Subtleties in the Mental Classification & Organization of Knowledge
Generalization & Abstraction
Human knowledge crucially depends on our innate ability to classify things into categories. Classification is useful since, once we can assign something to a known category, that something typically inherits the properties previously learned about the category. For example, if we can classify a never-before-seen thing as a dog, then we may automatically know a lot about it — e.g., that it likely chases cats.
This article discusses some of the underlying (perhaps mostly unconscious) ways we seem to mentally organize our knowledge. But before diving in to the subtleties, I would like to briefly comment on terminology. Scientists of all persuasions often establish specialized terminology to talk about their domains of interest in order to avoid misunderstandings and mere verbal disputes. I follow this practice here when discussing several nuanced distinctions, while trying to avoid being too pedantic. The terminology may also take on somewhat different meanings in other related contexts, but the terminology itself is not as important as the indicated meaning behind it.
Generalization
It should be no surprise that we tend to organize most of our categorical knowledge into hierarchies. We intuitively consolidate our concepts of everyday things into folk hierarchies, such as: animals, birds, robins (for living things); furniture, chairs, kitchen chairs (for artifacts); publications, books, paperbacks (for written works) ; and even moving, turning, spinning (for events). Such hierarchies extend from the more general to the more specific, and technically exhibit the type/subtype distinction. A given type, such as publication, can have subtypes, such as book, which itself can have subtypes like paperback.
The specific relation between a subtype and its type is often called a “kind” in English, allowing us to say things like “A paperback is a kind of book” or “A book is a kind of publication”. (The converse relation is “subkind”, so we can alternately say, somewhat more awkwardly, “A book has subkind paperback”, etc.) Moving from a subtype to its type is technically called generalization (not to be confused with abstraction), since the characteristics attached to a type are more general (ie, apply to more things) than those attached to its subtype. For example, the characteristics of birds typically include the characteristics of animals (like having a heart), in addition to their own (more specific) bird characteristics (like having feathers). From a wider perspective, categorical knowledge can be usefully represented (but only to a first approximation) as downward branching trees from general to more specific kinds.
Abstraction
In addition to our generalization hierarchies, we also organize knowledge into abstraction hierarchies. Consider an example, starting with a generalization hierarchy: “A cheetah is a kind of mammal” and “A mammal is a kind of animal”. Now we would also like to represent that Charlie is a cheetah. But while the terms cheetah, mammal, and animal are general category terms, Charlie is an individual, not a category. This is an illustration of the type/token distinction in philosophy, where the relation between a token and its type is commonly said to be one of exemplification (I prefer instantiation, but see note 2). The English proposition representing this knowledge is then something like “Charlie is an example of a cheetah” (or conversely “Cheetah has example Charlie”). Here, moving from an individual thing to its category is what I’m calling abstraction (note 3).
But abstraction can also involve moving from one category to a higher-level (more abstract) category as well, creating an abstraction hierarchy. For example, moving from Charlie to cheetah, and from cheetah to species spans two levels of abstraction. (The level could be further extended upward to biological taxon, if required — eg, to represent general knowledge about biological taxonomies.) In English, such knowledge might be expressed as “Charlie is an example of a cheetah”, “Cheetah is an example of a species”, and “Species is an example of a biological taxon”. Or more colloquially, “Charlie is a cheetah”, “Cheetah is a species”, “Species is a biological taxon” (note 4).
Note how different the abstraction hierarchies are from the generalization hierarchies: cheetah -> mammal -> animal -> organism (generalization) vs Charlie -> cheetah -> species -> taxon (abstraction). In fact, all of the concepts in the generalization hierarchies turn out to be examples (via exemplification) of concepts in the higher-order abstraction hierarchies, if consistency in knowledge representation is maintained. (Of course, we are not computers, and prefer to live with subtle inconsistencies, often to our own chagrin. Unfortunately, that usually makes for muddled thinking about abstract topics.)
For those interested in a deeper analysis of these kinds of knowledge representation & organization issues, feel free to comment, email, or see my text Contemplating Concepts: Exploring the Conceptual Landscape on Amazon.
Footnotes:
1. Cruse, D. A. (1986). Lexical Semantics. Cambridge University Press.
2. I’ve used the more uncommon term “exemplification”, rather than “instantiation”, to avoid confusion with a common philosophical use of “instantiation”. Which is to say that a predicate (or concept) is instantiated only when there exists an object satisfying the predicate in the physical world. Exemplification is intended to apply even to nonphysical objects — e.g., “Sherlock Holmes is an example of a fictional detective”.
3. The word “abstract” is also often contrasted with “concrete” to distinguish between extensional physical concepts, like my TV (concrete), and intensional concepts, like the set {1,2,3} (abstract). But this is not the meaning intended here.
4. Note, however, that the “is a” construction is ambiguous between a generalization reading as in “A cheetah is a mammal”, and an abstraction reading as in “Charlie is a cheetah”. English does not normally draw such subtle distinctions, often leading to misunderstanding.
