Given the formal system below:
Language:$$\left\{ *,\blacksquare ,\blacklozenge \right\}$$
Syntax: $$ <s>::=<star>,"\blacksquare ",<star>,"\blacklozenge ",\ <star> $$ $$ <star>::="*"|<star>,"\blacksquare "; $$
Axiom: $$ *\blacksquare *\blacklozenge ** $$
One possible interpretation here that makes the formal system consistent although not all consistent witl all interpretations is as follows:
$$ \left[ *\mapsto 1 \right. , $$ $$ **\mapsto 2, $$ $$ ***\mapsto 3, $$ $$ \vdots $$ $$ +\mapsto \blacksquare $$ $$ =\left. \mapsto \blacklozenge \right] $$
Question: how we can deduce please that system above is incomplete as we can not prove that 4+3 = 7?