A third [evolutionary] advance is in a way the most important, since it is the one used by paleontologists to distinguish reptiles from mammals. The lower jaw of reptiles contains several bones, of which two are important to us. One of these, the dentary, bears the teeth while the other, the articular, smaller and at the hind end of the jaw, forms part of the hinge between the lower and upper jaw (Figure 9-8). The other part of this hinge is the quadrate, a small bone in the head portion of the skull, or cranium. Immediately behind these two small jaw bones is the middle ear, within which sound waves are amplified and transmitted from a special nerve to the brain. In reptiles, amphibians, and fishes, this amplification is carried out by a single small bone. By contrast, the lower jaw of mammals consists only of the tooth-bearing (dentary) bone, which is hinged to another bone, the squamosal, also in the cranium. The two bones that form the hinge of the reptilian jaw have not disappeared. They are represented in mammals by two small bones in the middle ear connected with the counterpart of the single reptilian ear bone. In reptiles, amplification of sound waves in the middle ear, carried out by a single bone, is relatively inefficient. The three bones in the mammalian ear do this job much more effectively, so that the hearing of mammals is much better than that of reptiles.
In order to classify fossil animals neatly and clearly as either reptiles or mammals, most paleontologists and nearly all textbooks classify as reptiles all bony-limbed animals that have a liquid-filled amniotic egg and a jaw hinge formed by the two small bones, articular and quadrate, along with a single ear bone. Mammals differ in having the tooth-bearing (dentary) lower jaw bone articulated directly with a bone of the cranium (squamosal), plus three small bones in the middle ear. Tooth structure also helps in classifying them. Nevertheless, an animal that has almost mammalian teeth but a reptilian jaw hinge and middle ear bone is called a reptile. Mammallike reptiles are all classified as reptiles on the basis of this character, even though the advanced dog-tooth has teeth that resemble those of primitive mammals more than they resemble the teeth of the earliest mammallike reptiles or their immediate ancestors, the pelycosaurs. Likewise, the earliest animals having three bones in the middle ear are called mammals, although, like the primitive mammals of modern Australia—the spiny anteater and platypus (monotremes)—they may well have laid eggs, lacked nipples or teats, had skeletons showing some reptilian features such as shoulder girdles, and had chromosomes resembling those of reptiles.
— Stebbins - Darwin to DNA, Molecules to Humanity, pp. 289-91
I find this strangely profound: everyone knows the difference between a reptile and a mammal upon seeing one, but once all the fragile details are stripped away, there’s only a single, trivial difference between them; it’s this one silly little criterion that informs all of our (taxonomical) knowledge about species long-extinct. I suspect that the taxonomies of many disciplines are like this.
The text alongside fig. 9-8 reads:
A series of skulls showing a few of the numerous transitional forms that, via a series of adaptive radiations, resulted eventually in the origin of modern mammals (a)–(c): Three typical reptiles. (a) A primitive Captorhinus that, like early amphibians and modern turtles, has only one pair of openings in the skull in addition to the nostrils. (b) A primitive ancestor of lizards, Youngina. (c) A modern lizard, Varanus. (d)–(i): Six reptiles that were on or near the line leading to mammals. (d) and (e) Two pelycosaurs that were typical reptiles but show the beginnings of tooth differentiation. Note that the hindmost bone of the lower jaw (angular, a) is nearly as large as the tooth-bearing bone (dentary, dn). (f) and (g) Two early mammallike reptiles, showing further tooth differentiation, plus reduction in size of the angular bone. (h) and (i) Two later forms of reptiles that, with respect to tooth differentiation and reduction of the angular bone, were much like mammals. Diarthrognathus was almost completely intermediate between reptiles and mammals. (j)–(l): Three kinds of mammals. (j) Sinoconodon, the earliest of these, still retained a number of reptilian features. (k) A later form, Deltatheridium, was very similar to modern shrews. (l) A modern opossum (Didelphys). The skulls are drawn at different scales of magnification. Those in the center column are at natural size or somewhat reduced; those in the right column are somewhat magnified.