Then quit acting like you think I have some special definition for begging the question.
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.
If you agree that begging the question doesn't invalidate a deductive argument then you shouldn't feel the need to continue arguing like so:
"I am not aware of anyone who adheres to that notion of question-begging in practice, only when in philosophical discourse about the nature of logic etc." - Post#453
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.
You keep sounding as if you think some special kind of question-begging may still invalidate a deductive argument. If you want me to quit responding to that, quit equivocating.
I can not be more clear, syne.
Any equivocation you see is simply your desire to misinterpret to suit your own agenda.
But for purposes of clarity, let me explain again:
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.
See what I mean? "...as I understand begging the question" continues to bring into doubt whether you understand that no degree of begging the question, on its own, makes a deductive argument invalid.
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.
Begging the question is always a matter of soundness in a deductive argument. If you want to be very clear about deductive validity, you shouldn't be asking whether it begs the question at all. What you should be asking is whether there is an unstated/hidden premise.
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.
And where do you imagine in that quote that I am talking about a first cause?
When you refer to something as simply "first cause" and omit either an indefinite or definite article, it is a perfectly legitimate approach to address the distinction.
Note the term "if" in what I said.
And which of these definition are you disputing?
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.
Whether a premise is questionable is obviously a matter of soundness.
Well done.
Now where can you cite a definition of begging the question, that includes how it pertains to deductive validity (which is all you have been claiming it to pertain to), and in any way refutes these?
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...".
There are no two ways to understand question-begging and deductive validity. Begging the question never invalidates a deductive argument. It can only effect its persuasiveness or soundness.
Noone has said (since post #306) that it does invalidate a deductive argument.
You are clearly still hung up on this and it seems to be clouding your ability to comprehend what is written.