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Inverse View
It is not the case that Ian Hacking's early likelihoodism acknowledged this gap, conceding that likelihoods cannot adjudicate the choice of the hypothesis space itself.
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Reasons For
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Reason for
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1.
Hacking's concession may undermine likelihoodism's core claim to provide a complete inductive logic without external assumptions.
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2.
If hypothesis spaces require justification outside likelihood, likelihoodism becomes incomplete rather than foundational for inference.
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3.
This gap suggests Bayesian or information-theoretic methods might better integrate hypothesis space selection with likelihood evaluation.
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Reasons Against
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Reason against
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1.
Likelihood ratios only compare hypotheses within a fixed set; they cannot justify why that set exists rather than alternatives.
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2.
The hypothesis space itself reflects prior theoretical commitments, background knowledge, and pragmatic choices beyond likelihood calculations.
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3.
Acknowledging this gap prevents false claims that pure statistical methods can solve the prior problem of model selection.
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