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It is not the case that Skepticism about humans' ability to reach absolutely primitive concepts is not a fatal barrier to constructing a universal characteristic.
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Reasons For
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Reason for 1 of 2
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1.
Concepts that are primitive relative to human cognition are culturally and historically variable, undermining the universality required for a characteristic.
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2.
Leibniz's project requires cross-cultural and cross-temporal stability of primitives, which cognitively relative primitives cannot guarantee.
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3.
Without guaranteed stability, the characteristic becomes a parochial notation system rather than a universal science of concepts.
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Reason for 2 of 2
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1.
Frege and Russell's logicist program demonstrated that apparent conceptual primitives are often reducible to deeper logical structures, revealing hidden complexity.
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2.
If human cognitive limits prevent us from detecting further reducibility, we cannot distinguish genuine relative primitives from merely unanalyzed concepts.
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3.
A characteristic built on undetected non-primitives inherits systematic ambiguities that invalidate the inferential machinery the project depends upon.
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Reasons Against
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Reason against
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1.
Even if absolutely primitive concepts cannot be cataloged, concepts which cannot be further resolved by humans can serve as primitives relative to human cognition.
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2.
A characteristic can be constructed based on concepts that are primitive relative to us, even if not absolutely primitive.
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