A category is commonly understood as a generalization about someone or something; a general truth about a thing. That much we can usually agree upon. But when it comes to the details of what a category is, we have much less agreement. There is a lot of debate about what, in specific, a category is.

Among the many views about what categories are, two are most prominent. On the one hand, we have a classical approach to categories, which argues for necessary and sufficient conditions; and on the other hand, we have a prototypical approach, which argues for a probabilistic approach.  Let’s explain each further.

To start, let’s explain the similarities between the two approaches.

The prototype approach argues that categories are shaped by a handful of essential features, and that these essential features determine membership. For example, the category of book might depend on features like pages, spines, covers, and text; and so, in order for something to be a book, those essential features ought to be present. By that reasoning, the Critique of Pure reason, or the Wealth of Nations, are both books. They both fit into the prototypical notion of a book.

Similarly, though not exactly the same, the classical approach argues that categories are shaped by necessary and sufficient conditions. And that these necessary and sufficient conditions determine membership to a category. Put otherwise, something is either necessarily a book when pages, spines, and covers are present, or is sufficiently a book when two thirds, or some other degree, of the conditions are present.

Clearly, the differences, seemingly, are not large. Both approaches rely on a handful of features to determine category membership. But when we read into the views, a world of difference emerges within the details. These two views differ in ontology and epistemology, rather greatly.

Differences Between the Ontology and Epistemology of Category Theories

The prototypical approach often relies on a form of indirect realism for ontology. For the indirect realists, reality is a representation. Meaning, rather than see the world directly and plainly (direct realism), we instead see an interpretation, or a representation (indirect realism). That is to say, our sensory organs interpret the world and then the world is represented to us, like an internal simulation of sorts.

Comparatively, classical theorists rely on direct realism. They believe the world is seen directly, without interpretation of any sort. Which is to say, we are seeing a directly real world.

As a result of these distinct ontological stances, differences in the ontology of categories arises. For prototype theorists, categories exist inside the mind, whereas for classical theorists categories exist inside the world; prototype theorists view categories as creation, whereas classical theorists view categories as needing to be discovered. One believes categories are rational products of imagination, while the other believes categories refer to naturally occurring sets.

Another important difference in the epistemology of these two views refers to derivation of categories: how categories are derived.

The prototype theorists believe categories are based on statistical learning. After we see something enough times, we begin to develop a prototype which represents a cluster of objects. That makes prototype theorists empirically oriented. For example, when we see a water bottle, we formulate a prototypical representation of “bottles”; as such, we can say water bottles and wine bottles are both bottles: because both fit the prototype of bottle.

And for a prototype theorist, categories are derived through the senses as well. After we see enough objects, smell enough, or feel enough, we formulate the prototypical category. We rely on our senses to feed us data, and we then develop prototypical categories based on the data.

In comparison to the prototype theorist method of category derivation, the classical theorist believes categories are defined; that is, we can produce an axiom or statement which clearly defines or describes naturally occurring features in the world. They are more a priori oriented, insofar as they believe categories exist mind-independently, and we are simply discovering definitions which point to them.

So, for the classical theorist, categories do not preside inside the mind but are instead observed inside the world. And when we want to know a category, we must formulate a statement or axiom which refers to the collective set of objects inside the world.

Conclusion and Summary

To summarize and conclude, for a classical theorist, a tree is a tree only when a set of necessary and sufficient conditions arises, and for a prototype theorist, things are more or less trees, depending on how similar they are to the prototypical model: the empirical average. The classical theorist relies on definitions of necessary and sufficient conditions for entry to a set or category, whereas the prototype theorist places things on a spectrum composed of close-to and far-from end points. An object is either a member or not, according to classical theorists; but an object is more or less a member, according to prototype theorists.

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