[summary:Propositions are statements with a clearly defined truth value]

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.