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.