Spandrels of Truth (1?)
I am reading JC Beall's Spandrels of Truth this semester as part of an independent study. We've only made it through Chapter 1, but it's great so far: clear and interesting.
I, however, am having unclear (and probably uninteresting) thoughts about it. Specifically, I am wondering whether certain things Beall says are in tension with each other.
(1) "God could use only the T[ruth]-free fragment of English to uniquely specify our world. We are unlike God in that respect; we need a device that enables us to overcome finite constraints. That device is 'true'... [W]ere we God, or even just beings with infinite time or capacities, we wouldn't need to use 'true' in such generalizing contexts [e.g. 'Everything Pat says is true']." (p.1)
So (1a) God (or any other appropriately infinite being) can 'uniquely specify our world' without using the word 'true'. Furthermore, (1b) 'true' is only introduced to overcome a practical limitation.
(2) Our language, which contains 'truth,' gives rise to sentences like the Liar that are true falsehoods: these are sentences A such that both A and ~A are true. Beall calls such sentences 'spandrels of truth': they are unintended byproducts of introducing a truth-predicate.
(3) Beall uses the 'Routley star' semantics for negation. For those unfamiliar with this semantics, all that's needed for present purposes is that in a world where there are true falsehoods, that world's "star mate" cannot be the world itself, and must be an abnormal world (in an abnormal world, there is a sentence A such that neither A nor ~A is true, i.e. abnormal worlds exhibit truth-value gaps). (In brief: B is true in w* iff ~B is not true in w.)
(4) If a language contains no true contradictions, then abnormal worlds are completely superfluous. (We cannot show that the abnormal worlds do not exist, but they would do no semantic work not already done by the normal worlds.)
So now I will try to articulate my thought. If God can completely describe everything without using the predicate 'true,' then abnormal worlds are superfluous for a complete description. And if we subscribe to some sort of Ockhamian principle of parsimony, then such abnormal worlds don't exist. However, bringing 'truth' into our language requires (given Beall's other assumptions) that there must be abnormal worlds. That is unsettling enough: God needn't know about the abnormal worlds, even if God knows a complete description of everything.
Furthermore, the only thing that forces us to introduce abnormal worlds is a predicate that we introduced to overcome a practical limitation on our part. Devices for surmounting practical obstacles don't seem like the kind of thing that should be able to teach us about whether there are abnormal worlds or not.
I guess one response to this is to be a serious instrumentalist about the abnormal worlds: since they are unnecessary for the god's-eye view, we should (at least if we prune 'idle wheels' from our theories) say: they don't really exist, but we cannot give an acceptable semantics for a truth-predicate (satisfying certain conditions Beall finds natural) without them. But this response seems strange to me; though I cannot articulate precisely why, here's a try. If we ask: "Is our actual world's "star mate" a normal world or an abnormal world?", we would have to say 'From a God's-eye-view, no; but if we have a certain kind of truth-predicate in our language, then yes, the actual world's star-mate is an abnormal world.'
Hopefully, there will be further installments in my attempts to grapple with Spandrels... but I'm not making any promises.