Intensive and Extensive Abstraction

“When reflection, turning to the comprehension of chaotic experience, busies itself about recurrences, when it seeks to normalise in some way things coming and going, and to straighten out the causes of events, that reflection is inevitably turned toward something dynamic and independent, and can have no successful issue except in mechanical science. When on the other hand reflection stops to challenge and question the fleeting object, not so much to prepare for its possible return as to conceive its present nature, this reflection is turned no less unmistakably in the direction of ideas, and will terminate in logic or the morphology of being. We attribute independence to things in order to normalize their recurrence. We attribute essences to them in order to normalize their manifestations or constitution. Independence will ultimately turn out to be an assumed constancy in material processes, essence an assumed constancy in ideal meanings or points of reference in discourse. the one marks the systematic distribution of objects, the other their settled character.” (See George Santayana, "The Life of Reason"  , Chapter III – The Discovery of Natural Objects – )

In this way, Santayana points to the fact that human cognition shows two kinds of abstraction, one “intensive” (analytical) and one “extensive” (synthetic). The first is directed towards the object and “inwards” and it proceeds through separation and differentiation of parts. The second is directed to the context of the object (while this remains in view) and “outwards”, and it proceeds through aggregation and comparison with other objects in the field of observation.

In day-to-day conversation but also in academia, business, government and other “educated” exchanges, it is a custom to consider only one type of abstraction, which I call here “extensive.”  This is the sense in which the speaker will say that he or she does not want to discuss “abstractions.” By this –if there is any logical consistency, the speaker will mean some form of rejection of generalizations and collective terms. “Abstractions” are crudely associated with intellectual and academic efforts, while “facts” are assumed to be the the only worthwhile and practical subject of any discussion. Contrary to “abstractions,” “facts” are held to be “concrete” or “real.”

The problem is, though, that “facts” are produced by a different mechanism of abstraction but are otherwise not different—in respect to truth or relevance—to the supposedly vague “generalizations” rejected by the empiricist.

Facts are the result of “intensive” or analytical abstraction, i.e. of separation, isolation and fragmentation of the things observed. In this sense, “facts” without the explicit framework that produced them are as unreal and devoid of meaning, as bad generalisations and “vague” concepts despite the ideological preferences of whoever raises them to first-class elements of knowledge.

Any two distinctions can be articulated so to obtain a meaningful set of categories. Because of this, we must be careful with the possible combinations of cognitive distinctions and choose only those that are fundamental. Above all, it is important to avoid simple classifications and search for a model based on logic.

Intensive and extensive abstraction (in the sense described above) are fundamental and can be aligned one against the other to form a “logical square,” as shown in the following diagram.