by Jeremy Perret Mar 26 2016 updated Mar 27 2016

Propositions are statements with a truth value.

[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.