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    The subgroup description presupposes a determinate point-... — Carmelics
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    Challenges→The symmetry possessed by a geometric object F is described exactly by the subgroup of spatial automorphisms that leave F invariant

    The subgroup description presupposes a determinate point-set identity for F, but objects individuated by their symmetries face a circularity: identity conditions presuppose the very group structure they are meant to explain.

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    Key Terms

    Group structure(as used in mathematics and philosophy of mathematics)
    A mathematical system with a set of objects and rules for how they combine or relate to each other.
    Point-set identity(as used in mathematics and metaphysics)
    The idea that something has a clear, fixed identity based on the collection of specific points or elements that make it up.
    Subgroup description(as used in mathematics and philosophy of mathematics)
    A way of defining a smaller collection of objects by listing out their shared characteristics or rules.
    Symmetries(as used in mathematics and philosophy of physics)
    Properties or transformations that leave something looking the same or unchanged—like how a square looks identical when rotated 90 degrees.
    circularity

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    (as used in logic and epistemology)
    A logical problem where an explanation depends on the very thing it's trying to explain, going in a circle rather than providing genuine support.
    identity conditions(Metaphysics of mental states)
    The criteria that determine what makes an entity the same entity across time or contexts, i.e., what individuates it.
    individuated(Chodorow's account of boys' psychological development)
    Feeling oneself to be separate or distinct from others, as a result of identifying with an absent parent

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    Causation1 linkedModality & Possibility1 linked

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    The symmetry possessed by a geometric object F is described exactly by the subgr...

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