Inheritance

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This blog post is a continuation of my last entry: <a title="Common in the multitude" href="https://protesilaos.com/common-multitude/"><em>Common in the multitude</em></a>.

The properties of a set are inherited by its subsets. Apart from the patterns present in the world, inheritance of this sort can even be identified in classes of objects that are substantiated arbitrarily. If this webpage contains paragraph text p whose property is its white color, then the general rule for identifying its characteristics is p { color: white }. The webpage may have a certain structure for sorting and arranging its various elements over a given space, so that e.g. the content area is distinct from the sidebar, the footer etc. These sections are parts of the webpage and by that token their own paragraph text, where present, will inherit by default the aforementioned properties of p.

Such inheritance only has force where the general rule is not overridden by a particular one with higher priority. If the parts of the website are bestowed with properties of their own, then the general rule is either limited to parts with undefined features or is rendered void. On the flip side, the general rule will always take precedence over any particular one if it is given priority status, making the latter superfluous. Priority notwithstanding, inheritance is always downward. Even if the website as such were to have no rule for defining the text’s color, the particular rules, would not have upward, and hence general, application. The particular rule .sidebar p { color: grey } would only apply to the sidebar section and have no effect whatsoever on other parts of the website such as, say, the content or the footer.

As is the case with abstractions, the properties performing the function of discernment among the elements of a set cannot qualify as common in a multitude and, a fortiriori, cannot be considered properties of the abstract as such. In the case of fruit we may say that the taste sweet cannot be a property germane to it, for while it may be traced in peach it is not found in — and is in fact contradicted by — grapefruit. Since we hold that inheritance applies downwardly we may argue that if fruit were to be inferred from peach and grapefruit it could only be from properties common to both.

That emerging incompatibility in the possible upwardness of particular properties within a subset applies to abstractions from patterns in the world, as well as to categories with no natural presence, as with the example of the website and its parts. If that is indeed the case, it seems to reinforce the notion of the abstract as that which is the common in the multitude.

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