Can the specifications of domain of applicability be part of analytic statements?
The problem involves my reading of Quine's Two Dogmas, and trying to elaborate the "creatures with hearts" and "creatures with kidneys" argument. I'm finding that in order to maintain that these two classes are co-extensive, I need to add an axiom along the lines of "Given that we limit our consideration to the vertebrates that we know of today" (limited to vertebrates, since as far as I can tell only vertebrates have kidneys proper). Without it, one can consider an as yet undiscovered creature, say a fish that does all of it's excretion through its gills, but does not have kidneys. Once you allow that possibility, the two classes are not co-extensive, and Quine's argument breaks down.
So to me it looks like you either a) impose a specific assumption about the domain of discourse, in which case the equivalence of "having a heart" and "having a kidney" is derivable from that assumption by enumeration or (b) you have some kind of uncertainty about whether in fact these two classes are co-extensive, and thus you have uncertainty about whether the two classes can be interchanged with one another.
Option (a) looks like "having a heart" is synonymous with "having kidneys", at least in the exchange sense, is analytic; but maybe I'm mistaken on this. Option (b) seems to describe a situation irrelevant for Quine's argument, since that argument requires that the two classes are co-extensive.
My understanding of Quine's argument is that: If there is at least one pair of class labels that are not linguistic synonyms, but for which elements of one class are substitutable (in the Carnap sense) for the elements in the other class due to the two classes being coextensional, then being substitutable is different from being synonymous. The proof of the antecedent is by example: using the specific example of cordate & renate.
I'm questioning the validity of the argument; I'm just not finding the specific example fully compelling, unless I'm making a mistake somewhere else.