Armstrong's combinatorial theory of possibility faces a number of insuperable objections. In order to construct non-actual possible worlds from actual elements they must be fictionally recombined. I make three criticisms of Armstrong's reliance on fiction. First, fiction makes combinatorialism redundant. Second, fictionalism makes possibility insufficiently real. Third, Armstrong cannot provide an account of fiction within his own system that does not rely on possibility, mainly because of the essential role of dispositions in his theory of mind and, therefore, his theory of meaning. I continue by showing why possibilities cannot be confined to recombinations of actual elements, and suggest a somewhat neo-platonic theory of possibility that overcomes these problems.