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    The symmetry possessed by a geometric object F is describ... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    The symmetry possessed by a geometric object F is described exactly by the subgroup of spatial automorphisms that leave F invariant

    CausationModality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A geometric object F is a point set with a definite relational structure
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    • 2.Those automorphisms of space that leave F invariant constitute a group
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    • 3.That group captures precisely which transformations preserve all the relations constitutive of F
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Symmetry is an intrinsic structural property of F, not a relation between F and the ambient space of automorphisms.
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    • 2.Weyl's automorphism-group account makes symmetry extrinsically dependent on the choice of background space, which can vary without any change to F itself.
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    • 3.Hermann Weyl's own later work on the hole argument suggests that identifying geometric objects with their embedding space conflates intrinsic and extrinsic structure.
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    Reason against 2 of 2
    ?
    • 1.A geometric object can possess continuous or approximate symmetries that no discrete subgroup of spatial automorphisms captures exactly (Nozick's objection to structural definitions).
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    • 2.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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    Modality & PossibilityCausation

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    Philosophy of Language1 linked

    Related

    A geometric object F is a point set with a definite relational structureA geometric object can possess continuous or approximate symmetries that no disc...Hermann Weyl's own later work on the hole argument suggests that identifying geo...Symmetry is an intrinsic structural property of F, not a relation between F and ...
    +4 moreShow less
    That group captures precisely which transformations preserve all the relations c...The subgroup description presupposes a determinate point-set identity for F, but...Those automorphisms of space that leave F invariant constitute a groupWeyl's automorphism-group account makes symmetry extrinsically dependent on the ...

    Similar

    The full homogeneity or symmetry of space is described by its group of...77%Those automorphisms of space that leave F invariant constitute a group77%The group of automorphisms consists of the one-to-one mappings of the ...74%Congruence is defined entirely in terms of the transformations availab...74%

    Source

    AI-extracted1/3 agreementValid
    SEP: weyl
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    The amorphous four-dimensional differentiable manifold possesses a high degree of symmetry. Because of its homogeneity, all points are alike; there are no objective geometric properties that enable one to distinguish one point from another. This full homogeneity or symmetry of space must be described by its group of automorphisms, the one-to-one mappings of the point field onto itself which leave all relations of objective significance between points undisturbed. If a geometric object \(F\)
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit