essence, or is it the content that is accidentally attributed to the given thing? On the basis of this we determine as to what Predicable the given term belongs.
For example, the term 'rational' means some qualitative content. Therefore, logically, it belongs, as a term of first intention, in the Predicament 'Quality'. In the predication  " A human being ( = species)  is  rational "  this qualitative content is that what completes the incomplete Essence as it is expressed by the term 'animal'.  That is, here the term 'rational' is, as a term of second intention, a difference, that is, it belongs to the Predicable  ' Difference '.
So logically the term 'rational' belongs, as term of first intention, to the Predicament 'Quality', which is an accidental predicament, while as term of second intention it, as figuring in the predication  " a human being ( = species)  is  rational ",  belongs to the Predicable  ' Difference '.  And this means that although 'rational' is logically an accident its significatum does not reside in the phenotypic domain but in the genotypic domain of the given thing.
So ontologically the significatum of the term 'rational', as it figures in the predication  " a human being ( = species)  is  rational ",  is not something that is generated by the Essence (that is, is not a phenotypic expression of the Esssence), but is part of the Essence.
Realize, that the predicational context does not influence or determine the meaning (signification) of the term, but only its status, namely its ontological status (phenotypic, genotypic), as well as its logical status (as to what Predicable it belongs).
In our example we assume that 'rational' in the predication  " a human being ( = species)  is  rational ",  stands for the completion of the incompletely expressed Essence. The Essence is the specific dynamical law governing the dynamical system human being. The incomplete Essence is then the general dynamical law, while that what contracts this general dynamical law to our specific dynamical law is that what is supposed to be signified by the term 'rational' (We will return to this topic further below).

All this leads us to the question that asks what then indeed is the the distinction between predication and signification.
If there is a difference at all then it seems to be as follows :
Signification is the apprehension (simplex apprehensio) of the individual essence or, equivalently, the  quod quid erat esse  NOTE 71 ) of a thing, that is, the transforming of an object into a 'significant' object which exposes its 'pointe'. Next we apprehend the  quod quid erat esse  of another thing, and after that, of another thing, etc. And on the basis of the character of all these individual essences we form classes and subclasses.
This  quod quid erat esse  can also -- mutatis mutandis -- refer to a quantity, a quality, etc. The Predicaments signify the whatness, and that is here the most general whatness, of either an ontologically independent being (substance), or of an accidental or per se determination of it. In fact the predicaments signify always (also in the case of accidental predicates) the whatness of the thing (how it is determined in itself, or how it is determined  per accidens ) and, in so doing, they indicate the degree of interiority of this whatness [description].
The explicit emplacement of a thing (s.l.) or a group of things in a definite class by means of an assertion is then predication  ( 'Socrates is a human being' [Socrates is a thing belonging in the category of Substance],  'A human being is an animal' [Every human being (is a thing that) belongs in the category of Substance],  ' Redness is a color' [Redness is a thing that belongs in the category of Quality] ).
Summarizing :

Signification  is a relation (implicitly having it posited) between sign (signum) and signified (significatum), or, equivalently, between sign and the thing which corresponds to it outside the anima intellectiva (reason) :  This sign is first of all a so-called natural sign (intentio animae, Ockham, Summa Totius Logicae I. 1) which has a conventional sign as an effect (that is a spoken or written word).

Predication  is a relation between terms in virtue of their signification (meaning).

The  meaning  (significatio) of terms ( = incomplex signs) ultimately is formed by  ostensive definition (that is, via pointing to the signified (significatum) while at the same time mentioning the term).

As soon as we know the meaning of the terms (and if they are thereby univocal or considered as univocal) then we have a number of descriptions of things. If we make these descriptions as general as possible, then we are left with a number of fundamental ways or types of description (ways of signification), which indicate the whatness of a thing in as general a fashion as possible. These most general ways of description differ among each other, with respect to -- as has been said -- the degree of interiority of the description of the thing.
In this way we obtain the Categories or Predicaments. The supposita ( = that for which they stand) of these most general descriptions are  principles of being ,  as was stated earlier.

C1.  Meaning and Extension.  Distinction of Predicables revisited.

The meanings of terms also give directly their relative extensions. By means of these extensions (ranges of reference, which are themselves thus based on the meanings, significations of the terms) we can determine whether a given term belongs to the Predicable  accidens, proprium, genus, species or difference  ( In the context of discursive science the  species  does not belong here, while -- according to me -- it does so belong in the context of metaphysics). The relative extensions are, however, not sufficient. This is so, because, for instance, the relative extensions of accidens and species on the one hand, and the relative extensions of genus and species are identical :

(where Ext(X) = extension of X,   >  =  larger than,   <  =  smaller than,   acc = accidens,   diff = difference (differentia specifica) ) :

Ext(acc) > Ext(species)
Ext(genus) > Ext(species)

The other extensions are (the  species  not being accounted for) :

Ext(diff) < Ext(genus)
Ext(diff) = Ext(proprium)
Ext(diff) < Ext(acc)

Ext(genus) < Ext(acc)
Ext(genus) > Ext(proprium)

Ext(proprium) < Ext(acc)

So here we find the following equal relative extensions :

Ext(diff) < Ext(genus)
Ext(diff) < Ext(acc)

Ext(acc) > Ext(proprium)
Ext(acc) > Ext(diff)

Ext(genus) > Ext(proprium)
Ext(genus) > Ext(diff)

So in order to determine whether a given term belongs in this or that Predicable, the relative extension is not sufficient.
For to detect a distinction between, say,  genus  and  accidens  their extension with respect to that of the  difference  is of no use, because :

Ext(diff) < Ext(genus)  [ = Ext(genus) > Ext(diff) ]
Ext(diff) < Ext(acc)  [ = Ext(acc) > Ext(diff) ]

but also their extension with respect to that of the  proprium  is of no use, because :

Ext(genus) > Ext(proprium)
Ext(acc) > Ext(proprium)

How then must we discriminate between, say,  genus  and  accidens? This can only be done by considering the  way of predication  (predication  per se / predication  per accidens,  and within predication  per se :  predication  in quid  and predication  in quale,  and within predication  in quale :  predication  in quale quid ( = predication of the difference)  and predication of  a  proprium.
This way of predication takes place on the basis of the signification ( = meaning) of terms. From these meanings, that is to say, from the terms' intentions, the absolute extensions follow. The extensions consequently are the necessary result of the intentions. Nevertheless we discriminate between, for instance, an  accidens  such as 'white' and  a  proprium  such as 'capable of laughing' on the basis of how their extensions turn out to be :  Because 'capable of laughing' turns out to occur exclusively and always in the  species  MAN, we call it a proprium with respect to MAN.  And because 'white' turns out to occur also beyond MAN, it is in any case not a proprium with respect to MAN (as appropriate subject). Is it in the nature of WHITE also to occur in other things than humans? Probably so. Is it in the nature of CAPABLE OF LAUGHING to occur exclusively and necessarily in MAN? Probably so.
So the term 'white' signifies some formal content, and 'capable of laughing' also signifies some (other) formal content (implying that they both logically belong in the Predicament of 'Quality'). But their extension (range of signification) turns out to be different. In fact, WHITE  is  a  replaceable determination,  and so implies a substrate (on which it can be replaced by another determination [in te same Predicament] ),  while CAPABLE OF LAUGHING  is  a  non-replaceable determination (it is always present in any given human being), and thus does not imply a direct substrate (only an ultimate substrate, namely prime matter).
In this way we decide to which  Predicable  a given term belongs by considering the empirically assessed extension, in the case of  proprium  and  accidens (where the extension of  'capable of laughing'  suggests it to stand for a non-replaceable determination, while the extension of  'white'  suggests it to stand for a replaceable determination).
But with this we cannot ascertain whether the term 'capable of laughing' is  a  proprium  or  a  difference ,  because the extensions of  proprium  and  difference  are equal.
The distinction between  proprium  and  difference  could be that  a  proprium  refers to an ontologically dependent entity (while implying an appropriate subject), while the  difference  refers directly to the last over-forming, which has itself integrated as to become over-formed matter (integrated such that it is now over-formed matter) and is thus ultimately an ontologically independent entity NOTE 72 ).
A second distinction (related to the first one) could be that  a  proprium  is always and exclusively present with the Essence, without, however, necessarily following from it, while  a  difference  is a formal content that necessarily follows from the Essence, and that means here :  necessarily  is  the Essence :  the  difference  explicitly signifies the last over-forming and implicitly the rest, and thus it signifies the Essence.
However, these distinctions lack sense as long as we cannot objectively ascertain whether something, for instance that which represents CAPABLE OF LAUGHING, does or does not comply with the mentioned criteria. Does CAPABLE OF LAUGHING comply with the criterion that it is always and exclusively concurrent with the Essence (and with it with MAN) without necessarily following from that Essence? The first part of this criterion can be empirically verified, but as regards the second part we cannot indicate anything that would convince us that CAPABLE OF LAUGHING does not necessarily follow from the Essence, and that RATIONAL does necessarily follow from it :  RATIONAL is always and exclusively present at the Essence (that is, always present in MAN), but does it then necessarily follow from the Essence or not? Whatever answer we give -- in the present stage of the discussion (but see already NOTE 72) --, the answer is stipulative instead of being ascertained on the basis of enquiry.
Before we investigate this further, we can establish that the predicables  Genus, Species  and  Accidens  do not pose problems :

The predicable  accidens  has as suppositum NOTE 73 )  a  per accidens  determination ( = replaceable determination).
The predicables  genus  and  species  have as suppositum the Essence.
The  genus  expresses that aspect of te Essence that commonly occurs in the subsumed Essences (For example the genus animal refers to a common nature that is present in MAN, as well as in DONKEY, HORSE, DOG, etc.).
So genus  and  species  do not have as suppositum one or another  determination,  but the Essence itself.
But, as said,  proprium  and  difference  give problems, at least in Classical Metaphysics. In my revision (as has been laid down above, especially in NOTE 72, and as will be expounded further below) of this sproblem I have given an answer :  We can say that, with respect to MAN (but then generalizing all this), the features RATIONAL and CAPABLE OF LAUGHING are ontologically equivalent. Both are generated by the dynamical law, both are permanent and so do not involve inherence, both are phenotypic essential parts (namely certain material substructures of the human body), both are generated by that part of the dynamical law that we call the  difference.  This  difference  is the over-forming of the generic part of the dynamical law, and so is a genotypic essential part. In the definition of MAN we can (phenotypically) let represent this  difference  by either the feature RATIONAL or the feature CAPABLE OF LAUGHING.  Both are  propria.
That to which a  proprium  refers is phenotypic and not replaceable.
That to which an  accidens  refers is phenotypic and replaceable.
That to which a  difference  refers is genotypic and not replaceable.
In the following we will precisely and in more detail go through all this :

We have been able to established that the Essence of a genuine intrinsic complete being is identical to the dynamical law governing the dynamical system that can generate this being from basic elements.
In almost all cases (of such beings) we are not able to explicitly formulate this dynamical law (it is simply unknown). But for the exposition of the status of  genus, species, and  difference  this is not necessary. These status we can, and will, illustrate with the help of a number of simple abstract dynamical laws, expressed in a mathematical form  ( These laws are fictitious, i.e. without (possibility of) physical interpretation, but that is no obstacle because here it is about laws as laws). Such dynamical laws can come in all kinds of forms among which that of a polynomial (i.e. a mathematical expression involving more than one term). Let us give an example :

Xn+1 = 3Xn2 + 2Xn +7

Here Xn and Xn+1 refer to consecutive process states, and Xn2 means :  Xn multiplied by itself, that is, the square of Xn .
Xn ,  Xn+1 ,  Xn+2 ,  etc. are  variables,  and that means that they are each for themselves, as it were, a 'box' provided with  a  name  (that is, the name of the variable, as we have here for example "Xn", or "Xn+1", or "Xn+2" ),  and into such a box we can put one or another chosen or computed  value.  We then have a box with the name (pasted onto it), say, "Xn", and a value, say, 5 (put into it). We can change that value at will. So we can replace the value 5 in box Xn by the value 8. We then say that the variable Xn first had the value 5, while later the value 8 has been attributed to it.
The meaning of the above given expression (which is supposed to represent a dynamical law) is as follows :

The new process state, Xn+1 ,  is generated from the previous ('old') process state, Xn ,  namely -- in the present case --, as follows :  The new state, Xn+1 ,  becomes equal to :  Three times  the square of the old state Xn ( = 3Xn2 ),  plus  two times that old state ( = 2Xn ),  plus  7.

If we thus start with a value for Xn ,  then we can compute the value of Xn+1 as indicated above.
And then a new state is generated from the previous state.
From this new state a next state can in turn be generated (and thus calculated) by repeating the procedure. This we do by placing the computed value of Xn+1 back into Xn (that is, we rename the value that was computed for Xn+1 to "Xn" )  and introduce it back into the expression Xn+1 = 3Xn2 + 2Xn +7  (that is Xn ,  wherever it occurs in te expression, gets this new value). We can then calculate this next state. This can be continued as far as we want to, and what we get is a whole series of consecutive states. And because in this procedure every time the newly obtained value is intoduced back into the expression (the formula) as (now) representing the 'old' one (this we call 'iteratingNOTE 74 ) ),  we have to do with  a  feedback  system  ( feedback often occurs in organisms). Such type of dynamical system one calls  a  recursive system.
So here we have given an example of  a  polynomial  dynamical law (polynomial, because Xn+1 = 3Xn2 + 2Xn +7 is a polynomial, that is, it consists of more than one term, in the present case three [trinomial] ).
There are many such polynomial laws (to come up with) and these relate to each other as  genera  and  species.

In order to understand these  genera  and  species  we must have a closer look to the just given polynomial 3Xn2 + 2Xn +7 (which stands for the value of the state that follows upon Xn ,  or said differently, which belongs to the dynamical law Xn+1 = 3Xn2 + 2Xn +7 ) :
In this polynomial  '3'  is the  coefficient  Xn2 ,  '2'  is the  coefficient  of Xn  and  '7'  is  a  constant.
The highest power of Xn is here 2, and therefore we call  3Xn2 + 2Xn +7 ,  and of course also  3X2 + 2X +7,  a  quadratic polynomial (and  Xn+1 = 3Xn2 + 2Xn +7  a  quadratic  polynomial dynamical law).
The general form of such a quadratic polynomial can be denoted as follows :

a1Xn2 + a2Xn + a3

In the above discussed polynomial,    3Xn2 + 2Xn +7 ,  we thus have :
a1 = 3
a2 = 2
a3 = 7

There are, of course, also polynomials in which the highest power of Xn is larger than 2, as for instance the polynomial  2Xn3 + 5Xn2 + 7Xn +1  (where Xn3 means :  Xn times Xn times Xn ).  This is a polynomial in which the highest power of Xn is 3, and such a polynomial is called  a  cubic  polynomial. The general form of this type of polynomial is :

a1Xn3 + a2Xn2 + a3Xn + a4

We are now able to give the  most general form of  a  p o l y n o m i a l,  and with it, at the same time, the most general form of  a  p o l y n o m i a l  d y n a m i c a l  l a w :

Xn+1 = a1Xnm + a2Xnm-1 + a3Xnm-2 + .  .  .  + ak-2Xn2 + ak-1Xn + ak

where  a1 ,  a2 ,  a3 ,  .  .  .  ,  ak-2 ,  ak-1  are the coefficients of respectively  Xnm ,  Xnm-1 ,  .  .  . ,  Xn ,  and where  ak  is a constant.

The most simple polynomial is where the highest power of Xn is equal to 1. The general form of such a polynomial is :

a1Xn + a2

The dynamical law corresponding with this polynomial reads :

Xn+1 = a1Xn + a2

and such a law one calls  a  linear  dynamical law.  A species of it is, for example, Xn+1 = 3Xn ,  where, accordingly  a1 = 3,  a2 = 0 .

From the above given general form of a polynomial dynamical law, which we can consider to represent  an  Uppergenus,  we can derive a number  of  genera,  namely the Linear dynamical laws, the Quadratic dynamical laws, the Cubic dynamical laws, etc. These genera have, as direct subsumpts NOTE 75 ), not yet true  species,  but  subgenera.  But when we descend along the line general-special we'll finaly arrive at lowest  genera.
Every lowest genus consists of one or more  species (these latter are thus direct subsumpts of the former). An example of directly (i.e. skipping intermediates)  a  species  NOTE 76 )  of the (higher) genus  Linear dynamical laws  (which genus is :  Xn+1 = a1Xn + a2 )  is :  Xn+1 = 5Xn + 17 .

As we saw earlier, the genus  Cubic polynomials  looks like this :

a1Xn3 + a2Xn2 + a3Xn + a4

and the corresponding genus  Cubic polynomial dynamical laws  looks like this :

Xn+1 = a1Xn3 + a2Xn2 + a3Xn + a4

This genus is a high genus, that is to say that it contains possible subgenera as its (logical) subsumpts.

An example of a highest subgenus (of that genus) is :

Xn+1 = a1Xn3 + a2Xn2 + 14Xn + a4

A lower (and at the same time the lowest possible) subgenus is for example :

Xn+1 = a1Xn3 + 8Xn2 + 12Xn + 2

To the same group of lowest subgenera belongs for example :

Xn+1 = a1Xn3 + Xn2 + 6Xn + 4

To another group of lowest subgenera belongs for example the subgenus:

Xn+1 = 3Xn3 + a2Xn2 + 7Xn + 20

Because in such a (lowest) subgenus there is only one variable coefficient left, specification of it (that is, giving this coefficient a definite numerical value) -- and that is the determination of this (lowest) subgenus -- directly results in  a  species.  The just mentioned subgenus (but of course also all other lowest subgenera) can now also simply be called  a  genus.  It is then the  genus  of, for example, the following  species :

Xn+1 = 3Xn3 + 5Xn2 + 7Xn + 20

Another species of the same genus is for example :

Xn+1 = 3Xn3 + 7Xn2 + 7Xn + 20

Yet another species of this same genus is for example :

Xn+1 = 3Xn3 + 7Xn + 20

where the coefficient of Xn2 is thus equal to 0.

The Quadratic polynomial dynamical laws constitute, as has been said, yet another genus, the genus  Quadratic polynomial laws.  This genus has the following general form :

Xn+1 = a1Xn2 + a2Xn + a3

A lowest subgenus of it is for example :

Xn+1 = a1Xn2 + 5Xn + 2

species  of that lowest subgenus then is for example :

Xn+1 = 3Xn2 + 5Xn + 2

And another species is for example :

Xn+1 = Xn2 + 5Xn + 2

Another lowest subgenus is for example :

Xn+1 = 2Xn2 + a2Xn + 3

A species of this subgenus is for example :

Xn+1 = 2Xn2 + 18Xn + 3

Yet another species of this same subgenus (which we can simply call genus) is for example :

Xn+1 = 2Xn2 + 3

where  a2  has the value 0  NOTE 77 ).

We now have, by way of simple examples (of dynamical laws) an idea as to what we should understand by the suppositum NOTE 78 ) of a term that is predicated as the predicable  genus,  with respect to (genera of) true complete beings, and also the suppositum of a term that is predicated as  species  (also with respect to true complete beings).
In both cases the (often unknown, but nevertheless intended) suppositum is not  a  determination (of a being), but the Essence itself, either incompletely, or completely indicated.

If  we now inspect the two mentioned species of the genus

Xn+1 = 2Xn2 + a2Xn + 3  (where  a2  as coefficient shows the incomplete specification of the Essence),

namely (the species)

Xn+1 = 2Xn2 + 18Xn + 3


Xn+1 = 2Xn2 + 3,

then  the  differences (differentiae specificae) are, respectively :  {18} and {0}  
(where the notations are done in the form of sets :  "{18}" means :  "a set containing just one element, namely the number eighteen" ).

Upon generation of the respective  Totalities  as a result of those dynamical laws (if we assume that we here indeed have to do with Totality-generating dynamical systems), these  differences cause phenotypic  determinations,  such as RATIONAL (in the case of MAN) (these determinations are thus generated).
Such a determination accordingly represents an aspect of the Essence, said differently, such a determination is a phenotypic aspect of the corresponding aspect of the Essence (which itself is genotypic), or, yet in another way formulated, such a determination is the expression of an aspect of the Essence ( = dynamical law, which, as dynamical law of that  Totality-generating dynamical system,  was (and is) in operation).
Now suppose that  Xn+1 = 2Xn2 + 18Xn + 3  is the dynamical law (in its purely mathematical form) of every human individual NOTE 79 ).  And suppose further that its direct genus is :  Xn+1 = 2Xn2 + a2Xn + 3,  then the determination RATIONAL would be reducible to {18}  (the determination RATIONAL is a certain definite material [and thus phenotypical] substructure of the [brain of the] human body, and this substructure is co-generated by that what is signified by the term {18} [and indirectly by the term 'rational'] ).  The term {18} is predicated of the species as the  difference :

" Xn+1 = 2Xn2 + 18Xn + 3  ( = species)  IS  {18}  ( = difference) "

where  " IS  {18}"  means :  " has its coefficient  a2  equal to 18 ",
and where  Xn+1 = 2Xn2 + a2Xn + 3  is the genus.

In this proposition the specification of the genus, namely that  a2  in this genus is specified to be equal to 18, is predicated of the species (like we say HOMO est RATIONAL).  Here  "a2 = 18" (or simply "18") can be seen as the  name  of this particular  difference.  It signifies directly and explicitly that what precisely in reality is  "a2 = 18",  and indirectly and implicitly the genus, namely precisely that genus (Xn+1 = 2Xn2 + a2Xn + 3) of which  "a2 = 18"  is a specification, turning this genus into the species  Xn+1 = 2Xn2 + 18Xn + 3.
So if we say that a certain material substructure, 'making the difference' in the sense that it specifically qualifies a given Totality, is generated by that part of the dynamical law which is signified by the  difference term (which part of the dynamical law is the part that over-forms or specifies the generic part, and is the '18' in the above example), we must realize that we're here speaking about that what is directly and  explicitly  signified by the difference term. In fact the difference term in addition refers, but now implicitly so, to the rest of the dynamical law, and thus the mentioned material substructure is generated, not solely by the part of the dynamical law that is explicitly signified by the  difference term, but (is generated) by the whole dynamical law, i.e. the (fully) specified generic law (where, then, as a result, this generic law has become the the specific law).

Still to discuss is how to establish the distinction (if there is any) between  difference  and  proprium.
Earlier we already discussed this problem, and the results were summarized in the diagram above .
It is good to continue this discussion, because it will reveal more and more about the ontological status of determinations, and the ontological structure of several types of things. In this continued discussion we try out different solutions to the problem of the distinction between  difference  and  proprium.
The phenotypic feature CAPABLE OF LAUGHING (to stick with the HUMAN example) is present in every human individual and only in human individuals. This indicates that it must be an effect, a product, of the Essence and only of the Esssence. The same goes for the phenotypic feature RATIONAL. As such, both features can be penultimately reduced to certain material substructures of the human body.
We now stipulate that in that case in which we call  RATIONAL  a  difference  (and consequently not  a  determination), we then let the term 'rational' directly stand for a part or aspect of the dynamical law (as we did with the fictitious law above). The term thus refers to something that belongs to the genotypic domain. In the case, however, where we let RATIONAL to be  a  determination  (which is perfectly legitimate in another context), the term 'rational' refers to a particular material part of the human body, and thus it refers to something that belongs to the phenotypic domain.
But we can do the same with respect to the feature CAPABLE OF LAUGHING.
This feature must, like RATIONAL, ultimately originate from the over-forming of the generic part of the dynamical law.  If we see it as  a  determination,  then the term refers to a certian material structure of the human body. If we see it as  the  difference,  then the term directly refers to the mentioned part or aspect of the dynamical law.
Both features, whether as penultimately reduced to material structures (generated by the dynamical law) or as ultimately reduced to parts or aspects of the dynamical law (aspects that over-form the generic part), are permanent and thus belong to the carrier-only (either as essential parts in the genotypic domain, or as essential determinations in the phenotypic domain), while replaceable determinations do not belong to the carrier-only, but only inhere in it.
In the form of determinations both features are material parts of the Totality and can be expressed in a metaphysically correct way by a predication, as we have done this with the nose of Socrates (See the document  Revised Ontology of Determinations Part I  in the Non-classical Series of documents in  First Part of Website ).  This nose is, as the material structures under discussion, a material part of Socrates, and can in a physical context be predicated with HAS :

Socrates has a nose

Here we speak about two things, one possessed by another.
But if we want to express the unity of Socrates + nose -- and then we find ourselves in a metaphysical context -- we predicate with IS :

Socrates is nosed

Precisely the same we should do with the mentioned material structures representing the features RATIONAL and CAPABLE OF LAUGHING.
A special part of the dynamical law, namely that part which over-forms (that is, specifies) the generic part of the law, is responsible for the generation of specific and permanent determinations, like, for instance, RATIONAL and CAPABLE OF LAUGHING in MAN.  Terms directly referring to such a (specifying) part of the dynamical law (of whatever being) belong in the Predicable  difference.

The use we made above of a fictitious and simple dynamical law to indicate the supposita of  genus, species  and  difference,  of course embodies  a  very simplistic representation  of the real state of affairs. It only gives a rough simplified analogy of that what really is the case in the constitution of every human individual.
The real dynamical law of every human individual (which law, for the sake of the present argument, is held to be the same-qua-content in every human individual) is, of course, much more complex, and as such still unknown (much of it is [penultimately] contained in the set of instructions in his DNA).
However, what ontologically counts in these matters is to sketch an image of the general state of affairs with respect to the supposita of the predicables  genus, species, difference and  proprium.
In addition to all this we can be sure that there is no direct isomorphy (that is, a one-to-one mapping) present between the dynamical law and the generated determinations, that is to say, there is no direct correspondence between the particular parts of the dynamical law on the one hand, and the particular determinations (of the Totality) generated by that dynamical law on the other. Said differently, there is no direct correspondence between the structure of the dynamical law and the structure of the Totality (generated by that dynamical law). There are only certain definite relations of dependency, unknown to us, between dynamical law and Totality. The special relations of dependency between the parts of the dynamical law on the one hand, and the parts of the Totality on the other, which, as has been said, do not form an isomorphy NOTE 80 ),  are virtually unknown, except for a number of cases of known gene expression.

Earlier (in the above mentioned document in First Part of Website) we had found that  determinations  can in fact be reduced, (1) in some cases to corresponding  concrete parts  of, or  concrete structures  in, the Totality,  and (2) in other cases to  concrete interactions  of the Totality with external agents (these latter give the  per accidens  determinations).
The ultimate form, however, of many such  determinations,  such as (to be) RATIONAL NOTE 81 ) and the like, are  high-level features,  that is, features residing at a high structural (morphological) level of the given Totality, features which present themselves out into reality, it is true, but are not visible as a definite individual material local substructure, such as Socrates' nose. They are materially scattered all over the Totality, or (scattered) over a more or less large material part of the Totality, and this means that these features are not present anymore at a low level. They are called  emergent  features or phenomena. Said differently, they are  epiphenomena ,  they are generated on top of the lower morphological levels.
Of course there are also many  determinations  that reside at a low material level in the form of small parts of the Totality.

C2.  Again, the distinction between  Difference  and  Proprium.  Genotype and Phenotype.  The  per accidens  nature of  Determinations.

Earlier we have distinguished between  per accidens  determinations and  per se  determinations of a Totality.
However, Classical Metaphysics holds that all determinations are  per accidens,  even  a  proprium NOTE 82 )  (which is supposed to accidentally always go along (together) with the Essence).
Now it could be the case that this classical position is correct (or partly correct) after all, namely in virtue of the following reasons :
Determinations  belong (according to my revision) to the 'phenotypic' domain or range of a being, that is, they belong to the  concretum end  of the  principle-concretum duality, that is, the duality constituted by a principle and that which is determined by that principle)  ( The Essence lies in the 'genotypic' domain or range of a being, and with that it belongs to the  principle end  of that duality).
Determinations  (except those that represent the setting of the Totality with respect to Time and Place) are reducible to concrete parts (sometimes scattered) or concrete structures of the Totality, and thus originate (as to a certain aspect of them) necessarily from the Essence.
But it is possible that such a concrete part or structure later -- that is, after its generation -- becomes damaged, or even -- as a result of such an act of damaging -- totally disappears, without the Essence being changed or destroyed  (the latter would mean a substantial change of the Totality into one or more other specifically different Totalities). In this way a given human individual can, as a result of disease or accident, lose certain capacities, without causing the individual to die or lose its identity.
Crystals  are more sensitive in this respect (i.e. they are eidetically NOTE 83 )  less stable) :  A change in chemical composition (except where this is just a substitution of one atomic species by a different but similar atomic species) directly entails a substantial change, that is, the Totality turns into a specifically different Totality NOTE 84 ).
Only a substitution of an atomic species for a different but similar atomic species, or the replacement of atomic species, only at the crystal surface, by other atomic species (similar or strongly differing), for instance in the case of a light weathering of the crystal (surface), can be interpreted as just an exchange of a given determination (first case) or just an 'illness' of the crystal (second case) (and thus -- in both cases -- the crystal's specific identity staying the same), and need not be interpreted as a substantial change. The crystal remains what it was. Substitution or (superficial) weathering never involves a macroscopic anatomical part of the crystal (by means of that part being lost or replaced), because crystal doesn't have such parts, it is everywhere (i.e. at every location [larger than its unit cell] in the crystal) the same with respect to structure. So in the case of substitution or weathering the erasion of one or another existing  per se  determination  is out of the question. Rather  a  determination  is exchanged (in the case of substitution), or, in the case of weathering one is added :  weathered  (Of course we can, before that had happened, say that the crystal had the determination  unweathered,  but this looks more like  a  privation  of  a  determination). And the exchange between one particular ratio obtaining between two atomic species (in the crystal) and another such ratio (as such an exchange takes place in substitution) is  per accidens  with respect to the crystal's Essence. The same applies to the case of superficial weathering :  The determination  weathered  is  a  per accidens  determination, because it is induced by certain external factors that accidentally prevailed, and --ex hypothesi -- having affected the crystal's surface only.
But because a crystal has no (macrocopic) anatomical parts,  per se  determinations of it cannot (together with these parts) be erased while the Essence remaining the same. The  per se  determinations are all  all-pervading  determinations. In a crystal there are, in contrast to organisms,  no  per se  determinations intrinsically connected with certain macroscopic anatomical parts of the crystal (which parts could then get lost) resulting as such in such  a  'per se'  determination to be in fact -- abeit in a weak sense -- a  per accidens  determination (like we do see it in the case of RATIONAL or CAPABLE OF LAUGHING). In a crystal it is such that if there are  per se  determinations at all, then they are genuinely  per se  determinations. And this is denied in Classical Metaphysics.
In  organisms,  which always possess (macroscopic) anatomical parts, that can execute certain biological functions, and thus embody certain capacities, matters are, as we saw, different :  There  per se  determinations, if they are embodied in such anatomical parts, can be erased after their initial generation (as we said, as a result of disease or accident), making such determinations (insofar as they are phenotypic) weakly  per accidens  determinations.

So in complex beings, such as organisms, some  per se  determinations can -- while the Essence remains the same -- be erased or replaced by other determinations, making these determinations, in a sense (that is, in a very weak sense)  per accidens  determinations. Such determinations are, among others, RATIONAL and CAPABLE OF LAUGHING :  normally they remain -- as specific proprium -- present in the human individual, but they can get lost.
Such changes, as a result of damage of some local structure embodying a proprium, can result in privations, but also in an exchange of functions (the new 'function' is in such cases not always very useful for the organism involved).

Now it is possible to indicate the real distinction between  proprium  and  difference :

While  a  d i f f e r e n c e  can never be erased or exchanged (by another difference) without destroying or changing the Essence of the involved being, a  p r o p r i u m  can, in some cases, namely some propria in complex beings, be erased or exchanged while the Essence of the involved being remains the same.

difference  (that is, one or another  difference) directly refers to the Essence, as Classical Metaphysics asserts to hold, as I have shown above by means of example-laws (i.e. fictitious dynamical laws in their not physically interpreted mathematical form). As long as no substantial change takes place, the Totality (the thing, the being) does not experience an exchange of  difference  because it does not undergo an exchange of its Essence. The suppositum of the  difference  belongs to the 'genotypic' domain of the Totality, and is  per se  with respect to the Essence concerned.
The corresponding local material structure generated by the dynamical law, especially in virtue of its (specific) over-forming, is a  determination  and as such residing in the 'phenotypic' domain of the thing concerned. This material structure, can, where the causal path between it and the dynamical law is long, be erased or exchanged, making, as has been said, this  determination  a  per accidens  determination in a weak sense. Because the  difference  is a part of the dynamical law of the Totality it is, as the dynamical law itself, an  all-pervading  formal content, that is a content that is everywhere present in the Totality, it cannot be erased or exchanged by the destruction of some material part of that Totality.

proprium  (that is, one or another  proprium) always refers to a  determination  (as Classical metaphysics also holds), and therefore it always refers to something in the phenotypic domain of the Totality.
While the signification of a given  difference  goes all the way down to the dynamical law (that is, to the Essence of the Totality), the signification of a given  proprium  halts at the corresponding local material structure, that is, it remains in the phenotypic domain of the Totality.
The local material structure, which is the significatum of the given  proprium,  can, where the causal path between it and the dynamical law is long, be erased or exchanged, making also this  determination  a  per accidens  determination in a weak sense.
If the  proprium  happens to be an  all-pervading  formal content of the Totality, it cannot be erased or exchanged by the destruction of some material part of that Totality.

We can illustrate the case of non-erasable or non-exchangeable  determinations  by looking at crystals :
In crystals there is -- as in all simple beings -- a much shorter path of dependency between the genotypic domain (the dynamical law, or Essence) and the phenotypic domain of the Totality (that is, the individual crystal).
The  Space Group  of a given crystal is, as expounded in First Part of Website, the description of the total symmetry of the crystal, thus including that symmetry which is visible only at the microscopic level. From this it is evident that the Space Group of a given crystal is a (qualitative)  determination (and thus residing in the phenotypic domain of the crystal). This determination is, however, an  all-pervading  determination, that is, a determination that is present everywhere in the crystal. So it is not connected with one or another particular concrete part of the crystal. It is connected with the whole crystal individual. The Space Group concerned remains the same in all growing stages of a given individual crystal, but a number of other crystal species possess the same Space Group (that is, have the same total symmetry). So the Space Group is  a  generic proprium.
Something similar can be said about the  Chemical Composition  of a given crystal. It can also be considered as a (qualitative)  determination of the crystal. It is also an all-pervading determination, and also residing in the phenotypical domain of the crystal. And, like the Space Group, it is  a  generic proprium,  because other crystal species can have the same chemical composition.
The  Space Group PLUS Chemical Composition  (S + C) also remains the same in all growing stages of the given crystal, but does not as such occur in any other crystal species.
And of course also S + C is phenotypic, and therefore  a  determination (and thus it is not the Essence itself, it is generated by the Essence). So we can consider S + C to represent a proprium, namely  a   s p e c i f i c  proprium.
Hoewever, S + C is an  all-pervading determination  and cannot, therefore, as such be destroyed or exchanged while the dynamical law (the Essence) remains the same (as, in contradistinction to this,  is  so  with respect to RATIONAL and CAPABLE OF LAUGHING in the case of a human individual, because in a human individual the causal path leading from the dynamical law to the corresponding local material structures, respectively embodying these features, is much longer than the corresponding path is in crystals and other simple beings).
S + C (Space Group plus Chemical Composition in crystals) evidently is  a  direct  consequence of the dynamical law (which here is the relevant crystallization law).
S + C is the immediate (phenotypical) expression of the Essence of the given crystal.
Consequently, the proprium S + C (or, expressed better, the suppositum of the proprium S + C [where S, as well as C is named, and thus where "S + C" is a term] )  is  a genuinely  per se  determination ,  and not  a  per accidens  determination in any sense.
So indeed there exist  propria  that are truly  per se  with respect to the Essence of the given Totality, at least in crystals NOTE 85 ).
And, as we have seen in the NOTE just given, also organisms have such truly  per se  propria, namely in the form of their specific DNA structure, in addition to not truly  per se  propria, such as RATIONAL and CAPABLE OF LAUGHING.
Let's summarize these findings.

This is further summarized in the next diagram :

Figure above :  Causal connections between the dynamical law, DNA instructions, DNA chemical structure, generated material structures, and high-level features.
The complete set of DNA instructions forms the pen-ultimate dymamical law of the given organism.

In the next document we will continue with the Predicables, and reconsider them within a mereotopological framework, that is, we consider a given genus, species, difference, proprium, and accidens in terms of parts and boundaries, in this way supplementing our understanding of them.
Mereotopological theory has been developed in the document  A Supplementary Approach :  Mereotopology of reality  in the Non-classical Series of documents in First Part of Website .

e-mail : 

To continue
click HERE
for further study of the Theory of Natures, Part IIIa.

Back to Homepage

Back to Contents

Back to Part I

Back to Part II