Yes. He didn’t mention inductance except to admit he didn’t mention it. He implied he would give fuller explanations in part 2.
So what is your problem with him not (yet) talking properly about inductance? Do you see a problem with his experiment or arguments that this will address?
Maybe it’s me who’s wrong. But current in 1 wire inducing opposite current in a parallel wire is well understood. To discuss the phenomenon yet not name it seems strange.
Maybe a better experiment might have the switch and bulb on separate but parallel circuits. dunno.
