Irony has various forms, but what's common among them is the juxtaposition of an idea and its contradiction. I think what's meant by sincerity, here, is a clear and committed choice between the two.
You can have a sincere belief that an idea can coexist with its contradiction, but this is kind of a meta-sincerity.
That's sort of the point of post-modern irony, though, and it's also why metafiction is such an important part of the movement: Commitment is always premature, but that would mean that you can never say anything. Irony, in that sense, is a life-line that rescues you from silence, and allows you to treat your belief as a work in process. It's been one of the strategies that minorities have at their disposal, not only to talk, but also to think about their place in society. Language hasn't developed first and foremost with them in mind.
In other words: What ever you say will be wrong in some way, but if you shut up because of that you'll let others be wrong for you. "Wrong", here, is more politcal than true.
An example: When you insist that treating "God Almighty" ironically is inherently disrespectful, that puts me as both a social relativist and atheist in a bind. You may be expecting a sincere commitment to "God does not exist." That's what being "an atheist" is all about, right? The problem here is that "God does not exist," is not - per se - a positive belief item. It's not something I can say with any more sincerety than "God exists." Doesn't that mean I'm an agnostic? No, it doesn't. I am that, too, but when I say I am an atheist what I really mean is "I do not believe in God." Ideally, I wouldn't talk about God at all, but since I'm living among Catholics, God will come up, and then I will either have to react or hold myself back and accept because-god-says-so arguments - insincerely. There is not good way for me to respond to "Do this because God wants you to." The closest I get to sincerity would be "leave me alone with God", but that would only be sincere to the extent that it expresses frustration. Since I'm living in world that has you in it, too, I actually want to get along, and so I don't actually want you to hold back. I could maybe say "Please respect that I don't believe in God," or something like that, but you'll sound like a broken record, and eventually people will stop talking to you altogether. As an atheist who lives among Catholics (in Austria), let me tell you, irony is a life line. It helps keep conversations going, where a more commited response would only foster frustration. I may respond ironically, but by responding with content (even if not commited to a clear a position) I signal that I'm listening with interest, and without hostility. I like using absurd examples that no-one can take seriously, precisely to get at the structural point in an argument that I'm interested in.
But if people react to my irony with frustration, puzzlement, or (rarely) hostility, then there's really nothing left for me to say. Because I feel that what really causes offense is me "not knowing my place". People who believe in God have the home advantage in any of those conversations. Whenever I have to speak about God, there's part of me that
must pretend. I can't commit to any statement about God other than that I don't believe in Him.
Since I'm a social relativist, what kicks in when talk ironically about God, is a review of the things I can't see because I'm taking them for granted. At times, I will have to say what "I believe instead". But there's really nothing. Does that mean I'm a nihilist? No, it doesn't, because I won't commit to the idea that there's no meaning to anything either. So whatever I'm going to say is necessarily situational. I'm a soical, and not a moral relativist, so that means that I see the regularities in my behaviour, and I assume that I have blindspots as well as selective attention to certain details over others, etc. When I define myself in opposition to theists, I'll end up with slightly different beliefs, than when I define myself in opposition to secular humanists, for example. Because what I'll be saying is determined in part by where the conversation leads my attention (situational, remember?). And the conversation we're having (about God) is a conversation we'd not be having if you hadn't brought up the topic first. I would never bring up God - God is a topic I'd never come up with on my own accord. Theists are theists because they belive in a god/Gods; I'm an atheist, because theists believe in a God/gods (and I don't).
Defining yourself over what you're not is a weak position to argue from. You need something positive to hold against God, so you can anchor yourself: this is why some positions - social relativist, for example - are attractive to me. I can sort of identify with that. But it's not really a belief as much as it is a hypothesis about my lived morals (assuming I acquired some consistency behaviour-wise). However, situationally you still have to show committment or you're - quite simply - going under.
Irony is the bracket that holds situational believe, social expectations of consistency and a perceived distance between what you say and what you are togher. That was a very long-winded way of saying if you want me to talk about God, and if you want me to be sincere, then an ironic attitude towards what I'm saying about God is the only possibility. Without an attitude of irony I literally have nothing at all to say to you in a conversation about God.
But saying nothing often means that I will either have to defer to "God's" authority, or that I have to fight back from a position I hate (and thus won't be able to keep up emotionally).
So when I read the Remodernist manifest, and come across "the failure of post modernism to answer or address any important issues about being a human being", I have the strong urge to shut up and hide in bed and wait for death. Post modernism hasn't answered any important issues about being a human being, but that's not failure - that's the point. And it most certainly adresses important issues. All the time. Of course, that comes from someone who can't talk about post-modernism unironically.
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For what it's worth, here's what I think about how post-modernism relates to literature:
An employee of the chocolate company Milka is handing out free samples of their
I love Milka brand. If people spend 25 seconds looking the box's name ("I Love Milka"), they can have the box for free. A classical, a modernist and post-modernist character drop by. After looking at the box's name for 25 seconds:
The classical character extols the virtue of Milka in a loud voice. A nearby character (also classical in nature) takes issue, championing Lindt. They decide to settle issues through a duel. In the morning, the place the box of chocaletes (still wrapped in plastic so the due won't hurt it) on the ground, then turn around and walk each in the opposite direction. Lindt guy wins the duel. He walks over to the other guy, picking up the box Milkas. As he looks down at the corpse and declares: "Though you have been wrong, I admire your dedication." As the sun rises, he unwraps the box and eats the chocolates in tribute.
The modernist character is about to unwrap the chocolates, but then thinks it might be nice to share them with his with wife. On his way home, though, he suddenly notices advertisments everywhere: bilboards, shop window, in the streets, in the subways. He can't get rid of the image of the box and the line "I love Milka". A forced first person pronoun. Milkas certainly taste good, but is it fair to say he loves them? He participated because he wanted the chocolates, sure, but... It's not like the company pursuaded him, but at same time, what if... To what extent does he really like the chocolates? When he gets home he is in a strange mood. His wife asks what's wrong, but he just shrugs. Then he absentmindedly hands her the box. "I got these for free." His wife takes the box. "Mm, Milkas." She unrwaps them and pops one in her mouth. "Mm, they're good." This makes smile. He takes one, too. "They are, aren't they?" he says.
The post-modernist character unwraps the box immediately. He recites one love poem per praline. Originally, they're all supposed to be different genres, but he runs out of poems and cheats. When all pralines are gone, he launches into a blues number and sings how Milka always leaves him. He disappears around the corner.