Logic has nothing to do with Language
In the view of logic I endorse (and this is something that is also held by many if not all logical realists and kantians), logic has no (metaphysical) relation to language or, at least, to semantics: it is not about what “and” means or about what we do when we negate something, etc. It is about logical phenomena, centrally about the logical phenomenon of what follows logically from what, but probably about other phenomena as well. Thus, logical systems are logical theories or models that aim to explain what follows from what and why. Logical notions like ‘negation’, ‘disjunction’, ‘conjunction’, etc. are theoretical concepts that logic develops to make sense of these phenomena. That is why, they are not directly testable – think of them as the non-empirical analogue to non-observational notions in the empirical sciences. Yes, these notions may also be the semantic values of some expressions in (at least some) natural languages, i.e., the so-called logical expressions. But this is not ...