Mathematical statements are usually about some object or set of objects.
Before we can decide whether the statement is true or not, we have to specify exactly which object or set of objects we're talking about. This process is called quantification . There are only two kinds of quantification, both extremely common throughout mathematics. In fact, we very often do both in the same statement. The theorem applies to every set of three points not falling on a straight line, and it asserts that a circle exists through those three points.