 Solution

Some scientific classifications plausibly identify natural kinds; it does not follow that every useful theoretical category does. A good test asks whether the classification supports reliable inference because of relevant natural structure, rather than treating either practical usefulness or a precise verbal definition as sufficient.

A chemical element illustrates a strong case. Its atomic number fixes nuclear electric charge and constrains the electronic structure of the corresponding neutral atom. The classification thereby supports explanations of recurring chemical properties through quantum mechanics. Isotopes show why the claim must be qualified: equal atomic number does not imply equal mass, nuclear stability or every reaction rate. Whether a division is informative depends on which properties the investigation is trying to predict.

Biological classification need not have the same structure. The biological species concept emphasizes reproductive relations; a phylogenetic species concept emphasizes descent and diagnosable lineages. Hybridization, asexual reproduction and variation within a lineage make a single intrinsic essence an implausible universal criterion. A homeostatic property cluster theory instead asks whether interacting causal processes sustain a cluster of traits that supports induction, without requiring every individual to possess every trait.^[ref] These considerations can support realism about biological groupings without making all boundaries equally sharp.

There are also classifications whose role is expressly relative to a task. Calling a particle nonrelativistic compares its momentum scale with $mc$, or its speed with $c$. An investigator can set a tolerance for neglecting higher terms in an expansion. The boundary then depends partly on the accuracy required; it is not a newly discovered fundamental species of particle. Nevertheless, the approximation is constrained by measurable scales and can be objectively excellent or poor.

This prevents two opposite mistakes. Since a category is chosen for a purpose, it need not be arbitrary: a classification that repeatedly supports independent predictions has a better claim to natural grounding than an arbitrary grouping. Conversely, successful prediction does not uniquely identify the world's one privileged taxonomy. Different scales and explanatory questions may justify overlapping classifications of the same objects.

The defensible conclusion is selective and plural. Treat some kinds as tracking stable mechanisms, structures or historical lineages; assess the evidence for each classification and its intended domain. Retain useful idealized or conventional categories without pretending that every term in a scientific theory names an equally fundamental division of nature.