I don't think there's anything absurd or counterintuitive about us using the English language to describe possible (non-actual) or counterfactuals worlds. — Michael
The absurd and counterintuitive things occur because you have a contestable interpretation of how that works, just like your debate partners do!
If you're referring to C2 and C3 here, I do explain how we avoid them. The issue isn't with anything I have been saying but with the T-schema being imprecise (or misinterpreted). — Michael
I'm not. Nothing in what you've written seems relevant to the T-schema at all, you've got two different senses of interpretation, both of which could be analysed in terms of a T schema. "X" is true iff X. Your use of "true at" is making a different kind of model of the system of possible worlds the "right" kind of model for this scenario than "true in" would, and both senses of "true" could be T-schema'd.
I don't think there's anything absurd or counterintuitive about us using the English language to describe possible (non-actual) or counterfactuals worlds. — Michael
Which is what makes the above a bit tendentious. Because this discussion is bottoming out in the appropriate way to think of modelling networks of possible worlds. Which, honestly, is not the kind of thing everyday language settles at all.
You've shifted the debate terrain to a distinction between "true at" and "true in", but "true at" behaves exactly the same as your opponents' "true". If you call your opponents truth concept T_R, True at T_@ and true in T_I. Pick an element w of a world W, and call the sentence "there is w" S( w ) then the following have been stipulated to hold of existence claims:
A) S( w ) is T_R at W iff S( w ) is T_@ at W.
B) S( w ) is T_R at W iff w is in W.
C) S( w ) is T_I at W iff {w is in W & S ( w ) is in W}
D) S( w ) is T_R at W iff w is in W
T-sentences could be constructed for any sense of truth. The work they're doing is just by saying there's one sense of "true" without arguing about how the interpretation function should work with possible worlds - as if that interpretation function is innate in language. What you wrote above commits the same "appeal to intuition" which has been the unproductive engine of this entire thread.
My reading of what's gone on so far is the following clusterfuck:
A) S( w ) Is T_R at W iff S( w ) is T_@ at W
+
C) S( w ) is T_I at W iff {w is in W & S ( w ) is in W}
Gives you:
D) S( w ) is T_I at W iff {S( w ) is T_R at W & S ( w ) is in W)
which gives you:
E) S( w ) is T_I at W implies S( w ) is T_R at W
by taking one conjunct of the biconditonal then taking a conjunct of its right hand side through conditional proof.
In effect the conjunction doesn't save T_I and T_R from equivocating at W, you need an implication or another contraption. As in you somehow need T_I to only evaluate S ( w ) as true in worlds where S( w ) is and w is - a
restriction on appropriate interpretations of possible worlds, rather than of their domains. Or alternatively something like {w in W implies S( w ) is T_I}, which is what it was supposed to inhibit, and its contrapositive makes existence depend upon the existence of sentences.
It could be that you pick something not bivalent for the assignment function, or make it a partial function somehow, which would mean that worlds which have w in them but not an S( w ) simply don't assign any truth value for S( w ), or assign S( w ) a third truth value "mu" in a world where w is but S( w ) is not.
You'll probably claim that it's your opponents who are equivocating T_I with T_R, your opponents will claim you're equivocating T_R with T_I, and IMO everyone's right, but no one's actually arguing about what they disagree about.
Which is this:
In effect the conjunction doesn't save T_I and T_R from equivocating at W, you need an implication or another contraption. As in you somehow need T_I to only evaluate S ( w ) as true in worlds where S( w ) is and w is - a restriction on appropriate interpretations of possible worlds, rather than of their domains. Or alternatively something like {w in W implies S( w ) is T_@}, which is what it was supposed to inhibit.
Equivocating between the two can take the form "regardless of the status of language in the world, S ( w ) is true or false based on the entities in it" - which as I understand it is what you're picking a fight with, and are interpreting your opponents as saying. Or it can take the form "regardless of the status of language in the world, w in W implies S( w ) is true", in the latter case that true is a T_R... but it implies a T_I and a T_@, and it isn't T_I if there's no S( w )!
In terms of this:
A) S( w ) is T_R at W iff S( w ) is T_@ at W.
B) S( w ) is T_R at W iff w is in W.
C) S( w ) is T_I at W iff {w is in W & S ( w ) is in W}
D) S( w ) is T_R at W iff w is in W
Your opponents are hesitant to allow S( w ) to be a domain element, which means they might doubt C. You're not going to accept B, since you don't have a T_R, you have a T_I and a T_@. Your opponents and you believe in D, but you parse D as a definition of T_@ and they parse it as the definition of T_R - and you're both right.