Course:Phil150/necessaryandsufficientconditions

A set of conditions is necessary and jointly sufficient for some other condition when the former obtains only if the latter obtains, and the latter obtains only if the former obtains. Expressions of necessary and sufficient conditions usually take the form of 'if and only if' statements.

Examples:

You will pass a course and receive credits for it at the University of British Columbia if and only if you score at least a 50% as a total of all your assignments, exams, and quizzes in that course.

A human is dead if, and only if, their heart has irreversibly stopped beating.*

• Note that stated necessary and sufficient conditions are often controversial. For example, one might object here that a human might be alive even if their heart has stopped beating - suppose one could hook them up to a machine that served to bypass the heart but still pump blood, or suppose that there is life after death - then a stopped heart would be neither necessary nor sufficient for death. It can be difficult to find a fully satisfactory set of necessary and sufficient conditions for many things/states of affairs.