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    As Suppes and Winsberg have argued, mathematical models a... — Carmelics
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    Supports→Formal definitions of chaos may not be applicable to actual physical and biological target systems

    As Suppes and Winsberg have argued, mathematical models and their target systems inhabit distinct ontological domains, requiring explicit correspondence rules to bridge them.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Mathematical objects (infinities, perfect circles) have no physical instantiation, so models cannot directly represent physical systems without interpretation rules.
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    • 2.Successful applications of models across different domains (physics to biology) suggest models operate in an abstract space distinct from specific physical systems.
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    • 3.Without explicit correspondence rules, we cannot determine which mathematical features are physically significant versus merely computational conveniences.
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    Reasons Against

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    • 1.The distinction between 'mathematical domain' and 'physical domain' may be epistemological rather than ontological—a difference in how we know, not what exists.
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    • 2.Physical systems themselves may be partially mathematical in structure; if so, no bridging rules are needed, only accurate descriptions of shared properties.
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    • 3.Appeals to correspondence rules risk infinite regress: rules themselves are abstract entities requiring their own rules to connect to reality.
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    Related

    Appeals to correspondence rules risk infinite regress: rules themselves are abst...Formal definitions of chaos may not be applicable to actual physical and biologi...Mathematical objects (infinities, perfect circles) have no physical instantiatio...Physical systems themselves may be partially mathematical in structure; if so, n...
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    Successful applications of models across different domains (physics to biology) ...The distinction between 'mathematical domain' and 'physical domain' may be epist...Without explicit correspondence rules, we cannot determine which mathematical fe...

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