Quinean Ontological Commitment Derailed
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What should we believe exists? The Quinean response is straightforward: We should believe in all and only those objects over which we must quantify in our best scientific theories. Let us call this view Ontological Commitment = Quantifier Commitment, or OC=QC. The author draws upon resources from Jody Azzouni and Stephen Yablo, who reject this criterion to disrupt a central argument for platonism in mathematics. The project has two parts. First, the negative project is to argue that OC=QC is misguided because we ought not read our ontological commitments off of our quantifier commitments. Second, the positive project is to suggest an alternative criterion to OC=QC that allows us to accept the idea that statements that quantify over mathematical objects that would be abstract if they existed are indispensable to our best scientific theories, but nevertheless reject the existence of numbers.
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