There is a deeper puzzle about eliminativism.
(E) There are no A's. There are only B's.
(R) There are A's but A's are only B's.
Clearly (E) and (R) do not disagree about the basic ontology. They agree that there are only B's. But they fundamentally disagree about the definition of 'A'. The eliminativist (E) claims that an A, as the term 'A' is correctly and properly understood, cannot exist, because its definition would include features inconsistent with being a B. The reductivist (R) is saying that, as the term 'A' is correctly and properly understood, it is entirely consistent that an A can be a B, indeed that every A is a B.
But if it is merely a quarrel over definitions, why is there any disagreement at all? There is no disputing over definitions. Perhaps the answer lies in the difficulty that surrounds all philosophically interesting notions. The SEP says "Like many philosophically interesting notions, existence is at once familiar and rather elusive. Although we have no more trouble with using the verb ‘exists’ than with the two-times table, there is more than a little difficulty in saying just what existence is". That is, there are certain terms which we all understand and have no difficulty using with a standard sense in everyday life, but which we find terribly difficult to define. Hence there may be profound disagreement over which features are essential to the term, and hence profound disagreement between (E) and (R). Both agree that in using the term 'A' they are talking about the same kind of thing, and using the term in the same sense. But they disagree about what are the fundamental features of an A. The eliminativist believes that there is some feature of A's, correctly understood, that makes it inconsistent with an A being B. And since he believes there are only B's, he holds that there are no A's. The reductivist agrees that this feature is inconsistent with being B, but regards it is non-essential, and so it is possible - indeed true - that no A actually has the feature.
Considering the example of truth - which is as philosophically interesting as any - we have
(E) There is no truth. There is only warranted assertibility.
(R) There is truth, but truth is only warranted assertibility.
The disagreement here does not involve equivocation (as I previously thought). Both (E) and (R) both think they are talking unequivocally about the same thing: truth, an idea that we have no more trouble in employing than in using the two-times table. Both agree on the 'ontology': there is warranted assertibility and nothing more. Where they disagree is that (E) thinks that truth involves more than warranted assertibility, and is inconsistent with the ontologyl.(R) by contrast thinks that truth involves no more than that, and so its existence is consistent with the ontology.
So the disagreement is not about ontology or about which entities/features are to be eliminated. Both agree that 'truth involving more than just warranted assertibility' is to be eliminated. But (E) eliminates it by eliminating truth itself. (R) eliminates it by holding onto truth, but eliminating anything more than just warranted assertibility. The disagreement lies in the analysis of the everyday notion of truth, and not 'ontology'.
The deeper puzzle is how people can agree on the meaning of a term, and yet disagree about its definition. How can we agree on the meaning of 'existence' - a term which is no more difficult to use than a times-table, and yet disagree profoundly on how to define it? Why are there similar puzzles and disagreements over the nature of truth, individuation, identity, reference and all the rest? This problem goes back at least to Plato, and we appear to be no closer to solving it.