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It is not the case that A necessary condition claim about chaos cannot be grounded in a distinction that dissolves under mathematically equivalent redescription.
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Reasons For
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Reason for
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1.
Mathematical equivalence concerns abstract structure, not physical implementation; different formulations can correspond to distinct causal mechanisms.
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2.
Necessary conditions can be formulated relative to conceptual frameworks without being invalidated when frameworks prove mathematically equivalent.
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3.
A distinction dissolving under redescription may still track real differences in how systems behave or how we can intervene on them practically.
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Reasons Against
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Reason against
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1.
Mathematical equivalence preserves all structural properties; distinctions that vanish under such redescription lack intrinsic physical basis.
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2.
Necessary conditions must pick out objective features of reality, not merely linguistic or representational artifacts of our chosen formalism.
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3.
If two descriptions are mathematically equivalent, they encode identical information; grounding claims in one but not the other is arbitrary.
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