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    Armstrong's partial identity account cannot recover the f... — Carmelics
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    Challenges→Determinate similarity and comparability among lengths is explained by Armstrong's partial identity account.

    Armstrong's partial identity account cannot recover the full dense ordering of lengths without presupposing the real number structure it purports to explain.

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    1 reason for
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    Reasons For

    1 perspective
    Reason for
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    • 1.Partial identity only generates discrete similarity classes, not the continuum structure needed for dense ordering of all lengths.
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    • 2.Any attempt to derive real number properties from finite identity relations requires smuggling in limiting processes or cardinality assumptions.
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    • 3.Armstrong's account lacks resources to distinguish between rationally comparable and incommensurable lengths without prior metric structure.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Partial identity accounts need not derive reals from pure identity; they can posit primitive ordering relations independently defensible.
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    • 2.The charge of presupposition conflates requiring structure with presupposing real numbers specifically—intermediate frameworks exist.
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    • 3.Dense orderings are achievable through iterated divisibility and comparative relations without invoking full real number arithmetic.
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    Related

    Any attempt to derive real number properties from finite identity relations requ...Armstrong's account lacks resources to distinguish between rationally comparable...Dense orderings are achievable through iterated divisibility and comparative rel...Determinate similarity and comparability among lengths is explained by Armstrong...
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    Partial identity accounts need not derive reals from pure identity; they can pos...Partial identity only generates discrete similarity classes, not the continuum s...The charge of presupposition conflates requiring structure with presupposing rea...

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