Homogeneity inferences arise whenever an assertion implies a universal positive (every/both) and its denial implies a universal negative (no/neither). I present an account of homogeneity inferences based on two assumptions which together constrain the behavior of negation: rejection is non-classical, and vacuous models may be omitted (Neglect Zero). If both assumptions are enforced, the only definable negatives are universal (no/neither), predicting the homogeneity gap.
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Giorgio Sbardolini (2024) studied this question.
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