Deflating Existential Consequence, Chapter 3

Deflating Existential Consequence, Chapter 3 - 3 Criteria...

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3 Criteria for the Ontological Commitments of Discourse The classical version of the Quine-Putnam indispensability thesis involves two steps. The first step, which is the one opponents of the thesis have universally attacked, is to claim that indispensable application of mathe- matical doctrine requires our taking the mathematics so applied to be true. As I showed in chapters 1 and 2, it's hopeless to try to undermine the thesis by denying this claim. The indispensability thesis, however, is that the indispensability of applied mathematical doctrine commits us to the existence of mathemati- cal entities, and so we still need a path from the taking true of mathemati- cal doctrine to a commitment to entities. This requires a method for identifying what entities we are committed to by espousing a doctrine- the application, as it's commonly put, of a criterion for what a discourse commits us to. The criterion of choice (almost universally) is Quine's (1948). Here's the plot for chapter 3: I explore the reasons that Quine, and others, have given for his criterion, with a contrasting view implicitly in mind, that ontological commitment is to be carried not by the quantifiers but by an existence predicate instead. I will, in the process, go through a very long analysis of Quine's triviality thesis-this is because of the wide number of options that are possible defenses of it. I end this chapter on an indeterminate note: There is no good argument for Quine's criterion for what a discourse commits us to, at least when one restricts oneself to considerations about discourse. Chapter 4, therefore, naturally turns to other ways of determining a suitable criterion for what a discourse com- 49
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50 Truth and Ontology mits us to via the m ore metaph ysical-looking route ofa criterion for what exists. Let's begin. The version of Quine's criterion I like is this: First, any bod y of doctrine D mu st be regimented i nto an i nt erpreted first-order language tr: That done, we take commitment to be recognized by impli- cations of the f orm (3x)Sx, where Sx is any formula with variable x free. That is, if (3x)Sx is deducible from D' , th en D' commits its believers to Ss. As Qu ine' s (194 8) discussion makes clear, this criterion is supposed to apply to dis cour ses regardless of whether we take them as true. To the extent, therefore, that interpretation or tr anslati on of a discourse requir es agreement , this criterion is designed to apply even to discourses that we don't unde rstan d-p rovided, of cour se, th at we take them to be couched in first -order languages. A syntactic criterion suits this demand perfectly.' Very oddly, philos opher s often retain Q uine' s criterion while qu ite openly aban do ni ng the restriction to first- ord er theories. I worry ab out the cogency of th is (as doe s Quine ) because th e criterion, when restricted to first- order theories, really does off er a means of comparison between the ories. When, however, one language has m od al resources, for example, and an other doesn 't , it' s unclear why Qu
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