June 30, 2021

Introduction to Natural Kinds

From the Internet Encyclopedia of Philosophy:

A large part of our exploration of the world consists in categorizing or classifying the objects and processes we encounter, both in scientific and everyday contexts. There are various, perhaps innumerable, ways to sort objects into different kinds or categories, but it is commonly assumed that, among the countless possible types of classifications, one group is privileged. Philosophy refers to such categories as natural kinds. Standard examples of such kinds include fundamental physical particles, chemical elements, and biological species. The term natural does not imply that natural kinds ought to categorize only naturally occurring stuff or objects. Candidates for natural kinds can include man-made substances, such as synthetic elements, that can be created in a laboratory. The naturalness in question is not the naturalness of the entities being classified, but that of the groupings themselves. Groupings that are artificial or arbitrary are not natural; they are invented or imposed on nature. Natural kinds, on the other hand, are not invented, and many assume that scientific investigations should discover them.

Philosophical realists hold that things, loosely construed, exist independently of people and their perception of those things. Often, these things are grouped together in some way, facilitating their analysis by reference to their collection.

Some such collections, it is hoped, are natural, in the sense that they are described by some property that determines those collections uniquely and absolutely.

Under this reasoning, the class of all humans would be a natural kind, because (presumably) there is a property or set of properties that humans have and nothing else non-human has. By contrast, the class containing

  • a single human,
  • the color red, and
  • a random integer

would not constitute a natural class, because there are properties shared by these elements that are not exclusive to them, and because each has at least one property that does not hold of the others.

Getting More Precise

In other words:

  • the collection KP contains all things x such that property P holds of x,
  • there is no y in KP for which P does not hold, i.e. such that ¬Py,

We must also stipulate that no such property is the self-referential class-membership property:

  • KP cannot be given by Px = "x is a member of KP".

The extension to the case where K is determined by a family of properties is straightforward.

Where I’m Going

I’m not committed to metaphysical realism, or indeed most philosophical theses, but I found the basic premise approachable: collections of objects fully determined by one or more properties are abundant in mathematics, and tools from that field should find ready application here. In particular, if we relax the uniqueness property at least to uniqueness-up-to-isomorphism, we have (the object collections of) categories.

For example, in the category of groups Grp, all and only algebraic groups are present in the object class Ob(Grp), and every G in Ob(Grp) satisfies a family of properties called the group axioms.

Various structural approaches to natural kinds exist, which try to characterize what it means to be such a kind using formal tools rather than a natural-language analysis. My current work is translating these faithfully into the language of categories, and from there building connections to situate the theory of natural kinds within the broader mathematical landscape.

Further Reading

For a far lengthier discussion and tons of citations, check out the SEP page, or the IEP entry quoted above.