Here's something you frequently hear said about ontological commitment. First, that to determine the ontological commitments of some sentence S, one must look not at S, but at a regimentation or paraphrase of S, S*. Second (very roughly), you determine the ontological commitments of S by looking at what existential claims follow from S*.
Leave aside the second step of this. What I'm perplexed about is how people are thinking about the first step. Here's one way to express the confusion. We're asked about the sentence S, but to determine the ontological commitments we look at features of some quite different sentence S*. But what makes us think that looking at S* is a good way of finding out about what's required of the world for S to be true?
Reaction (1). The regimentation may be constrained so as to make the relevance of S* transparent. Silly example: regimentation could be required to be null, i.e. every sentence has to be "regimented" as itself. No mystery there. Less silly example: the regimentation might be required to preserve meaning, or truth-conditions, or something similar. If that's the case then one could plausibly argue that the OC's of S and S* coincide, and looking at the OC's of S* is a good way of figuring out what the OC's of S is.
(The famous "symmetry" objections are likely to kick in here; i.e. if certain existential statements follow from S but not from S*, and what we know is that S and S* have the same OC's, why take it that S* reveals those OC's better than S?---so for example if S is "prime numbers exist" and S* is a nominalistic paraphrase, we have to say something about whether S* shows that S is innocent of OC to prime numbers, or whether S shows that S* is in a hidden way committed to prime numbers).
Obviously this isn't plausibly taken as Quine view---the appeal to synonymy is totally unQuinean (moreover in Word and Object, he's pretty explicit that the regimentation relationship is constrained by whether S* can play the same theoretical role as we initially thought S played---and that'll allow for lots of paraphrases where the sentences don't even have the appearance of being truth-conditionally equivalent).
Reaction (2). Adopt a certain general account of the nature of language. In particular, adopt a deflationism about truth and reference. Roughly: T- and R-schemes are in effect introduced into the object language as defining a disquotational truth-predicate. Then note that a truth-predicate so introduced will struggle to explain the predications of truth for sentences not in one's home language. So appeal to translation, and let the word "true" apply to a sentence in a non-home language iff that sentence translates to some sentence of the home language that is true in the disquotational sense. Truth for non-home languages is then the product of translation and disquotational truth. (We can take the "home language" for present purposes to be each person's idiolect).
I think from this perspective the regimentation steps in the Quinean characterization of ontological commitment have an obvious place. Suppose I'm a nominalist, and refuse to speak of numbers. But the mathematicians go around saying things like "prime numbers exist". Do I have to say that what they say is untrue (am I going to go up to them and tell them this?) Well, they're not speaking my idiolect; so according to the deflationary conception under consideration, what I need to do is figure out whether there sentences translate to something that's deflationarily true in my idiolect. And if I translate them according to a paraphrase on which their sentences pair with something that is "nominalistically acceptable", then it'll turn out that I can call what they say true.
This way of construing the regimentation step of ontological commitment identifies it with the translation step of the translation-disquotation treatment of truth sketched above. So obviously what sorts of constraints we have on translation will transfer directly to constraints on regimentation. One *could* appeal to a notion of truth-conditional equivalence to ground the notion of translatability---and so get back to a conception whereby synonymy (or something close to it) was central to our analysis of language.
It's in the Quinean spirit to take translatability to stand free of such notions (to make an intuitive case for separation here, one might, for example, that synonymy should be an equivalence relation, whereas translatability is plausibly non-transitive). There are several options. Quine I guess focuses on preservation of patterns of assent and dissent to translated pairs; Field appeals to his projectivist treatment of norms and takes "good translation" as something to be explained in projective terms. No doubt there are other ways to go.
This way of defending the regimentation step in treatments of ontological commitment turns essentially on deflationism about truth; and more than that, on a non-universal part of the deflationary project: the appeal to translation as a way to extend usage of the truth-predicate to non-home languages. If one has some non-translation story about how this should go (and there are some reasons for wanting one, to do with applying "true" to languages whose expressive power outstrips that of one's own) then the grounding for the regimentation step falls away.
So the Quinean regimentation-involving treatment of ontological commitment makes perfect sense within a Quinean translation-involving treatment of language in general. But I can't imagine that people who buy into to the received view of ontological commitment really mean to be taking a stance on deflationism vs. its rivals; or about the exact implementation of deflationism.
Of course, regimentation or translatability (in a more Quinean, preservation-of-theoretical-role sense, rather than a synonymy-sense) can still be significant for debates about ontological commitments. One might think that arithmetic was ontologically committing, but the existence of some nominalistic paraphrase that was suited to play the same theoretical role gave one some reassurance that one doesn't *have* to use the committing language, and maybe overall these kind of relationships will undermine the case for believing in dubious entities---not because ordinary talk isn't committed to them, but because for theoretical purposes talk needn't be committed to them. But unlike the earlier role for regimentation, this isn't a "hermeneutic" result. E.g. on the Quinean way of doing things, some non-home sentence "there are prime numbers" can be true, despite there being no numbers---just because the best translation of the quoted sentence translates it to something other than the home sentence "there are prime numbers". This kind of flexibility is apparently lost if you ditch the Quinean use of regimentation.
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14 comments:
Hi Robbie, I wonder whether you might be able to get another option going here. Suppose we do have the relevant nominalistic paraphrase S* available, that does the same theoretical work that the target sentence does. Then we run some kind of contrapositive of the indispensability argument on the entities apparently invoked by the target sentence S. This leaves us with the choice between saying that S is false, or that it is an unregimented version of S*. For principle of charity style reasons we should say the latter.
As far as I can see this is compatible with thinking that the regimentation relation involves synonymy or that it involves translation and disquotational truth. But I'm not sure that you have to say either of those things (given your suggestion that those who talk about ontological commitment don't mean to be taking a stance on these issues). At worst you just have a simple normative notion of regimentation according to which its just the fact that S* plays the same theoretical role as S which allows us to read the ontological innocence of S* into S. Basically we're taking the suggestion in your final paragraph but insisting that theoretical elimination just is regimentation, and then allowing the theorists to argue about the details of regimentation later.
Of course that depends on helping ourselves to an answer to the symmetry objection, which I gloss above by saying something about dispensability. The idea is roughly that any demonstration that the existential entailments of S are dispensable will mean that we were never *committed* to their existence in using S - because we could always fall back to S*. I don't see the appeal of symmetry here: it isn't as plausible to say that the availability of S as a fall-back from S* shows that S* is ontologically committing. Given some independent reasons for taking S to be true and taking its ontological commitments at face value, we might then be able to use the principle of charity to show that S* should be interpreted in the committing way, but that's much weaker than symmetry.
Hey Daniel,
That's interesting. One thing I'd like to be clear on is how the notion of regimentation is going to save the truth of "there are prime numbers" if not through synonymy or translation.
Is it, for example, that though the regimented version isn't synonymous with the unregimented version, the (horizontal) content of the regimented and unregimented versions coincide?
It sounded a little as if you wanted rather to keep the notion of regimentation sui generis. So the idea would be that "there are primes" is true iff the extension of "prime" is non-empty; and "primes" applies to all and only primes; and yet the truth of that sentence isn't committed to primes.
Does either of those options correspond to what you intended?
I wasn't convinced by the symmetry worries. Why can't they be defused by appeal to, say, robustness (rather than deflation) about, say, R-schemas and satisfactions-schemas? Consider
(1) There are three holes in this piece of cheese.
(2) This piece of cheese is thrice-perforated.
We can imagine two theorists who both insist that (1) and (2) are synonymous. But one of them says "and they are both true because there are these things -- holes -- that bear the 'in' relation to this other thing -- a piece of cheese.' The other one denies this -- he says both sentences are true, but neither should be understood as ultimately predicating some sort of relation between a piece of food and three further things. In other words, something like the following schema is non-trivial:
x1...xn is F iff there are things identical to x1...xn that stand in F to each other (or satisfy "F", or what have you)
When we "regiment" something, we put it into the form where we'd then be willing to accept a schema of this sort. ...?
Robbie, what I was trying to suggest was meant to be neutral between synonymy, translation and a sui generis concept of regimentation. But I guess you're worried that unless there's a sui generis concept to fall back on, my account is just saying that the synonymy and translation accounts have *something* in common, which we already knew.
But here's what I was getting at by mentioning the principle of charity. Suppose I recognise that S* is a theoretical counterpart of S, but I don't want to commit myself to either synonymy or translation - is there anything else I can say to explain why S should be counted as true? Well, it isn't as if the people who accept S do so because they think they have had direct experience of the objects which S is apparently committed to; rather, they accept S for roughly the same reasons as the ones for which I accept S*. So we get to apply the Lewis-style principle of charity which says you should count the beliefs of others as true unless you have reason to think that their evidence is misleading etc. Perhaps if we had reason to deny that S was synonymous with (or was a good translation of) S* that would prevent us from using charity; but in the position where we are neutral on those issues I think charity is ok.
Hey Jason,
I'm not myself terribly sympathetic to the symmetry worries---I *do* think this is the place where they arise, but also that they might be resisted. My concern is rather that I don't know what sort of relation among sentences "regimentation" is supposed to correspond to. Obviously your story about what it is should meet constraints like: not being susceptible to symmetry worries. But at this stage I'd be happy if the options were put on the table.
I suppose the puzzle I'd have about your example is what the semantic properties of "there are three holes in this piece of cheese" are supposed to be. Are the semantic properties of the whole determined compositionally from the semantic propeties of the parts? Does the embedded quantifier get a usual quantifier-like semantics? If not, I want to here more about the metaphysics of semantic properties that allows us to say the things we want to.
Here's one way of meeting this challenge head on, though it's got metaphysical costs. Be robust about reference etc, and let that compositionally determine truth-conditions for some sentences. In addition, buy into a metaphysically robust synonymy relation, relating sentences whose truth-value is compositionally determined to other sentences. Then for a sentence to be true is for it to be synonymy-related to some sentence which is compositionally determined to be true.
That seems a picture on which we can handle the example you mention, and we've clearly got the asymmetry. And it doesn't seem impossible to give a metaphysically account of the synonymy relation (I can see how to fit it in to a Lewis-style interpretationist metasemantics, for example). But did you envisage a more lightweight treatment of the specific case?
Another thing we might do is get revisionary about the syntax: say that actually "there are three holes..." and "... triply perforated" were tokens of the same syntactic type, despite appearances. Regimentation would be a syntactic process of making the surface syntactic form mirror the "real" syntactic form.
As I said at the beginning, the agenda I have in all of this is just to figure out what the regimentation relation is. Without a grip on that, I don't know when people propose paraphrases in metaphysics papers how to evaluate their claim. So if the upshot was that regimentation made good sense, so long as construed syntactically, or construed as appealing to a robust primitive synonymy relation, that'd be great for me---I'd then know what a fictionalist who "paraphrases" there are numbers to "according to arithmetic, there are numbers" is actually saying. And for me, that'd be an advance.
Hi Robbie,
I'm not sure how to read what you're looking for. Is it (a) what do metaphysicians think they're doing when they give paraphrases/regimentation/whatever? Or is it (b) how should we properly interpret them to give them a plausible view?
I suspect there's no uniform answer to (a): some think "paraphrase" is declaring the paraphrased sentence false and offering a replacement; some have something like the semantic view outlined above (robust reference, robust synonymy), some have something like the semantic view outlined above, and some just haven't thought about it but see that this is how ontology is done and so start doing it themselves.
If (b), then that will depend a lot on your favored metasemantics, I'd think. For instance, I imagine that if you're wedded to the Lewisian interpretivist account, the thing to do would have a robust reference relation and a robust synonymy relation, etc. (Of course, this isn't yet to work out the details of the story...)
You suggest (or seem to suggest) that this has some costs, and ask if I have something more "lightweight" in mind. I'm not quite sure I know what the costs are or what the "lightweight/heavyweight" distinction is tracking here. Is the "weight" that there's too much metaphysical load-lifting already embedded in the meta-semantical picture?
Relatedly, it might be that on some metasemantical pictures, there's just no rational reconstruction of the paraphrase activities. (I think Hirsch probably thinks something like this.) So I suspect you're going to have to pick a metasemantics *first*, and then try to figure out how to understand metaphysicians' paraphrase schemes...
Hi Robbie,
just a few small points.
(I'm assuming that the regimented version S* belongs to a formal language, whereas the original sentence S doesn't.)
1) On one way of reading Quine, he doesn't think that looking at the regimentation S* tells you very much about the commitments of S. The question what the commitments of S are is simply rejected as not admitting of a decent answer - natural language is too ill-behaved or what have you to allow us to give a decent answer. If you accept S and are unsure about what kind of ontology to accept, look at the regimentations which do the job, pick whichever you like best, believe in the things it commits you to.
2) I find your presentation of the symmetry objection slightly puzzling. If S and S* are synonymous, certainly whatever follows from S follows from S* et vice versa. In particular, if certain existential statements follow from S (S*) but not from S* (S), surely they don't have the same OCs.
Or do you mean derivability when you say 'following from'?
Part of the point of regimentation for someone who accepts the synonymy-constraint may be that it allows removing ambiguities, 'reveals logical form', etc. pp., thus enabling to judge what consequences S* (and therefore S) has. No symmetry puzzles here, 'cause prior to regimentation, we're unsure what the consequences of S are.
Best, Stephan
Daniel:
Ok, I see. That sounds a bit like the "robust synonymy" model I was chatting to Jason about above. I.e. some sentences get robust truth-conditions determined compositionally; others get truth-conditions determined by robust synonymy with sentences that have compositionally determined truth conditions. And some kind of charity-involving metasemantics gives us a naturalistic story both about the synonymy relations and the reference relations.
Jason:
My main practical interest is how to write about people who appeal to paraphrases without too much explanation (e.g. some fictionalists). So I'm interested in what they think, but also what they should or could say---what the best possible view in the vicinity is. I'm interested in whether the decent views hereabouts involve some pretty major metasemantic commitments. I'm personally ok with interpretationist metasemantics. In fact, my own favoured take on ontological commitment, which doesn't involve regimentation, relies on interpretationism. It'd be dialectically useful for me if those who appeal to regimentation were committed to this too.
Overall, maybe the best way to express what I'm looking for is: what do you have to think about the nature of language for the regimentation methodology to make sense (and to make sense as a hermeutic project---i.e. not error-theoretic)?
Stephan:
Thanks for these. On (1)---S needn't be in natural language---it could be in some formal language. Predicate position quantification is one such issue. I do have some sympathy that the Quinean methodology here is to tell us to stop talking in 2nd order ways, and start talking set-theoretically.
There's an exegetical question, and a more general question about the range of coherent options available. On the first, I had thought that Quine was offering an answer to the question, asked from the perspective of one who's already adopted the advice to speak in set-theoretic ways: is the HO logician’s statement "(EX)aX" true, given the way the world is? Certainly Quine himself has the *equipment* to address this question---since he endorses, I guess, the translation/disquotation treatment of truth-attributions to sentences not expressible in one's own language. But obviously I should check this out.
I do think there's some pressure to talk about the OC's of pre-regimentation sentences, or at least give one’s opinion of whether they are true or not. Because it does seem important to know whether a philosophical theory implies that such-and-such piece of discourse is largely false, or meaningless, or whatever on the basis that it appears to talk about is philosophically dubious entities.
On the second issue you mention. I agree there are some cases---like regimentation to avoid ambiguity---where there's no sense in which the S has consequences that S* doesn't. But there seem to be cases where talking of "different consequences" captures something about the case, and we've got the theoretical burden of saying something about what that amounts to.
I’m thinking, for example, about a paraphrase from QML into counterpart theory, where "Possibly there are donkeys" is paraphrased into something involving existential quantification over worlds. Another would be the Lewis/Lewis example Jason uses of "there are three holes..." being paraphrased into perforation talk.
In the second case, apparently S itself is an existential statement. Its plausible that S follows from S, so it looks like an existential statement about holes follows from S. Does existential quantification over holes follow from S*? If it does, and entailing holes-quantification is a way of being existentially committed to holes (by the formulation of Quinean OC’s we’re considering, anyway), and the paraphrase doesn't get rid of the holes-commitments.
Of course there are things one can say. Suppose you went for the syntactic approach mentioned in a previous comment, so S really isn't syntactically existential (it's syntactic form is something that no linguist would ever attribute to it, matching S*). Then there's a good sense in which no existential claim follows from S* or S---S is merely “apparently” existential.
Suppose instead you go for the kind of synonymy approach mentioned above, where the content of S is determined by its being synonymy-related to S* which has compositionally determined content. Then one thing to say is that even though S is syntactically existentially, it isn't really an existential sentence, since its syntax is semantically irrelevant.
But I do think, if all we're told is that regimentation is normed by synonymy, then the prima facie symmetry puzzle is there. And then it takes further elaboration of one's view of how language works to say why the symmetry objection fails. That's how it looks from my point of view anyway---is there something I'm missing?
So here's just a small thought --- it won't answer your question, but it might suggest a few places to start looking. Suppose some working ontologist replies, "Well, I don't know a whole lot of metasemantics. But I do know that I said
(D) There is a dearth of food in the fridge
this morning, and I take it as desideradum on metasemantic-and-ontological theorizing that: (i) my utterance of D this morning was true; (ii) there are no such things as dearths, and (iii) an utterance of D is true (in a context) if and only if
(D*) There is no food in the fridge
is true in that context. And when I paraphrase a sentence S in terms of S*, you should take me as asserting a similar relation between S and S* as that which (we should all agree) holds between D and D*. If making sense of my claims about D/D* requires hefty metasemantic commitments, so be it --- I take it as a desiderata, before getting involved in fictionalism and the like, that we'll need these commitments just to make sense of D/D* pairs anyway."
I'm thinking a number of ontologists have thoughts along these lines (Peter van Inwagen springs quickly to mind, but perhaps some others as well) --- they don't have a particular view about what the S/S* relationship is, but they think we all grasp it just fine. And I think a lot of mathematical fictionalists (at the least) think that the D/D* relationship is precisely the sort of relationship that holds between, say, "there is an even prime number" and their complex mathematical "paraphrase" of it.
One potential asymmetry between common paraphrase strategies and D/D* is that the latter seems psychologically transparent to us --- if you just stress the word "dearth" right in "is there really a dearth in your fridge?", any competent speaker is going to say, "no, of course not, that's just a manner of speaking." It's not clear that you get the same psychological transparency with numerical talk, and you certainly don't get it with table-and-chair talk. So one place to press will be the degree to which the paraphrase scheme is supposed to be capturing something settled by our linguistic dispositions or other things transparent to us, and the extent to which it's settled "by the world" somehow.
I guess it's also an open question whether desideratum i--iii on D/D* can be satisfied by a decent theory of interpretation, but I think the example has enough intuitive force that philosophers of language ought to try to accommodate it. So I guess the real question is whether ontologists can use that basic picture to fuel everything they want to do with their paraphrases. But if they can, and if D/D* pairs can be accounted for by many metasemantic pictures (as I would have suspected in advance), then there may be no determinate answer to "what do you have to think about the nature of language for the regimentation methodology to make sense".
Quick clarificatory comment on the above. (Maybe this was obvious, but just in case it wasn't:) The idea behind the D/D* thing isn't that since we, as good ontologists, think it's crazy to think that there are dearths, a good metasemantics will find a way to make sense of the imagined speech. The idea is rather that competent English speakers are already disposed to endorse both of:
(D=) There is a dearth of food in the fridge if and only if there is no food in the fridge.
(D-) There are no dearths.
And since this is just a deliverance of ordinary people's language organs, good linguistic/phil. of language methodology should look for a way to make them both true.
I definitely agree that we should be interested in the OCs of natural language sentences, and for just the reasons I mention. My point was supposed to be merely that if someone starts out wondering about the OCs of S, then proposes regimentation S* and asks what S*'s OCs are, that person needn't expect the answer he gets to reveal the OCs of S - he may have thought it wise to change the question, perhaps because he found the original one to be intractable. (That kind of picture is stressed in Rayo's paper on OC, 13f.)
I also agree on the symmetry issue. My thought was not that all appeals to allegedly synonymous regimentations are unproblematic, but that regimentation by itself need not introduce symmetry puzzles.
FWIW, here's how I understand the symmetry worries.
Suppose that S* is the paraphrase of S, and suppose further that S* is intended to be deflationary.
The paraphraser wants S* to reveal the commitments of S (maybe its a more perspicuous representation of the truth-conditions, or something).
The Alston-style challenge is to give an explanation of why we think that S* deflates the ontological commitments of S, rather than thinking that S inflates the ontological commitments of S*.
The problem perhaps is clearest if we consider paraphrases into different languages. In the case of Sider-style naturalists, you get an answer to the question of why one language is privileged: it carves nature at the joints.
If you think of things in a full-blown Quinean way, however, you'll probably think that move is off limits. Sure, we might have *pragmatic* reason to prefer one language to another (maybe science goes easier) but that's all. The consequence is the infamous thesis of "ontological relativity". But that's badly named, as least as I understand it. It's not the thesis that what there is varies from some standpoint to another. Rather, its the thesis that there is no language for settling ontological committments that is the uniquely priviledged one.
So, I think that what you think about the symmetry worry will, to some extent, turn upon your metasemantic commitments.
Hi Jason,
I see your point. Here's one worry about the strategy. It seems to lean heavily on our being entitled to regard the paradigm cases (talk of dearths; or the average man, or whatever) being instances of a kind that could generalize to cover e.g. number-talk.
It seems to me a pretty bold conjecture to think we have a uniform phenomenon here. I'm not sure why the ontologists you mention would be entitled to it.
E.g. I remember that Jason Stanley somewhere talks about the syntax/semantics for "average man" and claims that it just doesn't function the way that one might naively expect it to. If there is independent reason to think that "the average man has 2.3 children" doesn't have the form "[the F]G" I guess this would misfire as an putative paradigm. For nothing like the specific story about "average" is going on with number-talk, I guess. And further, it's not at all clear how the usual paraphrase of average-man talk would fit in here. I don't think Stanley's story at all supports the idea that the usual paraphrase gives the underlying logical form. So when we look at the details, it would still be unclear what the significance of paraphrase is.
So: to think of paradigm examples as non-committal is one thing. To expect the story about how they're non-committal to involve the paraphrase relation in a significant way is quite some leap.
Of course, you didn't use the "average man" case. But it's a reasonably common thought that there's something strange about other, "dearth"-style cases.
From recollection, one of the points made about "dearth" style cases is that it isn't obvious that in embedded contexts they behave as you'd expect them too if one were to take the syntax and semantics at face value (I'm being woolly here because I can't remember the discussion---I'm thinking in particular of Crispin Wright's stuff about "reidentification of dearths". But the general thought I'm having is that it's far from clear that e.g. complex demonstratives involving dearths really make sense: "that dearth of food in the fridge". But if "dearth" just behaved in absolutely standard ways, why wouldn't this make sense? "that number I was thinking of" seems to make perfect sense, so this does seem like a disanalogy).
I don't think this is knock-down, of course, and the case of dearths is particularly woolly. But I do think it's worth highlighting that (a) there's an assumption in the methodology you sketch that the story about why "number-talk" is non-committal will turn out to be similar to the story about why "dearth-talk" (and the like) is non-committal; and (b) this story will involve the paraphrase-relationship in some interesting way.
I don't really see what the grounds are for endorsing either (a) or (b). In the case of "average man" I guess if Stanley is right the analogues of both are false. In the case of dearth talk, I'm inclined to be agnostic.
Of course, you might accept all this, and still think that it's the best description of what's going on in the literature. I'm inclined to think that it'd be much *better* to get committal here.
(By the way, I'm still not seeing how any old metasemantic story will ground synonymy relations that aren't reducible to sameness-of-compositionally-determined-truth-conditions. It seemed to me that the constitutive role of charity in interpretationist treatments was very important in allowing for this. On the other hand, I'm never terribly sure how causal or teleosemantic stories are going to generalize beyond the few paradigm cases of names and predicates for medium-sized dry goods, so maybe the complete story---whatever that is---will allow for them.)
Hey Robbie,
So, I was thinking the friend of dearths could do two things with the little example: first, use it as a paradigm for what's going on with paraphrases, and second, use it to argue that they don't need to take on any objectionable metasemantic commitments to make sense of what they're doing.
On the second thing: I wasn't thinking that it meant that any old metasemantic story will ground "synonymy relations that aren't reducible to sameness of truth conditions" (or whatever). I was thinking that the intuitive plausibility of the dearth case instead would let the ontologist argue: if a metasemantic story can't do this, then we ought to reject it as not fitting the data.
On the first thing: I take your point, simply picking a paradigm and saying "it's like that" leaves a lot to be desired. For one thing, it leaves the ontologist open to the charges that the semantic machinery in play in the paradigm isn't/can't be like the semantic machinery in play in the proposed paraphrase strategy.
For instance, when I used the "dearth" case, I had in the back of my mind the compositional nihilist who (like van Inwagen) wants to use paraphrases on ordinary medium-sized-dry-goods talk. One feature of "dearth" talk is that it doesn't behave inferentially the way ordinary quantificational talk does; the nihilist wants (at least some) apparently "ordinary" inferences to turn out invalid, too (for instance, statue/lump inferences involving Leibniz' law). And this seems to match up nicely with some of what Stephan was saying: the paraphrases wear their inferential forms on their faces (as it were), whereas the unparaphrased sentences look as though they should participate in inferences, given their (surface?) syntax that they in fact don't.
But (as you point out), one of the key features in the case of numbers is that we want to preserve *all* the inferential relations. So the "dearth" paradigm doesn't look so hot there. So, as I'm reading this, it's an argument that, *if* you say that your paraphrases are modeled on "dearth", *then* there is a good argument that there can't be paraphrases of number talk of the sort looked for. Am I tracking this right?
Just a couple of questions at this point about how we're thinking about regimentation and paraphrase:
(1) Does this have to be a sentence-to-sentence relation, or can giving (say) a semantics (the intended one, we allege) for S in a metalanguage that doesn't quantify over K's count as a "regimentation" of S that shows that it doesn't "really" commit us to Ks? For instance, if I show how to give, say, a semantics for quantification over times (e.g., "Joe was hungry at t") in a metalanguage using only Priorian tense operators, have I then "paraphrased away" apparent references to times?
(2) Does "regimentation" have to be a uniform phenomenon? I'm imagining a philosopher who started with the "dearth" case, read Stanley on "the average man", and then says, "Well, this just shows me that there are lots of ways for a sentence's surface structure to be misleading; some are syntactic, some are semantic, etc. So when I give a paraphrase S* of S, I allege only that (a) S's surface structure is somehow misleading, (b) S*'s surface structure is not misleading; (c) S and S* have the same truth conditions, and (d) the misleadingness of S is similar to either "dearth" misleadingness, or "average man" misleadingness, or...
Granted: doing this still opens the ontologist up to certain styles of arguments, of the form "every natural language instance of misleadingness has either property A, or B, or C... But the target sentences don't have A, or B, or C... so your paraphrase can't be right." But it seems to me that this is just evidence that metaphysics is hard -- not that there's something wrongheaded about the general methodological strategies...
(By the way: on the assumptions (a) and (b) you point out: when it comes to (b), I thought that would just follow from (a), because I thought that the methodology was stipulating was that what it is for S* to be a paraphrase of S just was for S* and S to bear the same sort of relation to each other that D* and D do. So I'm not seeing these as separate assumptions; but maybe there's something I'm missing here?)
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