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.


The critical thing to appreciate about Two Dogmas of Empiricism is its context. You mention the idea that we impose "specific assumptions about the domain of discourse" in Quine's analysis of the Cordate/Renate relationship - well, Rudolph Carnap's Logical Empiricist project was exactly about the processes and mathematics in formulating such domains formally to serve as the groundwork for a precise and mathematically rigorous language for scientific analysis, and it is that project's expression of two unanticipated Dogmas that Quine is addressing.

If you want to take the line that the domain introduces a new notion of synonymy, you might start by focusing on Carnap's use of State Descriptions. The idea here is that we think of analyticity in terms of a state space of propositions (potentially a probability distribution) whereby if two statements have equivalent truth values in all states, then they are synonymous. Of course if we have a state space in which in some possible state some animals have hearts and do not have kidneys (even if none in fact actually do) then it's not analytic that animals that have hearts have kidneys, but something synthetic, and that thus needs to be subject to synthetic evaluation.

The work that the analytic/synthetic distinction is doing for Carnap is to show that you can start from the grounding of mathematical axiomatics, and then add something further to this to help elaborate how scientific theorizing can be done in a formally rigorous way. The analytical truths are covered once we've accepted the legitimacy of the mathematical explication (which we suppose to be well-founded in mathematical practice), and the synthetic truths are those that are determined when you go out into the world and test.

But for Quine, it's not that simple. Carnap's theory of State Descriptions is, in principle, syntactic. When I give the suggestion above that there might be some possible state where animals have hearts and do not have kidneys, in Carnap's theory this is certainly a legitimate state to introduce into our framework prior to any sort of empirical investigation. It might so happen that we later on get to a stage where we realize that the only states that are consistent with the available evidence are ones where hearts and kidneys are indeed coextensive. But even then, we wouldn't say that the statement is Analytic. Indeed, we've had to go through a process of synthetic investigation to get to that stage. If we call things "Synonymous" at this stage and use this to ground a notion of "analyticity" then that's fine, but it's not going to be a notion of "analyticity" that does the work that Carnap wants to put it to.

So coextension alone doesn't decide the matter of what should be deemed prior analytical knowledge. What about situations where we might think that two statements are simply coextensive "simpliciter", by virtue of meaning? Quine points to the case of "All Bachelors are Unmarried" as a candidate example. But to point to "meaning" doesn't really help us out here. In Carnap's State Description framework, we start by identifying the full modality of propositions as distinct. If we want to say "John is a Bachelor" and "John is Unmarried" as expressing two distinct propositions in Carnap's proposal then we're going to identify a state (in fact a whole partition of the state pace) where one is true and the other is false. If we want to appeal to "meaning" then we need to add new, distinct postulates to tell us when two things mean the same and when they mean something different; this is the kind of external appeal that we were hoping to avoid by relying on the mathematics rather than theories of properties or forms.

Quine traces this idea of meanings and synonymy through the next few sections of his paper and ultimately can't see any way for Carnap to get out of it.

  • My hang up is in paragraph 4: when the example non-renate cordate (my hypothetical fish) is a member of the "set of symbols" used in the theory (language as per the linked Carnap article) then, the two classes are not co-extensive, and that "all creatures observed to date are both" is not analytic (as per same link). When you get to the final sentence you pull the rug out, and to my mind, re-define the problem such that, now, the "set of symbols" only happens to include (cordate and renate) items. But then you've baked the co-extension, and thus changeability, into the theory specification.
    – Dave
    May 15 '15 at 16:59
  • Yes, I think that's correct. But this is grist to Quine's mill, because he's arguing that this second notion of "co-extension" (that you might perhaps want to use to form a kind of "analyticity" to respond to the charge that analyticity is an unclear notion) is not epistemologically innocent. The "analytical" that Carnap seems to want to use for his epistemology can't be this notion without assuming a substantial relation of meanings, which then also needs to be argued for, and in my fifth paragraph I mention how Quine considers the first kind of "coextension" and finds it wanting as well.
    – Paul Ross
    May 18 '15 at 10:54

Quine may have assembled his example more carefully, if there was a substantive point behind it. But the difference between synonymy and co-extensionality is such a well-known and undisputed fact, that he did not need to bother.

You seem to object that the two classes "creatures with hearts" and "creatures with kidneys" might not be co-extensive after all. But I think that the more relevant angle is the opposite one: it is enough, for the sake of the argument, that the two classes could be co-extensive (synonymous they surely are not). And if they are co-extensive (as far as we know) then surely they also can be co-extensive. And that is all that is required.

There is no assurance here that the extensional agreement of 'bachelor' and 'unmarried man' rests on meaning rather than merely on accidental matters of fact, as does extensional agreement of 'creature with a heart' and 'creature with a kidney'..

  • I thought that at the time of Two Dogmas (and related works) the difference between synonymy and co-extensionality was still in dispute and that these works, and this argument in particular, was the "nail in the coffin". Is there someone earlier than Quine that he's building on?
    – Dave
    May 15 '15 at 22:28
  • @Dave The extension/intension distinction is ancient. See some of its history here. May 15 '15 at 22:59

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