The term ‘donkey sentences’ derives from the medieval philosopher Walter Burleigh, whose example sentences contain mention of donkeys. The modern philosopher Peter Geach rediscovered Burleigh's sentences and the associated problem. The problem is that natural language anaphoric pronouns are sometimes used in a way that cannot be accounted for in terms of modern predicate calculus. The solution lies in establishing a separate category of anaphoric pronouns that refer via the intermediary of a contextually given antecedent, possibly an existentially quantified expression.