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    The inference from 'separately warranted' to 'jointly con... — Carmelics
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    Challenges→If we have good reason to believe that p is true and good reason to believe that q is true, then we have good reason to believe that p and q are logically consistent, even without understanding how they could be mutually consistent.

    The inference from 'separately warranted' to 'jointly consistent' is precisely what Russell's paradox showed to be illegitimate in set theory.

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    Reasons For

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    Reason for
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    • 1.Russell's paradox shows that properties like 'self-membership' can be individually coherent yet collectively generate contradiction when combined.
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    • 2.Individual warrant for set axioms (comprehension principle) proved insufficient to guarantee the joint consistency of the overall system.
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    • 3.This demonstrates a general principle: separate justification of component premises provides no guarantee against collective inconsistency.
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    Reasons Against

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    • 1.Russell's paradox reveals a *domain-specific* failure in naive set theory, not a universal principle about inference from warranted to consistent premises.
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    • 2.Many mathematical systems (ZFC, Peano arithmetic) have separately justified axioms that remain jointly consistent, showing the inference can succeed.
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    • 3.The lesson may be that we need *better warrant criteria*, not that separate warrant is inherently insufficient for joint consistency.
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    If we have good reason to believe that p is true and good reason to believe that...Individual warrant for set axioms (comprehension principle) proved insufficient ...Many mathematical systems (ZFC, Peano arithmetic) have separately justified axio...Russell's paradox reveals a *domain-specific* failure in naive set theory, not a...
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    Russell's paradox shows that properties like 'self-membership' can be individual...The lesson may be that we need *better warrant criteria*, not that separate warr...This demonstrates a general principle: separate justification of component premi...

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