Wolfgang Schwarz

Suppose we set aside quantum physics for a moment. Suppose, with the philosophical mainstream, that propositions have truth values only relative to possible worlds. What will we say about your (1)?

(1) The photon got reflected

We don't say that it's true or false simpliciter; (1) is true at some worlds, and false in others. Whether, in a given context, we're happy to say that (1) is true will depend on which world we're talking about. But when the context is provided, we're happy to say that (1) is, say, true -- what we mean when we say that is that it's true relative to, say, the actual world.

So suppose that quantum physics shows that propositions are only true relative to branches. Then we should say the same thing. Even after we've made it clear which world we're talking about, either implicitly or by affixing, say, an 'actually', we'll still want to say that (1) is true relative to some branches and false relative to others. If we've settled on a branch, then we can just say that (1) is true, by which we'll mean it's true in the relevant branch.

I don't see a case to be made for just saying that the unqualified (1) is false on grounds like these. We wouldn't be tempted to say that for the worlds case. It's not like it's false that p just because p is false in some possible worlds.

Hey wolfgang, I am not sure if you had this in mind but the structure here is very much like the motivation for MacFarlane's relativistic semantics from the open future.

For him "There will be a sea battle tomorrow" uttered at t is not true or false absolutely -- but is true relative to an assessment point. The assessment point establishes a "branch". So, roughly speaking, future contingents only have a truth-value relative to a branch.

In both MacFarlane's relativistic semantics and the picture you sketch above there is no determinate branch on which an utterance takes place. This, I take it, is the reply to Ickikawa's suggestion: the context of utterance does not determine a branch but it does determine a world. So in the quantum case, like the future contingents case, there is no such thing as truth-at-a-context (unless we supervaluate or something).

Jonathan: if you're suggesting that we should say that propositions are ultimately true or false only relative to a branch, but that we may sometimes omit mentioning the relevant branch if it's clear from context, then I agree -- that's the most straightforward way of dealing with the issue. But it seems to me that this would not please people like Cappelen and Hawthorne and Soames, who deny that propositions are only true relative to something. Nor would it please all those people (e.g. Jeff King) who claim that propositions are only true relative to worlds, and not e.g. times. Superpositions present a challenge to these views which I haven't seen discussed yet. You're right that it does not present a special challenge to views according to which propositions are anyway true only relative to a shopping list of indices.

Brian: yes, the fact that there's often no "utterance branch" is one of the interesting aspects here. It depends a bit on whether there is collapse. Suppose not. Then if we measure the photon's position, we become entangled in the superposition -- on one branch, we see that it got reflected, on another that it passed through. On the first branch, we say "it got reflected", on the second we don't. So then there is an utterance branch, and what we said is true on that branch. I guess this is how the Frege sentence would come out as true in every context we can encounter. However, this only works if our utterances are suitably entangled with the relevant properties. E.g. if we haven't yet measured the photon's position and utter "the photon got reflected", then the photon is in a superposition relative to the utterance branch, so the proposition seems neither true nor false relative to that branch.

I think relativization-of-truth-to-branch strategies of this sort have indeed been considered in various places.

Many people read Everett's original work like this. He called his theory a 'relative state' interpretation and insisted that macroscopic objects only had states relative to a branch. Given some fairly uncontentious assumptions about truth, that gets you relative truth.

Simon Saunders was a bit more explicit about it. In some papers in the mid nineties (I think 'Naturalizing Metaphysics', in The Monist, is a good example - but see also the 'time, quantum mechanics and X' trilogy in Synthese) he pushed the line that Everett relativized 'value-definiteness' to branches. A doctoral student of Jeff Barrett's at UC Irvine called Christina Conroy has just written a PHD thesis defending this sort of line.

More recently 'branching-time semantics', Belnap-style, has been applied to the case of EQM. That's effectively a truth-relativization strategy as well. A few people have written on this, but it might be worth going straight to Belnap & Muller 2010 in the BJPS.

Having learned the trade in the shadow of Williamson and Hawthorne it's maybe not surprising that I don't have much time for truth-relativization strategies like this. In fact I've just written a paper arguing against it. I think I'll send you a copy. :)

Alastair, thanks for the pointers! I wonder if my talk of "branches" was a bit misleading: by a "branch" of a superposition I simply mean a projection, e.g. a determinate photon position. Whether or not time branches, or whether the "many worlds" have a branching structure, is an entirely different matter.