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It is not the case that A formal system that requires quantification over a domain carries commitment to that domain's existence, regardless of the theorist's instrumental intentions.
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Reasons For
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Reason for
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1.
Quantification can be formalized over empty domains or fictional domains without metaphysical commitment to them.
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2.
Theorists can adopt instrumental stances that treat quantification as useful notation without endorsing what appears quantified.
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3.
Distinguishing between formal system requirements and philosopher's ontological commitments preserves interpretive freedom.
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Reasons Against
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Reason against
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1.
Quantification in formal systems uses existential claims with logical structure that presupposes domain objects as referents.
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2.
The syntax and semantics of quantified formulas require interpretation models where variables range over actual entities.
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3.
Instrumental use doesn't eliminate ontological commitment—merely employing a tool that assumes X still commits one to X.
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