Given the importance of origins in biology, in that field we can make another distinction among essentialisms, according to how they answer the question: Can one kind of thing turn into another kind of thing? In the strictest interpretation, no one holds this; no sense can be made of it. Definitions (shared nature) and idealizations (type) don't change, although things defined can change definitions and things idealized can change so that they are no longer to be idealized in that way. Thus the useful meaning of the question is looser than this: given a population (of whatever size) of a given kind, can this population be modified to be a population (of whatever size) of another kind, in such a way that the latter population descends from the former population? There are a number of different answers.
Contrary to popular belief, the traditional Aristotelian essentialist is not necessarily committed to a negative answer, although, as a matter of fact, the only biological case analogous to such an evolution that was really considered at all was spontaneous generation. Aristotelians allow for substantial transformation; indeed, substances regularly transform into other substances in the Aristotelian view, as different substances are generated and corrupted. This is all that is required for the possibility of species transformation, whether it is actually accepted or not. By the nineteenth century, however, there were very few traditional essentialists around, and there have been relatively few since, so we can set this view aside entirely.
More interesting for the history of evolutionary thought is the believer in independent special creation. The independent special creationist says no; the kinds are immutable; to have a new kind, it must be independently created. Independent special creationists are Darwin's primary target in The Origin of Species:
Although much remains obscure, and will long remain obscure, I can entertain no doubt, after the most deliberate study and dispassionate judgement of which I am capable, that the view which most naturalists entertain, and which I formerly entertained — namely, that each species has been independently created — is erroneous. I am fully convinced that species are not immutable; but that those belonging to what are called the same genera are lineal descendants of some other and generally extinct species, in the same manner as the acknowledged varieties of any one species are the descendants of that species.
What I will call 'transformism' is a loose category of people who would answer 'yes' to the above question. There are a lot of different variations of transformists. Darwin again gives us a sense of some of the diversity in the Introduction to OS:
In considering the Origin of Species, it is quite conceivable that a naturalist, reflecting on the mutual affinities of organic beings, on their embryological relations, their geographical distribution, geological succession, and other such facts, might come to the conclusion that each species had not been independently created, but had descended, like varieties, from other species. Nevertheless, such a conclusion, even if well founded, would be unsatisfactory, until it could be shown how the innumerable species inhabiting this world have been modified so as to acquire that perfection of structure and co-adaptation which most justly excites our admiration. Naturalists continually refer to external conditions, such as climate, food, &c., as the only possible cause of variation. In one very limited sense, as we shall hereafter see, this may be true; but it is preposterous to attribute to mere external conditions, the structure, for instance, of the woodpecker, with its feet, tail, beak, and tongue, so admirably adapted to catch insects under the bark of trees. In the case of the misseltoe, which draws its nourishment from certain trees, which has seeds that must be transported by certain birds, and which has flowers with separate sexes absolutely requiring the agency of certain insects to bring pollen from one flower to the other, it is equally preposterous to account for the structure of this parasite, with its relations to several distinct organic beings, by the effects of external conditions, or of habit, or of the volition of the plant itself.
The author of the 'Vestiges of Creation' would, I presume, say that, after a certain unknown number of generations, some bird had given birth to a woodpecker, and some plant to the misseltoe, and that these had been produced perfect as we now see them; but this assumption seems to me to be no explanation, for it leaves the case of the coadaptations of organic beings to each other and to their physical conditions of life, untouched and unexplained.
So there are (at least) five kinds of transformist, all of which accept that biological species can transform , but which disagree on the mechanism: the pure variationist (external factors alone), the orthogeneticist (the 'volition' or tendency of the plant itself), the Lamarckian ('habit' or accumulation of characteristics), the saltationist; and the selectionist (Darwinian). While Darwin is primarily concerned with arguing against independent special creationists, he does give brief indications of why he thinks other forms of transformism are not sustainable. Saltationism doesn't really explain anything at all; the others are not adequate for explaining the sheer richness and detail of actual biological life.
Notice, incidentally, that Darwin's argument against other transformisms can be interpreted as the claim that they fail to explain biological kinds. Lest one consider this an illusion of reading just this passage, consider a few facts about Darwin's presentation. Darwin argues that 'species' on other views (and particularly on independent special creationist views) is a poorly defined concept. However, he does not simply leave it at that, but goes on to argue that his theory of natural selection provides the principle for natural classification. Darwin very clear believes there is a natural classification; and thinks that one of the major advantages of his theory over rivals is that it gives a way to make sense of it. As he says:
I believe this element of descent is the hidden bond of connexion which naturalists have sought under the term of the Natural System. On this idea of the natural system being, in so far as it has been perfected, genealogical in its arrangement, with the grades of difference between the descendants from a common parent, expressed by the terms genera, families, orders, &c., we can understand the rules which we are compelled to follow in our classification. We can understand why we value certain resemblances far more than others; why we are permitted to use rudimentary and useless organs, or others of trifling physiological importance; why, in comparing one group with a distinct group, we summarily reject analogical or adaptive characters, and yet use these same characters within the limits of the same group. We can clearly see how it is that all living and extinct forms can be grouped together in one great system; and how the several members of each class are connected together by the most complex and radiating lines of affinities. We shall never, probably, disentangle the inextricable web of affinities between the members of any one class; but when we have a distinct object in view, and do not look to some unknown plan of creation, we may hope to make sure but slow progress.
Moreover, we find elsewhere reason to regard Darwin as an essentialist; not least is his acceptance of the Unity of Type doctrine. Darwin's difference from an essentialist who merely accepts unity of type is that Darwin thinks descent explains unity of type, and is itself explained by 'conditions of existence'.
In my next post on this issue I'll say a little more about Darwin as an essentialist of a particular sort.