Integrative Levels Classification project scheme monograph references

« Arrays of levels

Chains of types

Each class in an array can be divided into a number of subclasses, which in turn form an array, to be ordered according to similar phylogenetic principles. Subclasses are particular types of their parent class. A type T of a class C is a concept belonging to C but more specific than it, such that it can be said that "all Ts are C" and that "only some Cs are T", eg all mollusca are animals, while only some animals are mollusca:

m	organisms
mf		fungi
mp		plants
mq		animals
mqm			mollusca
mqn			annelida
mqr			arthropoda
mqt			echinodermata
mqv			chordata (mostly vertebrates)
mqvg				cartilaginous fish
mqvh				ray-finned fish
mqvi				lobe-finned fish
mqvj				amphibians
mqvl				reptiles
mqvt				mammals

Each class, like mqvt mammals, thus belongs to a chain consisting of the ordered series of iself and its upper classes, like mqv chordata, mq animals, m organisms. (A further upper class, unexpressed in notation, is the stratum kVn life to which the level of organisms belongs.)

Like in all decimal classifications with an expressive notation, each further letter in the symbol of a class expresses a further degree of specificity: mqvo birds is a more specific concept than mqv chordata.

Chains of types are thus another component in a classification, orthogonal to arrays of levels: while an array expresses an evolutionary sequence of increasing derivatedness, a chain expresses a typological sequence of increasing degrees of specificity [Gno10]. These orthogonal components together represent what can be imagined like a big tree of all phenomena, and the relationships between them in terms of both origin and similarity.

This suggests some general guidelines on how a given phenomenon should be represented in ILC notation. It should naturally be listed near phenomena most similar to it, and not before the phenomena from which it presumably originated. More in detail, the question is to establish the appropriate degree of specificity (ie notation length) for the new phenomenon.

Let us consider the phenomenon of birds. They are clearly a kind of organisms, so have to be filed somewhere under m. Research in biological evolution found that birds originated from some ancient type of reptiles. Hence they cannot be listed before mqvl.

A purely genetic (cladistic) approach would suggest that birds can then be considered as a type of reptiles: mqvlX. However, classificationists paying more attention to morphology observe that birds have evolved into forms very different from those of their reptile ancestors, suggesting that they deserve a separate class. The establishment of the specificity of this class depends on how much different are birds from other organisms. The possibilities are:

A formal principle to determine the appropriate degree of difference would require a precise measurement of morphological difference, a parameter for which there are not absolute measures available. Therefore, classification usually proceeds in a more intuitive way. Zoological knowledge suggests that birds are different from reptiles, but still share most characters with the other chordata, so that their best placement is mqvX. As they originated from reptiles, X must be greater than l. The letter o can be chosen as it remembers of the word ornithology (notice that b from birds is not suitable as it is lesser than l):

mqv		chordata
mqvl			reptiles
mqvo		 	birds
mqvt			mammals

While we keep developing classifications in such intuitive ways, we may search for more formal and objective principles to establish the degree of similarity between phenomena. An important aspect of such research is measuring grades of organization, that should indicate the appropriate levels and sublevels (ie classes and subclasses) to which phenomena are to be assigned. Complexity theory has developed in recent decades a similar search for an absolute measure of complexity. A promising notion in our perspective is that of logical depth, someway expressing the derivatedness of a phenomenon: logically deep phenomena are derived from an evolution of shallower ones, with the accumulation of new properties in the process [Ben87-88; Gno06c].

To draft at least a simple model, a suitable case is provided by chemical elements. Indeed, each element differs basically for its atoms having one proton and one electron more from the previous elements: the addition of them is enough to determine most properties of the new element (as my high school physics teacher Clementina Morales once said: "aren't you shocked that, just by adding one electron, an atom becomes another one?!").

The periodic table of the elements illustrates very well one of the "laws" of the integrative levels, in that small changes in atomic structure are enough to make a clear difference between two neighbouring elements. [Fos61]

As elements are level e in the ILC schedule, let us represent by eb the most simple elements, having only one energy level, and by ebb the most simple among them, hydrogen (H), having one electron in its only energy level. Therefore we can say its notation x to be an ordered set of symbols:

x(H) = (e, b, b)

More in general, the notation x of any phenomenon p will be an ordered set

x(p) = (x1, x2, x3, ... , xn)

Now let us consider the next element, helium (He): it has two protons and two electrons, still in one only energy level. Comparing it with hydrogen, it has one additional character (having a second proton-electron pair). Hence we can suppose that logical depth D has increased by an order of magnitude 1:

ΔD = D(He) - D(H) = 10¹

To represent this, we can change the last symbol xn in our ordered sequence from b to c:

x(He) = (x1, x2, x3) = (e, b, c)

We chose to change the last symbol because the increase in logical depth is 10¹. More in general, in notation

x(p) = (x1, x2, x3, ... , xi, ... , xn)

we will change the symbol xi where

i = n + 1 - log &DeltaD

Moving to the next chemical element, lythium (Li), we find not only one more proton-electron pair, but also a new energy level: indeed, the new electron is not at the same level as the previous two, but at a more external and energetic level. Therefore, logical depth has increased by two orders of magnitude:

ΔD = D(Li) - D(He) = 10²

This means that

i = 3 + 1 - log 10² = 2

so that this time we have to change symbol x2:

x(Li) = (x1, x2, x3) = (e, c, b)

In this way, we obtain a schedule of chemical elements whose notation expresses their progressive increase in organization:

eb 	atoms with one energy level
ebb 		hydrogen
ebc 		helium
ec 	atoms with two energy levels
ecb 		lythium
ecc 		berillium
ecd 		boron
ece 		carbon
ecf 		nitrogen
ecg 		oxygen
ece 		fluorine
ece 		neon
ed 	atoms with three energy levels
edb 		sodium
edc 		magnesium

Deictics »


Integrative Level Classification. Structure. Chains of types / Claudio Gnoli – ISKO Italy : <> : 2009.04.10 - 2011.07.29 -

  Integrative Levels Classification project scheme monograph references