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Inverse View
It is not the case that Visser and Lindström demonstrated that mutual interpretability strictly weaker than synonymy, so interpretability underdetermines theoretical identity.
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Reasons For
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Reason for
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1.
The notion of 'theoretical identity' is unclear—identity for what purpose? Pragmatically equivalent theories may suffice.
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2.
Synonymy itself is notoriously problematic; grounding identity in a stronger but equally disputed concept doesn't resolve underdetermination.
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3.
Mutual interpretability might be precisely what theoretical identity requires; calling for more may conflate identity with metaphysical sameness.
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Reasons Against
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Reason against
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1.
Mutual interpretability allows theories to translate all propositions bidirectionally, yet they may carve reality at different joints.
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2.
Two mutually interpretable theories can have distinct ontologies and inference rules, suggesting identity requires something stronger.
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3.
If interpretability alone determined identity, empirically equivalent but conceptually incompatible frameworks would be identical.
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