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    Carmelics

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    Made withinDC&Austin
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    Inverse View

    It is not the case that If logical validity requires variable sharing, then classical logic's most central structural rules—including ex falso quodlibet—are rendered invalid, contradicting centuries of logical practice endorsed by Frege, Russell, and Hilbert.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Variable sharing is a feature of some logical systems, not a universal requirement; multiple valid logical frameworks coexist without mutual invalidation.
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    • 2.Classical logic's structural rules can be justified through semantic models and proof-theoretic properties independent of variable-sharing constraints.
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    • 3.Rejecting classical logic's central rules requires demonstrating practical failures, not merely philosophical objections to their intuitive appeal.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Variable sharing principles reflect genuine logical principles about relevance that classical logic obscures but cannot eliminate.
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    • 2.Endorsement by historical figures doesn't establish truth; classical logic's acceptance may reflect unexamined assumptions rather than validity.
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    • 3.Ex falso quodlibet's counterintuitiveness (anything follows from contradiction) suggests it lacks genuine logical warrant independent of formal convention.
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