note taking:

"Hmm. Does the law of non-contradiction admit of degrees of adherence?"
Can the law of non-contradiction be applied to human society, and
can it be applied to any human society that we could consider just?

A modernist would say yes/ a post-modernist would say no.
An 18th century Philosoph would say yes/ a 16th century Humanist would say no.

And there's a difference between relativism in an absolute sense and relativism as an acceptance of what we can know of the world. Relativism of some sort is a necessity for a democracy, otherwise if you want to follow Plato fully take the politics too.
The dream of a perfect grammar in politics becomes a defense of authoritarianism. That's the post-modern and the pre-enlightenment (still secular humanist) critique of modernism and of the enlightenment and the age of revolution.

And Engels in a different context your words could have been written by a someone at Volokh arguing with Jack Balkin, or Brian Leiter mocking Bruce Ackerman. Your argument is fundamentally conservative in that to follow it results in conservative [read: anti-democratic] policy.

References follow:

Thus the Renaissance conception of humanitas had a two-fold aspect from the outset. The new interest in the human being was based both on a revival of the classical antithesis between humanitas and barbartias, or feritas, and on a survival of the mediaeval antithesis between humanitas and divinitas. When Marsilio Ficino defines man as a “rational soul participating in the intellect of God, but operating in a body,” he defines him as the one being that is both autonomous and finite. And Pico’s famous ‘speech’ ‘On the Dignity of Man’ is anything but a document of paganism. Pico says that God placed man in the center of the universe so that he might be conscious of where he stands, and therefore free to decide ‘where to turn.’ He does not say that man is the center of the universe, not even in the sense commonly attributed to the classical phrase, “man the measure of all things.”
It is from this ambivalent conception of humanitas that humanism was born. It is not so much a movement as an attitude which can be defined as the conviction of the dignity of man, based on both the insistence on human values (rationality and freedom) and the acceptance of human limitations (fallibility and frailty); from this two postulates result responsibility and tolerance.
…The humanist, then, rejects authority. But he respects tradition.

Erwin Panofsky, “The History of Art as a Humanistic Discipline" in Meaning in the Visual Arts

“Humanism- Most generally any philosophy concerned to emphasize human welfare and dignity, and optimistic about the powers of unaided human understanding.”

Simon Blackburn, The Oxford Dictionary of Philosophy.

Two definitions of Humanism. I prefer the first. Not hard to do considering I'm not a Modernist.
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In for a penny:
"It sounds as if you are denigrating modernity"
I'm not denigrating modernity. Or maybe I am but we're stuck with it. We're modern. Modern-ism is something else: enthusiasm and optimism regarding the technological advancements of modernity. Modernism involves a conflation of technological and moral progress. It gets more complex when you're dealing with someone like Eliot who is called a modernist when he's more a regretful modern. It's the same when thinking about humanism. Do you mean the humanism of humane irony or the later humanism of clarity and optimism? I think of the latter as a variant of post or anti-humanism. But I'm not any bigger on the optimistic enlightenment than I am on modernism. And for the record Surrealism and Duchamp weren't dealt with seriously in this country until the 60's and 70's, with the moves against Greenbergian modernist idealism. Surrealism is more a touchstone of post-modernism than modernism itself. See Rosalind Krauss.

Quine's naturalism begins with the arch rationalist's assumption that the self is a stable thing: acting and not reacting. And if that's not his argument then that doubt should be applied back to any speaker. This ties in in the 50's I guess to a distaste for behaviorism. A distaste that's more moral than logical.
But what happens when you apply formal systems or assumpions to the complexities of the social world? If you want to treat language as formal system go ahead, but don't delude yourself that it will still function as a representational one, representative that is of our experience. Numbers may or may not function as models but words are used in mimesis and mimesis is very personal. Don't even begin to talk about politics. It seems more like an escape from politics or with social engagement outside the academy.

If you want to talk about philosophy in the world look at the relation of ideas and behavior. You may want to see your ideas as representing yourself in the world, but actions do a better job of that. Arguing that we should all live by rules when we live (at our best) by principles and prudence is arguing for abstract reason from wishful thinking. Successful politics is always founded in empiricism, both the politics that civilized people despise and that they praise. But it's a functional streetwise empiricism, a different form of "realism" than that discussed here. What sort of a naturalized epistemology can we have when the agent of naturalization is so prone to going off?
And this means specifically that no one should confuse my argument with anti-realism. The relevant question to me is not the existence of the outside world but the problem of access and of moral responsibility. Someone should respond to my question about SCOTUS. And in general: if you don't have the capacity to describe your existing relations to the world: of social life; and politics, then you have little business discussing philosophy. And I say that assuming that for anything to be of broader philosophical interest it has to be seen to model something other than itself.

As to post-modernism. There is another division. There's the librarian model of de Man and Borges which is a sort of literary epicurianism (of language divorced from the world) which is connected to decadence and even anti-humanism but which helped lead towards a return to humanism. I think Garcia Marquez called Borges something like 'necessary', which wasn't meant simply as a compliment. And again: Duchamp and Surrealism and Krauss. Don't rely on Danto for Duchamp. Duchamp goes back to Baudelaire. He didn't want to be called a dumb painter because as he said: no one ever got called a stupid poet. And Eliot used readymades too, as collage: "Hurry up please, it's time." Duchamp is a literary trickster and if anything as conservative in his way as Eliot.
Playing off of outmoded forms of narrative that he couldn't quite let go of. He was a perv of the old bourgeois, but the pervy bits got him street cred with the punks.

Between modernity and modernism it's a mish-mash but they aren't identical. And the same with what follows, but if you want to imagine the American equivalent of European pomo-theorists you won't find them in the American academy. The unreliable subject is the subject of literature, and from there it became one of continental philosophy. The American academicized version of continental theory is like the perfect replica of the Parisian bistro in NY: a simulacrum without the context. And the unreliable author, whether Derrida, Deleuze, Zizek , Philip Roth or Norman Mailer, becomes in the academy the very very reliable expert in Unreliability Studies. The American academy is predicated on the reliability of American academics, when they are no more reliably aware of the external world than the rest of us. Humanism on the other hand, I am being snarky here is founded on the hope of a worldly academy, even occasionally a vulgar one.

And in relation of ideas to literature, complaining that the Europeans are just ripping off Montaigne is like saying Proust is ripping off Lady Murasaki. The point is the communication of ideas in the language of the present. It's the present that's being observed and described in literature. The world is the subject being represented through mimesis in language. People have been making chairs for thousands of years. If you and a friend are looking at a room full of chairs at the Metropolitan Museum you're not going to talk about the one thing they all have in common. If you're talking about novels you're not going to pretend the stories are "true." But there's probably more truth in the collected lies of Philip Roth than there is in the collected truths of Donald Davidson. The difference is that all Roth is trying to give an objective description of his subjective experience.
And maybe the Continentals are all lousy poets but in a very real sense what they were trying to describe was post-war Europe, while their American contemporaries were trying to describe absolutes. But maybe all the Americans succeeded in describing was post-war America. And that is what makes the Europeans smile.