Aside: It took a while in the 20th century to realize that logic was not about logical truth but rather about validity of inference. In classical logic can you treat these interchangably, but not all (rough logics vs smooth logics - whether the consequence relation can be determined by the set of all theorems). Dummett has written about this issue.
What if we picked some other vocabulary (other than logical) to hold fixed? E.g. substituting non-theological vocabulary for non-theological vocabulary. “If justice is loved by the gods then justice is pious”. If no matter what we substitute for justice the inference is good, we might say the sentence is true in virtue of its theological form.
Philosophy of logic (See Quine’s and Putnam’s books both titled The Philosophy of Logic) has two classic questions:
a demarcation question: what makes something logical vocabulary?
Quine disallows second order quantifiers and the epilson of set theory, whereas Putnam allows them.
a correctness question: which logical consequence relation to use:
Classical? Intuitionistic? etc.
Sellars challenges this tradition (logical empiricism) by pointing out there is a concern conceptually prior in the order of explanation to philosophy of logic: materially good inferences.