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It is not the case that If the CCP admits physically realized exceptions, probabilistic independence cannot be derived from mere absence of causal relations between error terms.
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Reasons For
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Reason for
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1.
Absence of causal relations between error terms already entails probabilistic independence in standard causal models by definition.
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2.
Physical realizability and formal independence are distinct questions; conflating them obscures rather than clarifies the issue.
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Reasons Against
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Reason against
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1.
Physical realizability introduces contingent constraints that mere absence of causal relations cannot capture or explain.
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2.
Independence requires positive warrant; lack of causal connection is necessary but insufficient without additional structural constraints.
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3.
Systems with physically realized exceptions exhibit dependencies that formal causal graphs alone cannot represent adequately.
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