Abstract

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages