Definition:Premise/Historical Note

Historical Note on Premise
In the early days of (mathematical) logic, there was a significant distinction between premises on the one hand, and assumptions on the other hand.

Premises ought to be essential for the validity of the argument, while assumptions were expected to be discharged at some point in the argument.

Over the years, through abstraction and change of perspective on (symbolic) logic, this distinction is becoming less important; however, it still retains considerable conceptual value.

For example, the Rule of Assumption of natural deduction is a symbolic representation of both these concepts, but allows to distinguish between them to make it easier to convey the overall structure of a proof to the reader.