I've always been puzzled by the following problem. The setting for it is the metaphysical Aristotelian concept of a "species", not the biological one (in the biological sense this is easy). How do we know that women and men are the same species? I.e., how do we know that the species that we belong to is human rather than there being two species, woman and man?
I think a partial answer can be given by taking into account the following observation (I've learned it from David Alexander here who attributes it Peter Geach, though neither may endorse my application): In general, from the fact that x is a good F and x is a G, one cannot infer that x is a good G.
Here, I intend "is a good F" to mean something like "flourishes at F-ness" or "is good at being an F". Moreover, I am thinking here in the context of Greek notions, so that to be a good human includes both having the virtues of the intellect and will, as well as the excellences of the body. This is at times a somewhat awkward use of "good", but I shall adopt it.
I shall be rough here. I know what I say is not exactly right. For full precision, one needs to work not with the coarse tools of entailment and necessity, but with more finegrained tools of explanation and truthmaking. But what I shall say seems approximately right.
Despite what I said above, sometimes inferences like the ones questioned above seem exactly right:
(1) If x is a good lieutenant in a military force, then x is a good officer in the same force.
(The "in the same force" condition is needed, because a spy might be an officer in more than one army, but is unlikely to be a good officer in more than one.) The converse I am less sure of, but it is also plausible:
(2) If x is a good officer in some military force and x is a lieutenant, then x is a good lieutenant in the same force.
Suppose, now, that F and G are kinds such that, necessarily, all Fs are Gs but not conversely, and necessarily x is a good F if and only if x is a G and x is a good G. I shall say that "F is normatively subordinated to G".
Conjecture 1: If F is a species and G is a higher genus, then F is not normatively subordinated to G.
Conjecture 1 embodies an Aristotelian notion of the primacy of species, in the normative realm. And I think the normative aspect of species-hood is central for Aristotelians (I would like read the characterization of the essence as to ti ên einai as normative, though it may be stretching the Greek: what [the thing] was [supposed] to be). The species encodes the normative properties for the individuals of that kind. If we can explain the normative properties of an x insofar as it is an F in terms of its aptness at fulling G-ness, then F-ness is not the normatively basic property here. F-ness specifies the x further, but does not add any nomrative force. For reasons of explanatory power, we should try to find as general a kind as we can without sacrificing any normativity when we are searching for. To be a good human is more than just being human and being a good mammal. One can be really good at mammality while being far from human flourishing. The converse, I think, is false, though: if we fully flourish at humanity, we also flourish at mammality.
Now one is a good woman if and only if one is a woman and a good human; similarly for a man. This is a controversial claim, but I think correct. Therefore woman and man are normatively subordinated to human. If woman and man were species, then human would be a higher genus, and hence Conjecture 1 would be violated. Hence, if Conjecture 1 holds, woman and man are not species.
An interesting question is whether one can come up with a full characterization of species in similar normative terms. Here is something that might come close.
Conjecture 2: A natural kind G is a species iff both (a) G is not normatively subordinated to any larger natural kind, and (b) if F is a proper natural subkind of G such that any good F is necessarily a good G, then F is normatively subordinated to G.
(The "F is normatively subordinated to G" condition in (b) can be replaced by "necessarily a good G who is an F is a good F", because more than half of the definition of normative subordination is implied by the antecedent of the conditional in (b).)
For instance, mammal is not a species. For human is a proper natural subkind of mammal such that to flourish at being a human entails flourishing at being a mammal, but human is not normatively subordinated to mammal. One can be really good at mammality while a miserable failure at all other dimensions of humanity. But one cannot be really good at humanity and a woman while being a failure at being a woman.
A different way to look at the above is to note that the flourishing of a man or a woman as such is basically no different--it is just a particular form of the flourishing of a human.