Armstrong and Dretske's nomic necessitation framework requires that natural kinds be defined by intrinsic, repeatable universals that can enter into second-order relations with other universals.
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A way of explaining how laws of nature work—the idea that certain properties or features are connected by natural laws in a way that makes one necessarily follow from another.
Repeatable(as a property that kinds must have)
Able to occur multiple times in different places at different times—for example, the pattern 'being a dog' can repeat in many individual dogs.
Second-order relations(as connections between universals in this framework)
Relationships between abstract properties themselves (rather than between concrete things)—like how the property of 'being red' might relate to the property of 'being colored'.
natural kinds(Water is offered as a paradigm example of a natural kind individuated by microstructure)
Categories of things in nature that share an essential microstructure, used to ground essentialism about species and substances
universals(Debated in Lefèvre's Disceptatio de universali between two students of Chrysippus's academy)
Either what particular classes of things share, or what those who reason say they share (decided by convention)