What's the meaning of the sentence?

I judge we might now discuss the matter in more detail, clarifying our respective positions; do you not agree

Cleared the air means to settle a gripe. For example, if you and I were debating or in a conflict, we would clear the air by coming to some sort of common agreement. We would settle our gripes, thus eliminating conflict.

The conversational part asking, "don't you" is about the person asking you if you feel agreeable to thosw terms or is there a consensus.

I have a feeling that you are mainly uncomfortable with the phrase "don't you" being part of the same sentence, rather than a separate sentence. An intuitive approach to good grammar would make us think that, indeed, "don't you?" should be separate from the rest of it. But in common colloquial usage it's customary to make it a part of the same sentence. It's done all the time, don't you see?

It's not only possible, Smarty, it's exceedingly common in English. These are called tag or mini questions. We use them not so much to ask a real question, but to seek confirmation or agreement where we already have some knowledge of a situation or the answer is what the speaker sees as the expected answer.

As a full question, it would be,

"Don't you think it's time we cleared the air?"

Some more examples of tag/mini questions:

1. You like [+] pizza, don't [-] you?

2. You don't [-] like broccoli, do [+] you?

We NORMALLY use a negative tag with a positive statement [see 1.] and a positive tag with a negative statement [see 2.]

In 1, the tag question is framed with a positive statement because there is an expectation that what the speaker wants or expects is a 'yes' reply.

In 2, the tag question is framed with a negative statement because there is an expectation that what the speaker wants or expects is a 'no' reply.

This doesn't mean of course, that the answer will/must be the expected one.

It's gonna rain, isn't it?

Moscow is in Russia, isn't it?

Putin is Russia's leader, isn't he?

Gorbachev isn't Russia's current leader, is he?

Australia isn't in the Northern Hemisphere, is it?

We can make tag/mini questions out of any real question.

Dale meant to put a question mark at the end of that sentence but he forgot.
Otherwise it wouldn't make any sense at all.

I judge we might now discuss the matter in more detail, clarifying our respective positions; do you not agree?

Joe(Do you not agree?)Nation

Piffle, Merry, a big load of piffle.

Not actually Joe. It’s one of scores of shortcuts to simplify my life at 81 with only 5 years to go

Likewise the omission of the period

That's a pretty big assumption, Joe. We don't have any question marks in speech yet things all seem to make sense.

In fact the question mark is redundant and redundancy is one of the big peeves of many prescriptivists. I guess they forgot this one or more likely, independent thinkers that they are, no one has mentioned it to them yet.

Thank you JTT for your support, rare in this diriment of convoluted procrustean conation
One of the reasons is that many folk terribly angry at all times about almost everything are drawn to the Internet forum as a means to anonymously express their frustration

Hence they’re ever busy looking for something wrong, however trivial. The fanatics are especially drawn to forum admin posts where they can make up rules for us to follow and criticize or even ban us for the slightest infraction

I hasten to add however those supervisors of a2k are exceptionally liberal in that respect. Any other forum by now I would have been banned. You think I’m kidding

In fact I was banned from one such ostensibly because they didn’t like the punctuation in my postings

What we have in speech in inflection, emphasis and, for lack of a better term, silence.

Try speaking in a monotone without indicating an inquiry or excitement or stressing a particular word. It's fun. It's an old acting exercise, done to make the actors pay attention to the structure of the lines, and it's a lot harder to do than you think. It's not just 'robotspeak', it's the removal of any indicators.

The next step was to say the lines from behind a scrim so that the person listening couldn't have any visual clues.
~~

Dale: It's actually younger people who leave out all the punctuation marks and paragraphing, it's more out of laziness and ignorance than anything else, but they are surprised when someone replies to a text or an email with "Whathefuck'?"
Look at some of the posts here where people type two hundred words without any indication of where the points or thoughts being expressed begin and end.

It's not critical, it's just annoys me.

Next will be the elimination of spacing between words, whatisthepointofthatanywayicansaywhatiwantandspeelitthewayiwantnnebodywhoduzantlikitcankissmyass

Joe(itz da modern wurld)Nation

Very pertinent Joe you should so remark. If we listen closely to the lines of TV commentators, actors, etc, often that very emphasis is missing or misplaced, showing they don’t fully understand the script

I hadn’t noticed that but myself and I’m 81. However I too deplore the latter

That’s me, exactly

I get that sort of response but surprisingly, very rarely; partly ‘cause I seldom word a q for instance so it’s not obviously a q. Even more surprisingly nobody has yet objected to my abbreviation of “question,” saving me millions of aditional keystrokers


Yea Joe it’s positively deplorable


I often skip altogether such a posting

Actually some of that is the fault of incompetent software, for instance like the a2k routine that doesn’t immediately provide you the scroll bar in edit window

..or when you”re replying, doesn’t select the last page nor scroll to the bottom

..or typically for instance one for years that sent me screaming, “...annoys me. [/quote]...”if you delete space between “me.” and "[/quote]”, deletes also the left bracket
..but then as an erstwhile writer and compulsive commentator I guess I’m just a fussbudget