In the standard account of ambiguous political rhetoric, ambiguity is equated with voter uncertainty: a politician takes an ambiguous stance on an issue by announcing to the voters a lottery over the positions he might take on that issue. The present account equates ambiguity with multiple meanings: a politician takes an ambiguous stance on an issue if his rhetoric admits of different meanings in different contexts. The linguistic account of ambiguity is based upon the formal logical concept of a piecewise definition. Piecewise defined terms provide the politician with the means of uttering statements each of which has seperate meanings for different voters. This paper formalizes the multiple-meaning account of ambiguity and traces the implications of the formalization for political strategy. The findings are: ambiguous rhetoric is often optimal; the conditions under which it is optimal are simple; and the selection of optimal ambiguous rhetoric is rarely simple.