Ordinary language is all right.
One could divide humanity into two classes:
those who master a metaphor, and those who hold by a formula.
Those with a bent for both are too few, they do not comprise a class.
Socrates never loses control of himself; he doesn't need to compose his thoughts in writing. If connected, these facts would suggest that we, with our need for writing, find some of our thoughts, or their disorder, disquieting.
It could be that what disquiets us is the feeling that they must be given more order, or made to fit one.
One can imagine Socrates taking time to think, but not: not being ready to publish.
It's not clear whether philosophers think of the gist of an argument as what is persistent about it, or as what it's been reduced to.
You can imagine Socrates asking an interlocutor how an argument goes—but as a prelude to the old routine, extracting something like a full performance from the interlocutor. Professional philosophers, in contrast, can seem to be suspended in rehearsal. They defer the performances: 'Let me just get it right first, how does it go again?'.
If you ask a musician 'how does it go?', he might sing a bit of it to you. Even if he's not a singer; even if he could, say, play it on the piano there.
He probably won't go look for a recording of it, either.
—Which shows something about what we do with arguments. It's hard to imagine someone being convinced by the gist of an argument. Or, in some settings, being asked, 'just gimme the gist of it'. By a judge in open court, for example. (On the other hand, in closed chambers, with just the lawyers…)
We say not only 'what's the argument?', but also 'how does the argument go?'. —We think there is such a thing as the gist of an argument.
My favorite guilty verdicts are the ones where the whole gallery gasps.