The synthetic distinction and the a-posteriori distinction together yield four types of propositions:

  • the 3 non-contradictory proposition types will account for all propositions possible

Analytic(predicate concept is contained in subject concept)

Synthetic
(predicate concept is NOT contained in subject concept)

A Priori
(justification does not rely on experience)

  • analytic a priori
  • all bachelors are unmarried
  • synthetic a priori
  • 7 + 5 = 12

A Posteriori
(justification does rely on experience)

  • analytic a posteriori - self-contradictory
  • N/A
  • synthetic a posteriori
  • all bachelors are unhappy