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The Limits of Quine's Criterion for Ontological Commitment

Marcus Rossberg, University of St Andrews (16 Apr 2005)

Third SPPA Seminar Day, University of Stirling

Statements for Quine's criterion for ontological commitment can be found in many of his papers. A characteristic one is, ``entities of a given sort are assumed by a theory if and only if some of them must be counted among the values of the variables in order that the statements affirmed in the theory be true." (W.V. Quine [1953]. From a Logical Point of View. Cambridge, MA: Harvard UP, p. 103.)

Quine not only sees this as a tool to figure out the ontology a theory commits us to, but also draws the requirement from it that everything is to be formalised in standard first-order logic. It has been widely discussed and criticised that the paraphrase Quine prescribes is not as innocent as he wants us to believe. The first part of my paper diagnoses where this problem arises. A circularity in Quine's project is brought to light. The second half argues, independently of that, that the criterion simply does not work generally. Trying to apply it to just slightly more interesting theories than Quine usually considers as examples, it becomes clear that either commitments to sets or other higher-order entities must already arise in classical polyadic first-order theories -- a consequence that is contrary to the spirit of Quine's project, and unacceptable to Quine in general -- or that theories that clearly have interesting ontological implications come out as having no \emph{Quinean} ontological commitment at all.

Quine's criterion seems to work for monadic first-order theories only. It is no wonder then, the paper concludes, that it yields such counterintuitive conclusion for, e.g., higher-order theories. Quine famously claimed that the use of higher-order quantifiers commits to sets, irrespective of the intended subject matter of the theory. As a consequence of his criterion this cannot be argued for without admitting the same for polyadic first-order theories, too.

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