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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that A position number system with zero as a placeholder allows an infinite set of natural numbers to be represented using only a finite set of symbols

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Representing a number and instantiating it are distinct: finite symbols can denote infinite numbers only if an infinite medium (time, space, or computation) is available for arbitrarily long strings.
      ?

      Think about whether this reason is strong or weak

    • 2.Wittgenstein's rule-following considerations show that no finite set of symbols autonomously determines its own extension to infinitely many cases without an interpreting practice.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The claim conflates potential infinity (always being able to add another digit) with actual representability, a distinction Aristotle and later Cantor took to be philosophically significant.
      ?

      Think about whether this reason is strong or weak

    • 2.A number requiring n digits demands a physical token of length n, so unbounded natural numbers are not representable by finite means but only by a finite scheme applied indefinitely.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Zero functions as a placeholder that encodes positional magnitude
      ?

      Think about whether this reason is strong or weak

    • 2.Any finite set of symbols combined with zero can represent arbitrarily large numbers by varying digit positions
      ?

      Think about whether this reason is strong or weak

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