A class is derived from the identification of the common in the multitude between objects and their properties. It is an object of thought representative of a pattern: it is an abstraction. The classification of objects proceeds from the discernment of the properties they have in common. That property which is essential to the object — without which the object would not be — is definitive of it and, hence, it is ultimate.
The abstraction which is reduced only to ultimate properties, represents the highest-order object of its class — it is its form. A lower-order object partakes of the ultimate properties of its class, while extending and complementing them with properties that are not definitive or characteristic of the form, but only of the object as such and of its own extensions. Arrays may therefore be traced that group together objects at every level of abstraction; objects whose very properties are classifiable in arrays of their own. Engendered from this and subject to the factors of the consideration, there are descriptive and synthetic arrays of objects and properties.
If “motorcycle” is an abstraction that extends a higher abstraction “vehicle”, it can encompass an array of objects such as “Scooter”, “Cruiser”, “Off-road”. These objects partake of whatever properties may be germane to “motorcycle”, yet they also have properties of their own, distinguishing them from their higher-order abstraction — “motorcycle” — and from the objects in their very own array. These definitive properties are a descriptive array of a given object. Thus the definitive properties of, say, “Scooter” are not found in either “Cruiser” or “Off-road”.
However, a property in itself cannot be definitively descriptive of an object so that e.g. “four-wheeled” may be a property of “car”, yet it may also be found in “truck” (two more extensions of “vehicle”). Still, the object “truck” may be considered as sharing in “eight-wheeled” that could be a property also identifiable in the object “bus” (yet another extension of “vehicle”). In naming and classifying, it is therefore mandatory to specify both the object and the property, so that the descriptive array is stated clearly and precisely in the context of the broader, synthetic array of objects.
Consider a further example: this blog post can be given the category “philosophy” and the tag “logic”. If “post” is an object in a certain database and if “philosophy” and “logic” are, in this case, properties of it that foster a taxonomy of a sort, then another object “book” that is also categorised as “philosophy” and tagged with “logic”, will not be grouped together with “post”. Should the formal structure of such data be o(c, t), where o signifies “object”, c “category” and t “tag”, then the database for “post” and “book” would have to contain the following two distinct arrays:
- post(philosophy, logic)
- book(philosophy, logic)
This manner of identification allows for a greater degree of precision in the discernment and classification of objects and of their properties. It contributes to the reduction or elimination of ambiguity and conflation, for — to return to the latter example — it becomes crystal clear that the category “philosophy” for the object “book” is technically not the same category as that which happens to have the same name but is specific to another object, namely “philosophy” for “post”. The classification is not about the content that we may assume as specific to “philosophy” or “logic”, for these perform the function of properties in the aforementioned scenario. Yet, their possible presence as objects in cases beyond the one now considered, cannot be denied.
Additionally, should a category have an array of its own of, say, “philosophy” being further extended to e.g. “Platonic” and “Aristotelian”, it too would have to be properly named. The synthetic array that would emerge would therefore be of a structure such as o(c(p,a), t) where the descriptive array of the category is included in the array of data and, in this case, where p _stands for “Platonic” and _a for “Aristotelian”.
To recapitulate, the above do not imply exclusivity. Their use only concerns proper naming and ordering in the discernment and classification of objects. The purpose is to make use of a method of analysis that facilitates precision of statement and, moreover, further improves our knowledge’s degree of clarity. In that regard, the allusion to an ultimate property must be understood as referring to an object that is inconceivable without _it, though not that said property is _necessarily specific to any given object.
The identification of ultimate properties fosters higher level thinking, in terms of the orders of abstraction, yet in the absence of proper names, these ultimate properties would not be sufficient in discerning with certainty objects and their consequent classification in descriptive and synthetic arrays.
More to follow. UPDATE May 10, 22:39 CET: the follow-up post, Descriptive and synthetic arrays, is published.