No, I have raised the only definition that directly pertains to deductive validity. Remember deductive validity...it's what you've gone on about for quite some time now. So far, your only rebut has been to reassert the simple definition of an informal fallacy that has no bearing on validity. Guess what, it is trivial. If you think there is a hidden premise, state it, and quit jerking around about begging the question. The conclusion is valid, because it is both entailed in the premises and relies on no hidden premises. If there is a hidden premise, it is not valid. So your 'Either the conclusion is valid...' is disingenuous, since you immediately say it 'invokes a hidden premise'. So you are basically saying either it is invalid or it is invalid. Can you see why I keep doubting your understanding of validity? While begging the question doesn't, itself, effect validity, a hidden premise does. What do you think the hidden premise is? So which is it? A hidden premise or unnecessary premises? What do you think the hidden premise is? Which do you think are unnecessary? If you cannot answer all of these, you are obviously just trolling and avoiding being pinned down on any assertion at all. The lack of justification in a premise is an issue of soundness. Begging the question is a form of circular reasoning, which is also known as circular justification. Hence, soundness. The fallacy of petitio principii, or "begging the question" is committed when someone attempts to prove a proposition based on a premise that itself requires proof. - https://en.wikipedia.org/wiki/Begging_the_question#DefinitionA premise that requires its own proof is unjustified and unsound. Now that proof may be in the form of a hidden premise (which would invalidate the argument), but we don't know that until we've addressed soundness. Between an informal fallacy and an actual issue of validity? Question begging is only an issue of soundness. If you want to attack validity, you should assert what hidden premise there may be. But as soon as you do, we'll be discussing the soundness of particular premises. There's no two ways about it. What do you think the hidden premise is? Which do you think are unnecessary? What? That is ignorant. '...invalid unless one introduces a (or reveals a hidden) premise that directly assumes the conclusion'? If there is a hidden premise (and you can successfully demonstrate what it is), it is invalid. If there is a hidden premise, then 'a single premise' does not assume the conclusion, since it needs an extra, hidden premise. And even if a single premise did, it wold not be invalid, only vacuous. This is really just a bunch of arm waving to avoid soundness. It's getting old.