Ironically, of course, Popperian falsifiability is itself unfalsafiable, and therefore does not meet its own definition as a member of itself.
Popper knew this, by the way. So the inverse to the trap you point out here is the claims that "if not falsifiable, then unable to be true/useful", which is just as specious.
Popper knew this, by the way. So the inverse to the trap you point out here is the claims that "if not falsifiable, then unable to be true/useful", which is just as specious.