In this NOTE we reproduce the argument (as it is represented in the Document om Mereotopology in First Part of website) that leads to a correct characterization of the carrier-only, and to the correct assessment of the boundary between the genotypic and phenotypic domain of an intrinsic being (a true Totality). Of course the references in the text (for instance references to definitions) relate to places in the original document on Mereotopology in First Part of Website.

Before we reproduce the argument we must recapitulate as to the content of certain important concepts :
We can discriminate between the following types of  Concrete things :

1. True Aggregates.
   These are scattered entities, that is, entities of which the parts are totally separate from each other, and which do not form a repeatable and characteristic pattern. The boundary of such an aggregate is, if present at all, totally extrinsic with respect to the aggregate. A true aggregate (scattered aggregate) has no Essence, because its 'pattern' is not related to an inherent dynamical system.
   Examples :  (1) a heap of stones,  (2) a volume of liquid,  (3) a volume of gas.

2. Non-scattered aggregates, that is, entities of which the parts are more or less contiguous. The parts do form a recognizable and characteristic pattern, but it is not precisely repeatable, only globally so. Here a boundary is always present, but it is partly or wholly extrinsic with respect to the aggregate. A non-scattered aggregate has no genuine Essence, because it is only a fragment of a dynamical system.
   Examples :  (1) a granite pebble (here we see a more or less characteristic pattern consisting of contiguous mineral grains (crystals), and a clear boundary (although this boundary is extrinsic),  (2) a detached arm of a human body (partly exstrinsic boundary, repeatability of the pattern of constituents is only possible in the context of a complete dynamical system that generates a whole human body),  (3) a machine.

3. True Totalities, that is entities with contiguous parts or no actual (macroscopic) parts at all. The pattern of macroscopic parts (if present) and the pattern of microscopic parts is typical and repeatable, because such a Totality is generated by one single definite dynamical system whose dynamical law is the Essence of the Totality. The boundary of the Totality is wholly intrinsic with respect to this Totality. If the actual boundary of the Totality turns out to be extrinsic, then, in the case of true Totalities, there is still an intrinsic boundary too, albeit implicit (from which the extrinsic boundary is a deviation).
   Examples :  (1) an individual organism, an individual single crystal,  (2) a molecule,  (3) an atom.

Of  these,  2  and  3  are called  Mereo-totalities  (concrete things in the broad sense)  ( 1  is not a mereo-totality at all, but a multitude of mereo-totalities), while  3  is a true Substance in the broad sense, that is the individual substance together with its accidents (the fully determined substance). Also a mereo-totality in the broad sense ('fully-fledged' mereo-totality) is a fully determined mereo-totality.
A mereo-totality in the strict sense (and thus also a substance in the strict sense) is called the  carrier-only  (carrier or substrate for determinations) and turns out to be equivalent to the historical individual.
Although we speak of the carrier-only with respect to substances as well as with respect to non-scattered aggregates (and thus speaking of the carrier-only of mereo-totalities), the carrier-only of a non-scattered aggregate is only a carrier-only in an analogous sense, because such an aggregate has, like a scattered aggregate, no Essence. A most strict and true carrier-only contains the Essence of the thing.
Let's now proceed with the reproduction of the mentioned text on mereotopology :

(1).  There is no partition of X into mutually separable parts (Definition 8). This means that the carrier-only must be a complete unity, and this in turn means that it is not a contiguum (like the two billiard balls), even not a tight contiguum (See the next Figure).

Figure 8.
(1).   Contiguum     (2).   Tight Contiguum

(2).  X does not involve inherence (Definition 8).

(3).  X is not a substantial part (Definition 12), i.e. it is not a proper part of a carrier-only.

As we see -- in (2) -- a carrier-only, insofar as carrier-only, does not involve entities that are one-sidedly specifically dependent on it (Definition 4). Such entities (Accidents) are conceptually removed (from a full-fledged Mereo-totality) resulting in the carrier-only.
What exactly is (conceptually) removed?
Well, only those entities that are removable at all, i.e. they should be removable without destroying the specific identity of the Mereo-totality. If we would remove all determinations whatsoever, then we would end up with just Prime Matter, the ultimate carrier. But according to Definition 12 X should have at least a boundary (which is already a determination ), so X cannot figure in that Definition as just Prime Matter.
The only entities that are (conceptually) removable, without destroying the specific identity of the Mereo-totality, are the occurrent entities, i.e. the replaceable determinations (Accidents), like being tanned by the summer sun.
So after the removal of such entities we should be left with the carrier-only. And this carrier-only will still possess several determinations, namely the ones that cannot be removed. These are determinations -- or sequences of them, each sequence consisting of a series of successive determinations, which (sequences) are then each for themselves (interpretable as) single determinations - that are directly caused by the Essence of the Mereo-totality. They are consequently not just compulsorily presupposed types of determination, which are (also) not removable, but are completely specified individual determinations that are necessary for the (content of the) Mereo-totality's specific identity. They are essential parts, essential structures, of the Mereo-totality. They cannot be just potential or virtual.
This needs some further elaborations :
In the dynamical systems approach a necessary sequence of successive determinations (of an individual Mereo-totality) represents a necessary series of successive system states. Such a sequence is therefore a direct effect of the dynamical law (= the Essence of the Mereo-totality), and indeed as such is an essential part (discussed further down) of the Mereo-totality (which should in this context be a genuine Substance). But each individual determination (as a member) of such a successive series will eventually and necessarily be replaced by another determination, namely by the next one in that successive series. And then by the next one, etc., according to the dynamical law.
So only the series-as-a-whole is not replaceable, i.e. the same series will appear in other individuals of the same species, while its members -- the individual determinations making up the series -- are (replaceable).
And if a determination is replaceable in the context of a (full-fledged) Mereo-totality, then it is removable in the context of (obtaining) a carrier-only. Thereby it should be understood that a replacement of a determination is a physical operation, while a removal of such a determination is only a conceptual operation, in order to obtain (i.e. isolate) the carrier-only.
So now we can better assess which determinations are removable (in order to conceptually obtain the carrier-only), and which are not :

(1). Necessary determinations, that are constantly present - i.e. persistent - in the Mereo-totality, are not replaceable, and consequently not removable. When such a determination would nonetheless be removed, or even just replaced by another, the original specific identity of the relevant Mereo-totality is destroyed.

(2). Per accidens determinations are triggered by extrinsic agents. Such a determination can be replaced by another, without destroying the specific identity of the Mereo-totality, and consequently it can be (conceptually) removed.

(3). Determinations, that are members of necessary successive sequences, are replaceable only in a certain restricted sense. Such a determination can indeed be replaced by another, without destroying the specific identity of the Mereo-totality, provided it will be replaced by the next member of the particular necessary successive series of determinations. And because it can be (so) physically replaced, it can conceptually be removed (in order to isolate the carrier-only).

The determinations of (1) are strongly implied by the Essence of the Mereo-totality. They are in fact not determinations of a substrate, but the substrate itself -- albeit not the ultimate substrate -- i.e. they are the substrate for the other determinations. This can be expressed by calling them essential determinations (or essential parts). They belong (already) to the carrier-only, because they cannot be removed.

The determinations of (2) are not at all implied by the Essence of the Mereo-totality. Such a determination can be physically replaced by virtually any determination from the same (Aristotelian) category. Therefore it can conceptually be removed, and consequently does not belong to the carrier-only.

The determinations of (3) stand more or less in between :  as successive sequences they are essential parts, and (already) belong to the carrier-only, while each individual member of such a sequence is - albeit in a restricted sense - physically replaceable, and thus conceptually removable, and consequently not (already) belonging to the carrier-only.

It is important to realize that for a full-fledged Mereo-totality no determination can be removed just like that. It can only be replaced by another determination belonging to the same (Aristotelian) category. When we speak of really removing a determination, we leave the domain of a full-fledged Mereo-totality (from which that determination is supposed to be removed), and enter that of a carrier-only. Such a removal indeed destroys the full-fledged Mereo-totality (because it is then not full-fledged anymore) and leads to the intended isolation of the carrier-only. The removal is in this case a just conceptual operation (while a replacement is a physical operation).

For the full-fledged Mereo-totality to actually be able to exist it must involve a complete set of types of determinations, intrinsic and extrinsic.
If that Mereo-totality is viewed over the whole time span of its existence, then not all determinations, implied by this set, need to be completely specified (For example, Socrates' length is not a once and for all fixed quantity, it varies during his life time). But some of them, namely the essential determinations, should be so specified. If, on the other hand, that (same) Mereo-totality is viewed as a here-and-now entity, then all determinations, implied by the above mentioned set of types, must be completely specified (For example, with respect to a quality : it should not be specified as just (a) COLOR, but (specified) as, say, (a particular nuance of) RED). In general, the Mereo-totality should be at a definite space-time location, it should have definite quantities, qualities and relations.
A non-completely specified, general, determination can at one point in time become specified (actualized) as (being determination) A, and at another point in time become specified as (being determination) B, while the specific identity of the Mereo-totality remains the same, and with it its essental parts (which are caused by, or derived from, that identity (Essence)) (Later we will expound that the difference between the essential parts on the one hand, and the Essence on the other, boils down to a difference of (ontological) domain : The essential parts are phenotypical expressions of the Essence which itself resides in the genotypical domain of the Mereo-totality).
These essential parts will surely involve partitions.
When we stipulate that the interstices that are involved in such partitions intrinsically belong to the Mereo-totality, and thus converting them into partitions into non-separable parts, the Mereo-totality is then a (albeit heterogeneous) continuum, because the parts, resulting in virtue of such a partition, are then only substantial parts (They are not themselves Mereo-totalities or Substances), but are nevertheless actual (also their boundaries are actual).  Here we meet a new kind of continuum :  The continuity of such a Mereo-totality, that is a Mereo-totality consisting of cells and interstices (and thus being partitioned, although partitioned into non-separable parts), is a continuity only with respect to 'belongs to' :  If we go through such a Mereo-totality we never come across regions not belonging to it. So we can call it a 'belonging-to' continuum. But because the cells are actual, such a Mereo-totality cannot at the same time be a mathematical continuum, unless we interpret the cells as just being determinations, and then (in this latter view) the cells are as cells only virtually existing while as determinations they are actually existing. In this way such a Mereo-totality would be a heterogeneous continuum.

If the Mereo-totality is now viewed (only) insofar as it is the carrier-only , then all occurrent entities (i.e. all Accidents) are (conceptually) removed. This means that the carrier-only cannot be viewed as a here-and-now entity (because, among other things, a definite point in time - the answer to the question when the Mereo-totality is - has been (conceptually) removed), and this in turn means that in the carrier-only only the essential determinations are completely specified, and thus actual. All other determinations (namely all replaceable determinations, i.e. Accidents) are only potentially present.
Further, the above (mentioned) stipulation about the status of the interstices of the Mereo-totality, implies that also the carrier-only of such a Mereo-totality is a (heterogeneous) continuum.
So far so good, but what then is the difference between, on the one hand, the carrier-only, and, on the other hand, the corresponding Mereo-totality considered over the whole time span of its existence , i.e. the historical (individual) Mereo-totality?
Well, there is no difference.
The historical Mereo-totality IS the carrier-only.
The Mereo-totality is a totality of its determinations. Some of them are necessary determinations, others are replaceable determinations. The dynamics of the replacement of one Accident by another implies a substrate. This substrate is the whole Mereo-totality minus the Accidents actually involved in that (particular) dynamics, and this substrate is the carrier-only. It is the carrier-only with respect to those particular Accidents actually involved in that dynamics of replacement. The carrier-only, so conceived, does not involve inherence with respect to those particular Accidents, but it does involve inherence with respect to all the remaining Accidents.
And when we now consider all replaceable determinations (Accidents) 'simultaneously' involved in such a dynamics of replacement, we finally have (conceptually arrived at) the (genuine) carrier-only just like that, after we have removed those determinations.
This carrier-only is the result of the (conceptual) exclusion of all occurrent entities. However, as has been said, each necessary successive sequence of determinations, seen as a whole, is not excluded. They are, together with the intrinsically constant determinations, considered as essential determinations, because successive replacement is (ex hypothesi) a necessary pattern.
And in this way we obtain the 'Substance' as it was understood already for a
long time : That which lies under the replaceable determinations.
It comprises the Essence, and all entities that are directly and necessarily caused by, or derived from, it, insofar as they are not replaceable.

There are two categories of concrete real things (Mereototalities) :

• Mereototalities-but-not-yet-genuine-Substances (A table, a granite pebble)
• Mereototalities that are also genuine Substances (An organism, a single crystal)

• As carriers-only
• As concrete wholes

Back to main text