In his paper on “Carnap, Quine, Quantification, and Ontology,” Gregory Lavers holds forth — mostly quite instructively — on the connections between Carnap’s and Quine’s conceptions of ontology, and on the connections between these and their respective conceptions of explication. He misses a few critical details, though, and it seems to me that these apparently minor omissions undermine some, at least, of the points he wants to make.
I will start with something that looks quite trivial, but sheds (perhaps unintended) light on his understanding of the texts he discusses. His footnote 20 on p. 20 claims that his account of the relation between explicandum and explicatum (in their Carnapian senses) agrees with that of Howard Stein. What he says in the passage to which this footnote is appended, though, is this:
We just saw that, relative to an explication of number, numbers exist. And relative to an explication of the notion of reference for an arithmetical object language, numerical terms refer. One might say at this point, yes, relative to this newly introduced sense of ‘refer’, numerical terms refer, but is this the correct sense of refer — is there actually an object for which these terms stand? Since Carnap has offered an explication of the term ‘refers’ as it relates to the object language, he would say there is no question of whether the account of reference is correct. An external question then is one that asks, of ‘exists’ or ‘refers’ in some reconstructed system, if they agree with reference and existence in the unreconstructed sense — a sense Carnap saw, in Syntax and right through his semantic period, as being sufficiently unclear as to invite philosophical confusion. (pp. 19-20)
Whereas what Stein writes in the passage to which Lavers refers in his footnote is the following:
An explication is a proposed exact characterization of a concept. If the proposal is adopted, the concept so characterized is an explicatum — that is, an ‘explicated’ notion. There is a perhaps somewhat delicate issue whether the explication is to be regarded as a clarification of a notion already present before the explication has been achieved. In typical cases, something like this is so; and Carnap calls the preexisting, not fully clarified notion the explicandum: ‘that which requires explication’. That this state of affairs involves the well-known ‘paradox of analysis’ is clear — indeed, this is precisely the paradigm situation of that alleged paradox; I need hardly elaborate. That on the other hand there have actually occurred what should quite reasonably pass for successful explications in this full sense seems to me uncontroversial; for instance, although Quine is unhappy with Carnap’s account of logical truth, he is famously happy with first-order predicate logic — and would presumably agree that the exact construction of this system clarified the preexisting, insufficiently clear and precise, notion of logical inference.
Now, Carnap’s distinction between ‘external’ and ‘internal’ questions, which was introduced in his paper on ontology and is deprecated by Quine, has — if one accepts it (which means: if one agrees to use it) — an obvious application to the process of explication in general. The explicatum, as an exactly characterized concept, belongs to some formalized discourse — some ‘framework’. The explicandum — if such there is — belongs ipso facto to a mode of discourse outside that framework. Therefore any question about the relation of the explicatum to the explicandum is an ‘external question’; this holds, in particular, of the question whether an explication is adequate — that is, whether the explicatum does in some appropriate sense fully represent, within the framework, the function performed (let us say) ‘presystematically’ by the explicandum. (Stein’s paper ‘Was Carnap Entirely Wrong, After All?’, 1992, p. 280)
Stein, unlike Lavers, does not address the question whether an explication is “correct” — he very carefully describes the question he raises as “the question whether an explication is adequate — that is, whether the explicatum does in some appropriate sense fully represent, within the framework, the function performed (let us say) ‘presystematically’ by the explicandum.” What is the difference? Well, the difference is precisely the one Carnap goes to considerable trouble to make clear in ESO: external questions make no sense as cognitive questions (Lavers is clear about this part), so they should instead be taken as practical questions, i.e. as normative ones — about which it makes no sense to ask whether an answer is “correct” or “incorrect.” They become questions about whether a proposed explication is “adequate” or sufficiently useful or elegant or appealing relatively to the purpose it is being proposed to serve. Answers to such questions, for Carnap (who was a non-cognitivist — in fact, he invented the term), are not amenable to truth or falsehood; they can be consistent or inconsistent with systems of normative statements (or “comprehensive value functions,” as he called them), but not true or false.
(Later in his paper, Lavers appears to understand all this, but still does not quite spell it out.)
In another passage (p. 10), Lavers cites Quine’s well-known remark that he was Carnap’s disciple for about six years, which Lavers suggests was from about 1933 to 1939, and that during the early part of this period, Quine read the Logical Syntax as it emerged from Ina’s typewriter. Here another apparently insignificant detail gets in the way. The summer in which Quine read what emerged from Ina’s typewriter was 1932, not 1933. And why does this matter? Because it was in late 1932 that Carnap abandoned his quest for a canonical syntax language and adopted the principle of tolerance instead — perhaps the single most significant turning point in Carnap’s career. The Syntax that Quine read as it emerged from the typewriter was the first draft of the book, which still promoted its “system language [Systemsprache]” as the canonical language of science; in the second draft (written in 1933), this became Language I (one of an “open sea” of possible choices). The Carnap whose disciple Quine says he became, in other words, was the pre-tolerance Carnap.
This becomes relevant in what follows. “The concept of explication,” Lavers says, “became a central pillar of Carnap’s thought, but Quine also saw the notion of a Carnapian explication as very important.” He goes on to list the writings in which Quine mentions explication; what he omits to mention (though he was clear about this in an earlier  paper) is that in “Two Dogmas” Quine actually rejects Carnapian explication, since he regards it as just as dependent on pre-existing synonymies as ordinary definition (From a Logical Point of View, p. 25). He later, in Word and Object, accepts a form of explication, but essentially just this reduced form of it, in which an explication regiments a “core” meaning to get rid of meaningless clutter adhering to a concept from ordinary language or traditional associations. “Explication is elimination,” he says in a passage that Lavers quotes explicitly, claiming that it “amounts to the same thing” (p. 12) as Carnapian explication.
But this is not Carnapian explication. (See also Gustafsson.) For Carnap, ordinary language remains as it is. To adopt the metaphor Carnap uses in his reply to Strawson, we rarely need a microtome for everyday purposes; the ordinary pocket knife will do just fine — it goes on doing its job and is not eliminated. As we saw in the elucidatory second paragraph of the quotation from Howard Stein above, the explicatum is in a different language from the explicandum; questions regarding the analogy or similarity in function (or, say, “partial synonymy”) between the explicatum in its more precise language and the explicandum in ordinary language are external questions (or else empirical questions belonging to descriptive pragmatics).
Quine, as Lavers points out, persisted in regarding ontological questions as language-transcendent, and thought there was a “core meaning” to the question “what is there?” that persisted from ordinary (and traditional philosophical) language into his attempted explications of this question. For Carnap, it was of central importance that this made no sense; from sometime in 1924, ontological claims were self-consciously regarded as nothing but façons de parler; ontological questions were purely internal to a language framework. The “philosophical” final chapters of both the Aufbau and the Syntax are largely devoted to this priority; Carnap can’t be accused of not putting his cards on the table. But as Gary Kemp and Andrew Lugg point out, the question of what really ultimately exists was on Quine’s mind throughout his early career; they quote him saying: “In my youth I thought of the question of existence, or what there is, as perhaps the most basic question of philosophy and science. In the fullness of time the scales fell from my eyes.” They generously see his “youth” as stretching through Word and Object; certainly it includes the years when Quine claims to have been Carnap’s “disciple” — which raises the question how he could have missed this obvious, and pretty central, doctrinal clash between supposed master and supposed disciple.
Even more curious is the critique to which Lavers himself subjects the Syntax for its failure to engage with ontological worries. On this front, he says, the book is an “unsatisfactory patchwork,” and “not very convincing” (p. 4). But as he himself acknowledges, the existence assumptions of Carnap’s that might raise such worries, in this or that sensitive soul, are entirely logical and mathematical. And he further acknowledges that Carnap’s response to such worries is to say something like “Sure, the axiom of choice makes certain existential assumptions, but we are unconcerned with these since we need only care about the material interpretation of descriptive sentences.” (p. 6) Nonetheless Lavers objects to this response on the grounds that “adopting this instrumentalist view concerning existence assumptions of the logico-mathematical portion of the language is to dismiss rather than address (or dissolve) ontological concerns.” Precisely! — and that is Carnap’s whole point; he wants to dismiss ontological concerns in principle, root and branch. This is practically the main point of the entire book — the main philosophical point, anyway (apart from the principle of tolerance, which depends on the exclusion of ontology and was added late in the composition process, unfortunately getting little exposure in the final chapter). To criticize Carnap for failing to engage with the ontological worries raised by the axiom of choice is a bit like criticizing Hume for failing to engage with the doctrine of transsubstantiation (which of course becomes entirely moot if we accept his more general arguments against supernatural agency).
Still, doesn’t Carnap’s conception of explication, just like Quine’s, advocate replacement that need not be fully synonymous? — so isn’t Quine right to align his own view to Carnap’s, and isn’t Lavers right to elide them and say they amount to the same thing? What possible difference, he might ask (like Patrick Maher, p. 23, footnote), could there be between “replacement” and “elimination”? For Quine, there is none. For Carnap, though, there is a very important difference that goes to the heart of his philosophy. Elimination, in the context of reductive analysis in the Russellian tradition, is inherently an ontological project. Composite concepts are reduced to simple concepts, and the ultimately simplest concepts, at the end of this analysis, are those to which the language in question is “ontologically committed.” Elimination by Occam’s Razor is part of an ontological program for (at least the “early”) Quine, just as it had been for Russell. Carnap, too, entertained such programmatic proposals. But for him they were linguistic proposals, not ontological ones. Acceptance of a linguistic proposal, for this purpose or that, was a practical decision analogous to the decision to use a chain saw rather than an axe for trimming a certain tree branch. And in Carnap’s non-cognitive conception of normative statements, there is no possible inference from such a practical decision to an empirical or theoretical statement regarding the existence of some entities (as he pointed out in ESO). Linguistic proposals were to be judged by their suitability as tools for some purpose or another. They did not — in addition to their suitability for that purpose — also need to meet further philosophical qualifications. (It’s just this further requirement Quine imposes on candidate explications, that they meet philosophical qualifications beyond anything “pragmatic,” that so exercised Michael Friedman in his — appropriately named! — Howard Stein Lecture at the University of Chicago back in 2006.)