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It is not the case that If mathematics were a separate calculus, it could not play its explanatory role in scientific theories expressed in natural language.
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Reasons For
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Reason for
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1.
Physics successfully explains natural language observations using mathematics precisely because math is formal and independent.
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2.
Translation between mathematical formalism and natural language occurs routinely; separation doesn't prevent explanation.
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3.
A calculus needn't share language substrate to explain phenomena—only produce predictions matching natural language observations.
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Reasons Against
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Reason against
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1.
Scientific explanation requires bridging abstract mathematical structures to empirical phenomena described in natural language.
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2.
A separate calculus would lack the shared conceptual vocabulary needed to connect formal models to observable world descriptions.
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3.
Mathematics' explanatory power depends on its integration with language-based scientific discourse, not isolation from it.
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