Between a conditional's antecedent and its consequent: Discourse coherence vs. probabilistic relevance

•We tested a pragmatic account of why missing-link conditionals (“if a fish has eyes, it swims”) are odd.•Our experiment compares two explanations: probabilistic relevance and discourse coherence.•Discourse coherence relations linking antecedents and consequent are not sufficient.•Antecedents must be relevant for consequents for conditionals to be assertable.

Reasoning with conditionals is central to everyday life, yet there is long-standing disagreement about the meaning of the conditional. One example is the puzzle of so-called missing-link conditionals such as “if raccoons have no wings, they cannot breathe under water.” Their oddity may be taken to show that conditionals require a connection between antecedent (“raccoons have no wings”) and consequent (“they cannot breathe under water”), yet most accounts of conditionals attribute the oddity to natural-language pragmatics. We present an experimental study disentangling the pragmatic requirement of discourse coherence from a stronger notion of connection: probabilistic relevance. Results indicate that mere discourse coherence is not enough to make conditionals assertable.