Indicative conditionals, that is sentences of the form “If p, then q,” belong to the most puzzling phenomena of language. On the majority of accounts of indicative conditionals, the truth of p and q suffices for “If p, then q” to be true or highly acceptable. Yet, many conditionals with true clauses, even if there is a meaningful connection between them, sound odd. The most common reaction to this phenomenon is to attribute the oddity of conditionals with true clauses to natural language pragmatics. We present an experimental study investigating how the presence or absence of a connection between the clauses affects the assertability of conditionals and conjunction expressing generic and specific kind of content. The results refute the standard pragmatic explanation.