# Propositions

Logic is usu­ally stud­ied through lan­guage. In for­mal logic, we at­tached a sym­bol (e.g. $$S$$) to a state­ment (e.g. “Socrates is a man”). This state­ment has a truth value: ei­ther Socrates is a man, and $$S$$ is true, or Socrates isn’t a man, and $$S$$ is false. We call this kind of state­ment a propo­si­tion. In clas­si­cal logic, there is no mid­dle ground: ei­ther a propo­si­tion is true, or false. This is the law of ex­cluded mid­dle.

By defi­ni­tion, a propo­si­tion could be at­tached to any state­ment, as long as it has a truth value. For ex­am­ple, “Socrates is a man” or “The Moon is made of cheese”. We usu­ally don’t care if the state­ment is true or false, only that it can be true or false.

Parents:

• Logic

Logic is the study of cor­rect ar­gu­ments.