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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that If necessity were solely grounded in what subjects are, mathematical truths about physical objects would require no empirical supplementation, which Aristotle denies in Physics II.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Mathematical truths about physical objects (e.g., 'this sphere has volume') may be deducible from definitions without empirical input about specific matter.
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    • 2.The claim conflates two distinct questions: whether mathematics needs empirical grounding versus whether applying mathematics to nature requires observation.
      ?

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    • 3.Aristotle denies that necessity is *solely* internal to substance, but this doesn't establish that empirical supplementation is always required for mathematical claims.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Aristotle distinguishes form from matter; mathematical properties inhere in form alone, yet physical instantiation requires empirical knowledge of matter.
      ?

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    • 2.Knowing a triangle's angles sum to 180° tells us nothing about whether bronze or wood instantiates it—this requires sensory observation of particulars.
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    • 3.Physics II.1 emphasizes that natural objects unite form and matter; mathematical necessity governs only form, leaving material determination empirical.
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