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    A genuine ordinal number must occupy the same ontological... — Carmelics
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    Challenges→The order type Omega of the natural order on ordinal numbers is itself one of the ordinal numbers

    A genuine ordinal number must occupy the same ontological category as the ordinals it orders, which NFU's stratification systematically prevents.

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    Reasons For

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    Reason for
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    • 1.Ordering relations typically hold between entities of the same type (e.g., numbers order numbers, not apples).
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    • 2.NFU's stratification creates type hierarchies where ordinals inhabit different levels than their elements, violating type uniformity.
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    • 3.A number that orders itself must share the same categorical status as itself—stratification prevents this reflexive identity.
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    Reasons Against

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    Reason against
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    • 1.Ordinals needn't be in the same ontological category as ordered items—a ruler (different category) orders lengths successfully.
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    • 2.Stratification is a feature preventing paradox, not a flaw. Type distinctions allow NFU to be consistent where naive set theory fails.
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    • 3.The claim conflates 'genuine ordinal' with 'metaphysically simple ordinal'—NFU's ordinals function adequately despite stratification.
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    Related

    A number that orders itself must share the same categorical status as itself—str...NFU's stratification creates type hierarchies where ordinals inhabit different l...Ordering relations typically hold between entities of the same type (e.g., numbe...Ordinals needn't be in the same ontological category as ordered items—a ruler (d...
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    Stratification is a feature preventing paradox, not a flaw. Type distinctions al...The claim conflates 'genuine ordinal' with 'metaphysically simple ordinal'—NFU's...The order type Omega of the natural order on ordinal numbers is itself one of th...

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