Mutatis mutandis

Mutatis mutandis is a Medieval Latin phrase meaning "the necessary changes having been made" or "once the necessary changes have been made". It remains unnaturalized and is therefore usually italicized. It is used in English and other European languages to acknowledge that a comparison being made requires certain obvious alterations, which are left unstated. It is not to be confused with the similar ceteris paribus, which excludes any changes other than those explicitly mentioned. Mutatis mutandis is increasingly replaced by non-Latin equivalents, but is still used in law, economics, mathematics, linguistics, and philosophy. In particular, in logic, it is encountered when discussing counterfactuals, as a shorthand for all the initial and derived changes which have been previously discussed.