Necessary vs Sufficient Conditions

  • Necessary condition = A condition \(A\) is said to be necessary for a condition \(B\), iff the falsity of \(A\), guarantees the falsity of \(B\)
    • “Air is necessary for human life”
    • “Without air, human beings do not live”
    • “If a human is alive, then that human has air to breathe”
      • In an if-then statement, the clause that follows “then” (consequent) states the necessary condition for the antecedent (clause followed by “if”)
    • A necessary condition is not a sufficient condition
    • All sorts of conditions may be necessary for others, but do not (by themselves) suffice or guarantee those others
  • Sufficient condition = A condition \(A\) is said to be sufficient for a condition \(B\), iff the truth of \(A\) guarantees the truth of \(B\)
    • While air is a necessary condition for human life, it is not a sufficient condition, i.e. it does not, by itself, guarantee human life
      • There are many necessary conditions for human life
    • “Having four sides” is a necessary condition for a square, but that single condition by itself is not sufficient for something to be a square
      • Some four sided things are not squares

References