You have effectively raised a definition that trivialises it with regard deductive reasoning, and is different to the definition used by most other people here.
Why should I not?
You are using a notion that makes the term redundant but does nothing to address that which is was raised to criticise.
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.
Either the conclusion (line 4) is valid, but by being so invokes a hidden premise that question-begs the conclusion directly, or the conclusion is invalid.
Thus, despite your ongoing protestations about mixing the two notions (validity and question-begging), the two are linked in this instance.
That is not to say that question-begging in this case invalidates the conclusion, but the opposite: question-begging of the conclusion directly is the only way the conclusion could be valid.
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?
I am distinguishing between the notion you use (that all deductive arguments beg the question) and the notion I use, where question-begging is where the conclusion is assumed not across all the premises but in one premise.
The difference between the question begging (your notion) that is in the Socrates is mortal syllogism, and the "A therefore A" kind.
If you can not yet comprehend this distinction then I can only assume you are being deliberately obtuse.
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.
As mentioned to Yazata, question-begging is not about soundness at all.
It is neutral on the matter of veracity of the premise.
One can neither demonstrate or falsify a premise, or an argument, through question-begging.
Thus it is neutral.
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#Definition
A 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. I am not disputing either as legitimate definitions in their place, but I am disputing your insistence on not being able/willing to distinguish between the two, and address the points raised with the definition intended and pointed out.
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?
For hopefully the last time: line 4 is invalid unless one introduces a (or reveals a hidden) premise that directly assumes the conclusion - i.e. question begs - not simply in the way you hold that every deductive argument begs the question but in the way that a single premise assumes the conclusion.
To quote wiki... "To beg a question means to assume the conclusion of an argument—a type of circular reasoning. This is an informal fallacy, in which an arguer includes the conclusion to be proven within a premise of the argument...".
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.