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    If the shared geometric features do not track the causall... — Carmelics
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    Challenges→Chaotic models can give us understanding of the behavior in corresponding actual-world systems through topological or geometric similarity, not trajectory isomorphism.

    If the shared geometric features do not track the causally relevant properties of the system, they cannot ground genuine understanding per Woodward's interventionist account.

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    Reasons For

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    • 1.Woodward's interventionism requires understanding how manipulating variables changes outcomes; geometric features divorced from causation cannot satisfy this.
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    • 2.Understanding involves grasping why systems behave as they do; purely structural descriptions without causal information leave the 'why' unanswered.
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    • 3.Two systems with identical geometry but different causal mechanisms would mislead us if we treated geometric features as explanatory without causal grounding.
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    Reasons Against

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    • 1.Geometric features often *are* causally relevant properties—a triangle's angles determine load distribution; separating them assumes a false dichotomy.
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    • 2.Understanding in mathematics and physics sometimes succeeds through structural relationships alone, without explicit causal language or interventionist manipulation.
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    • 3.Woodward's account may be too strict; understanding could be graded or pluralistic, allowing geometric grounding even if it's not interventionist-sufficient.
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    Related

    Chaotic models can give us understanding of the behavior in corresponding actual...Geometric features often *are* causally relevant properties—a triangle's angles ...Two systems with identical geometry but different causal mechanisms would mislea...Understanding in mathematics and physics sometimes succeeds through structural r...
    +3 moreShow less
    Understanding involves grasping why systems behave as they do; purely structural...Woodward's account may be too strict; understanding could be graded or pluralist...Woodward's interventionism requires understanding how manipulating variables cha...

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