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.

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In this paper, new evidence is presented for the assumption that the reason-relation reading of indicative conditionals ('if A, then C') reflects a conventional implicature. In four experiments, it is investigated whether relevance effects found for the probability assessment of indicative conditionals (Skovgaard-Olsen, Singmann, and Klauer, 2016a) can be classified as being produced by a) a conversational implicature, b) a (probabilistic) presupposition failure, or c) a conventional implicature. After considering several alternative hypotheses and the accumulating evidence from other studies as well, we conclude that the evidence is most consistent with the Relevance Effect being the outcome of a conventional implicature. This finding indicates that the reason-relation reading is part of the semantic content of indicative conditionals, albeit not part of their primary truth-conditional content.

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According to virtually all major theories of conditionals, conditionals with a true antecedent and a true consequent are true. Yet conditionals whose antecedent and consequent have nothing to do with each other—so-called missing-link conditionals—strike us as odd, regardless of the truth values of their constituent clauses. Most theorists attribute this apparent oddness to pragmatics, but on a recent proposal, it rather betokens a semantic defect. Research in experimental pragmatics suggests that people can be more or less sensitive to pragmatic cues and may be inclined to differing degrees to evaluate a true sentence carrying a false implicature as false. We report the results of an empirical study that investigated whether people’s sensitivity to false implicatures is associated with how they tend to evaluate missing-link conditionals with true clauses. These results shed light on the question of whether missing-link conditionals are best seen as pragmatically infelicitous or rather as semantically defective.