Let me begin with a mantra of 20th-century math education: “ ‘but’ means ‘and’.” We all know that this makes partial sense: namely, if one says “John is poor but happy” one is asserting both “John is poor” and “John is happy”. Nevertheless “but” is a major component in the structure of thought (like “nevertheless”), and the version having “but” as the connective is not the same as the conjunction of the two simple assertions. Many English speakers would find “John is poor but happy” cogent but not “John is rich but happy”. You will easily find more and subtler everyday examples. Examples within mathematics are subtler, inexhaustible, but [!] more elusive; […]Even when but takes on the meaning of and, but stays syntactically asymmetric.
Keywords: natural language, coordinators, mathematics, logic, reasoning, precision
 Chandler David: The Role of the Untrue in Mathematics. The Mathematical Intelligencer Summer 2009, Volume 31, Number 3, pp. 4-8.