Philosophy Index


In logic, a proposition is any sentence that expresses something that is either true or false.

For example, the following are all propositions:

  • All penguins are birds
  • The Earth orbits Mars
  • Socrates is mortal
  • Reason causes leprosy

Propositional Variables

By convention, propositions in logic are symbolized using uppercase Roman letters, which indicate propositional variables.

For example, we may symbolize each of the propositions above by letters. For example, we may use the letter P to refer to “All penguins are birds” and the letter S for “Socrates is mortal”. We can then perform logical operations on these words, and say something like P ∧ S, or “All penguins are birds, and Socrates is mortal.”

It is a convention, or tradition, to use the letters beginning with P and Q when referring to argument forms where the specific propositions are unknown or unimportant.