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We know that 'scientific disciplines divide the particulars they study into kinds'. But there are also taxonomy categories that rank above a kind (of particulars). In that case, the kind mediates that higher category and a particular: it acts as a middle category between them. For example, a biological species mediate a relevant particular and a genus, a member of which the species is itself. In this case, the name for the middle category is a species and for the higher one genus.

Now consider an example I am specifically interested in. Each object is characterised by the property of color (a higher category here); furthermore, we do not have one color but instead many kinds of color (white, yellow etc.--a middle category) which are instantiated by objects in the form of actual particular instances of them (a particular).

What would be right words (names) for the middle and higher categories in this example (for I doubt that the 'species' and the 'genus' could fit there)?

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    For the middle and higher categories, we often resort to the phrases "division and subdivision", "category and subcategory", "class and subclass", "genre and subgenre".
    – TimR
    Commented May 16, 2017 at 17:03
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    Every field has its own taxonomy. So, it depends on the field. Species and genus are for plants and animals. Not colors. By the way, you may want to take a look at color theory and the color wheel. Colors have hues and tints and all sorts of things.
    – Lambie
    Commented May 16, 2017 at 19:53
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    As Lambie says, ever field has its own taxomomy. For nudibranchs, a particular genus and species may exist in several colours: the correct term is colour variant. For domesticated dogs, Canis Lupus Familiaris is classified as a sub-species and, as we know, there are many variants of size and shape within the sub-species: these are called breeds.
    – JavaLatte
    Commented Jul 9, 2018 at 8:14

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Any system of naming categories is a taxonomy ("taxo-" = arrangement + "-nomy" = name).

For example: military aircraft nomenclatures (F/A-18, V-22, etc) are a taxonomy. The Dewey Decimal system is a taxonomy. The set of job titles a company uses are a taxonomy.

"Species" and "genus" are categories in a specific taxonomy (phylogeny), and are not part of most taxonomies. You could borrow them if you were laying out a new system, but there is no universally applicable hierarchy of taxonomic categories.

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Linnean biological taxonomy is a strictly hierarchical system, in which an organism is a member of a species, a species is a member of a family, and on up through such categories as order, phylum, and kingdom. These terms belong strictly to this particular system.

Not all fields of study group their subjects into strictly hierarchical taxonomies. Some use orthogonal sets of categories, in which an object or area od study may be a member of two or more categories, neither of which is a subset of the other. Most theories of color do not, for examp-le divide colors according to a hierarchical set of categories. (This is an area I know a little about, my father was a psychologist specializing in color vision.) Hue and saturation are orthogonal dimensions of perceived color, and are related to but not identical to wavelength and intensity of physical color.

There is no general term for what you refer to as a "middle category" across all fields of study, or even most fields.

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