Necessary and sufficient membership conditions are neither a sufficient test of naturalness nor a plausible universal prerequisite for scientific classification. They can characterize some natural kinds very successfully. The mistake is to turn that success into a requirement that every scientifically useful grouping must satisfy a single essentialist pattern.
First distinguish three demands. A classification may have an exact extension, scientists may know an exact test for membership, and membership may be grounded in properties that members necessarily share. These are different claims. Ignorance of an exact test does not show that no common constitution exists. Conversely, an exact definition alone does not show that a category tracks a scientifically significant structure. “An object with mass below one kilogram or temperature above 300 kelvin” specifies necessary and sufficient conditions, yet offers no general reason for a common underlying explanation or reliable extrapolation.
Chemical elements provide a favourable case for a comparatively sharp criterion. In the usual classification of atomic nuclei, carbon has atomic number six, meaning six protons. Different isotopes need not have the same mass, and ionization changes electron number without changing the chemical element. The underlying criterion explains why superficially varying samples can belong together. It also distinguishes a defining physical structure from a readily observed stereotype: ordinary appearance is a poor general test of a chemical element. Even here, the claims must be scoped to the relevant physical objects; an arbitrary mixture containing some carbon is not thereby one carbon chemical atom.
Species make the universal requirement much less attractive. The biological species concept organizes sexually reproducing populations through reproductive relations, but an infertile organism can still belong to a species. Universal actual interbreeding is not required, and asexual organisms demand other classificatory resources. A species is historically extended: descent, gene flow, shared development and environmental interactions help explain similarities without requiring every individual to possess every diagnostic trait. Distinguishing members by a list that merely records all actual individuals would not explain why their similarities support further predictions.
Richard Boyd's homeostatic property cluster theory supplies an alternative. Properties can tend to co-occur because processes maintain their association, while individual members lack some traits and boundaries remain imperfectly sharp.[ref]
Homeostasis, Species, and Higher Taxa by Richard Boyd. sections 0.0–0.1: explanatory classification, property clusters and indeterminate membership
For a species, shared ancestry, gene flow and common developmental resources can help maintain such a cluster. “Homeostatic” here need not mean a literal fixed physiological set point. The proposal concerns processes that explain a persistent association of traits.An objection is that a cluster account merely turns every convenient resemblance into a natural kind. The reply must add a constraint: the grouping should support successful inquiry because it tracks relevant causal or historical structure. Similarity of two laboratory samples due only to the current lighting gives little basis for extrapolating their chemical behaviour. Shared constitution, by contrast, can support predictions under changed illumination and independent testing. This distinguishes useful tracking of nature from a category selected solely to fit a past sample.
A second objection is that vague membership makes disagreement impossible to settle. Sometimes sharper operational criteria are needed, but different research purposes may legitimately attend to different processes. A classification useful for reproductive isolation need not settle every question about descent. That is a reason to state the relevant species concept and domain, rather than to require the scientific world to contain one unique partition for every purpose.
Thus exact membership conditions remain valuable where an explanatory common structure supplies them. Their absence is not a decisive reason to reject a proposed natural kind. The better standard is whether the classification reliably supports explanation and inference through a defensible account of the processes that sustain it.
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