MEPX
Chapter 5 of 10All chapters
  1. 1What an argument is
  2. 2Validity and soundness
  3. 3If, then
  4. 4All, some, none
  5. 5Necessary and sufficient
  6. 6Deduction against induction
  7. 7Formal fallacies
  8. 8Informal fallacies
  9. 9Logic puzzles
  10. 10Using it in real arguments

Chapter 5 of 10

Necessary and sufficient

The distinction that clarifies arguments.

Two roles

A necessary condition must hold for the outcome. A sufficient condition guarantees it. Oxygen is necessary for fire; a lit match in a fuel tank is sufficient.

  • If P then Q means P is sufficient for Q, and Q is necessary for P.
  • If and only if means each is both.

Where it bites

Policy and legal arguments constantly confuse the two. Asking whether a proposed cause is necessary, sufficient, both or neither usually clears the fog immediately.