I should apologise for the very incoherent post. However, I thought it’s better than nothing! I don’t think I can get a chance to write a serious post for a while. So here we go…
[update: Oh, I've chosen a fancy title, now I feel guilty for such an incoherence and unclear post! ]
Me, Howard Kelly and Joe Razavi were talking about truth-conditional semantics and justficationist theories of meaning† and in a big chunk of the discussion we were talking about the inadequacy of the principle of bivalence. The interesting thing is that we could see the principle of bivalence should not hold for general case in our philosophy, by the logical structure and by the fact that it was a necessary condition to get rid of the circularity of truth-conditional semantics. However, we couldn’t come up with a good example in natural language. No matter how complicated the situation was, we could always find a realist response to that. The only examples in which the realist could not say anything was examples from quantum mechanics. All other tries to come up with an example in natural languages were fail!
Independently, I raised this question: I think the claim should be easily verifiable if we could make a statement consisting of atomic facts. Basically because from the simplicity of our logical structure I had this feeling that if we could come up with examples of atomic facts it should be intrinsically different. However, we knew that we weren’t the first people who tried to find an example of atomic facts and failed. So we tried to, at least, make sense of what Wittgenstein and us were saying! Joe, whose fresh thoughts always open new perspectives to my mind suggested that if we think about it scientifically, atomic facts must be a set of bases which span the state space of our facts. However, the set is not unique (in the same way, intuitively, that the spanning bases for Euclidean 3-space isn’t unique). And since we don’t have the tools for it (as we do in sciences) it would be upsetting to look for such atomic facts.
I find the idea brilliant. It made me think if the same mysteries which exist on the boundaries of classical and quantum theories also exist on the boundaries of atomic facts and the large scale natural languages as well as thoughts! And whether there is chance to find something like the decoherence theory for philosophy of language!
†chapter 4 and 5 of Thought and Reality by Michael Dummett (It’s actually a very important book in philosophy of language which I would recommend buying it.)