Actually I saw him give a talk on this. I should definitely work through it properly though.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bsl/1255526080

Seemed like it’d be right up your alley.

I don’t know much about the operator theories of truth, either. Probably the most worked out theory in this vein is the prosentential theory (Grover, et al). I guess the generalization issue is this: the truth predicate allows us to generalize over sentences using out regular old first-order quantifiers (the truth predicate allows for semantic ascent). On an operator theory of truth there’s no “semantic ascent” going on; we’d still need propositional or substitutional quantification in order to generalize over the true sentences. So we’re introducing a new kind of quantification to play the generalizing role that the truth predicate was intended to play.

I’m glad you commented actually, as I’m coming to this with basically no knowledge of the literature at all. What is the well known result you mentioned in your second sentence? Is there anything written on the operator versus predicate theories of truth? (After writing this I realised that I’m still not crystal clear why one turns out to be consistent.)

Incidentally, I’m not sure I agree with your point about the generalization capabilities of the operator theory. At least, if you’re willing to accept that name*s are illegitimate then can’t you just formulate the generalizations using propositional quantification?

Part of the problem of with the operator theory of truth is that it doesn’t yield the generalization capabilities of unrestricted predicate type theories. So it’s not really a good candidate if you’re a deflationist. That fact is born out here in an interesting way: the weak Kleene theory doesn’t allow generalization over the ungrounded sentences at all.

Sorry for not getting back to you sooner.

Part of the problem with that was that you can construct models where is true but actually Fred denotes different individuals in different worlds (as does the variable x on the assignment that makes this sentence true.)

Another point is that we have the following two claims:

1) Necessarily “Aristotle” denotes Aristotle

2) It’s contingently the case that “Aristotle” denotes Fred.

If we followed the suggestion at the end of the post we could existentially generalize to get the result that “Aristotle” both contingently denotes some object and necessarily denotes another. So if we were following you’re suggestion it woulb both be a rigid and an accidental designator.

The claims I wanted them to agree on were the material conditional versions: i.e. necessarily either Socrates was a philosopher or Fred was Plato and Ned was Aristotle, and necessarily either Socrates was never a philosopher or Fred was Aristotle and Ned was Plato.

So the question becomes: is there something that tribe A could learn about tribe B’s use of “Fred” and “Ned” that could cause them to accept these claims (and vice versa for tribe B and “Aristotle” /”Plato”.)

On the one hand, if Aristotle and Plato differ over their essential properties then one could distinguish Fred and Aristotle by their modal properties. But I think that we can then make a good case that tribe B are speaking a very unnatural language.

If we chose to reformulate the argument with objects that have no non-haecceitistic modal differences, like two twins in a symmetric universe, then the two languages seem more on a par in terms of naturalness. But then I also can’t see what fact they could ever come to learn that would make them accept (1) and (2).

That said, in the latter case I can’t think what would make them come to agree that Fred was necessarily twin1 and Ned was necessarily twin2 either. My inclination is to say there is no matter of fact in such cases. (Compare the case with two mathematician tribes who independently come up with names for the roots of -1. One tribe calls them i and -i, the other / and \ and it seems there’s no matter of fact whether to translate i as / or \.) I need to spend some more time sorting this out in my head though.