It is commonly assumed that one can write a generative grammar while adhering to three methodological restrictions: (1) that neither semantics nor statistics enter into either the statement or the evaluation criteria of the grammar; (2) that the grammar be finite; and (3) that the grammar generate strings of morphemes, or, equivalently, that the last rules of the grammar be of the form X → a, b, c,…, where X is some grammatical abstraction (such as ‘noun‘) and a, b, c, … are morphemes or words (man, thing, happiness.) I shall attempt to demonstrate that it is not possible to write a grammar while strictly adhering to all these restrictions, and advance some arguments in favor of eliminating the last.