Per the Oxford Concise:
1. of or belonging to citizens
That there is my preferred meaning.
Citizens -- people who have responsibilities in and to civil society.
In a democracy, citizens have the responsibility to behave transparently. To speak, when they speak on matters of public policy, honestly, in good faith, and with respect for both their interlocutors and the whole body of other citizens.
Civil discourse is discourse in which each party strives to convey its message transparently -- to state clearly what the message is and to state the real reasons why it is being conveyed -- and to understand and acknowledge the message, and meaning, being conveyed to it.
People engaged in civil discourse may well speak harshly and may not always be friendly. But they always speak truthfully and completely, and listen attentively to what is said to them and respond to what is said to them. They do not divert the discourse, or disguise their message, or pretend not to understand what is said to them or that what is said to them is something other than what it was. True respect, true civility, lies in doing that.
Rote rules about "personal attacks" and the like really have not the first thing to do with civil discourse. In true civil discourse, for instance, lies are never tolerated; misrepresenting one's interlocutor's words or meaning is never tolerated; offering less than the whole truth is never tolerated; employing deceptive reasoning is never tolerated; claiming to speak from some exalted high ground while concealing one's personal interest and what one stands to gain from one's position atop that moral mountain is never tolerated; appealing to others' anti-democratic, selfish impulses rather than to the shared, democratic values of the citizenry is never tolerated.
I merely muse, variations on the theme of "civility", which I will never go along with characterizing as speaking in pretty words. And of course I invite anyone who might ever catch me out in any of those tricks, who ever sees me offer disrespect in return for respect, or bad faith for good faith, to call me out.
Civil society. Civil discourse is just about its most important foundation stone and guarantor. In fact, the preservation of civil society pretty much depends on its citizens' commitment to civil discourse.
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