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Aristotle's doctrine of the Predicaments has, since St Thomas Aquinas (and here and there already by St Thomas himself) undergone changes, and in order to obtain a good understanding of the Predicaments it is useful to succinctly discuss these changes. We begin with the first Predicament :

d₁.  Substance.

The term 'substance' is a term of first intention and signifies disjunctim ( = disjunctively, that is, with  or .  .  ., or .  .  .) several individual things which exist ontologically independently.
First we note that the concept 'substance' does not delimit itself clearly from the concept 'aggregate of substances' :
It is possible that many individual, and even specifically different, crystals (which each for themselves are individual substances in the metaphysical sense) have come together in a regular pattern, forming higher-order individuals, as we see it for example in graphic granite, where quartz and feldspar crystals interweave regularly. From here we see in Nature a gradual transition to a lesser and lesser regular aggregation of (for instance) crystal individuals, corresponding to the crystal lattices of the component crystal species becoming less and less compatible with each other. Eventually we end up at an aggregate of randomly oriented crystal individuals as we see it in normal granites.
Also in the organismic world it is, especially in the case of lower organisms, often hard to establish what really is 'the' individual, the truly 'unum', for example in the case of Sponges and many plants. Here the distinction from 'colonies' (that is, clear multiplicities) becomes increasingly more vague. Indeed, Van MELSEN, A., Natuurfilosofie, 1955 speaks (for example on p.140) of the 'analogy' of the concept 'substance' (as ontologically independent entity) ( NOTE 87 ).  It is, according to him, a typically philosophical concept (analogous or equivocal concepts never were accepted by men like Duns Scotus and William of Ockham).
But the concept of 'substance' does not to be abandoned because of this. It does become, however, much more theoretical, that is, that for which the concept of 'substance' stands is not directly observable anymore, as all theoretical constructions are. This is because of their higher degree of being fundamental  ( The true significatum of the term 'substance' is, as carrier-only, the historical individual, that is, the complete sequence of consecutive states, which (sequence) is as such not observable :  what we observe is always a here-and-now state of affairs). The same we've seen in the case of the significatum in re ( NOTE 88 )  of the concept 'difference' (differentia specifica). Here this significatum is not something like RATIONAL (in the case of man) but the dynamical law AS SPECIFIED ( = dynamical law as specifically over-formed), and such a law is not as such observable anymore.

d₂.  Substantia dupliciter dicitur :  subiectum et essentia ( NOTE 89 )

According to AERTSEN, p.60, St Thomas, in  De Potentia, 9, 1, finds out that the Philosopher ( NOTE 90 ) distinguishes, within the notion of substance, between substance as  ipsum subiectum ( NOTE 91 ),  which cannot be predicated of something else,  and  substance as  forma vel natura subiecti ( NOTE 92 ),  which can be predicated of something else :  "Socrates is a human being". Here "Socrates" is first substance, while "human being" is second substance.
The term 'human being' is supposed to signify the so-called essence of Socrates (not as Socrates), and this term signifies it in the way of a whole, that is, it signifies the essence as if this essence were some whole, which in turn means that 'essence' is, in this signification, taken, not as something abstract (such as 'humanity'), but as something concrete (such as 'human being')  (See St. Thomas in his  De Ente et Essentia (Leonina edition), Cap.III, lines 20-25), namely :  the term 'human being' explicitly signifies the essence, and implicitly and indistinctly it signifies all what is in the (given) individual. Therefore direct predication of the term ('human being') of an individual is possible ('Socrates is a human being').
If, on the other hand, we take the essence precisely as it is in itself, and only as it is in itself, then we must disregard everything not belonging to that nature :  See De Ente et Essentia, Cap.II, from line 253 :  Si autem significetur natura speciei cum precisione materie designate [medieval spelling] que est principium individuationis, sic se habebit per modum partis, et hoc modo significatur nomine humanitatis, humanitas enim significat id unde homo est homo. Materia autem designata non est id unde homo est homo ...  ( NOTE 93 ).
Indeed, St Thomas agrees with Avicenna ( NOTE 94 ) that the quidditas (whatness) is not the same as the composite (compositum), despite the fact that the quidditas as forma totius is also a compositum :  immo oportet quod sit recepta in aliquo quod est materia designata (still, De Ente et Essentia, Cap.II, at about line 270) ( NOTE 95 ).
The Essence is thus taken up into one or another subject which directly individualizes it :  By reason of distinguishing between substantia prima (first substance) and substantia secunda (second substance) St Thomas is forced to assume a principle of individuation which is perhaps hard to defend, for he states (1) that it should be imagined as originating from matter, but this matter is pure potentiality, and (2) (he states) that the Essence is supposed to be received into a subject which embodies the accident Quantity, and this is also not without problems ( NOTE 96 ).
Not all medievals took things this way :  According to Ockham, for instance,  to be  and  to be an individual  are identical :  Only individuals exist, if something is, it is automatically individual. There are no universals that allegedly must be 'contracted '  to an individual :  For this is a turning point :  The fact that St Thomas sets up a principle of individuation indicates that he, in the problem of universals, (moderately, it is true) adheres to a realistic position ( = universals do exist in extra-mental reality), which is disputed by Ockham :
Only individuals exist. Consequently there is no need for a principle of individuation.
In the first part of his Summa totius logicae Cap.7 Ockham presents a proof of the theorem  ' homo est humanitas '  ( = man is humanity). This statement is meant to show that there is no distinction between first substance (homo) and second substance (humanitas).
The point of departure of the proof is the (assumed) fact that the term  ' Socrates '  means, also for the opponents of Ockham, exactly the same as the term  ' Socratity ' ( NOTE 97 ). For if they would mean different things, then by  'Socratity '  the individuality of Socrates would not be co-signified, an then  'Socratity '  could also refer to Plato, precisely as  ' humanity '  refers to Plato as well as to Socrates. And then there would be no distinction between  ' humanity '  and  'Socratity '  [which there must be, because  'Socratity '  is more specific than  ' humanity ' ].  So Socrates = Socratity. From here, the argument is continued :  It is clear that the term  ' humanity '  is the more general term (i.e. it refers to more individuals) as compared to  'Socratity ' ,  and, consequently, also more general than the term  'Socrates ',  and thus the term  ' humanity '  can be directly predicated of   'Socrates ' :  Socrates est humanitas ( = Socrates is humanity), instead of Socrates habet humanitatem ( = Socrates has humanity). And this immediately means that the term  ' humanity '  does not signify cum praecisione (that is, as a part) anymore, but as a whole (Said differently :  the term  ' humanity '  is not an abstract term anymore). So, contrary to the opinion of St Thomas, direct predication (that is, predication with "is")  is  possible (Socrates is humanity). And as soon as we realize that this same argument also holds for Plato, Peter, etc., we can, generally, say :  man is humanity (homo est humanitas). So there is no distinction between first substance (exemplified by homo) and second substance (exemplified by humanitas).
Nevertheless Ockham does not consider the term  ' man '  and the term  ' humanity '  as mere synonyms :  The abstract term  ' humanity '  is, so he says, not purely significative, because in a concealed way syncategorematic terms ( NOTE 98 ) are included in it, resulting in the fact that  ' humanity '  can only be understood in a propositional context of necessity :  ' humanity '  then means  man qua man  (man, considered only insofar as man), or (it [equivalently] means)  man necessarily is .  .  .  ( The term  ' humanity '  signifies all the [relevant] individuals coniunctim [that is, as  and ..., and ... ] instead of disiunctim [that is, as  or ..., or ... ] as does the term  ' man ' ).
This means that the abstract term can be eliminated and can be reduced to a propositional context of necessity in which now the term appears in its concrete form. The fact that terms, from the Category of Substance, while being concrete terms, have abstract counterparts, (such as the concrete term  ' man '  having  ' humanity '  as its abstract counterpart), has persuaded many a philosopher to interpret concrete terms (such as  ' man ' )  as connotative terms, precisely as is the case in the concrete terms from the Category of Quality. Thus because a white thing is white in virtue of the whiteness (as accident) which it has (which resides in it), one also went on to say that a human is human in virtue of the humanity (as essence) which resides in him (the term  ' white '  connotes whiteness, the term  ' man '  connotes humanity). This directly involves the Problem of Universals and the Problem of Individuation (See the above mentioned document What is an Individuum? Part II [First Part of Website, Classical Series] on the individuation principle as worked out by St Thomas, and our thematic discussion directly follwing it).
Because in the view of St Thomas  ( De Ente et Essentia, Cap.III, line 23) still the Essence, expressed by the term  ' man ',  implicitly contains all what is in the individuum (that is to say, the term  ' man '  signifies the Essence as if it were the whole individual (itself)), it is precisely in virtue of this (only) 'implicitly'  that in fact an Essence is referred to by the term  ' man ' ,  an Essence which explicitly is not the whole individual. Therefore the term  ' man '  signifies (at this place in De Ente et Essentia) something universal, that is to say, a universal essence, and not just a universal term ( NOTE 99 ).
But, following from the Ockhamistic result, expressed in 'Socrates est humanitas', it would appear that an Essence is not (as proper part) in Socrates. And when we now say :  'Socrates est homo', the term  ' homo '  cannot signify such an essence as part. It must signify the whole individuum, implying that, qua being individual, the term  ' Socrates ' and the term  ' homo '  do not differ. Basing himself on such considerations, Ockham denies that there is a difference between first and second substance.
However, according to me, the term 'Socrates' refers to a contingent state of affairs, while  ' man ' ,  although signifying something individual, nevertheless signifies something not-contingent, because  ' man '  either signifies the individual Socrates, or the individual Plato, or the individual Melissus, etc., that is to say, the term in its signification gives up the aspect of particularity, but does not give up the aspect of individuality. The absence of particularity in the signification of the term  ' man ' , or of its equivalent  ' human being '  (homo),  lets the predication  ' Socrates is a human being '  be a predication of something non-contingent (predicate) of Socrates (subject), who, as particular, is contingent. Therefore there is a difference between first and second substance after all. But this difference is, as it seems, only a difference within the logical order  ( The mind gives up the aspect of particularity). It must still be investigated whether or not this difference within the logical order is based on a(n) (difference within the) ontological order. This, because metaphysics precedes logic.

The interpretation of the remaining categories (we had just considered the category of substance) has not always been the same. It undergoes a number of remarkable changes, to begin with in the opinion of St Thomas :
Already his doctrine about the Trinity forces ( NOTE 100 ) him to distinguish between accidental (predicamental) relation  and  a different kind of relation :  not the seemingly natural alternative relatio rationis ( = a relation residing in the mind only), but a relatio rationis cum fundamento in re ( NOTE 101 ) (as such with respect to content and meaning, but not yet expressed by fixed terms, in In I Sent. d.31, and in Summa Theologiae, I [this  " I "  is often denoted as Ia, meaning prima (pars), first part], q.42) ( MARTIN, G., Wilhelm von Ockham, Untersuchungen zur Ontologie der Ordnungen, 1949 (first edition of that year) ).
Duns Scotus ( NOTE 102 ) already speaks of  transcendental relations  (Rep. par. II, d.1. q.6, 22, 555b (cited in MARTIN, 1949¹  ,  p.127 )) :  'to be a creature',  for example, is such a relation that transcends all categories (predicaments) and therefore is transcendental (every being whatsoever, so also every auxiliary being, that is, every accidental determination, has been created (by God)). Also with respect to  number  (thus the quantitas discreta) Duns Scotus already doubts its merely accidental character (that is, he doubts that all there is to say about the being of  number  is that it belongs in a certain predicament, namely Quantity).
This process continues in Ockham :  For him, all categories, except Substance and Quality, are transcendentals (transcendentalia) ( NOTE 103 ). To be transcendentals means that they are automatically implied by Being (latin :  ens), meaning further that they themselves do not have (with respect their mutual difference and also with respect to their difference from Being) reality, they only have existence in the mind (latin :  in mente) ( NOTE 104 ).
So it is, for example, with space as quantitas continua :  Space has, apart from things (as supposed to be residing in space), no reality. Later this was also acknowledged by Leibniz and Kant (against Newton), and in our days by Einstein. But while space has no reality of its own,  place  does have it, according to Aristotelian, and especially Thomistic metaphysics  (See the document The Impetus as Variable Quality, in Fourth Part of Website ,  Part XXIX Sequel-5 ).  For Aristotle the accidents do not have ontologically independent reality, it is true, but they nevertyheless have reality. The same is the case with length, width, and also with everything in the quantitas discreta, such as number (as a result of counting).
The fact that for Ockham Quality still has a reality of its own, is a result of considerations about the Eucharist. According to Ockham Quality is a genuine being. And although in the natural order it resides in a subject, it is a being of possible independency. In all this we must realize that much of Ockham's polemic is not so much directed against St Thomas, but against Duns Scotus. For Ockham the categories (except Substance and Quality) have no reality outside the anima intellectiva ( = reason), while with respect to most categories this is still the case (they still have reality) for Duns Scotus. St Thomas, has, as we know, already weakened this reality, by accepting, following Aristotle, the analogy of Being (which 'analogy' here must be understood as the  pros hen  character of Being [See Part I of present website] ).  For Duns Scotus (and also for Ockham for that matter) Being is not equivocal, but univocal. This, and the position of Scotus that all accidents are real, implies that Scotus views the accidents as genuine things, and it is this view which Ockham disputes (except with respect to Quality).
For Kant there is, however, also no need to ascribe reality to Quality anymore, resulting for Quality also to become a transcendental, that is to say, that it does not really differ from the other transcendentals (Perhaps we could express this as follows :  Quality, as it is in itself, does differ from the other transcendentals, that is, they formally differ [have different definitions], but because they -- as transcendentals, do not add anything to Being, they do not differ materially), and this now also holds for the term  ' substance'  (See NOTE 103), because now  ' substance'  refers to  ' all '  categories, namely Substance, for there are no other categies left (According to this view, all so-called accidents coexist with Substance, and therefore Substance is rendered convertible with Being).
In this way the Aristotelian doctrine of categories has become for Kant transcendental philosophy :  All 'Categories' now have the same transcendental status :  They all are for themselves the most general determinations (for Kant, determinations a priori) of Being qua Being ( NOTE 105 ).

This important discovery as regards the historico-thematic development of the doctrine of categories and that of transcendentals, is largely accomplished by G. MARTIN, 1949¹ in his work about Ockham (mentioned above) and in other works from his hand :  according to us a splendid piece of thematic and historic research!

d₄.  Substantia dupliciter dicitur revisited (See   d₂    ).

We return to Substance where we had found the possibility :
man is humanity, in which the abstract term can be eliminated (discussed in Section d₂) and only the concrete term remains. This concrete term is now not connotative, but absolute, that is to say, the term signifies only the different individual substances and doesn't connote anything :  'Homo' signifies Plato or Socrates, or Peter etc. ( NOTE 106 ).
There is no duality (catallelism) of suppositum (homo) and essence (humanity) anymore (in which  'essence'  would be :  suppositum minus materia signata).
Ockham also does not distinguish between a potential part and an actual part in Substance, because everything is actual :  If there is something potential, then it is actual :  Potential being is no more than a certain way of predicating, namely one of the modal predications (praedicatio de possibili ( NOTE 107 )).
Substance, viewed in this way would not be such that it can be asked about (that is, if we point to a given substance, say a crystal, we cannot ask what it is). If, however, knowledge about it is nevertheless possible, then either this view of Substance is false, or the criterion of questionability is false, or this knowledge must originate from a science different from discursive science. ( NOTE 108 ).
As regards this problem we could, to begin with, remark that knowledge comes in two sorts :  discursive and intuitive as Aristotle expounds it in the beginning and at the end of the Posterior Analytics. Something that is qua catallelism questionable (such as Socrates, in :  ' Is Socrates a human being?' ), can discursively be proved as conclusion of a syllogism :  The two 'alleles' are, respectively, the minus (small term) and the maius (large term). A middle term then proves their connection (See Part II, VIA QUAESTIONIS, b. ).
But discursive knowledge always presupposes non-discursive knowledge (intuitive knowledge) as its principle. This latter is not an 'aliquid de alio' knowledge (that is, knowledge of something through something else), but an 'aliquid de seipso' knowledge (that is, to know something wholly through itself, or, equivalently, to know something not in virtue of something else, but in virtue of itself), which is knowledge via definitions ( NOTE 109 ).
And in this sense something which is not catallel (i.e. does not, ontologically, consist of two different 'parts' )  is questionable (i.e. it can be asked for as to what it is). The answer to the question, however, is produced in an intuitive way. That which must, in the case of such questioning, be known is the definitio quid nominis (nominal definition). Moreover we, in the Section VIA QUAESTIONIS (f.), have discussed a possible catallel transformation as regards Substance (Essence) (forma totius and forma partis).
Nevertheless all this urges further thought about what 'essence' really is. Therefore we present a modest attempt to gain more insight in this problem. In the VIA DIFFINITIONIS we will, naturally, return to these matters.

e.  The Essence.

In Cap.II of De Ente et Essentia (editio Leonina) St Thomas expounds (1) where Essence, among (ontologically) composed things can be found. It is found as forma totius which consists of matter and form (that is, designated matter and pure form), and (2) he prepares for a discussion in Cap. III with respect to the relation of the logical intentions genus, species and difference on the one hand, to the Essence of the (composed) things on the other (said differently :  he discusses our way of coming to know things about the Essence, or just, the way of knowing the Essence).

• The genus (for example the first intentions 'animal', 'organism') is, with respect to its explicit content, taken from that what is material in a thing, while the genus thereby does not include any further determination, containing these only implicitly, the latter resulting in the fact that the genus refers to a whole, making it predicable of an individuum.

• The difference takes its explicit content from the formal part of the thing, while it, in its signification, does not exclude the material part, but implicitly contains it. Therefore the difference also refers to a whole.
  Genus and difference each for themselves refer to the species (each in a different way) and through the latter also (refer to) all what is referred to by the species, that is, all what is in the individuum.

• The species (for example Homo) explicitly refers to a whole, namely the forma totius, but now undifferentiated. And implicitly it refers to the carrier of this forma totius. And according to St Thomas, the abstract term (for instance  ' humanitas '  [ = humanity] refers only to the forma totius, under the 'cutting off '  of the so-called materia signata (matter insofar as it is the principle of individuation).

• The definition refers to the same whole as does the species, but then in a differentiated way  ( This differentiation is logical, not metaphysical. De Ente et Essentia, Cap.II, line 207).

1. either at the Essence absolutely considered, or
2. (at the Essence) as residing in the singulars (i.e. to be present in the singulars), or
3. (at the Essence) as residing in the intellect (mind).

For the time being, we conclude that St Thomas (at least in his De Ente et Essentia) has not yet succeeded to indicate the distinction between the logical differentiation in the Definition on the one hand, and the possible ontological differentiation in a finite being (that is, a material being) on the other. Of course the one is in the mind (in mente) while the other is outside the mind (extra mentem), but having only this difference at our disposal the metaphysical expositions about the ontological constitution of beings look little more than not-yet-well-argued thingifications of the structure of thinking and language (and thus in fact some brand of (Neo)platonism, as we see it, for example in Proklos) ( NOTE 125 ).  It is, generally, precisely this problem, namely the problem of purifying metaphysics from exclusively logical 'entities', which occupied William of Ockham, and he shouldn't therefore be called 'anti-metaphysical '.  For Ockham the matter-form distinction (and, consequently, also the potency-act distinction) is no more than a logical distinction (it figures in a propositional context of modalities, namely of being-possible and being-real )  as we already have said earlier ( NOTE 126 ).

St Thomas, following Aristotle, criticises at many places (in his works) the Doctrine of Ideas of Plato. There are, however, many indications that their interpretation of Plato  (In the case of St Thomas, the doctrine largely came down on him via Aristotle and Neoplatonism, and thus not (much of it) directly from Plato himself)  is not correct in all respects, and even if it were correct, this doctrine of Ideas may still be a possible point of departure in an attempt to interpret Reality ontologically. The fact is, whatever possible metaphysics we consider, sooner or later we will find out that a certain amount of Platonism cannot be avoided.
Aristotle sees in the Doctrine of Ideas some sort of unnecessary doubling of beings, but we doubt whether Plato meant it that way ( NOTE 127 ).  The being of (1) Idea and of (2) observable entity probably involves an analogy or is perhaps more or less comparable with the 'ways of being' distinguishing Kant's noumena and phenomena. Anyway, they do not belong to the same order of Reality, in the same way that, say, the  sign  (insofar as it is sign, not insofar as it is a physical thing or structure) and the  signified  do not belong to the same reality order ( NOTE 128 ).
Something comparable we find in Ockham's critique with respect to, among others, the Categories (except Substance and Quality) :  Also here Ockham denies for instance the reality of Quantity :  " Two substances " do not constitute a per accidens compositum of (1) the pair of substances, which then would be a carrier, and (2) the really existing accident  ' twoness '.  This is a kind of Platonism that he refutes convincingly. The twoness is not something apart from the pair of substances, i.e. we do not have a (single) general independently existing  ' twoness '  that sometimes 'goes out' to find possible substrates to land on. The twoness must already be anticipated by each one of the mentioned substances totally in virtue of those substances' own content ( NOTE 129 ).
But the view of a really and independently existing accident (as refuted by Ockham) is, as we've said earlier, not so much the view of St Thomas ( NOTE 130 ),  because he has weakened the reality of accidents by means of the concept of equivocity (in scholastic writings called analogy), something that Ockham does know to be sure, implying that his critique is in fact not directly aimed at St Thomas, with respect to these matters, but at others such as Duns Scotus. So St Thomas holds a peculiar intermediate position between those of, say, Scotus and Ockham. Therefore it is of no surprise to us when it turns out that the metaphysics of St Thomas Aquinas, precisely because of this intermediate position, has a large survival value.

In the following discussion we hope to gain still further insight into the Categories (Predicaments) and the Predicables, because it looks as if philosophers, in a more or less unconstrained way, invent all kinds of concepts and constructions, so that they are subsequently perplexed about them, and then go to investigate the next 2000 years as to what then they in fact are, as if they were given by God as natural structures.
Nevertheless in philosophy things go that way with respect to such constructions :  One 'feels' that there must be 'something' like that. Theoretical considerations together with observation almost inevitably lead to them. But as evident they initially appear to be in rerum natura ( NOTE 131 ),  so un-detectable they turn out to be, as soon as they either are of a very fundamental nature, or just plain mistakes. We must continue to critically investigate these traditional and for a long time cherished constructions and concepts, with the preparedness to reject them all, if necessary. After all, isn't it all about the verum, that is, the truth?
May the next discussion contribute to obtaining this verum.

AERTSEN, p.56 (Natura en Creatura, 1982) writes that a per se predication ( NOTE 132 )  is based upon a causal relation between the subject (or a part of it) and the predicate. It is evident that here a logical relation is thought as it to be (also) ontological (subject and predicate causally connected), that is, the relation between a subject and a predicate, which is a logical relation, is supposed to be based on a "causal" relationship between subject and predicate, which must, therefore, necessarily be re-interpreted as substrate and determination, and the relation between a substrate and its determination is evidently ontological. And, as far as we know, all this is asserted without being demonstrated (something which indeed was not the task or intention of the book Natura en Creatura).
Indeed, predication is a relation between terms, not, without qualification, between things.
That it is not just like that a relation between things, can be shown with the following (accidental) predication ( NOTE 133 ).  We do not show this in the sense of an established truth concerning these matters, but we show that 'ontologization' of parts of a predication is not undisputed, even already in the Middle Ages :

If we say  " This stone is spherically formed ",  then it may be argued that the term  ' spherically formed '  does not signify something that would be different from that stone. For why could a substance itself not be spherically formed, (also) without that particular entity spherically formed (that is, an entity apart and distinct from that substance)? Said a bit differently :  Couldn't we imagine that a substance can, all by itself, and thus not by involving something else, be spherically formed? Couldn't the content  ' spherically formedness '  be already be an integrated part of the given substance, which part cannot be different from the substance's content because it also belongs to this content? ( NOTE 134 ).
Ockham determines this as follows :  The term  ' spherically formed '  is, as concrete term, connotative :  It signifies primarily one or another substance (i.e. individual real thing) and secondarily (i.e. connotes) the truth of a certain proposition  ( That which is connoted is consequently not something in extramental reality, but a meta-object :  ' Truth of a proposition '  is a term of the meta-language ( NOTE 135 ),  a term of second intention, not a term of the object language (see previous NOTE), not a term of first intention ).  This connoted proposition puts that the conditions for attributing the term  ' spherically formed '  are satisfied, for example in virtue of an observation. And indeed all this refers to a here-and-now individual. Only when considering the  historical  individual can  'spherically formed '  be predicated of the carrier (substrate, logically, of the subject) because the historic individual is the carrier.
The abstract counterpart of  ' spherically formed ',  namely  ' spherically formedness ',  is a so-called incomplete symbol (just like the term  ' humanitas '  in the category of Substance) and is analyzable in terms of a context which involves necessity :  ' spherically formedness '  is spherically formed qua spherically formed ( = what  being spherically formed  simply, as spherically formed, necessarily entails). So the abstract term is reducible to a concrete term.

This whole treatment of  ' spherically formed '  is,  if taken maximally general (resulting in the supreme genus Quality), thus as qualitative property as such,  a description of a transcendental term :  (sensible) substance is coexistent with quality, that is to say, with to be a quale, and this latter therefore is also coexistent (convertible) with Being  ( We here give up on possible non-sensible substances, substances, nevertheless expressible by the object language, because their existence is far from demonstrated :  At most we can presuppose them within a broadened speculative perspective ( NOTE 136 ) ).  So we see that the parts of a predication do not necessarily stand for corresponding parts in extramental reality ( NOTE 137 ) :  In the mentioned example spherically formedness did not have separated reality with respect of the thing which was spherically formed (that is to say, did not enjoy an existence apart from the thing which was spherically formed). There only was a distinction secundum rationem, a distinction, which, as distinction, was formed by our intellect (ratio), and thus referring not to things or states of affairs in extramental reality, but to our way of knowing. So the distinction is not ontological but logical. This must be understood as follows :  It is  not  ' spherically formed '  that is (only) secundum rationem, but the distinction, in the sense of separation, of stone and spherically formed is (found out to be) (only) secundum rationem ( NOTE 138 ).  And this forces us to think more about the pretense of the VIA PRAEDICATIONIS to providing knowledge of extramental reality.
As a preparation we must consider the following :
A Being (ens), whether it be a substance or an accident ( = weakened being), is always one, is always an unum. An unum, as can be found in extramental reality, is always a being, an ens, whether it be a substance or an accident (an unum is a holistic totality of whatever elements).
UNUM is, consequently a transcendental term, that is, it transcends every classification whatsoever of types of Being, especially the classification expressed in the Table of Categories (Predicaments). The same applies to all other traditionally conceived transcendentals, such as VERUM (true), BONUM (good), RES (thing), etc.
According to Ockham QUANTITY is also a transcendental term  ( This, for him, with respect to created Being, and this thematically means :  with respect to Real Being, especially [when the immaterial angels are created beings] material beings, sensible beings ),  because  every  being is quantitatively determined (or said better, is quantitative [and, of course, not only quantitative), which means that every being whatsoever has a certain size, involves certain numbers, etc. We might add that this is only correct if all other accidental categories are also not considered to be beings, because, say, quality is, with respect to its very formal content, not quantitative (it at most involves quantity, in the sense that it must be co-existent with quantity), and if it were a being, then we would have a being that is not quantitative)ly determined). So in denying being (that is :  denying to be a being) for all accidental categories (making them to be no Categories of Being anymore), there is only one Category of Being left :  Substance. And then of course QUANTITY transcends all categories.
So as such, QUANTITY is transcendental ( NOTE 139 ) ( NOTE 140 ).
But this is, according to me, not the case with respect to the  species ( = lowest subgenera) of Quantity, that is to say, according to me no species of Quantity is transcendental, and also no species of any other accidental Category is transcendental. One or another substance can be 1.50 long. But not every substance is 1.50 long (and with respect to Quality :  A substance can be spherically formed, but not every substance is spherically formed. And also :  A substance can be red, but not every substance is red).  So  ' 1.50 long ',  ' spherically formed '  and  ' red '  are not transcendental terms.
We could hold that  Quantity  is a principle of Being (one among many such principles), where we limit "Being" in the expression "principle of Being" to real Being, which in the present context is :  material being. This principle guarantees that every material being is quantitatively determined.
A same type of consideration can be applied to Quality, and a number of other transcendental determinations.
So here we find a number of principles of Being which  ' horizontally '  pervade all real and full-fledged beings. In this way we come close to Nicolai HARTMANN's doctrine of Categories (and if we take those principles to be a priori categories of reason, then we come close to KANT's epistemological theory).
And thus an Aristotelian-Scholastic study of transcendentals could lead to a variant of the Hartmannian ontological doctrine of categories, or to a Kantian epistemological doctrine of a priori categories.
In a doctrine such as Hartmann's the 'Gebilde', the Totality ( = individuum) is not central anymore. The many Totalities together make up one single domain of Being (possibly consisting of several Layers of being), which is pervaded, and thus held together, by universal principles of Being.
In Fourth Part of Website we have expounded this Hartmannian doctrine. Here, however, that is in the present (Fifth) Part of Website, our point of view lies elsewhere. It lies at the Totality, that is, at the thing (as thing).

A given Substance can have, at the same time, several quantitative determinations such as  being 1.50 m long,  having a volume of 500 cc,  or  consisting of three parts,  but these determinations can vary in Time. This is evident when we, in stead of the here-and-now individual, have the historical individual in mind. Only then we can speak about replaceable determinations (accidents), replaceable with respect to a given being. The 'replaceable' is, it is true, also detectable in the context of here-and-now individuals, namely as we go from one such individual to another of the same species (Socrates is now tanned, while Plato is not). So this 'replaceability' appears be distinguishable also in a Nominalistic context of (only) here-and-now individuals. But this is not so, because speaking about  "replaceability of determinations in individuals of the same species"  necessarily implies the acceptance of an Essence that remains the same while determinations are replaced by others. And such an Essence is denied by Nominalism.
The discussed case of some given being which was determined to be spherically formed referred to a stone (with a spherical shape). In the argument the stone was imagined to be a genuine Substance (while it in fact isn't) in order to give an analysis of the determinations that further determine this substance. After all it here concerns a general exposition about determinations as such.
Nevertheless it is, in the present context, important to realize that, generally, a stone is not a pure being (ens), not an intrinsic Totality, but an aggregate (here, a tight contiguum). A stone (a rock) is, except when it consists of one single crystal only, such as a grain of sand, an aggregate of crystals (thus an aggregate of beings) that are randomly oriented with respect to each other (and are in many cases even belonging to different crystal species).
In the case of an aggregate (such as a stone) it is relatively simple and clear to speak about extrinsic determinations of this aggregate (taken to be a being), because a genuine (but still more or less tight) aggregate has few intrinsic features, this in contrast to a genuine being (a Totality, a genuine Substance). So the shape of a given aggregate (and thus, say, the shape of a given stone) is almost totally determined by external factors (otherwise it wouldn't be a genuine aggregate).
As regards real full-fledged beings, intrinsic Totalities, on the other hand, there is a much larger proportion of intrinsic determinations (which is, for example, obvious in the case of a molecule :  Here there are only very few extrinsic (and therefore replaceable) determinations (such as position and orientation with respect to the medium in which the molecule resides).

We were discussing the status of determinations, and found that these may only then be viewed nominalistically when they are taken as maximally generalized. And if we do not do this, then we must explicitly have in mind a here-and-now individual.
Quantity, for instance, is, in this Nominalism, not something that in itself has one or another form of reality alongside the reality of that something which has quantity (which is quantitative). (Something) to-be-quantitative is (only) a certain way of  description  (by us) of one or another being.
Viewed non-nominalistically, Quantity (and also the other accidental supreme genera) could be considered to be a principle of Being, as we had found out earlier. The species of Quantity (such as 1.50 cm long, 500 cc volume) -- and also those of the other accidental categories -- cannot be viewed nominalistically, because they are not transcendental, are not convertible with Substance, and are thus something else than Substance.
In a different sense they can be viewed nominalistically, namely when the following conditions are satisfied :

1. Only individuals exist.
2. These individuals are always (viewed as) here-and-now individuals.
3. (As consequence of [1] )  There doesn't exist something like an 'essence' (which remains constant under replacement of determinations).

To recap, consequent Nominalism asserts that all so-called accidental predicates do not refer to beings, even not to mere auxiliary beings. So a predication, although its (linguistic, or syntactic) form suggests it, does not express that something is added to something else (that to which the predicate term refers added to that to which the subject term refers).
On the contrary (still according to Nominalism), it only emphasizes some aspect of that what is signified by the subject term. And this means that the accidental term is in fact not an accidental term, but a transcendental term. So, according to Nominalism, all accidents are transcendentals. There exist, to be sure, even according to non-nominalistic and therefore classical metaphysics, genuine transcendental terms such as UNUM (unity), ALIQUID (something [else] ),  RES (thing), etc. But in contrast to this non-nominalistic classical metaphysics Nominalism says that, in addition to these traditional transcendentals, also all 'accidental predicates' are transcendental terms.

A transcendental term can be characterized in two ways:

• It is applicable to all types of Being, which means that it transcends every possible classification of types of Being, especially its classification into the ten types of Being derived from predication, the Predicaments (Categories).
  So such a term thus not only applies to Substance, but also to Quantity, Quality, etc.

• It says something directly of a being, that is, not by adding something to it, but expressing some aspect of it, an aspect that is in no way apart from it.

A true accidental term, on the other hand, says something about something else. It, namely, adds something to Substance. It adds to it by being ontologically carried by it, recepted by it, supervened to it, inhering in it.

Now, Nominalism (as we see it for instance in Ockham) asserts that, to begin with, also Quantity is a transcendental (at variance with traditional substance-accident metaphysics).
How can we demonstrate that Quantity is a transcendental?
Does it apply to all Categories? Evidently it does not :  While it does apply to the Category of Substance, it does not apply to the Category of Quality, because Quality as such, although necessarily entailing quantity (See Van MELSEN, A., Natuurfilosofie, 1955, p.252), is itself not Quantity (because Quality can never totally be reduced to quantity (See Van MELSEN, A., Natuurfilosofie, 1955, p.249. ( NOTE 141 ) ).
All this is, of course the reason why Quantity and Quality are recognized as different categories. They are obtained by maximally generalizing individual cases of quantity and quality.
So this shows that Quantity is not a transcendental (because there is at least one Category [other than itself] for which it does not apply, and that is Quality).
Of course, if we deny (as Nominalism does) that the accidental categories in any way stand for beings (of some sort), then we mean by this that they -- in a predication -- do not add anything extraneous to that of which they are predicated. In such a predication we just emphasize some intrinsic general aspect of that which is signified by the subject. And thus denying the accidental categories to stand for beings (of some sort) is equivalent to saying that they are transcendentals. Therefore this denial is not a demonstration that they are transcendentals, and if nevertheless considered as a demonstration, it is a circular argument.
So if, and only if, accidents are shown to be not beings (accidental terms not signifying beings), they are (shown to be) transcendentals (which implies that transcendentals are not beings).
But in the document  The Nominalistic Critique  ( First Part of Website , Critical Series) we found out that they are indeed not beings, because they are, although individual, not individuals (individua) ( NOTE 142 ) ).  From this it would follow that they are transcendentals.

Only when we hold that something which is UNUM as well as ALIQUID (see previous NOTE), that is, when it is undivided in itself and at the same time divided from the others, is not necessarily already an individual, but is individual, then an accident satisfies being a being (because an accident is individual). And indeed, the notion of accident, as developed in Part III and Part IIIa, namely as  a  phenotypic replaceable determination of which the content partly overlaps with that of the carrier in which it inheres  ( where the 'overlapping' is only implicit, in the sense of an anticipation by the carrier of a possible determination by that particular accident ),  complies very well with such a determination (only) being individual but not an individual. It derives its individuality from the individuality of its substrate (carrier).
Of course, when one asks whether Substance (which is the first Category) is a being (that is, whether the term 'substance' refers to a being), we should perhaps reply that it cannot be a being, because 'substance' is not individual :  the term is general. However, it can be general in a disjunctive way :  It signifies a multitude of individuals by means of  or ..., or ...,  and so the significatum of the term 'substance' is something individual after all. The same applies to the term  ' quantity '  (second Category, first accidental Category), and to the term  ' quality '  (third Category, second accidental Category), etc. :  The term  ' quantity '  refers to :  this length of 1.90 cm,  or  to  that length of 200 m,  or  to  that volume of 500 cc,  or  to ... .
So all the terms of the Categories, thus including all accidental terms, signify INDIVIDUAL entities (while logically they are supreme genera of Being).
The classical definition of  ' an individual '  is :

Something that is undivided in itself and divided from others.

And only if the  ' divided from others '  means  spatially  divided from others, we have defined a true individual (an individuum). And if the  ' divided from others '  is spatial, then it is (always) spatially separated from others, whether it shares the same essential content with all other members of the (same) species (one individual salt crystal, another individual salt crystal), or differs with respect to content from the others (an individual sugar crystal, an individual salt crystal).
But if, on the other hand, the  ' divided from others '  means :  (only) qua (formal) content divided from others, then we have not defined something to be an individual (because it then is not distinguished from other members of the same species), but only something which is different, like redness differs from blueness.
And at least a(n) (unseparable) part of any given accident (any given replaceable determination), namely that part of it that 'sticks out' of the substrate, is, in addition to undivided in itself, also divided, qua formal content, from others (which here, first of all, is the substrate in which that accident inheres), and thus the accident complies with its being different (qua formal content). And only when such a something is either a part of, or inheres in, something individual, it is itself individual.

Now let us see what the ontological status is of something, let us call it X, that is formally different and individual (and only individual).
X then distinguishes itself qua formal content from its 'environment' and at the same time, in order for X to be individual (and no more than that), it must be a proper part of an individual.
What then is X when it satisfies these characterizations?
X cannot be some given Substance (like an organism or a crystal, which are individuals), because X is not an individual (for we know that a Substance is either a historical individual [= carrier-only], or a here-and-now individual, so it is always an individual).
X can also not be an essential part of something, because an essential part does not differ with respect to formal content from that of which it is an essential part (and an essential part always (only) refers to an atom (in the mereotopological sense), not to a molecule). The formal content of an essential part (whether of a substance [carrier-only] or of an accident) is an all-pervading content, and so it indeed does not formally differ from that of which it is an essential part (for instance the space group symmetry is not some qualitatively different region or part of the crystal. It is not separate, neither spatially nor formally).
What is left then for X to be, is (for it) to be a replaceable determination, that is, an accident.
So if an entity X is formally different and at the same time individual (but not an individual), then X is an accident.
And because a (concrete) term, signifying an accident (such as the term  ' sectored-plated ' ),  can be predicated of a substance (as substrate for  ' sectored-plated ' ), such as in  " This snow crystal  is  sectored-plated ",  we predicate a term signifying a being of some sort, let us call this term T_x ,  of another term, T_s ,  signifying another being.
And it is then clear that the term T_x cannot be a transcendental term, because it adds something, namely the being X, to something else (the substance as substrate).

And this means that the accidental terms (quantity, quality, etc.) are not transcendental terms  ( Every accidental term, also when it is taken maximally general (and then being a Predicament) signifies an individual entity, and this entity differs with respect to formal content from its substrate ).
We see, all this boils down whether or not we consider accidents as beings of some kind, which in turn depends on whether or not we consider something that is  formally different and (at least) individual  to be a being.
That Quantity (as an example of an accident), as represented by, say, 1.90 cm length, is individual, is evident, because it inheres in an individual substrate. But also that which is signified by the term  ' quantity '  is, as we saw above, individual.
That Quantity is (formally) different from the substrate or carrier, is shown in Part III and Part IIIa. It is different, because we have shown that the formal content of any accident does by far not completely coincide with (a corresponding part of) the substrate. Only insofar as the substrate anticipates the accident there is some overlap as regards formal content. Indeed, all accidents are each for themselves formally different from the substrate because they are replaceable by formally different determinations, while in such a replacement the formal content of the carrier or substrate (including all its anticipations of possible determinations) remains the same.

REMARK :
One could object that we here assume something to remain the same, while a determination is replaced by another. But that this can actually be the case can be shown in crystals :  When a growing crystal, because of changing environmental physical conditions, changes its actual shape, its space group symmetry remains exactly the same. Also its chemical composition remains the same. And these features belong to the substrate. See next Figures :  In the first one we reproduce the diagram of NOTE 72 in Part III.  This diagram depicts the ontological constitution of a material being in general. The second diagram depicts this (same) ontological constitution (but now) of a sectored-plated snow crystal :

With respect to a certain per se predication as it was brought up as an example, St Thomas, in the first book, lectio 10 of his commentary on Aristotle's Posterior Analytics, appears to hold a moderate nominalism (as discussed earlier, while this is, as we shall see, in a lesser degree the case with respect to the attribution of accidental predicates to a given subject [accidental predication,  per accidens  determinations] ) :  St Thomas discusses two examples of  a  per se  predication as given by Aristotle, namely the predication

and the predication

These predications are  per se  because in the definition of  ' triangle '  the term  ' line '  occurs, and in the definition of  'line '  the term  ' point '.  This means that  ' line '  is necessarily implied by  ' triangle '  and  ' point '  is necessarily implied by  ' line '.
And St Thomas adds to this explicitly :  Quod non est intelligendum quod linea ex punctis componatur, sed quod punctum sit the ratione lineae, sicut linea de ratione tringuli ( NOTE 143 ).  This, according to me, should mean that the concept of  ' point '  is logically prior to that of  ' line ',  which further means that we must have at our disposal (or must invent) (and then use) the concept  ' point '  in order to define a line, while it is indeed not advisable to assert that a line is made up of points, because a point has no dimensions, and so cannot form something that suddenly does have one or more dimensions (a line has one dimension) ( NOTE 144 ).  A triangle does consist of a joining together of lines. The boundaries of these parts are the three angular points. The triangle is a contiguum.
The definition of  ' triangle '  has as its part the concept  ' three lines ',  and these three lines actually exist in every triangle. So here parts of the definition correspond to ontological parts.
The definition of  ' line '  on the other hand, in some way involves points (for example as boundaries of potential parts, or as making up a non-denumerable one-dimensional ordering as such constituting the line), and thus rendering the concept  ' point '  to be a part of the definition, but such a part does not necessarily have corresponding ontological counterparts, because we just don't know whether points are present in a line as line.
So also for St Thomas, the parts of the definition are here (that is in  per se  predications such as definitions) not automatically ontological parts. And this is the moderate nominalism of St Thomas with respect to  per se  predication, as noted above. The definition always refers to an UNUM within the context of metaphysics ( NOTE 145 ).

It is certainly plausible that, in the case of predication per se, first mode ( = predication of the definition) ( NOTE 145a ),  the parts of the predicate ( = parts of the definition) correspond in extramental reality with an UNUM, that is to say, the definition, although consisting of parts, has as its significatum a whole ( NOTE 146 ).  This latter is affirmed by St Thomas :  The catallelism ( = duality) in the definition cannot traced back in that entity in extramental reality that is signified by the definition.

But such a catallelism, assumed on the basis of a model of predication, St Thomas does pose with respect to accidental predicates :  These are then going to stand for 'auxiliary beings'. According to St Thomas, as expressed in the last Capitulum of his De Ente et Essentia, such an auxiliary being always must have mentioned in its definition (that is, a definition, not of an auxiliary being as auxiliary being, but of some given auxiliary being) its inherence in a substrate. And because such auxiliary being (accident) does not consist of matter and form, it is not possible that here the genus (as first part of the definition) is taken from the material part and the difference from the formal. The genus of the definition of the (given) auxiliary being must be taken from the way of being.
In general, quantity, for example, is a measure of the given substance, and quality a disposition of that substance. The carrier (substrate) is the material cause of the auxiliary being. Therefore the explicit content of the genus (figuring in the auxiliary being's definition) must be taken from the carrier ( = that to which the subject term refers).
In Summa Theologia, I-II, q.53, 2 ad 3, St Thomas poses that the accidental can be signified in two ways, viz., concretely, such as 'white', and abstractly such as 'whiteness'. Always the term signifies a relation between auxiliary being and carrier, in which the concrete term lets this relation begin at the carrier and end at the auxiliary being, and in which the abstract term lets begin the relation at the auxiliary being and end at the carrier.
The white (concrete) is that something (the carrier) that has whiteness (the auxiliary being).
Whiteness is that ( = auxiliary being) in virtue of which something (the carrier) is white.
A little bit more precisely we can express this as follows :
The concrete term '(the) white (thing)' signifies that something in extramental reality (namely the carrier) which has whiteness (the auxiliary being).
The abstract term 'whiteness' signifies in extramental reality that something (the auxiliary being) in virtue of which something (the carrier) is white.
It is striking that St Thomas here considers not only the concrete term, but also the abstract term to be connotative (it connotes the carrier) ( NOTE 147 ),  while this is not the case in Ockham :  According to the latter the abstract term 'whiteness' is not connotative but absolute and signifies directly that something which is distinguished from the carrier, and possibly independent of that carrier, implying that the carrier is not essential. This means that this carrier (logically the subject) does not need to be present in the definition of 'whiteness'. So this is Ockhams view of what precisely an accident, a predicament, is. 'Whiteness' belongs in the Category of Quality, and Quality is for Ockham the only predicament that is left, that is to say Ockham does not acknowledge that Quantity, and all the other accidental predicaments (categories), except Quality, are indeed predicaments, by denying that they are beings of some sort (the exception allowed for Quality has reasons connected with theological doctrine). For Ockham, consequently, whiteness and that which carries it, are two things, both with an Essence of their own, while for St Thomas the (degree of) reality of, for example, whiteness has already been weakened as a result of the analogia entis (the equivocity of Being) implying that whiteness does not possess an Essence of its own anymore :  it is an entis ens ( = a being of a being) ( NOTE 148 ).

In what comes next we (continue to) follow the discussions of St Thomas which (discussions) try to ontologically distinguish between  Proprium, First Substance, Essence (Second Substance), and Accidens.  Thematically we have already gone a long way toward a possible solution of this problem, symbolized and summarized in the above depicted diagram .  Here we will consider St Thomas' efforts, simply because they are instructive, but always with our own solution in mind.
In De Ente et Essentia, Cap.VI, from line 123, however (that is, in contrast to Summa Theologiae, I-II, 53, 2 ad 3), St Thomas still holds that the abstract term does not signify the carrier (which is to be expected of an abstract term), resulting in a signifiation as takes place also in the case of Substance, as he adds in In VII Metaphysica, lectio 1, nr.1254, whereby he, however, explicitly says that in extramental reality the accident is always inhering in a subject (substrate, carrier).
While in the definition of a given  a c c i d e n s ( NOTE 148a )  one or another carrier must be mentioned,  in the case of  a given  e s s e n t i a l  p r o p e r t y  (proprium) ( NOTE 148b )  that carrier, which  per se  belongs to this property, must explicitly, and with respect to content, be mentioned in the definition (of that given proprium), that is, it must be mentioned as proper subject. The definite substrate (carrier), referred to by the subject term (proper subject), becomes as term, a part of the definition of the given proprium.
Predicates, which do not occur in the definition of the subject and which also in their definitions do not mention the proper subject but only (mention) the inherence as such (that is, inherence in some substrate [where the latter is signified by the subject term] ),  are accidental predicates, that is, predicates that figure in accidental predications, and signify replaceable determinations. Such a predicate is, for example, 'white' (in a predication referring to skin color) with respect to man (St Thomas in In I Post. An., lectio 10). ( NOTE 149 ).  See next diageam.

Diagram above :  per accidens and per se predications.
    Upper image :  A predicamental term (i.e. a term belonging in some Predicament), in the diagram represented by its definition, is said of a subject term (also represented by its definition) by way of an accidental predication. It is an accidental predication because the formal contents of subject and predicate are totally discrete.
    Bottom image :  A term, signifying a given proprium (represented by its definition) is  per se  predicated of the subject (represented by its definition), because the formal content of the subject (as is given by its definition) is contained in that of the predicate (as is given by its definition).

Human forms an unum with Socrates, it also forms an unum with Plato, etc. This, because Socrates is  per se  a human, not, however, on the basis of a definition, because the term 'Socrates' refers to an individual (and of a[n] [given] individual there is no definition). But Human does not follow  per se  from Socrates as Socrates, but it does so follow from Socrates-as-a-case-of-being-a-human. Socrates as Socrates is only a human  per accidens  ( This object, called Socrates, happens to be a human). Socrates-as-a-case-of-being-a-human,  on the other hand, is  per se  a human ( NOTE 151 ).
Socrates and his whiteness (in the sense of paleness) do perhaps form an unum if we take Socrates as a here-and-now individual. But during his whole existence the color of his skin can be replaced by another color (for instance in the case of tanning), and, in addition, this color is, if we go from one human individual to another, from 'time to time' (in fact, from place to place) also replaced by another color,  while in all these cases of replacement the Essence of Socrates-for-example, which consists in being a human, is not replaced. And this is in fact an indication that whiteness does not form  a  per se  unum with Socrates after all, also not in the case of a here-and-now individual.
So while the Essence and whatever accidental determination are both subject to residing in something, the accidental determination is being replaced (is replaceable), while the Essence is not (not in the same individual, and not over the [con-specific] individuals :  Socrates is a human, but also Plato, etc.).
Now we have already spoken about the Essence which allegedly would be taken up into a subject which individualizes it, and shown that this is not simply a matter of fact. This becomes evident as soon as we assume that only individuals exist in extra-mental reality, as Nominalism holds. And that such an essence should form  a  per se  unum with that subject, is, in the context of Classical (non-nominalistic) Metaphysics, surely not directly evident :  Me thinks only the Essence itself  is  a  per se  unum (namely as soon as we have the genotypic essential parts in mind, which together form the one dynamical law). So in fact this (classical) metaphysics stipulates such a  per se  unum in the case of  Essence-in-an-individualizing-subject  and a non-umum in the case of an  accident-(also a proprium)-and-its-subject.
The just mentioned persistence of the Essence in Socrates is nevertheless an indication for the existence of such an unum to which the  human-socrates  refers. However, in Classical Metaphysics this also applies to a proprium.
From a different perspective we have, however, to do with  a  twoness  as regards the  human-socrates, namely the duality of genotypic and phenotypic domain (as we use these terms in the dynamical systems approach, that is, in a meaning that goes beyond mere genetics), said differently, (we have to do) with the duality of principle and concretum. The Essence itself, that is, the dynamical law, surely is an unum.

If we, however, hold on to the Thomistic confirmation as to the existence of first and second substance, then the characterization of a predicamental accident, that is to say the characterization of, respectively, the predicable 'accidens' and the predicable 'proprium' (which are, within the framework of Classical Metaphysics, both predicamental accidents) should read as follows :

A non-essential determination (accidens) must always reside in one or another subject (this we had already established above), without, however, it to belong  per se  to that subject-as-a-specific-carrier-for-it ( NOTE 152 ),  and without forming either a necessary unity with the subject (exclusion of an essence in a subject), or a necessary twoness (exclusion of proprium). It (that is, the non-essential determination) forms a contingent twoness with the subject.

An essential determination (proprium) ( NOTE 153 )  also must always reside in a subject, which latter, however, is at the same time the specifically proper substrate for it, whereby the proprium does not form a per se unum with that subject (exclusion of essence in a subject), but also not a contingent twoness (exclusion of non-essential determination). The essential determination forms a necessary twoness (necessary, because the proprium is always present [that is, always inhering in the given subject], which is at least an indication for a necessary connection to exist between the subject and the proprium).

In this way we hope that we have clarified (and further elaborated on) the distinction (accidens-proprium) as it is held by St Thomas.

Every organism is mortal
Man is an organism
Ergo :  Man is mortal

Here 'mortal' is a proprium for organisms. Therefore it can be demonstrated for man.
'Organism' is (part of the) definition of 'man', and is the middle term of this syllogism.
Man is necessarily mortal, because of the presence of a cause. And this cause is :  the fact that man is an organism. So  being an organism  is the cause of the fact that man is mortal.
But of course this is only a 'cause' in the sense of a formal condition, while a genuine cause is a state (of a dynamical system) that directly or indirectly precedes a given state, which latter state is called the effect.
On the other hand, the nature of the human body is such that it is an organismic body, and this directly implies all the processes of ageing, finally resulting in death. So being mortal is a direct consequence of the nature of the dynamical system which is the organismic body. And this nature is such that the necessary series of consecutive system states eventually ends up in states that can be characterized by a progressing erosion of the organic body, eventually resulting in its disintegration.
So being mortal is the effect of some intrinsic structural feature of an organismic body, and as such the organismic body itself, and as a whole (because the mentioned structural feature pervades the whole body), insofar as it is organismic, is the cause of being mortal. It is, hoerver, a formal cause, not an efficient cause.

According to me the  'per se  (which is as such) pointing to a causal relation'  cannot apply to the first mode of 'per se' (see NOTE 145a), because here, apparently, we have to do with identity (Also AERTSEN says this at p.64). And (also) St Thomas himself has said somewhere that something cannot be its own cause, because there cannot in any way be some priority of X with respect to X.
St Thomas (In I Post. An., lectio 10) says, however, that a predication of an essence is an attribution in virtue of the formal cause. This must then be the forma partis ( NOTE 155 ),  for otherwise there would be identity of cause and effect ( NOTE 156 ).  Only in this way it can, according to me, be defended that  essence  has a cause, and that thus the predication of this essence "points to a causal relation", and this, now in a metaphysical context (in contrast to the context of (natural) science).
Predicating the definition of the definiendum ( = that what must be defined) (per se predication 1st mode) can also not be a conclusion of a syllogism (See Part II, VIA QUAESTIONES,  b. )  ( NOTE 157 ),  and is as such not demonstrative knowledge. This in contrast to the demonstration of a proprium  (for example, being mortal is a proprium for organisms, and can thus be demonstrated for man [which is subsumed under organisms], or capable of laughing is a proprium for man, and can consequently be demonstrated for Socrates [ = an individual that is pointed to by the finger] ).  That something to which the definiens ( = the definition) refers could only be a consequence (conclusion) of that something to which the definiendum ( = that what must be defined) refers, if there were no identity ( NOTE 158 ),  thus when we assume that  in  homo ( NOTE 159 )  resides  rational animality (as a proper part),  or, the other way around, that  in  animal rationale  resides  humanitas ( = humanity) (as a proper part), which nobody is likely to accept, because homo already  is  the Essence, and in the same way animal rationale  is  the Essence (all this in the sense of total coincidence). The Essence has, it is true, a cause (the forma partis), but this causality cannot be derived from the definition (because there a middle term is impossible, a (middle) term signifying the cause).

On page 67 AERTSEN (Natura en Creatura, 1982) says :  " The horizon of the quaestio 'quid est' [what is it] is a squire [scire] per viam diffinitionis" (...... is knowing along the way of definition). The question quid est is the question that asks for the Whatness or Essence of the subject (See Part II, VIA QUAESTIONIS, a. ).  So to rewrite the above phrase :  What is expected from answering the question 'what is it?' is a knowledge through definition ( = as a result of definition).
The definition, namely, belongs to the principles of knowledge :  For these principles consist of

1. Some non-demonstrable but evident propositions (such as the principle of contradiction), and
2. The definitions (these already directly belong to the individual sciences, and are not propositions but signs which refer to the Essence, for example  animal rationale ( NOTE 163 )).

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