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It is not the case that Tense operators are better analyzed as quantifiers over times rather than as shifters of a time index in circumstances of evaluation.
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Reasons For
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Reason for
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1.
Indexical shift theories better explain how 'now' functions differently in reports of past belief without adding ontological commitment to times.
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2.
Quantifying over times requires metaphysically substantive temporal objects; indexing merely shifts evaluation parameters without ontological burden.
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3.
Natural language tense markers (morphology, auxiliaries) function more like indexical anchors than explicit quantificational operators.
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Reasons Against
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Reason against
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1.
Quantifier analysis unifies tense with other domains (modality, plurality) under standard first-order logical apparatus.
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2.
Index-shifting cannot easily explain complex tense interactions like 'will have been,' which quantifiers over times handle naturally.
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3.
Quantifier semantics preserves compositionality: tense operators combine with predicates via standard logical rules without special machinery.
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