Are "Gap-Fillers" Missing Premisses?

Identifying the missing or unstated premisses of arguments is important, because their logical quality depends on them. Textbook authors regard enthymematic syllogisms (e.g., "Elvis is a man, so Elvis is mortal") as having an unstated premiss - the major premiss (e.g., "All men are mortal"). They are said to be such because these syllogisms become formally valid when the major premiss is added (i.e., it is a gap-filler). I argue that unstated major premises are not gap-fillers: they support a part of the argument that is already given implicitly - the inference claim ("If the premisses are true then the conclusion is true"). As such, their logical status is the same as that of an unstated proposition that supports the minor premiss, which is not part of the argument. Therefore, the so-called "major premiss" is not an unstated premiss of the enthymeme