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    Made withinDC&Austin
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    Perspectives
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    Topics
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    Metric geometry is neither true nor false. — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Metric geometry is neither true nor false.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.We cannot verify which metric geometry is true.
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    • 2.We cannot empirically determine the metric geometry of space in principle.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Quine-Duhem holism entails that geometric hypotheses face empirical tribunal collectively with physical laws, not in isolation.
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    • 2.If geometry and physics form an indivisible empirical package, then joint geometric-physical claims are truth-apt and can be falsified.
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    • 3.Therefore the conventionalist severing of geometry from empirical truth-aptness misrepresents how scientific theories actually confront evidence.
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    Reason against 2 of 2
    ?
    • 1.Einstein's general relativity empirically distinguishes spacetime geometries via predictions about light deflection and gravitational redshift.
      ?

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    • 2.If rival metric geometries yield observationally distinct predictions when embedded in a physical theory, then at least one geometry is empirically false.
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    • 3.Poincaré's underdetermination argument assumes a fixed Newtonian physics backdrop, but that assumption was itself empirically overturned by 1915.
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    Topics

    Modality & PossibilityTruth & Knowledge

    Notable Defenders

    Euclidancient
    Alberto CoffacontemporaryCoffa 1986
    Alfred TarskicontemporaryTarski's model-theoretic conception of logical consequence
    Bertrand Russellcontemporary
    Bertrand Russellcontemporarydeveloper of ramified type theory
    Elie Zaharcontemporary
    Ernest NagelcontemporaryNagel 1939, 1979
    Ernst Zermelocontemporary
    Georg KreiselcontemporaryKreisel 1960
    Gerhard HeinzmanncontemporaryHeinzmann 1995
    Giuseppe Peanocontemporary
    Hans ReichenbachcontemporaryGlymour and Eberhardt 2012
    Henri Poincarécontemporaryproponent of the predicativity principle
    Jaakko HintikkacontemporaryHintikka 2012
    Janet FolinacontemporaryFolina 2020: 293
    Janet FolinacontemporaryFolina 1992
    Janet FolinacontemporaryFolina 2020
    Janet FolinacontemporaryFolina 2020
    Jeremy GraycontemporaryGray 2008
    Joan RichardscontemporaryRichards 1994
    John WorrallcontemporaryWorrall 1989
    Katherine DunlopcontemporaryDunlop 2016, 306
    Louis RougiercontemporaryRougier 1920
    Michael DetlefsencontemporaryDetlefsen 1992: 349, 360, 366; 1993: 272
    Michael Friedmancontemporary
    Moritz Schlickcontemporary
    Moritz SchlickcontemporarySchlick 1925, 91–92
    Nelson GoodmancontemporaryGoodman 1969
    Paul LorenzencontemporaryLorenzen 1955, 1965
    Rudolf Carnapcontemporary
    Rudolf CarnapcontemporaryAufbau
    Solomon FefermancontemporaryFeferman 1964
    W. V. O. QuinecontemporaryQuine 1986: 401
    W.V.O. Quinecontemporary
    Warren GoldfarbcontemporaryGoldfarb 1988
    Øystein LinnebocontemporaryLinnebo 2011
    Augustin-Louis Cauchymodernco-author of a proof of the fundamental theorem of algebra
    Bernhard Riemannmodern
    Bertrand Russellmodern
    David Hilbertmodern
    David Hilbertmodern
    David HilbertmodernFoundations of Geometry (1899)
    Emil MeuniermodernMeunier 1919
    Emile Boutrouxmodern
    Ernst CassirermodernCassirer 1910
    Ernst Machmodernprinciple of the economy of thought
    Ernst Machmodern
    Ernst Machmodern
    Ferdinand von LindemannmodernLindemann 1904
    Georg CantormodernCantor 1991: 188
    Gottlob Fregemodern
    Gösta Mittag-Lefflermodern
    Henri PoincarémodernPoincaré 1898
    Henri PoincarémodernPoincaré 1902: 158; 2017: 104
    Henri PoincarémodernPoincaré 1902; 1905b; 2017; 1913b
    Henri PoincarémodernPoincaré 1908: 23–30; 1913b: 371–375
    Henri Poincarémodern
    Henri PoincarémodernPoincaré 1902: 26; 2017: 3–30
    Henri Poincarémodern
    Henri Poincarémodernfrom 1905
    Henri PoincarémodernScience and Hypothesis
    Henri Poincarémodern
    Henri PoincarémodernPoincaré 1908: 212–213; 1913b: 484
    Henri PoincarémodernPoincaré 1882: 1167
    Henri PoincarémodernPoincaré's discussion of the sciences in sequence (arithmetic, magnitude, geometry, classical mechanics, physics)
    Henri PoincarémodernPoincaré 1905b: 94; 1913b: 272
    Henri Poincarémodern
    Henri Poincarémodern
    Henri Poincarémodern
    Henri Poincarémodernoriginator of the vicious circle principle
    Henri PoincarémodernPoincaré 1902: 152; 2017: 100
    Henri PoincarémodernPoincaré 1898: 41
    Henri PoincarémodernPoincaré 1902:107; 2017:56,68; 1898:42-43
    Henri Poincarémodern
    Henri Poincarémodern
    Henri Poincarémodern
    Henri Poincarémodern
    Henri PoincarémodernPoincaré 1899: 274; Poincaré 1905b: 174
    Henri PoincarémodernSchlick 1925, 91–92
    Henri PoincarémodernPoincaré 1905b: 165–166; 1913b: 335
    Henri Poincarémodern
    Henri PoincarémodernPoincaré 1902: 166; 2017: 109
    Henri Poincarémodern
    Henri Poincarémodern
    Henri PoincarémodernPoincaré 1905b: 104; 1913b: 280; 1921: 137
    Henri PoincarémodernPoincaré 1905b: 23; 1913b: 209
    Hermann WeylmodernWeyl 1918
    Hermann von Helmholtzmodernreferenced in Poincaré 1905b: 174
    Hermann von Helmholtzmodern
    Hugo DinglermodernDingler 1931
    Immanuel Kantmodern
    Immanuel Kantmodern
    Immanuel Kantmodern
    James Maxwellmodern
    Jean-Robert Argandmodernco-author of a proof of the fundamental theorem of algebra
    Jules Lacheliermodern
    Ludwig WittgensteinmodernRodych 2011
    Luitzen Egbertus Jan BrouwermodernBrouwer 1912: 124–125; Brouwer 1907: 176
    Moritz Schlickmodern
    Nikolai Lobachevskiimodern
    Pierre Duhemmodern
    Poincarémodern
    Sophus Liemodernreferenced via Lie's classification
    William Jamesmodern

    Connections

    2 topics

    Skepticism2 linkedPerception1 linked

    Related

    Einstein's general relativity empirically distinguishes spacetime geometries via...If geometry and physics form an indivisible empirical package, then joint geomet...

    Source

    AI-extracted1/3 agreementValid
    SEP: poincare
    View source passageHide passage
    The existence of relatively consistent non-Euclidean geometries leads him to the view that geometric propositions cannot be determined by a priori intuitions and that it is necessary to study “the structural relations between Euclidean and non-Euclidean geometry” (Nye 1979: 111). Poincaré established a famous dictionary translating concepts and propositions of Lobachevskii’s geometry into Euclidean geometry in order to create a model to show the relative consistency of Lobachevskii’s geometry (P
    Extraction notes

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

    Details

    If rival metric geometries yield observationally distinct predictions when embed...
    Poincaré's underdetermination argument assumes a fixed Newtonian physics backdro...
    +4 moreShow less
    Quine-Duhem holism entails that geometric hypotheses face empirical tribunal col...Therefore the conventionalist severing of geometry from empirical truth-aptness ...We cannot empirically determine the metric geometry of space in principle.We cannot verify which metric geometry is true.
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit