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It is not the case that Conflating nomological structure with physical substance commits a category error that reifies mathematical description into ontology.
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Reasons For
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Reason for
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1.
The distinction between 'laws' and 'substance' may itself be conceptual artifact rather than metaphysical fact. Modern physics suggests they're inseparably intertwined.
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2.
If physical substance has only the properties describable by laws, claiming substance exists apart from nomological structure is epistemically inaccessible and metaphysically idle.
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3.
Mathematical structures successfully predict and explain physical phenomena because they capture real structural features. This explanatory success suggests mathematical description reaches ontology.
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Reasons Against
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Reason against
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1.
Laws of nature describe regularities; substance is what instantiates them. Conflating these distinct ontological categories mistakes the map for territory.
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2.
Mathematics is a tool for representing physical structure, not identical to it. Treating equations as fundamental entities smuggles idealism into physicalism.
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3.
Category errors occur when properties of one logical type are attributed to another. Assigning mathematical properties (abstractness) to physical entities commits this error.
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