Wrong conclusions are inevitable and commonplace. Godel’s Theorems apply to all formalisms.
A tangent, but Godel’s incompleteness theorems simply show that for sufficiently powerful formal systems:
There are statements which are true, but unprovable
If the system is consistent, “this system is consistent” is such a statement.
Neither of which show that all formal systems are unsound. That is, if a statement is provable in a formal system, the corresponding property is true in all models of that formal system. So this point is not correct because of Godel (though it could be practically correct for other reasons, such as the world being complicated).
A tangent, but Godel’s incompleteness theorems simply show that for sufficiently powerful formal systems:
There are statements which are true, but unprovable
If the system is consistent, “this system is consistent” is such a statement.
Neither of which show that all formal systems are unsound. That is, if a statement is provable in a formal system, the corresponding property is true in all models of that formal system. So this point is not correct because of Godel (though it could be practically correct for other reasons, such as the world being complicated).