Putnam (1975) famously argued that no notion of meaning can satisfy both of the following two plausible assumptions:

 

1) Meaning is a (narrow) mental entity.

2) Meaning determines reference. 

 

I argue that Putnam's supposed dilemma can be resolved by interpreting 2) in terms of a probabilistic determination principle, a principle that is weaker than Putnam's supervenience interpretation of 2). I contend that there are no good reasons to believe that the supervenience principle is true, but that we do have reason to believe that the probabilistic principle is true. I substantiate this by giving a mathematical argument that underwrites the probabilistic principle in the context of a narrow form of inferential role semantics.