Referring to Mathematical Objects via Definite Descriptions

Linsky and Zalta try to explain how we can refer to mathematical objects by saying that this happens through definite descriptions which may appeal to mathematical theories. I present two issues for their account. First, there is a problem of finding appropriate pre-conditions to reference, which are currently difficult to satisfy. Second, there is a problem of ensuring the stability of the resulting reference. Slight changes in the properties ascribed to a mathematical object can result in a shift of reference and this leads to various problems, e.g., it makes inferring knowledge much harder than it is.