Continuing background to Shtulman paper.
Given confusions on this score it might be useful to say a few things about the claim that Darwin is not an essentialist. A major reason why this has become popular is Ernst Mayr, as in his Crafoord Prize speech. In that speech Mayr identifies six features of the 'Darwinian Zeitgeist', all of which he traces back to Darwin's principles. Of these six there are two that are unexceptionable (population thinking and descent of man; with regard to a third (scientific foundation for ethics), while it's controversial whether Darwin has actually done this, it can be conceded that Darwin heads in this direction. For the rest, however, Darwin would not qualify as a Darwinist in Mayr's sense. (1) Darwin, who has a very sophisticated understanding of the issues surrounding design arguments, is not so naive as to think the theory of selection does away with all design arguments. Indeed, he is very clear that it does not; it only does away with one narrow form of it. To do more you have to add other, more purely philosophical considerations. (For those who haven't read it, I recommend on this point Francis Darwin's The Autobiography of Charles Darwin and Selected Letters.) (3) Far from making the invocation of teleology unnecessary, Darwin's principles were understood at the time by three great early evolutionists (Gray, Huxley, and Darwin himself) to do exactly the reverse. That is, Darwin understood his own theory to reintroduce teleology, in the form of Cuvier's conditions of existence, which were widely understood to be an appeal to final causes, by giving it the key explanatory role. (4) Whether Darwin's principles do away with determinism is a bit more controversial. Darwin himself makes no such claims. As he says in Chapter 5, 'chance' is "a wholly incorrect expression, but it serves to acknowledge plainly our ignorance of the cause of each particular variation." This epistemic sense of 'chance' does not and cannot rule out deterministic causation. It is true that Darwin does think, far more than most, in probabilistic terms; but even determinists at the time wouldn't have had a problem with this. (The tendency to think of 'probabilistic' and 'deterministic' in opposed terms is a back-formation from a redefinition of the terms in physics; this opposition has nothing to do with the old question of whether there is real chance in the world, because it's an adaptation of the terms to a different type of question.)
This leaves (2), that Darwin opposes essentialism. It is clear that this is true if you mean that Darwin is not an independent special creationist; but, as I noted above, Darwin seems clearly committed to another form of essentialism. That variation is "nonessential and accidental," as Mayr puts it, is utterly irrelevant to the question; nobody in their right mind thinks that species are the process of variation. The fact that there are intermediate kinds between kinds, such that by descent one kind may be related to another, does not show us that there are no kinds at all. It does seem that a Darwinian can be either a shared nature essentialist (as Huxley seems to me) or a type essentialist (as seems closer to Darwin's view), or both; but to reject both would be to deny that biological organisms can be classified (except as a purely arbitrary matter of convenience). Either organisms share a nature or approximate a type; or else taxonomy indicates nothing about the world. Of course, as I pointed out above, one of Darwin's points is that one of things the theory of descent does is give us a clear and straightforward way of saying that taxonomy can and does indicate something about the world.
I find it, by the way, impossible to tell what Mayr means by 'essentialism'. He clearly has in mind shared natures -- the triangle example requires this; but he calls it 'typology', and type essentialism has generally been more popular in biology than shared nature essentialism. As I noted before, things are constrained by natures but to types. But, more relevantly, Darwin appears to be a type essentialist; otherwise it's unclear how he manages to accept, as he claims, unity of type. What Darwin rejects is not types but, as he says in the Recapitulation to OS, the claim that kinds are independently created according to type "without any apparent adequate cause." In other words, he rejects type essentialisms of the independent special creationist variety. He rejects it by proposing that descent from a prototype explains unity of type; and he explains this descent by natural selection. He does not reject types but argues that, with his theory of descent, types become "intelligible facts". And indeed, elsewhere in OS he notes that organisms are constrained to type by natural selection. However, Mayr is right that in doing this Darwin is making use of 'population thinking' and rejects the constancy of populations.
Faced with this there are two reasonable alternative ways to go. (1) We can say that Mayr and others who use Darwin to attack (certain versions of) essentialism (other than independent special creation) have strayed from the truth, and are really just trying to smuggle controversial philosophical claims under the cover of solid scientific theories and facts. Such philosophical parasitism is and has always been common: a philosophical position is put forward as the only one science allows, when closer examination shows that the only serious link between the philosophical position and the scientific claims is a vague and unanalyzed analogy. It wouldn't be the first time someone has misused Darwin in this way. (2) We could go the other way and say that Mayr is actually right; but that what makes him right is not Darwin but what biologists have discovered since Darwin. Because biology has discovered a lot of things since Darwin, this is a reasonable claim to make (if we're willing to back up the claim with facts); but I would have to see (a) what the facts appealed to really are; and (b) what sort of essentialism is being criticized. I think it's fair to say that since Darwin other forms of essentialism have gone by the wayside (certain forms of vitalism, for instance). It does not follow from this, however, that evolutionary biology isn't consistent with some modest forms of essentialism, or that there are neither types nor shared natures. These are stronger claims, and seem on the surface to be contradicted by certain facts of biological practice (taxonomy and comparative physiology, for instance); they would need a rigorous defense.
So that's the rough glance around. When I post on this again, I'll look at the Shtulman paper.
UPDATE: Those who found this post interesting should read John Wilkins's post, Essentialism Revisited, which offers a corrective to a few things above.