If we're talking about fallacies, we're invoking old-fashioned classical logic.
The nice thing about having a notion of strict deductive reasoning is that it gives you an idea of what arguments might persuade someone of basic good faith, but who very much doesn't want to be persuaded. If you and your interlocutor don't both accept modus ponens then you won't get anywhere, but that's pretty unlikely in practice.
(And I'd actually argue that we each invent logic on our own and then notice that the logics are equivalent, but that's straying into metaphysics.)
The nice thing about having a notion of strict deductive reasoning is that it gives you an idea of what arguments might persuade someone of basic good faith, but who very much doesn't want to be persuaded. If you and your interlocutor don't both accept modus ponens then you won't get anywhere, but that's pretty unlikely in practice.
(And I'd actually argue that we each invent logic on our own and then notice that the logics are equivalent, but that's straying into metaphysics.)