Semantics circle: Oddness, logical compatibility, and granularity

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Abstract

Disjunctions featuring logically compatible disjuncts like (1), are generally odd (Singh, 2008).

1. # Jo is from Russia or Asia.

Yet, conditionals derived from them via the equivalences A ∨ B ≡ ¬A → B ≡ ¬B → A exhibit an asymmetry (a novel observation inspired by Marty & Romoli, 2018). Descriptively, (2a), whose antecedent talks about a country (Russia) and whose consequent talks about a continent (Asia), is odder than (2b), whose antecedent’s and consequent’s roles are reversed.

1. a. ?? If Jo isn’t from Russia, he is from Asia.

     b. ? If Jo isn’t from Asia, he is from Russia.

This is puzzling given that Asia and Russia play completely symmetric roles at the logical level. To account for this, we formally model the intuition that Russia is finer-grained than Asia, considering the partitions of the Context Set these expressions evoke. The resulting "granularity" difference, we argue, first makes it impossible to disjoin Russia and Asia (capturing #(1)); and second, makes (2a) (but crucially not (2b)) violate a new Incremental

Relevance constraint inspired by Lewis (1988) and Roberts (1996, 2012). More generally, coarse- to fine-grained conditionals will be predicted to be fine, while fine- to coarse-grained conditionals will be predicted to be odd (regardless of the presence of overt negation). Moreover, if the partitions evoked by antecedent and consequent mismatch is a perfectly symmetric way, oddness is predicted across-the-board. The talk will further discuss to what extent this last prediction is borne out.