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Life on the Range: Quine’s Thesis and Semantic Indeterminacy

  • G. Aldo AntonelliEmail author
Part of the Synthese Library book series (SYLI, volume 373)

Abstract

This paper explores the ramifications of Quine’s Thesis that ontological commitment is determined on the basis of the range of quantified variables in light of a non-standard semantics for the first-order quantifiers analogous to Henkin’s general interpretations for second-order logic. On such a general semantics, the specification of the meaning of the first-order quantifiers requires, besides the selection of a first-order domain D of objects (as is customary), also the further identification of a second-order domain of subsets of D. In the absence of such a further identification, the semantics of “there is” and “for all” is radically indeterminate. Moreover, the general semantics might well be “transparent” in that no semantic facts might be available to discriminate the general from the standard interpretation. The general semantics is rich in consequences for Quine’s thesis: the paper shows how the two halves of the thesis, i.e., the symmetric claims that being the value of a bound variable is necessary or, respectively, sufficient for ontological commitment fail, albeit in interestingly different ways. The result undermines the prospects of philosophical ontology construed as the quintessentially armchair project of extracting ontological commitments from the semantic analysis of quantified statements.

Keywords

Ontological Commitment General Interpretation Binary Quantifier Existential Generalization Definable Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I am grateful to Sean Ebels-Duggan, Robbie Hirsch, Elaine Landry, and Adam Sennet for helpful comments.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Philosophy DepartmentUC DavisDavisUSA

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