Abstraction

The term abstraction derives from the Latin abstractio which in turn takes up the Greek one of “αφαίρεσις” (aphàiresis). Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon (removing characteristics from something in order to reduce it to a set of essential characteristics), selecting only the aspects which are relevant for a particular subjectively valued purpose. In a generic sense abstraction is the process of thought for which an element is isolated from all the others to which it was connected and is considered as a particular object of research.

In philosophy, abstraction together with generalization is a logical method for obtaining universal concepts from the knowledge of particular objects by retaining their common characteristics and putting aside those that appear only in some. The abstractive method, known since the origins of Greek thought, was theorized and arranged by Aristotle and then taken up by Boethius and adopted by all medieval philosophy according to which there are three gradual types of abstraction:

  • the physical abstraction, which omits the individual characteristics of particular objects but retains their material nature;
  • mathematical abstraction, which also disregards the sensitive characteristics of matter but not the intelligible ones inherent in the extension of matter itself;
  • the metaphysical abstraction which merely consider the entity as an entity, putting aside even every connotation connected to the extension.

Abstraction is also talked about in the physical-mathematical sciences when instead of resorting to the abstract concept (for example that of direction) we list the conditions for which two objects (for example the parallel straight lines) have in common precisely that concept (that is, the direction is what the straight lines have in common). 

Outside of metaphysics, in which abstraction has the function of reducing the object to being only, we speak instead of generalization when thought attributes these known characteristics to all objects not only to those present but also to that past and future in the which it assumes those notes are, have been and will be present. The generalization regards in particular mathematics and physics when new symbols are introduced and new hypotheses elaborated for which the previous field of investigation is enlarged which becomes a particular research sector with respect to the larger one that now contains it. For example, relativistic mechanics is a generalization of classical mechanics.

Already Plato in the De Republic placed among the functions of dialectics that of distinguishing one idea from another, so as to be able to account for it to oneself and to others (VII, XIV, 543). Aristotle believed that intelligible forms existed only in sensible objects, as sources from their universal characteristics, and that the soul could, through abstraction, bring them out in their purity so as to realize through this process its ability to know them (De anima, III, 7,8).

In the Middle Ages St. Thomas saw in abstraction the faculty of knowing universals, which exist as models of things (ante rem) in the divine intellect and are present in the things themselves (in re), which incorporate them, obtaining them as universal concepts abstracted from the things themselves (post rem).

Scholasticism distinguished various types of abstraction: negative abstraction, whereby an object is determined insofar as it does not possess a characteristic, e.g., “this tree is not red”; precisive abstraction, whereby one characteristic of the object is considered, but others, which it also possesses, are disregarded; formal abstraction, whereby the form that determines a particular object is considered, such as the hardness of a hard body; total abstraction, whereby the common characteristic of many objects is considered their universal essence, e.g., humanity as opposed to individual men.

In contrast, Locke considered abstraction to be the faculty, proper to the intellect, of separating the attributes common to several objects from those proper to each object, which enables it to arrive at a universality that in itself is nothing more than a product of intellectual activity (Essay, III, 3,7). Abstraction is in such a way the very faculty of affixing general names to those phenomena which are observed with some frequency in similar circumstances. This thesis may be said to be characteristic of empiricism in general.

A new conception of abstraction was arrived at with Hegel: abstraction, abstract thought, was no longer considered by him as the pure setting aside of what is perceptible in the object in order to grasp the intelligible, according to the conception that was seen to be proper to the Aristotelian tradition, but as the reduction of matter, as pure and simple phenomenon, to the concept as substance. The abstract itself was seen by Hegel as what is separated from the totality and therefore is finite and limited, destined to a surpassing in the process in which the Idea becomes. Thus we see in Hegel an evaluation of abstraction that is positive and negative at the same time.

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