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! 
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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!
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†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.)
February 20, 2011 at 12:13 am |
What do you mean by the set of atomic facts not being ‘unique’. If you mean that the set of atomic facts has the status of a set of axioms, then complex propositions will only be true relative to the set of atomic facts, of which there can be different versions. But this yields relativism rather than realism. Your mention of Euclidean space may mean that different sets of atomic facts represent different possible worlds. This seems to be a more tenable position.
February 20, 2011 at 1:23 am |
Here I didn’t mean to treat it as axioms, but as basis vectors. I don’t think the atomic facts, as they are described, are any similar to axioms of a theory. And by not being unique, I meant the same way you can span a vector space with different basis vectors, which in the end they are spanning the same space. This doesn’t necessarily have to change our view on realism or anti-realism. Because here our reference is not necessarily reality, but the possible states of language. A realist might say the possible states of language is determined by reality and an anti-realist could say reality is what could be justified.
In case we find any relationship between atomic facts and language as a whole (the same way we seek for classical and quantum mechanics) supporters of either realism or anti-realism might find it interesting. (Nevertheless, it might naturally fit into one better than the other, the same way that an anti-realist approach to quantum mechanics is more natural and publicly more acceptable than the realist one.)
February 20, 2011 at 9:44 am |
C. S. Peirce, Putnam, and others have sought to define truth in terms of that which would be agreed to by someone possessing *all* possible data. I wonder if you have something like this in mind on the anti-realist side. On such a view, complex propositions would still be resolvable into atomic propositions, in some sense, because we could trace the ground of complex propositions to discrete atomic data. Moreover, we could do so without falling into Sellars’s Myth of the Given.