The Principle of Individuation

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Introduction

When one carries out observations or experiments in the physical sciences one will obtain some information as a result of these observations or experiments, i.e. information with respect to certain cases, namely the cases of just those observations or experiments. The next step consists of a generalisation to ALL relevant cases. Doing so natural science presupposes that the same results would be obtained for all relevant cases on the basis of observations or experiments, when these would indeed have been carried out for all those cases under the same conditions. This is called induction. Stated differently : Natural science presupposes that processes in the Real World are repeatable, and that means that those processes proceed according to certain constant laws. This boils down to the presupposition that we are allowed to speak about a collection of beings (things) having each for themselves the same nature ( and another collection of beings also having each for themselves the same nature, but different from the nature of beings of the first collection. The same can be said with respect to other collections). The fundamental presupposition in scientific induction can now be reformulated as follows :

Things having the same nature will always behave according to that nature.

This does not mean that those things always behave in the same way, because that same nature will generally behave differently under different conditions, but still according to that nature. Under exactly the same conditions (which are seldomly realized) those things (having the same nature each) will behave in exactly the same way. Also the same thing will always behave according to its nature, whereby it is presupposed that this nature is constant for the thing. The mentioned behavior of the thing is always an interaction with other things, also having a certain nature, and so also behaving accordingly. This is equivalent with the presupposition that the natural laws are constant. So a thing can in principle be multiplied resulting in a collection of ' cases '. These cases behave in the same way (under the same circumstances), they all behave according to their nature, which is the same for every one of them, but they are different cases nonetheless. They differ numerically, they do not differ specifically, because their nature, their species, is the same for each of them. Accordingly natural science presupposes that every uniform thing (i.e. not a mixture of things) consists of two fundamental principles : a principle of individuality, and a principle of specificity. Expressed in another way : Every uniform thing is metaphysically a composition of two ' moments ', intrinsic causes, (which are not themselves things!), (1) an intrinsic cause of individuality and (2) an intrinsic cause of specificity (specific whatness). In Philosophy these two intrinsic causes are identified with " Matter " and " Form " respectively. Matter was already established as a principle of the possibility of radical change : When we assume radical change of a thing (into another totally different thing) possible, then we have to postulate a last substrate of all content of a thing (i.e. an ultimate substrate which carries the content -- the quantitative and qualitative determinations -- of the thing). If we would not postulate such an ultimate substrate then a radical change, i.e. a most radical change, could not be distinguished from the destruction (i.e. disappearance ) of the thing followed by the creation of the new thing. So ONLY by postulating a last substrate, which has no content (only potential content) and which remains during and after the radical transformation (radical change), can we speak of something that has changed. We see the connection of this last substrate with individuality. This last substrate is called ' matter ', more precisely PRIME MATTER, because we can call a ' last ' substrate also a FIRST substrate, depending on the direction we look. This prime matter is always informed by content, which is called Form, or nature. Said differently, the prime matter carries the Form or nature of the thing in question.
So by way of the presuppositions in the method of natural science, induction, we have found something like a PRINCIPLE OF INDIVIDUATION, and this principle is somehow represented by Prime Matter.
It is however necessary to elaborate more on these first results, in order to show in what way exactly prime matter individuates a certain nature (individuates a certain Form).

Here-and-now individual and Historical individual

Individuals occur in two varieties : Let us elaborate on that. An individual is a Totality, a uniform being, generated by a dynamical system. Generally this resulting Totality is not static but is subjected to the ongoing process of the dynamical system that generated that Totality in the first place. This results in the fact that the Totality is a succession of states. Every such state belongs to the current system state, it is an aspect of this system state, it participates in the global current system state. When we contemplate such a state (of the Totality) at a certain point in time we contemplate a here-and-now individual, which we can also call a semaphoront , meaning a bearer of distinguishing marks. And when we contemplate the complete succession of states (of that Totality), we contemplate the historical individual.
This is easily applicable to a human being. A human being goes through a more or less well defined succession of states (also during its adult lifetime). One such state (i.e. each state as such) is the semaphoront, for example Socrates, here-and-now (i.e. considered at a certain point of his lifetime). The complete series of states is the historical individual, it is just Socrates in all his life stages, i.e. Socrates during his complete lifetime. It is clear that what we normally understand by something being an individual is the historical individual, and our investigation must largely be directed to this type of individual.

The role of Quantity in individuation

We must now try to establish the principle (or principles) of individuation in more detail.
Generally the principle of individuation is that in the thing which causes it to be an individual. We located this principle, in a preliminary way, as being the prime matter of the thing. But prime matter as such has no content and is as such only potential (it can be informed by content).
Every being consists of quantities and qualities. And it is clear that a principle of individuation must somehow be related with quantity because individuals of the same species (having the same nature) can in principle be identical concerning content, but nevertheless be different : They must differ at least numerically. In order for this to be possible the (mentioned) content must be spatially extended. And only when it is thus extended it can be interpreted as being divided and as such has given rise to numerical different cases of this same content (or with other words, that same content can be considered as being multiplied). Stating the same differently : If there are to be many things of the same specific nature, they cannot be distinguished from each other by a formal distinction, because they are formally or specifically the same. If they are simultaneously to be many, each must have extension (spread-out-ness), dimensive quantification, i.e. a claim to a relative position or situation of its own ( See, for example, BOBIK,J., 1954, Philosophical Studies 4, p.60-79 ). So it is clear that quantity is involved in individuation. But quantity in itself cannot exist, it must be quantity of something. And a certain quantity, say, a length of 1.50 meter , can occur and exist in several things. So quantity cannot on its own accord be ' a this '. Only a quantity of something can do the job. Not until then it becomes this quantity. This means it needs a substrate. This substrate we know as ' matter ' (Do not confuse this matter with physical matter). So the principle of individuation must somehow be : QUANTIFIED MATTER, more precisely, quantified prime matter.
Let us elaborate on this further.
There are two main species of quantity : Time cannot have contiguous parts for none of the parts of time has a permanent or semi-permanent existence, and that which does not remain and abide can hardly have position.
Also with numbers we cannot have parts having a relative position or situation to each other, and we cannot state what parts are contiguous. This can only be done metaphorically, for example to map the numbers on a spatially extended something.
So for locating the principle of individuation we need quantity which permits something to have parts outside (other) parts, quantity involving position or situation, dimensive quantity , because only then many things having a same formal content can be divided over those parts and so can be many. The parts of the dimensive quantity are only potential, they constitute possible divisions of the dimensive quantity. Actual division generates actual parts. And because (1) quantity can only exist as quantity of something , and (2) this something is an ultimate substrate, we must say that individuation involves (prime)matter-quantified-by-dimensive-quantity.
Now we can consider dimensive quantity twofold.
Firstly as it is in itself. Considered just in its own proper nature, i.e. taken precisily in its distinctive quantitative nature, dimensive quantity excludes any qualitative completives or determinations, especially terminations by figure and the consequent limitation in measure (i.e. magnitude). It is just extension.
Secondly with respect to their (having received a) delimitation (termination) to magnitude, length or volume, and to form (i.e. external figure, and so implying quality (see " Quality " in the Essay on Substance and Accident), and as such it is a complete accident (see " The System of Categories " in the same Essay). But as such, i.e. as delimited, they cannot be a principle of individuation, because we know that in the very individual, i.e. the historical individual, those delimitations vary constantly during, and because of, the succession of states, and also because of extrinsic factors. And if dimensive quantity as delimited would be the principle of individuation), this would result in a multitude of individuals instead of one and the same individual. When an animal breathes it changes its figure, and also when it goes through its successive states it changes its figure and magnitude, but while doing so it remains the same individual nevertheless. So the principle of individuation must involve dimensive quantity insofar as the dimensions are considered as not delimitated. In philosophy such dimensions are called interminated dimensions, in contradistinction to terminated dimensions.

Although the very individual is the Historical Individual, the only individual which really, i.e. actually, exists is the here-and-now individual or Semaphoront. The historical individual is already a more or less theoretical construction. So our analysis must proceed from the Semaphoront to the Historical Individual.
In the individual nature (in contradistinction to the specific nature) we can detect three aspects which together play a role in individuation :

Numerical Unity

The individual nature has numerical unity, it is undivided in itself, it is ONE thing. First and foremost this is guaranteed by dimensive quantity. Here it is constituted by interminated dimensions, making prime matter dimensive matter. And in this way a situation or position is possible.

Last Subject

An individual is a last subject . It is separated from other individuals. It cannot rest on yet another substrate, it already involves an ultimate substrate. It cannot be communicated to inferiors. Logically (i.e. in terms of Logic) this means : It cannot be predicated of another subject. While we can say Socrates is human, predicating the term " human " of the term " Socrates ", we cannot say X is Socrates-here-and-now unless we mean by " X " exactly the same as by " Socrates ", and thus enunciate the meaningless proposition Socrates is Socrates.
So being a last subject the individual is not ' downwards ' communicable anymore (in contradistinction to the specific nature, like HUMAN [= the species MAN] which can be predicated of a subject, and thus being communicable to an inferior, say, Socrates).
It is Prime Matter that causes a substance to be a first substance (See the Essay on Substance and Accident for the distinction of first substance and second substance), i.e. becoming itself a last subject. This subject cannot be instantiated any further and so it is unique, and in this way prime matter guarantees this aspect of being an individual. In short, prime matter takes care of making something a last subject.

Determination towards the here-and-now

But interminated (unterminated) dimensions do not actually exist. They always are terminated dimensions , only considered as unterminated, i.e. considered in their pure nature, in their nature of (being) dimensions. The dimensions considered as terminated (the actually -- always in a subject -- existng terminated dimensions) involve a determined magnitude and figure, and guarantee the (being of the) semaphoront, i.e. the individual here-and-now. This quantitative and qualitative determination changes from one here-and-now (individual) to the next, giving rise to the historical individual. But speaking about the semaphoront we do not consider these changes.

Determination towards the historical individual

When we do consider those changes, i.e. those alternating determinations of dimensive quantity, then we are speaking about the historical individual. We can observe these changes in the successive states of the uniform thing (Totality), especially clearly in the metamorphosis of certain Insects. That such (sometimes even major) changes can happen without loss of individuality, i.e. without generating a whole series of individuals, is guaranteed by the unterminated dimensions, because the variation will proceed along these dimensions (playing the part of axes in a space of distinguishing marks, or parameter space : At different moments in time the individual will occupy different positions in this space). In this way a being can, in spite of these changes, remain in existence and continuously exist under (changing) here-and-now conditions. Said differently, the unterminated dimensions result in an individual which is numerical distinct from other individuals, but keep open the possibility of variation within an individual, while the terminated dimensions again and again determine a here-and-now situation. In this way numerical unity is conserved.

Explicit, but preliminary, Interpretation of Individuation in terms of Dynamical Systems

The concrete Essence of a uniform thing (= general Matter + Form) is the dynamical-law-inherent- in-the-systemelements, and, after the generation, by the dynamical system, of the Totality (= uniformed thing), this Essence is also inherent in that Totality. In the order of generation the dynamical law, as being inherent in the system elements (before the generation of the Totality), is existing in a more fundamental way, than as existing in the Totality (which is formed afterwards). As such, i.e. as inherent in the system elements, this law is dispersed (not necessarily repeated) over the multitude of system elements (the dynamical law never resides in only one system element). These system elements are themselves beings, complete things, or, consisting, each for themselves, of more than one complete thing. In this way dimensive, determined, quantity is already implied with the (existence of the) concrete dynamical law.
Individuation of the dynamical law, takes place when this particular (in a specific sense) dynamical law locally -- here and there -- starts to operate. This directly implies the individuation of the Totality being generated, in fact it implies the individuation of its Essence.
In the static, i.e. constitutive order, the principle of individuation is the constitutive cause of individuation (the effect).
This principle is :

Matter under unterminated dimensions .

It is the principle for something to be a Historical Individual, i.e. the complete series of process states of the Totality.
The principle of individuation is also :

Matter under terminated dimensions .

As such it is the principle for something to be a Semaphoront, i.e. one particular process-state of the Totality. This we can also express in a different way : Matter under terminated dimensions is an effect of matter under unterminated dimensions (as a cause), namely when these latter individuate the Totality (their subject, their carrier) and when this subject in turn individuates the matter under unterminated dimensions towards matter under terminated dimensions. The unterminated dimensions possess out of themselves the character, the nature, of individuation, while the terminated dimensions do not. The terminated dimensions obtain their individuality from their subject.
These terminations (determinations) alternate again and again with the continual or discrete transitions from one process-state of the Totality into another. During all this the dynamical law remains the same (if it changes we have to do either with just a partial law of which the change (of this partial law) is governed by a more comprehensive law, or we have to do with a specifically new Totality being generated). But the variations (alterations) always remain within certain limits. These limits are specific and are set by the dynamical law, the Essence of the Totality.
The same dynamical law can start to operate at more than one locality, implying several different initial conditions, and in this way several INDIVIDUALS of the Totality, governed by specifically the same dynamical law, are generated.
When we speak of the " individuality of (terminated) dimensions ", we mean that such dimensions are individual, they are NOT individuals. Only the Totality (the first substance in question) is an individual (A first substance is individual as well as an individual).

Conclusion

So prime matter is the principle of individuation, but only when it is informed by unterminated dimensions. Only then numerical diversity is possible. This diversity is constituted by an actual division of unterminated dimensions resulting in terminated dimensions giving rise to different positions, and thus the possibility of a multiplication of a certain formal content, giving rise to several here-and-now individuals of the same species. At each position the terminations can change from one moment to the next, together giving rise to historical individuals.
If unterminated dimensions are considered in their distinctive nature as unterminated dimensions they individuate their subject. If they are considered as accidental form, i.e. as inhering in their subject, they are individuated , meaning that they are rendered the dimensions of this subject , (and so are individuated) by that subject, like every other accident. Those dimensions are then individual, but they are not of course individuals .
Prime matter, the receptive root of every change, guarantees the possibility of variation of the determinations. The (formal part of the) Essence or substantial form of the thing, i.e. the (formal part of the) dynamical law of the dynamical system that generated (or can generate) this thing, is that which checks the variation and holds it within the limits which are demanded by it.
Summarizing succinctly, prime matter under dimensive quantity-considered-in-its-pure-nature (i.e. involving unterminated dimensions) is the principle of individuation concerning the historical individual. Prime matter under dimensive quantity-considered-as-involving- terminated -dimensions is the principle of individuation concerning the semaphoront (the here-and-now individual), or, said differently, the termination, and thus the individuality, that goes with matter under terminated dimensions, is the effect of the individuation of the subject. This individuation of the subject took place by the information of prime matter by unterminated dimensions. This informing is part of, and is governed by, the informing of prime matter by the substantial form. All this results in terminated dimensions. We can still explicate further : Dimensive quantity, considered as an accident, inhering in its subject, is individuated by the unterminated dimensions through the mediacy of the subject. Dimensive quantity considered as unterminated means that the dimensions are terminated (they always exist as terminated), but, only having one determination or another, not having this determination. And as has been said, the variations in the determination are set within specific limits demanded by the Essence of the thing. Unterminated dimensions so conceived is pure quantity, (and so) quantity not considered as an accident inhering in this subject. Only quantity as terminated (dimensions) is an accident, inhering in this subject.

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