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    If the set of possible magnitudes has no upper bound or i... — Carmelics
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    Challenges→There is a thing x and a magnitude m such that x exists in the understanding, and x exists in reality, and m is the magnitude of x, and it is not possible that there is a thing y and a magnitude n such that n is the magnitude of y and n > m.

    If the set of possible magnitudes has no upper bound or if maximal values for distinct properties conflict, then no x satisfying the magnitude condition can be well-defined.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Well-definedness requires identity conditions; unbounded magnitudes prevent establishing when x reaches completion or uniqueness.
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    • 2.Conflicting maximal values create logical contradiction: x cannot simultaneously satisfy incompatible property requirements.
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    • 3.Mathematical objects with undefined bounds (like open intervals) lack the determinate identity needed for singular reference.
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    Reasons Against

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    Reason against
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    • 1.Well-definedness concerns reference and consistency, not achieved magnitudes; unbounded limits can still define x precisely via properties.
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    • 2.Conflicting maxima may be resolvable through weighting, context-dependence, or treating x as genuinely indeterminate without loss of definition.
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    • 3.Mathematical functions with unbounded ranges (e.g., f(x)=x) are well-defined; boundedness is insufficient for definedness itself.
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    Connections

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    Natural Theology1 linked

    Related

    Conflicting maxima may be resolvable through weighting, context-dependence, or t...Conflicting maximal values create logical contradiction: x cannot simultaneously...Mathematical functions with unbounded ranges (e.g., f(x)=x) are well-defined; bo...Mathematical objects with undefined bounds (like open intervals) lack the determ...
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    There is a thing x and a magnitude m such that x exists in the understanding, an...Well-definedness concerns reference and consistency, not achieved magnitudes; un...Well-definedness requires identity conditions; unbounded magnitudes prevent esta...

    Details

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