Implicit properties in objects

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The present article shall be treated as a continuation of the analysis that took place in two recent posts: (i) Discernment and classification of objects, (ii) Descriptive and synthetic arrays. The reader who is acquainted with their content will find it easier to appreciate the themes here considered.

In classifying objects, properties are specified that engender discernibility. If object¬†O¬†features property¬†a¬†and if object¬†Q has property b, where a ‚Ȇ b and where these properties are constitutive of their respective objects,¬†and should no other information be considered, then¬†O ‚Ȇ Q. Examined as such, this information describes a certain state of affairs. The¬†knowledge derived therefrom¬†is commensurate with¬†the degree of correspondence the information¬†has to the state of affairs it refers to; it is correlated¬†to the truthfulness of the information.

When the exercise of classification increases in scale, arrays of objects are formed, which serve the purpose of revealing the_ structure_ peculiar to these objects. The array Fruit(Apple, Banana, Grape), to the extent that it is truthful, conveys the following quantum of knowledge:

  1. Object ‚ÄúFruit‚ÄĚ is a higher level abstraction than ‚ÄúApple‚ÄĚ, ‚ÄúBanana‚ÄĚ, ‚ÄúGrape‚ÄĚ (its extensions);
  2. The extensions stand at the same order of abstraction;
  3. The properties constitutive of ‚ÄúFruit‚ÄĚ are to be found in its extensions, though not vice-versa;
  4. The extensions are related to one another by virtue of all partaking of their abstraction ‚ÄúFruit‚ÄĚ and the properties thereof;
  5. The properties of the abstraction will be numerically less than those of its extensions, since the abstraction encapsulates what is common in the multitude, rather than encompassing all that is specific;
  6. The extensions of ‚ÄúFruit‚ÄĚ cannot be part of what negates it, though they do belong to whatever higher-order abstraction ‚ÄúFruit‚ÄĚ may be an extension of.

An array that is descriptive will document the properties germane to each object, so that a group of data can be formed, such as:

  • Fruit(plant, edible)
  • Apple(green, bitter)
  • Banana(yellow, starchy)
  • Grape(red, sweet)

The _synthetic _array encompassing all this data would therefore be Fruit(plant, edible)[Apple(green, bitter), Banana(yellow, starchy), Grape(red, sweet)]. If truthful, it would engender an awareness as to what are the objects under consideration and in what ways do they differ qua objects with properties.

Discernibility by association

There are however cases where an array need not be enumerative to foster discernibility; where properties can be inferred from linguistic, conventional and situational parameters. Let us elaborate on an imaginary case:

A. If this¬†Article¬†A¬†where to be described in the database of this website, it would among others be classified under¬†the¬†content type¬†to which it belongs: Post. Furthermore, it¬†would be grouped in accordance with the¬†taxonomies peculiar to Post, such as ‚Äúcategory‚ÄĚ and ‚Äútag‚ÄĚ. A¬†synthetic array of such sort could therefore be¬†Post[A(philosophy, logic)]. Assuming acquaintance with the applied methodology, a human (or machine) parsing this¬†data¬†will know that A¬†is an object that partakes of the content type Post, is categorised as¬†philosophy¬†and has the tag¬†logic.

B. Along these lines, another type of content featured on this website’s database could be Book. There may be an instance where an object belonging to book, such as the Book B, could also fall under the taxonomies specific to Book, such as the category philosophy and the tag logic. Hence, the synthetic array would be Book[B(philosophy, logic)]. Again, whomsoever is familiar with the manner in which such information is formatted, will know that B is an object that partakes of Book, is filed under the category philosophy and bears the tag logic.

C. In comparing this latter array with the former, we are presented with two sets of data that describe objects whose properties appear to be identical, which renders their differentiation seemingly meaningless. The data does not tell us explicitly how it is that one object is discernible from the other, apart from the fact that their label (name) is different. Labels may not be sufficient to draw delineations between classes. A second article A2 also under the category philosophy and the tag logic would still be an extension of Post. Same for any additional object under the content type Book. What is therefore at stake, is to appreciate the factors of implied discernment germane to Post and Book.

Factors of implied discernment

The linguistic: In common language we already attach properties to concepts/objects named by words, so that any agent who knows the meaning of the words can understand the differences in their¬†significations. One can tell that a blog post on philosophy and logic¬†is not the same as a¬†book on philosophy and logic, by virtue of attaching distinct meanings¬†to the terms¬†‚Äúpost‚ÄĚ and ‚Äúbook‚ÄĚ. In terms of the scenario here discussed, the choice to distinguish between two types of content may therefore be predicated on the willingness to make¬†linguistic familiarity¬†a contributor¬†to the website‚Äôs functionality.

The conventional: On the same scenario, consider that one website database is merely drawing delineations between types of content for the sake of specialising their presentation. All that belongs to Post could feature a section for user comments, while all that shares in Book could have a shopping cart functionality. These different functions, if exclusive to each one, would make the two content types distinct from one another. The implication is that properties of such objects, even when they have the same label, are in fact distinct by virtue of being treated as properties, not objects. So e.g. the philosophy category for Post can be one kind of taxonomy and the philosophy category for Book can be another if such a choice is made.

The situational: An implied property can also be identified in an object that exists in a given way within a certain situation. If Post and Book are to be parts of the website, then not only are they content types, having the imaginary properties mentioned above, but they mostly are such inasmuch as they also are characterised by their presence on that website. Their relation to the broader website itself bestows on them their very status while, furthermore, it is indicative of the fact that they can inherit the properties germane to the website.

Whether these implied properties are actual or perceived, is secondary to the possibility _of them being inferred. Implicit properties might not be germane to the objects they are attached to. They may not be _necessary _and _sufficient elements that are constitutive of the very nature of the object in question.

However, objects that are not treated in nothing but rather in the constitution of the case where they are made manifest, can be inextricably bound up together with their implicit properties, whether these are linguistic, conventional or situational. Perhaps then, any exercise of classification must, at the very least, specify the constitution of the case it is describing, and be prepared to provide arguments as to the reason(s) certain orders of abstraction are stipulated.

The point remains: the classification of information ‚ÄĒ which is the classification of knowledge where the information is true in describing states of affairs ‚ÄĒ can deliver precision of statement when it rests on clarity of concept, ultimately fostering greater certainty.