Descriptive and synthetic arrays
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To complete the process of thought initiated in the last post on the Discernment and classification of objects, let us pay closer attention to the separation of arrays in descriptive and synthetic. The objective is to illustrate the qualitative difference between sets of information whose function is to enumerate objects or enlist properties of objects.
A descriptive array presents the properties of an object. It is limited to the object it names even if that may be connatural to other objects and even where these also feature some or all of the properties there presented. A descriptive array is therefore all the information characteristic of an object, regardless of whether such information is or not exclusive to it. As such, it does not necessarily indicate a definitively discernible object; it rather documents the information descriptive of one in the milieu where it is made manifest.
A synthetic array denotes an abstract object that encompasses [a number of] its extensions. The extensions of the abstraction partake of the properties germane to it, yet they do have more of their own that contribute to their further specification/concreteness and, hence, discernment. A synthetic array is a tacit or explicit combination of descriptive arrays, for the enumeration of objects does not, in and of itself, imply that such objects are treated as devoid of the properties that define their very being and which render sensible their classification.
The correctness or falsity of the knowledge derived from an array is commensurate with the comprehensiveness of the data gathered in the examination of the case. Furthermore, such data is contingent on the analyticity of the case, of whether the case is examined at its formal _or _constitutional level. That is a determinant of the accuracy, the degree of correspondence of said case to a state of affairs in the world or the thinkable.
To the extent that the information is correct and its classification meaningful, the result shall be bestowed with the epistemic value of context-specific knowledge. Assuming correctness of data, its classification can either be meaningful and consistent or not, thus it will either foster context-specific knowledge or its results shall be incorrect when juxtaposed to the case under consideration — they shall be nonsensical.
What can be an opinion is either a belief that the information is comprehensive and accurately descriptive of a real state of affairs or any proposition about the arrays that is not contained in them; any speculative claim external to the information. In other words, an opinion on this can be the presumptuous or subsequent evaluation of the information, the inferences drawn from it and the judgements made thereon.
Consequently, the element of error in the array itself shall be identified in the adequacy and degree of completeness of the information in regard to its depiction of the case and then in the validity and consistency of the classification of the data derived therefrom. Anything other than that is to be treated in its own capacity.
Putting things together
To flesh out the points raised above, let us consider the following:
The general structure of an array is A(n), where A stands for “array” and n for the item(s) named.
In a certain case under examination, we identify three objects: “Grape”, “Apple”, “Banana”.
By tracing the common in the multitude between them, we derive the abstract object of which they are extensions of: “Fruit”.
Our synthetic array of such information can therefore be presented as Fruit(Grape, Apple, Banana).
Such presentation only contains objects at different orders of abstraction. It does not describe these objects in terms of the properties peculiar to them.
Whereas a descriptive array would be Fruit(plant, edible), while the same method would be applied for the objects that extend their respective abstraction: Grape(red, sweet), Apple(green, bitter), Banana(yellow, starchy).
Should the synthetic array be enumerative rather than generic, it would have to be written as follows: Fruit(plant, edible)[Grape(red, sweet), **Apple(green, bitter), Banana(yellow, starchy)]**. Note that the properties of the abstraction, of which the extensions also partake of, need not be specified for each object. That they share these properties is already entailed in the very order of these objects qua extensions of a more abstract entity in their own class.
We can then formalise this dataset in a more indexible format using unique identifies, such as: F(f1, f2)[G(g1, g2), A(a1, a2), B(b1, b2)].
The use of such unique identifiers is in line with the suggestion made in the previous post, concerning the attachment of proper names. Its usefulness becomes evident when another object with its own properties is added to the array. Consider, for instance, this new descriptive array: Strawberry(red, sweet).
The new “strawberry” array seems to duplicate the names of properties that are to be found in “grape”, namely “red” and “sweet”. While the names may indeed be identical, the classification of the data must not conflate “grape” and “strawberry”, for it is a mere coincidence that such similarity exists and that another object also features certain properties that were already documented. In light of this exercise of classification, the properties listed above describe only the object — they are not self-refential.
For the sake of presenting the objects with their respective properties, the new synthetic array that will also encompass “strawberry”, will be like this: F(f1, f2)[G(g1, g2), A(a1, a2), B(b1, b2), S(s1, s2)]. The use of unique identifiers only denotes properties specific to an object, preempting any ambiguity that could arise in the use of common words attachable to different things.
What can therefore be argued concerning the similarity of names, is that the information thus presented is somewhat incomplete, appearing as exhaustive in the enlistment of names when it is most obviously not, for two objects there referred are described as having the exact same properties, making it unclear how it is that one is discernible from the other, apart from the differences among their own name.
Where ambivalence of statement is found, the classification must be seen as false or incomplete, since it fails to make manifest the [claims to the] discernibility of the objects it treats, pointing to the need for further research that will either force a thoroughgoing revision aiming at improving the adequacy and comprehensiveness of the data for the sake of achieving internal consistency and overall clarity, or lead to the recognition that the entire project rests on dubious foundations and is erroneous to a degree that necessitates its abandonment.
Comprehensiveness of information in the depiction of the case, accuracy in the correspondence of the data to a state of affairs, validity and consistency of the classification of such data, are therefore the additional parameters to the exercise of clear and precise discernment of objects and of their properties, other than the use of proper names that was explicitly suggested in the last post on the Discernment and classification of objects.