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It is not the case that Probabilistic relevance requires a well-defined probability space, which itself presupposes determinate logical or causal relations between propositions.
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Reasons For
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Reason for
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1.
Probability spaces can be defined axiomatically without prior commitment to causal or logical structure—set theory alone suffices.
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2.
Empirical systems exhibit probabilistic patterns without determinate underlying logic; randomness itself may be fundamental, not derivative.
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3.
Relevance relations can be discovered inductively from data rather than presupposed deductively from prior logical or causal frameworks.
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Reasons Against
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Reason against
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1.
Probability assignments require a sample space of mutually exclusive, exhaustive outcomes, which logically presupposes prior determinate distinctions.
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2.
Without causal or logical structure, propositions lack the definitional boundaries needed to calculate their conditional probabilities meaningfully.
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3.
Bayesian updating depends on identifying which propositions affect others, implying causal relations must be antecedent to probability calculations.
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