But despite its fundamental role, logic’s place is in the background of what we do, not the forefront. From here on, the beautiful symbols $$\wedge$$, $$\vee$$, $$\Rightarrow$$, $$\Leftrightarrow$$, $$\sim$$, $$\forall$$ and $$\exists$$ are rarely written. But we are aware of their meanings constantly. When reading or writing a sentence involving mathematics we parse it with these symbols, either mentally or on scratch paper, so as to understand the true and unambiguous meaning.