This is a very silly question, and strictly speaking not a mathematical one. Feel free to downvote.
Definition. We fix a signature $S$, which is a set that may contain relation symbols, function symbols, and constant symbols. We assume that function symbols and relations symbols have an arity $\geq 1$. A string over the alphabet $\{\forall, \exists, (, ), \land, \lor, \rightarrow, \neg, =\}\cup S\cup \{v_1, v_2, \dots, v_n, \dots\}$ (the symbols $v_i$ are assumed to be variables) is said to be a first-order formula if and only if this can be shown with the following rules:
- If $R$ is an $n$-ary relation symbol, and $x_1, \dots, x_n$ are terms, then $Rx_1 \dots x_n$ is a formula. Also, if $x,y$ are terms, then $x=y$ should be a formula.
- If $\phi$ and $\psi$ are two formulas, then $(\phi)\land(\psi)$, $(\phi)\lor(\psi)$, $(\phi)\rightarrow(\psi)$, and $\neg(\phi)$ are formulas.
- If $\phi$ is a formula, and $v$ is a variable, then $\forall v\phi$ and $\exists v\phi$ are formulas.
Some authors require the sets $\{\forall, \exists, (, ), \land, \lor, \rightarrow, \neg, =\}$, $S$, and $\{v_1, v_2, \dots, v_n, \dots\}$ to be pairwise disjoint in order to prohibit conflicts. Is this requirement necessary? Can there really occur situations where the readability isn't unique if one, say, allows that $\forall$ can be a relation symbol? One could think that based on the position of $\forall$ in a formula one can always reconstruct if $\forall$ acts there as a quantifier or a relation symbol.
Edit: Allowing $\forall$ to be a relation symbol is just an example. One could also ask whether it causes readability conflicts if one allows $($ to be a variable, or whatever stupid example one might come up with.
Suppose $x$ is both a variable and a $2$-ary relation, and suppose $=$ is also a variable. Then
would mean both that $=$ and $y$ had the property $x$, and that $x$ was equal to $y$.