Summary of the Thomistic view of Individuality

It concerns the intrinsic causes (principles) of individuation. These are accordingly the conditions IN the (material) thing which are required for it to be an individual. The extrinsic causes of individuation presuppose these intrinsic conditions. Furthermore it exclusively concerns the individuation of a suppositum, which is something that is not in something else, and moreover a complete something, a first substance.
According to St Thomas the principle of individuation for bodily substances is jointed, i.e. it contains several aspects or 'parts', together constituting that principle.

The FIRST ASPECT is prime matter. Prime matter is the first principle of individuation. Prime matter makes a manifold of individuals within one and the same species possible. Here it concerns a numerical distinctness of individuals.
At the end of the opusculum (= small treatise) De Principio individuationis it is asserted that prime matter alone cannot be a principle of individuation because it is communicable over several forms, either the same with respect to content or different. By Quantity, however, matter is delimited in space-time to a definite 'point' and then it is not communicable anymore. In the Opusculum this is expressed as follows :

"...because this quantity cannot go together with another form under a same determination."

Prime matter ( materia prima), as the ultimate principle of potentiality in a bodily substance, makes possible the reception of its own substantial form and also of its own accidental forms, among which first of all the form of quantity. This always proceeds via the substantial form. In its function of corporality (that is one of the substantial form's many functions) it demands this quantity (in this way the substantial form attributes to the principle of individuation, i.e. it is an aspect of the principle of individuation). Quantity is nearest to matter and consequently nearest to :  non esse in alio (not residing in something else). And this means 'being a first subject', which is a condition for being individual, because this in turn means :  not communicable to something else anymore, i.e. not further instantiable anymore.
Prime matter, taken in itself, is indistinct and cannot (because it is indistinct) individuate the form it receives. It must first of all be made distinct. A form can, as this form, only be received in this matter, distinct from that matter and from that matter, and then by implication be individuated. And this is accomplished by quantity. The dimensive quantity disperses the matter, confers to it extent and consequently potential parts.
Determined dimensive quantity makes those parts actual, resulting in the ability to receive numerically different forms (of the same species) into those different parts and so individuation is accomplished :

"After all, the form is not individuated because it is received in matter, unless insofar as it is received in this matter or that matter, distinct and determined to the here and now. But matter is divisible only by means of quantity..."

The substantial form demands, as has been said, in its function of corporality, that the matter, in which it is received, has three dimensions. Because the individual possesses its own substantial form, it itself formally demands a three-dimensional extent. All this is possible by virtue of the participation of that individual in prime matter. The substantial form further determines the limits between which the size and outer form (figure) of an individual of a species can vary.

The dimensiones interminatae (undelimited dimensions) as a(n) (aspect of the) principle of individuation.

The dimensiones terminatae are the totally determined delimitations of size and figure of the here-and-now individual (the semaphoront, i.e. the bearer of diagnostic characters, See NOTE 1 ). In fact something exists at all only within a here-and-now 'location', and TO EXIST implies total determination and consequently a (status of) TO-BE-AN-INDIVIDUAL.
But these dimensiones terminatae cannot be a principle of individuation, and that means here : they cannot be a principle of TO-BE-A-HISTORICAL-INDIVIDUAL. The quantities (size and figure) are constantly changing in such an individual, that would be dissolved into a very large number of individuals WHEN the dimensiones terminatae were a principle of individuation. No, it is the dimensiones interminatae which are a principle of individuation, because they leave, by virtue of their relative indeterminateness, room for the changes mentioned, changes in the historical individual.
There is a kind of causal relation between the historical individual (as cause) and the here-and-now individual, the semaphoront (as effect):
The dimensiones interminatae individuate, as quantity, the subject. But the subject individuates all its accidents, and consequently also the dimensiones interminatae. It individates them to dimensiones terminatae (The latter always exclusively relate to the semaphoront):

"so that also the very terminated dimensions, which are founded in the complete subject, are individuated in some way by the matter, which is individuated by the interminated dimensions..."

In considerations about the individuum, seen, not as semaphoront, but as historical individual, it is always presupposed that something-with-content remains constant, together with the fact that 'always being quantified to one or another determination' also remains constant: So we read for example in BOBIK, 1953, La doctrine de saint Thomas sur l'individuation des substances corporelles, p. 27:

"Le fait qu'il est toujours quantifié est principe de sa constante identité numérique et de l'individuation qui en est la conséquence."

"The fact that it is always quantified is the principle of its constant numerical identity and of the individuation which is the consequence."]

It is this "il" (meaning "it") that is presupposed to remain constant. But this constitutes a problem, for instance for Nominalism, because a constant numerical identity is already presupposed by using the term "it", and so a principle for such an identity doesn't seem to be necessary. Nominalism rejects such a presupposition and holds that all what is real IS already individual all by itself (So no individuation principle is needed).
At the same time we see how important the issue of individuation is for an evaluation of the Thomistic Metaphysics in the context of a nominalistic critique. Nominalism does not accept the reality of any general concept, such as an Essence, or a species, i.e. it denies that a general concept corresponds to something in extramental Reality, something that would be present in a number of individuals. Such a general concept is -- according to Nominalism -- just a name (nomen), that belongs to our way of knowing and signifying. The only items that do exist in extramental Reality are individuals, whereas Thomistic Metaphysics admits of the existence of repeatable principles, i.e. principles (like an Essence) that can be multiplied, and so distributed, over several individuals.

De Principio Individuationis and De Ente et Essentia are treating the individuation-to-the-semaphoront.
The commentary on Boëthius' treatise on the Trinity treats of the individuation-to-the-historical-individual.
As far as I know, the precise relation between the two is not expounded.
Only the semaphoront exists (and is consequently totally determined).
The historical individual is already a theoretical construct, based on our own self-consciousness.

Thematical Discussion about Individuation

1. Individuum and Person.
2. Dimensive Quantity.
3. Individuum as Semaphoront.

See for such considerations for example
JANTSCH, E., 1980, The Self-organizing Universe, SCIENTIFIC AND HUMAN IMPLICATIONS OF THE EMERGING PARADIGM OF EVOLUTION . Further :
BRIGGS, J., and PEAT, F., 1984, Looking Glass Universe, THE EMERGING SCIENCE OF WHOLENESS .
And from the same authors : Turbulent Mirror, AN ILLUSTRATED GUIDE TO CHAOS THEORY AND THE SCIENCE OF WHOLENESS , 1990.

In the three mentioned subsections we do not intend to fully solve the (interesting) problems of which they treat. For suggestions concerning possible solutions, see the first part of this Website (that is, the first main Section of  'First Part of Website' [the latter is where we are now] ,  that is devoted to a modern revision of the Substance-Accident Metaphysics in terms of dynamical systems. See also Fifth Part of Website ,  where these topics are taken up again.

Individuum and Person

"By definition the individual is undivided in itself and divided from other things by the last of all divisions".

"After this (last of all divisions), a further division will make it specifically different (i.e. the thing will become something else). Because when we are going to divide an individual (cut it into chunks), we will obtain different substances"

Here it concerns a problem that relates to substantial change :
Van MELSEN, A., Natuurfilosofie, 1955 (An English precursor of this work, by the same author, The Philosophy of Nature, was edited by Duquesne University Press, Pittsburgh, USA, 1953, second edition 1954.), distinguishes two types of substantial change :

1. One in which a substantial form (i.e. the intrinsic nature of the thing) is substituted by another form (with another content) (or sometimes by more than one, but then we have to do with the generation of more than one substance differing in content, out of one substance).

2. The division of (numerically) one substance into numerically many substances (two or more) which are, however, identical (concerning content) to each other as well as identical to the original substance : eaedem specie, diversae numero (the same in species, numerically diverse).

"After all, the form of the whole in them, because of which they have a certain unity of (their) nature, over and above quantitative unity, is, according to the total intelligible content of that form, present in every part of such things : Thus when a division has taken place the essence of the same form remains in those parts that are diverse among each other. After all, every part of fire is fire, and every part of a stone a stone."

"Yet there is in those divisions a certain similitude with corruption and generation, not that new forms are generated by the division of such things, but because the being, or equivalently, the (more) prior act(uality), is being removed by that division and the potency is lead to its proper act [ I.e. the potency is actualized ]. So it goes in the case of the imperfect living beings like plants, and certain imperfect animals, like articulate animals."

1. The one substantial form which directly conveys being.

2. A form which is, it is true, present in the thing, but which does not confer being (a form-without-being-just-like-that), because otherwise -- when that second form would indeed confer being -- there would be TWO (genuine) substantial forms present in one substance, implying that that one substance would be several substances at the same time.

"After all, that form, on which the quantity as of its origin depends, is per accidens divisible."

However we, as has been said, now know that also the very small beings, like freely existing molecules (for example in a gas or liquid), although lower beings, are nevertheless not divisible idem specie : A division of them always results in something specifically different. In what way individuation of such small beings is accomplished is not directly completely clear, but it seems to me that also concerning them the Thomistic theory of individuation applies.
Moreover, in the case of molecules it happens to be that they are -- apart from their spatial situation (i.e. their orientation in space), their place (location), and more of such external factors -- insofar as we know, identical to each other, i.e. the individuals of the same molecular species are identical to each other, while this is not the case with complex substances like higher organisms and man. There each individual is unique in a high degree (and this not only with respect to their space-time situation, but also with respect to content : Socrates strongly differs from Plato, despite the fact that they are individuals of the same species, namely HUMAN BEING). The reason for this is that being-a-human-being (and this also applies to all higher organisms) is in one way or another eidetically (i.e. with respect to intrinsic content) more stable than the small molecules. For these latter a small change has more impact than for the former.
Moreover, individuals of higher organisms, including man, besides displaying an eidetical (species-specific) stability, display also a strong degree of individual stability : Socrates remains what he is, despite the many changes (changes with respect to all kinds of features on him) in the course of his individual existence. The 'steady root', remaining identical in Socrates, is thus not only his being a human -- this is also in the same way present in Plato -- but also his being-Socrates. And this being-Socrates is, with respect to content, different from being-Plato.
With the inorganic beings we encounter this in a much weaker way : The development of faces of, say, a crystal of sodium chlorate, can vary during growth because of a change in the growing environment, i.e. a certain set of faces could start to grow faster (than before) (always in a direction perpendicular to those faces), ultimately resulting in their disappearance, causing the crystal to obtain a totally different outer form than it had before. The crystal remains thereby specifically the same, but whether it also remains individually the same, or that it changes individually (comparable with the case in which Socrates changes into Plato), is hard to assess, when such a view of individuality applies at all to inorganic beings.

The phenomenon of personal individuality, especially in the case of human beings, implies that we not only can speak about Socrates, Plato, etc., as individuations of HUMAN BEING, but that also the here-and-now Socrates is an 'individuation' of Socrates (as historical individual, i.e. the here-OR-there-and-once-OR-now-OR-then(next) Socrates). The historical individual has a constanly changing but nevertheless complete (= total) determination. This changing takes place in Time (for instance with respect to Socrates), but it can also take place in Space, for example when we first look to Socrates, and then to Plato, then we see a change-in-space of complete determination : From the complete determination S of Socrates, to the complete determination P of Plato, where S is different from P.
S is a complete determination in one direction, whereas P is a complete determination in another direction. It seems evident that the dimensiones interminatae (unterminated dimensions) account for the possibility of these changes of complete determination, in space and in time. That however Socrates remains Socrates, and Plato Plato, while they remain different from each other in a characteristic way, cannot be explained with those dimensions.

In the first ON THE CONTRARY of the 2nd Article of Question 4 in St Thomas' Commentary on Boëthius' treatise on the Trinity (See Part Two), St Thomas refers to Porphyry who says that every individual contains a unique collection of accidents, which is moreover constitutive for such an individual. At the end of the Body of the Article St Thomas says that some accidents, namely those which directly relate to dimensions, take part in individuation, and that the remaining accidents are not (related to) the principle of individuation, but principles of the possibility of perceiving and recognizing individuals. Our ability to distinguish between human individuals is accordingly based on unique combinations of accidents, we can also say, on typical properties, and these could be the individual propria ('propria' are  per se determinations, [genuine] properties), each one of them being already sufficient for recognizing. These propria undoubtedly come from some fixed root, and that is first substance. In this way Socrates is a different substance from Plato, and this not only numerically, but also with respect to content.
This last mentioned phenomenon is not explained with the Thomistic principle of individuation, but can also not be explained on an eidetical basis (the basis of the specific nature), because both Socrates and Plato are a HUMAN BEING (i.e. both are specifically the same). The aspect of numerical individuality can, as has been said, be explained, albeit in a preliminary way, by that Thomistic principle of individuation, but not the personal. Also the 'soul', (considered) as substantial form, does not explain this, because it is the same for each human being (The soul as substantial form even does not explain numerical diversity, it explains, as substantial form, specific diversity only). And if we interpret the soul as being moreover something else besides being a substantial form, we'll, according to me, run into ontological problems, and shift the problem of the personal to that of the (in that case interpreted as a personal) soul, which doesn't yield anything.
So Socrates and Plato have nothing eidetically in common (i.e. they are not only numerically different but also with respect to intrinsic content). They just look like each other, causing us to place them, together with others, in a certain class, that we call HUMAN BEING, without there being anything in them in which they match exactly.
In this way we end up with a nominalistic position, or -- and this is perhaps a better position -- we should descend one level lower in all of this : Socrates is an individual of a possible monovular twin (or a monovular multiple), and so is Plato, resulting in the fact that Socrates and Plato are two substances differing in content (and of course also numerically). A monovular twin is the result of the development of two individuals from one and the same egg-cell. Their genetical make-up is consequently the same.
I will elaborate on this below.

Dimensive Quantity

The possibility of a qualitative determination of something, for example it to be white, is implied by the undeterminate dimensions. The limits within which the variation of those qualitative determinations (each for itself) can take place are set by the substantial form, thus by the whatness or specific identity of the thing, and the same is valid with respect to sizes. Not only there is such a controlled variation in each accidental determination within the species, but also (for example in humans) within an individual : Socrates varies within certain limits, causing him to remain recognizable as Socrates. It is not clear whereupon this last mentioned control is precisely based, it is the problem of (assessing) the individual person.

Individuum as Semaphoront

This predication is possible because Socrates is (here) still communicable to inferiors as long as we take Socrates to represent the historical individual (which is also the usual interpretation of "human individual").
While this (kind of predication) is being denied in all Peripatetic (= Aristotle-oriented) and Scholastic (later Middle Ages) writings!
The determined dimensions are, through matter, responsible for the semaphoront.
Prime matter is responsible for being a last subject, i.e. for the incommunicability to subsumed beings. And this is the case, not with the historical individual, but with the semaphoront.
The undetermined dimensions are, through matter, responsible for the historical individual, because it can still vary during its existence. So

THE LAST SUBJECT IS THE SEMAPHORONT.

Accepting this implies that (the) first substance is not Socrates, but Socrates here-and-now. This calls, as has been said, for the question of the difference between the fixed root in Socrates-as-a-historical-individual, remaining constant under the varying determinations of the here-and-now (i.e. the different determinations belonging to successive here-and-now's), AND that fixed root in Plato, also remaining constant under the successive here-and-now's. This cannot be their being a HUMAN BEING, because that is supposed to be the same in both. Perhaps Socrates and Plato are, afterall, two substances differing not only numerically but also with respect to content, two substances, which each for themselves are divided into semaphoronts. As has been said we then come close to a nominalistic position, that holds that there is not something in Plato and Socrates in which they exactly correspond. They only look like each other.
However such a (nominalistic) view is problematic.
If we interpret Socrates and Plato as two substances, differing in content, implying that HUMAN BEING becomes a genus instead of a species, then Socrates and Plato belong, it is true, to the same biological species, but not metaphysically so. The historical individual Socrates then is not an individual anymore, but a species. This species remains constant under the changes of conditions (= under the successive here-and-now individuals), implying again a non-nominalistic view, with the only difference that we have descended to a next lower logical level. The here-and-now cases of Socrates would then be the 'individuals' of (the species) SOCRATES. A very remarkable contra-intuitive conclusion by the way, because such 'individuals' are constantly connected with each other in time and space, and accordingly miss the ' divisum ab alio ' (i.e. the separateness from others).
We can go about a solution to this problem as follows :
The individuals of the species SOCRATES are not the here-and-now individuals of Socrates, but members of a possible monovular twin (or more than two, that is, a monovular multiple) of Socrates. In reality (i.e. in the case of the real Socrates) we only have one such member (a monovular singular), but this is of course accidental. Such a member is a historical individual and is (in time) divided into a succession of here-and-now individuals, i.e. into a continuous series of semaphoronts.

Let us now further solve the problem mentioned, applying new insights (and in so doing refer to our results laid down in the Non-Classical Series of Essays), and consequently deviating from classical positions :

We are going to interpret the HISTORICAL INDIVDUAL as the INDIVIDUUM, but this historical individual 'Socrates' belongs to a different species (metaphysically) as the historical individual 'Plato' does. The species SOCRATES has, as was in fact the case, only one member (consisting of one individual), and so also with respect to the species PLATO.
In the Classical Series of Essays I have argued that, say, the individual Socrates is in fact a DYNAMICAL SYSTEM, that displays a series of consecutive states (stadia). The succession of those states is dictated by the DYNAMICAL LAW of that particular dynamical system. The complete series of these stadia (We can legitimately call these stadia SYSTEM STATES) is the historical individual, while each separate state is a here-and-now individual (semaphoront). Also Plato is such a system, but subjected to a different dynamical law. Such a dynamical law accordingly is the law of the dynamical system that generates a being from basic elements (A "being" is, also in this context, interpreted as an intrinsic Totality, in this case as a totality-resultant of the corresponding dynamical system), and this law will be metaphysically interpreted as the ESSENCE of that being.
Now we are able to state the problem and its solution more clearly :
In the classical conception one first Substance (for example Socrates as historical individual) can, and will, differ from another con-specific first Substance (say Plato). The differences involved can then be assessed trouble-free as being accidental, because both are still human beings.
But if we accept, for good reasons, that the first Substance (= last Subject) is the semaphoront, implying that Socrates as first Substance must be the here-and-now Socrates, then we have a problem.
That problem consists of the fact that now a whole series of semaphoronts (representing Socrates) differs, in a persistent and characteristic way, from another such series (of semaphoronts, representing, say, Plato). Such a persistent and characteristic difference obtaining between two series can hardly be seen as just accidental.
The solution of this problem consists in (1) interpreting Socrates and Plato as two specifically different dynamical systems, and (2) (consists) in interpreting Socrates as a member of a possible monovular twin (or more than two) of Socrates. And the same goes for Plato. They are now two specifically different Substances, and their (persistent and characteristic) differences are now substantial differences, while the members of any such monovular twin differ little from each other. The difference involved in the latter can now be assessed trouble-free as being just accidental differences. Moreover, in terms of dynamical systems theory the members of a monovular twin can be seen as two separate systems, each governed by the same dynamical law, but originating from slightly different initial conditions. Indeed it now is to be expected that they are very similar, while strongly differing from other twins (or singletons), because the latter difference is specific, and thus substantial.
The reason why the members of monovular twins are so similar is their identical genetic make-up. Their differences relate to accidental determinations, like location and time (in the case that one dies earlier than the other), and influences of environmental factors that differ from location to location.
The problem of the personal, namely the fact that Socrates differs relatively strongly, and persistently from Plato is now solved, because now we do not need to interpret two such beings, differing so strongly and persistently, as two members of the same species. They belong to different species. Individuals of a same species are now the members of a monovular twin --Where no such twin exists the species comprises only one member - say (the members) Socrates-1 and Socrates-2 (and correspondingly Plato-1 and Plato-2), and such members do not differ so much (because of their identical genetic make-up) implying that the problem of the personal is solved :
Now, just like in any other case, be it human or non-human, (and be it) organic or inorganic, con-specific beings are very similar to each other, while beings belonging to different species differ strongly and persistently. It is now not the case anymore that the person Socrates-1 (magically) remains - during all his life - so clearly recognizable and (so clearly) distinguishable from the person Socrates-2, because they aren't.
So in Ontology we now can dispose of the term 'person' to indicate the special status of human individuals, because they don't have this special status in this respect.
In the hypothetical case of an actually existing monovular twin of Socrates we have to do with, Socrates-1 and Socrates-2  ( In which case we assume that the dynamical laws of monovular twins are identical, basing this assumption on their identical genomes (See NOTE 5) ).  Socrates-1 then shows a series of stadia and thus is a historical individual. And this series is separate from the series of stadia of Socrates-2, implying that these individuals (Socrates-1 and Socrates-2) now also show the divisum ab alio (being separated from other individuals, including from each other). In this way the problem is now completely solved.

Let us present all this in a systematic way, in which we also assume the existence of a monovular twin for Plato :

The dynamical law (the Socrates-dynamical law) is the same for Socrates-1 and Socrates-2. Their (penultimate) initial conditions were, however, slightly different.
The dynamical law (the Plato-dynamical law) is the same for Plato-1 and Plato-2. Their (penultimate) initial conditions were, however, slightly different.
The Socrates-dynamical law is different (with respect to content) from the Plato-dynamical law.

"Socrates-1(say)b  is  Socrates-1"   (see table above, stadium S1-b)

Where Socrates-1b is a semaphoront and last subject.
What then is the relationship between carrier-only and last subject?
Well, although this should be investigated further, we can, for the time being, state that the  carrier-only  is the subject-explicitly-without-replaceable-determinations, while the last subject refers explicitly to its downward ontological independence, while only implicitly referring to its character as carrier-only.