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John Stuart Mill explained the artificial nature of the Linnaean classification and suggested the following definition of a natural classification:"The Linnæan arrangement answers the purpose of making us think together of all those kinds of plants, which possess the same number of stamens and pistils; but to think of them in that manner is of little use, since we seldom have anything to affirm in common of the plants which have a given number of stamens and pistils.""The ends of scientific classification are best answered, when the objects are formed into groups respecting which a greater number of general propositions can be made, and those propositions more important, than could be made respecting any other groups into which the same things could be distributed." "A classification thus formed is properly scientific or philosophical, and is commonly called a Natural, in contradistinction to a Technical or Artificial, classification or arrangement."Ridley (1986) provided the following definitions: "artificial classification. The term (like its opposite, natural classification) has many meanings; in this book I have picked a phenetic meaning. A classificatory group will be defined by certain characters, called defining characters; in an artificial classification, the members of a group resemble one another in their defining characters (as they must, by definition) but not in their non-defining characters. With respect to the characters not used in the classification, the members of a group are uncorrelated. "natural classification. Classificatory groups are defined by certain characters, called 'defining' characters; in a natural group, the members of the group resemble one another for non-defining characters as well as for the defining character. This is not the only meaning for what is perhaps the most variously used term in taxonomy ...

=== Taxonomic monism vs. pluralism === Stamos (2004) wrote: "The fact is, modern scientists classify atoms into elements based on proton number rather than anything else because it alone is the causally privileged factor [gold is atomic number 79 in the periodic table because it has 79 protons in its nucleus]. Thus nature itself has supplied the causal monistic essentialism. Scientists in their turn simply discover and follow (where "simply" ≠ "easily")."

== Examples of important taxonomies ==

=== Periodic table === The periodic table is the classification of the chemical elements which is in particular associated with Dmitri Mendeleev (cf., History of the periodic table). An authoritative work on this system is Scerri (2020). Hubert Feger (2001; numbered listing added) wrote about it: "A well-known, still used, and expanding classification is Mendeleev's Table of Elements. It can be viewed as a prototype of all taxonomies in that it satisfies the following evaluative criteria:

Theoretical foundation: A theory determines the classes and their order. Objectivity: The elements can be observed and classified by anybody familiar with the table of elements. Completeness: All elements find a unique place in the system, and the system implies a list of all possible elements. Simplicity: Only a small amount of information is used to establish the system and identify an object. Predictions: The values of variables not used for classification can be predicted (number of electrons and atomic weight), as well as the existence of relations and of objects hitherto unobserved. Thus, the validity of the classification system itself becomes testable." Bursten (2020) wrote, however "Hepler-Smith, a historian of chemistry, and I, a philosopher whose work often draws on chemistry, found common ground in a shared frustration with our disciplines emphases on the chemical elements as the stereotypical example of a natural kind. The frustration we shared was that while the elements did display many hallmarks of paradigmatic kindhood, elements were not the kinds of kinds that generated interesting challenges for classification in chemistry, nor even were they the kinds of kinds that occupied much contemporary critical chemical thought. Compounds, complexes, reaction pathways, substrates, solutions these were the kinds of the chemistry laboratory, and rarely if ever did they slot neatly into taxonomies in the orderly manner of classification suggested by the Periodic Table of Elements. A focus on the rational and historical basis of the development of the Periodic Table had made the received view of chemical classification appear far more pristine, and far less interesting, than either of us believed it to be."

=== Linnaean taxonomy === Linnaean taxonomy is the particular form of biological classification (taxonomy) set up by Carl Linnaeus, as set forth in his Systema Naturae (1735) and subsequent works. A major discussion in the scientific literature is whether a system that was constructed before Charles Darwin's theory of evolution can still be fruitful and reflect the development of life.

=== Astronomy === Astronomy is a fine example on how Kuhn's (1962) theory of scientific revolutions (or paradigm shifts) influences classification. For example:

Paradigm one: Ptolemaic astronomers might learn the concepts "star" and "planet" by having the Sun, the Moon, and Mars pointed out as instances of the concept “planet” and some fixed stars as instances of the concept “star.” Paradigm two: Copernicans might learn the concepts "star", "planet", and "satellites" by having Mars and Jupiter pointed out as instances of the concept “planet,” the Moon as an instance of the concept “satellite,” and the Sun and some fixed stars as instances of the concept "star". Thus, the concepts "star", "planet", and "satellite" got a new meaning and astronomy got a new classification of celestial bodies.

=== HornbostelSachs classification of musical instruments === HornbostelSachs is a system of musical instrument classification devised by Erich Moritz von Hornbostel and Curt Sachs, and first published in 1914. In the original classification, the top categories are: