This is the most natural, the most spontaneous, and the most ancient method of classifying living organisms. The idea is to use one or two apparent properties (like wings or legs for animals, and spiral arms for galaxies) to build a classification. Of course, when the objects are a little bit complex, then this choice is subjective.
If we take the matrix:
| c1 | c2 | c3 | |
| A | 0 | 0 | 1 |
| B | 0 | 1 | 0 |
| C | 0 | 1 | 1 |
we get several different and incompatible classifications (“ABC”, “A” and “BC”, or “AC” and “B”) depending on the choice of the “obvious” parameter. c1, c2 or c3. There is no objective argument to tell the best.
This kind of classification can be useful, but this is necessarily limited to simple cases.
Biology
First classification of plants and animals arose very early. At those time, classification was intended for direct practicality, like whether a plant was eatable, could be grown, could provide some medicine, or whether an animal can be domesticated. The known diversity was not very large, so that a general classification was not necessary.until the Greeks, and particularly Aristotle, who began to think about the World. Many criteria were introduced, like the very anthropocentric ones above, or more related to the living organisms themselves, like the means the animals move (legs, wings), their blood temperature, the size of plants, their leaves or the colors of their flowers.
This way of classifying was surely an intellectual and cultural step forward since all living organisms were supposed to belong to a class. Hence the entire diversity could be understood with only a few simple and logical properties. Indeed, this approach to classification was so successful that it lasted until the 17th century.
Astrophysics
Galaxies have been discovered in 1922 by Edwin Hubble. This is a very young field as compared to biology. Hubble, thanks to his comprehensive works, obtained a complete knowledge of the diversity of galaxies in the Universe known at that time. He essentially had only one observable at hand: the morphology of galaxies as observed by imaging. Naturally, in front of too many objects, he tried to build a classification that could synthesize his catalogs. Consequently, diversity for Hubble meant morphological diversity.
He thus identified ellipticals, spirals and irregulars, and among the spirals separated the objects showing a bar. These four classes make the well-known Hubble classification, based on simple and logical properties of galaxy, and still largely used today.
Limitations of the traditional approach
During the Middle Age, travels developed and so the discovery of new species increased dramatically. The number of classifications increased accordingly since the subjectivity of the traditional approach allowed travelers and biologists to create their own taxonomy. Both criteria and names were arbitrary, so that the different classifications were difficult to compare, and even sometimes contradictory. A given plant or animal could belong to several classes with different names, or to none. Things became really unbearable in the 18th century.
Adanson (1763) wrote what we would call today a review of all existing classifications. Names were multiple, and sometimes were small phrases describing the living organisms with the chosen criteria. It could look like a multivariate classification, but very awkward: if a given class contains plant with yellow flowers, it was impossible to include a plant with red flowers and otherwise identical. This precluded the discovery of more fundamental properties. Naming objects with a few descriptors is blocking our quest of a global picture of diversity which follows the evolution of our knowledge.
In astrophysics, the essentially unique global classification of galaxies is based on the morphology as observed in the visible light. Van den Bergh (1998) gives a review of all proposed classifications from the Hubble’s discovery of galaxies. All are variations of the original one by Hubble. They thus have all the same drawbacks:subjective (classification is made by eyes), using a single criteria (morphology) defined in a very anthropocentric way since it uses the visible light. Problems arise when looking in other wavelengths. But one of the main critical point is that newly discovered galaxies very far from us (at high redshift) do not fit into this classification.
However, if one looks at the literature, many more classifications are used, proving by this that the Hubble classification has a limited usefulness, none being intended to be as general as the Hubble classification. These classifications are all based also on a very few number of observable properties, and most often depend on the wavelength (like radio, infrared, ultraviolet, X-ray or gamma-ray sources). Classes can also be defined from some quantity derived from the models.
Confronted with the explosion of the observational means, the astrophysicists have created several hundreds of names, often acronyms, to clarify the galaxy diversity. A whole “zoology” has thus appeared: dwarf galaxies, field or isolated galaxies, Cd, starburst, radio, ULIRG, disky or boxy ellipticals, merger, quasar, active (Seyfert, BLlac, OVV, blazar, Faranoff-Riley I and II, …), blue, compact, Lyman 
There is thus an astonishing parallel between the current situation in astrophysics and the one for biology in the Middle Age…
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ADANSON, M., 1763. Famille Des Plantes. volume Num. BNF de l’éd. de, Paris : INALF, 1961- (Frantext ; R263Reprod. de l’éd. de, Paris : Vincent).
HUBBLE, E.P., 1922. A general study of diffusive galactic nebulae. Astrophysical Journal 56, 162–199.
Astrocladistics 