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It is not the case that A paraphrase sentence (N) that preserves truth conditions must quantify over the same entities as (P), preserving the original commitment.
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Reasons For
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Reason for
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1.
Many true paraphrases succeed by shifting quantificational structure while keeping truth conditions materially equivalent.
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2.
Some entities (abstract objects, fictional characters) can be paraphrased away without changing truth conditions meaningfully.
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3.
Truth conditions can be preserved through ontological commitment shifts if the same facts remain true in possible worlds.
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Reasons Against
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Reason against
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1.
Truth conditions are determined by what entities a sentence commits us to believing exist and have properties.
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2.
Paraphrases that introduce or eliminate quantificational commitments change what must be true for the sentence to hold.
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3.
Preservation of truth conditions is the minimal criterion for genuine paraphrase rather than substantive reinterpretation.
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