In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. Wikipedia

Apparent contadiction in metamathematics Wikidata

The paradox where, given the observation that certain English phrases unambiguously define real numbers while others do not, there is an infinitely long list of English phrases that unambiguously define real numbers, yet (using a similar technique to Cantor's diagonal argument) it is possible to generate another such phrase not in the list. Wiktionary