Polysemies, or "colexifications", are of great interest in cognitive and historical linguistics, since meanings that are frequently expressed by the same lexeme are likely to be conceptually similar, and lie along a common pathway of semantic change. We argue that these types of inferences can be more reliably drawn from polysemies of cognate sets (which we call "dialexifications") than from polysemies of lexemes. After giving a precise definition of dialexification, we introduce EvoSem, a cross-linguistic database of etymologies scraped from several online sources. Based on this database (publicly available at http://tiny.cc/EvoSem), we measure for each pair of senses how many cognate sets include them both-i.e. how often this pair of senses is "dialexified". This allows us to construct a weighted dialexification graph for any set of senses, indicating the conceptual and historical closeness of each pair. We also present an online interface for browsing our database, including graphs and interactive tables. We then discuss potential applications to NLP tasks and to linguistic research.