Quantifier Variance and the Collapse Theorems

1. Quantifier VarianceIn philosophy, we often find ourselves confronted with multiple inconsistent answers to some question, each of which can be embedded into an internally coherent body of theory, and such that there is no agreement about how any new observations we could make would bear on the issue. A certain thought experiment can be instructive in such situations. For each of the sentences cp,, . . . , cp" expressing the rival answers to our question Q, imagine isolated communities C,, . . . , C", speaking languages syntactically like ours, and like us in other respects, except that the members of C, treat cp, as if it were obviously and unproblematically true, and treat the transitions licensed by the internally coherent theory containing cp, as if they were obviously and unproblematically truth-preserving. The members of C, thus behave rather like real-world proponents of cp, , except that (being isolated) they do not argue or agonise, and their dispositions with respect to cp, are stable, rather than varying between "theoretical" and "everyday" environments like the dispositions of certain philosophers. Now ask the following interpretative question: does each cp, express a truth in the language of C,? Call the affirmative answer to this question conciliationism about Q.1This question is worth thinking about, even for those who do not care about puzzles in radical interpretation for their own sake. For there are ways in which the answers might lead towards interesting conclusions about the significance of the real-life debate about Q, or about the right methodology for answering Q, or about the nature of the properties Q is about, or about the right way to characterise the underlying issue in the debate about Q. For example, if conciliationism about Q is true, there are arguments to be made that the appearance of disagreement about Q in the actual world is misleading, or that there is no fact of the matter about Q, or that arguments from ordinary language should be given great weight in answering Q. And if conciliationism about Q is false, there are arguments to be made that we should be more open to revising our pretheoretical beliefs about Q, or that we could never know the answer to Q.2Conciliationism has been widely discussed of late for questions about the ontology of material objects, including, Under what circumstances do some material objects compose something? and Under what circumstances does a material object have a shorter-lived part that coincides with it whenever it exists? Eli Hirsch is the most prominent defender of conciliationism about these questions. Hirsch uses conciliationism to motivate the views (a) that the right methodology for answering these questions is roughly that of ordinary language philosophy, and (b) that the debates as they are normally approached are misguided and lacking in "substance" (Hirsch 2011, xiii). However, the inference from conciliationism to (a) and (b) is controversial. Dorr (2005) endorses conciliationism for questions about composition while rejecting Hirsch's methodological morals, and Sider (2009, 2013) is also open to such a view.There is a widespread consensus that if conciliationism about these ontological questions is true, then the languages of the relevant communities Ct, . . . , C" assign different meanings to quantifier-words like 'something', 'every', and 'most'. One argument for this claim (see Sider 2000, §3.2) turns on the premise that the languages assign different modal profiles to sentences built up entirely from quantifiers, 'and', 'not', *=', and 'concrete' (such as the first-order translations of 'There are n concrete things') together with the premise that the languages agree in the meanings of 'and', 'not', *=', and 'concrete'.3 Another argument (Dorr 2005, §2) turns on the idea that we can provide a more economical explanation of the posited differences in the meanings of sentences by attributing them to differences in the meanings of quantifiers than by attributing them to differences in the meanings of predicates. …