So good, interesting arguments have a further virtue in addition to soundness. That is they're potentially convincing. Now, this depends on where you start. Potential convincingness depends in part on who is in a position to be convinced. We'll define it like this:
An argument is potentially convincing for a person when, prior to being confronted with the argument, the person believes the premises but doesn't believe the conclusion, and the person is in a position to see that the argument is valid.
So if the argument is potentially convincing for you, then because you believe the premises before being confronted with the argument, you'll be inclined to accept all of those premises. And because you're in a position to see that the argument is valid, you'll be in a position to see that, given that the premises are true, the conclusion, too, must be true. So you're in a position to be persuaded that the conclusion is true.
Strangely, none of my 3 books on logic, or this Coursera course Think Again: How to Reason and Argue, introduced the bolded terms above. They only discussed 'validity' and 'soundness' for arguments. A Google search cites uses only from the lecture above.
So are there other names for the bolded? If not, why is this 3rd key quality of arguments omitted?