 (where the symbol ‘\(F\)’ is a placeholder for a name of a particular formula of the object language). In fact satisfaction reduces to truth in this sense: \(a\) satisfies the formula \(F\) if and only if taking each free variable in \(F\) as a name of the object assigned to it by \(a\) makes the formula \(F\) into a true sentence. So it follows that our intuitions about when a sentence is true can guide our intuitions about when an assignment satisfies a formula. But none of this can enter into the formal definition of truth, because ‘taking a variable as a name of an object’ is a semantic notion, and Tarski’s truth definition has to be built only on notions from syntax and set theory (together with those in the object language); recall Section 1.1. In fact Tarski’s reduction goes in the other direction: if the formula \(F\) has no free variables, then to say that \(F\) is true is to say that every assignment satisfies it.