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Inverse View
It is not the case that If no method can rule out nihilism, then no method can rule out non-nihilism either, making the asymmetric skeptical conclusion self-undermining.
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Reasons For
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Reason for
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1.
Burden of proof differs: Nihilism requires positive evidence for sweeping negation; non-nihilism only requires doubt of that negation. Asymmetry is justified.
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2.
Symmetry fallacy: Logical form doesn't determine evidential weight. Ruling out a positive claim differs from ruling out its negation due to content.
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3.
Default rationality: Accepting ordinary claims (non-nihilism) needs no method to refute alternatives; extraordinary claims (nihilism) require special justification.
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Reasons Against
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Reason against
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1.
Logical symmetry: If a method cannot eliminate hypothesis H, it cannot eliminate ¬H, since both require the same evidential standard.
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2.
Self-refutation principle: A rule that permits rejecting non-nihilism while forbidding rejection of nihilism violates its own criteria uniformly.
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3.
Underdetermination applies equally: Evidence underdetermines all metaphysical conclusions equally, so asymmetric conclusions lack rational justification.
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