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    Carmelics

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    Made withinDC&Austin
    Statements
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    Home/Original/inverse
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    Inverse View

    It is not the case that The necessity of '2+2=4' depends on prior definitional choices, and definitions are conventional, not logically necessary.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.All number systems represent the same underlying cardinality relations; renaming symbols doesn't make '2+2=4' contingent—only its expression.
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    • 2.Definitions are conventional, but once adopted, logical entailment is *not*—'2+2=4' follows necessarily from the definition of those terms.
      ?

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    • 3.Necessity means 'true in all possible worlds given those definitions'; this is logically necessary even if definitions themselves are chosen.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Different number systems (binary, base-12) encode arithmetic differently, suggesting the form of truth depends on representational conventions.
      ?

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    • 2.Before defining '+' and '=' and '2', no mathematical truth exists to discover—definitions create the conceptual framework enabling the statement.
      ?

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    • 3.Societies have used non-decimal systems successfully, showing '2+2=4' is not universally necessary but contingent on decimal convention.
      ?

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