The property of being the implementation of a computational structure has been argued to be vacuously instantiated. This claim provides the basis for most antirealist arguments in the field of the philosophy of computation. Standard manoeuvres for combating these antirealist arguments treat the problem as endogenous to computational theories. The contrastive analysis of computational and other mathematical representations put forward here reveals that the problem should instead be treated within the more general framework of the Newman problem in structuralist accounts (...) of mathematical representation. It is argued that purely structuralist and purely functionalist accounts of implementation are inadequate to tackle the problem. An extensive evaluation of semantic accounts is provided, arguing that semantic properties are, unlike structural and functional ones, suitable to restrict the intended domain of implementation of computational properties in such a way as to block the Newman problem. The semantic hypothesis is defended from a number of recent objections. (shrink)