There is at that world no sentence "there is gold in those hills" that is either true or false; and yet there is still gold in those hills. Hence it is truth that there is gold in those hills, and that the sentence "there is gold in those hills" is true. — Banno

You appear to be switching between truths in a world and truths at a world, given that you start by saying that there is no sentence that is either true or false and then end by saying that there is a sentence that is true.

The nature of this oddity is that the sentence (proposition may be a better choice here) is not one of the things in the world, but a construct from those things. This is shown by the substitutional interpretation, but hidden by interpretations that treat sentences as what we might loosely call something like "substantial" things such as hills and gold...

In a second-order logic sentences such as f(a) and ∃(x)f(x) are not in the domain. — Banno

I still don't see the problem with the premise. Do you find anything objectionable about the below?

1. If the King of France is bald then the King of France exists

Perhaps performing a T-schema substitution will make it clearer:

1. If "the King of France is bald" is true then "the King of France exists" is true

And then, using modus tollens:

2. If "the King of France exists" is not true then "the King of France is bald" is not true.

1. If "the King of France is bald" is true then "the King of France exists" is true — Michael

What about 'If "the king of France is bald" is false then " the King of France exists" is true?

What about 'If "the king of France is bald" is false then " the King of France exists" is true? — Janus

What about it?

It should be obvious to you that I'm asking if you think it follows.

That's an ambiguous question.

Given that no King of France exists, a case can be made that "the King of France is bald" is neither true nor false, and is why I specifically phrased my conclusion as "not true" rather than "false".

With that in mind, the case can be made that "the King of France is bald" is false if and only if the King of France exists and is not bald, and so yes, it would follow.

Makes sense to me.

You appear to be switching between truths in a world and truths at a world — Michael

Well, yeah. Even Leon has to be able to say there is no gold at a world with no language, while presumably maintaining that there is gold, somehow, in order to even set out his proposal. So that's not problematic, surely. We are using a Tarskian semantics, after all. What else is there.

1. If the King of France is bald then the King of France exists — Michael

I don't see how introducing such dubious stuff helps. As you say, the truth functionality of "The king of France is bald" is contentious. The set of present Kings of France is empty. "The gold in those hills" is not empty.

The set of present Kings of France is empty. — Banno

And the set of truth bearers in a world without language is empty. Therefore if truth is a property of truth bearers then the set of truths in a world without language is empty (even if the set of gold in a world without language is not empty).

Per your view there aren't many truths in the present either.

Per your view there aren't many truths in the present either. — frank

Yes, we’re not saying many true things in the present.

But there are many mountains and planets and so on.

This is a pretty cool truthbearer:

repeating an erroneous argument doesn’t make it correct. Even if you say it three times.

I'm repeating it because you don't seem to be addressing it. You seem to think I'm saying something I'm not and addressing that instead.

From Truth in a World vs. Truth at a World

One way for something to be true with respect to a world requires the truth-bearer to exist in the world and be true there. Another way is for the truth-bearer to “correctly describe” the world, where this does not require existing in the world.

...

The conceptualist may claim that propositions can be true at worlds without being true in them, by analogy with the examples from Pollock and Buridan. A proposition like <there are no propositions> is true at certain possible worlds but true in none.

All I am saying is that there are no truths (true propositions) in a world without language. Either this is true or platonism is true, and I don't believe that platonism is true.

See here for a visual representation.

With that established we can then consider something like the T-schema:

"it is raining" is true iff it is raining

This can be interpreted in one of two ways:

a. "it is raining" is true in world A iff it is raining in world A
b. "it is raining" is true at world A iff it is raining in world A

If we interpret the T-Schema according to (a) then we are left with the other argument I gave:

P1. "it is raining" is true in world A iff it is raining in world A
C1. Therefore, it is raining in world A iff "it is raining" is true in world A
P2. If "it is raining" is true in world A then "it is raining" exists in world A
C2. Therefore, if it is raining in world A then "it is raining" exists in world A
C3. Therefore, if "it is raining" does not exist in world A then it is not raining in world A

You took issue with P2, but if you understand what it means for something to be true at a world but not in that world then you should understand what it means for a proposition to exist or not in a world.

That leaves us with either accepting C2 and C3 or rejecting P1.

If we reject P1 then we can re-interpret the T-schema according to (b) and/or we can amend P1 to:

P1. If "it is raining" exists in world A then "it is raining" is true in world A iff it is raining in world A

Either option allows us to avoid C1 and C2.

The conceptualist may claim that propositions can be true at worlds without being true in them, by analogy with the examples from Pollock and Buridan. A proposition like <there are no propositions> is true at certain possible worlds but true in none. — Michael

The world isn't empty without language in it though. There'll still be rocks and gold. Which will mean statements like "this is gold" evaluates to true in that world, not just at it.

A world absent propositions in such a logic would be quite different again, since propositions aren't world objects. As in, "there is gold in this world or there is not gold in this world" is a statement true even of an empty world (with an appropriate logic) since it's a tautology of that logic, but there is no gold.

Treating propositions as world objects also commits an odd kind of syntax error. An example, saying "there is gold", would mean that world has gold as an element in it. The presence of the propositional symbol "{the sentence "there is gold}" doesn't entail anything about whether gold is in that world. So in that world "there is gold" is true even though {the sentence "there is gold"} isn't a domain element.

In effect you've stipulated a flavour of logic by specifying an interpretation mechanism for worlds - every interpretation of worlds which interprets "there is gold" as true must have a domain element {the sentence "there is gold"}.

This isn't to say that the distinction you've used between truth in and truth at a world is a bad one, it's just that it behaves more like a stipulation about modality which should be defended on its own terms. How you're using it would have to defend that a world which has a set of entities T but no corresponding "there is..." sentences would have the same theorems about it as an empty world - even though gold could be an element of the first world and not in the second.

In terms of the metalogic, that makes the truth of the matter whether there is gold in the world depend upon whether there is a person there to see it. But in a vacuous sense, since there are no descriptions to be true or false.

The world isn't empty without language in it though. There'll still be rocks and gold. — fdrake

I know.

Which will mean statements like "this is gold" evaluates to true in that world, not just at it. — fdrake

If the proposition "there is gold" is true in that world then platonism is correct, and I do not believe that platonism is correct. If platonism is incorrect then "there is gold" is only true at that world.

But in a vacuous sense, since there are no descriptions to be true or false. — fdrake

And that's all I've ever been saying. If nothing is being said then nothing true is being said. The notion that there are truths and falsehoods without something true or false being said makes no sense to me.

If you think that truths are required for something to exist (and that falsehoods are required for something to not exist?) then that's on you. I certainly don't think it follows.

I know. — Michael

It would just be that "this world has objects in it" isn't true when you deprive a world of of language. But if you can somehow speak "about" the world, like "at" the world, I have honestly no idea what the point of this discussion is. If we were trying to avoid speaking about worlds when they have no truthbearers why are we suddenly allowed to have an entire new modality associated with the ability to speak about worlds that have no truthbearers in them? The "true at" concept is free floating - interworldly, doesn't care about whether speakers exist in this or that world - in precisely the same manner as the one being criticised.

I have honestly no idea what the point of this discussion is. — fdrake

I am simply saying that truth is a property of truth-bearers and that truth-bearers are features of language (i.e. platonism is wrong), and so therefore nothing that exists in a world without language has the property of being either true or false.

I don't think that this is anything controversial (unless you agree with platonism) or substantial, and so I don't understand the resistance I'm facing. I can only assume that people think I'm saying something I'm not.

and so therefore nothing that exists in a world without language has the property of being either true or false. — Michael

Entities aren't true or false though? Unless they're sentences. "there is a rock" is true or false. The rock isn't true or false. This might be a pedantic point but I don't know.

I don't think that this is anything controversial (unless you agree with platonism) or substantial, and so I don't understand the resistance I'm facing. I can only assume that people are thinking I'm saying something I'm not. — Michael

It's presumably because the things you're saying appear to entail lots of absurd and counterintuitive things. Much like the idea that propositions are somehow trans-world and nevertheless language items, which you're criticising.

Mostly as @Srap Tasmaner said earlier. It's quite silly to have a discussion where everyone's appealing to uncontroversial common sense.

Entities aren't true or false though? Unless they're sentences. "there is a rock" is true or false. The rock isn't true or false. This might be a pedantic point but I don't know. — fdrake

Yes, that's the point I have been trying to make for over a week.

It's presumably because the things you're saying appear to entail lots of absurd and counterintuitive things. — fdrake

If you're referring to C2 and C3 here, I do explain how we avoid them. I don't think the issue is with anything I have been saying but with the T-schema being imprecise (or misinterpreted).

Much like the idea that propositions are somehow trans-world and nevertheless language items. — fdrake

I don't think there's anything absurd or counterintuitive about us using the English language to describe possible (non-actual) or counterfactuals worlds.

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.

This is the kind of thing I am arguing against:

It misleads Michael to think that truths only exist when sentences exist. — Banno

I am saying that a truth is a true sentence, much like a falsehood is a false sentence, and that, contrary to platonism, a sentence (whether true, false, or neither) only exists if a language exists, because sentences are not mind-independent abstract objects.

That is all.

That is all. — Michael

You're a philosopher, you can't say just what you've said. That's not how it works. You say all the things you might be committed to under some utterly insane interpretation, which also happens to be your own when held up to the light in the court of reason.

What insane interpretation? I am simply making two simple claims:

1. "a truth" means "a true sentence"
2. Sentences are not mind-independent abstract objects à la platonism

Do you disagree with either of these?

I am simply saying that you are simply refusing to play ball.

I am simply saying that you are simply refusing to play ball. — fdrake

With what? The problem as I see it as that you and others think I'm saying something I'm not and now you're criticising me for not defending what I'm not saying.

With what? The problem as I see it as that you and others think I'm saying something I'm not and now you're criticising me for not defending what I'm not saying. — Michael

I am not simply saying that you're simply saying something that you're not saying, I'm saying that what you're not saying simply is part of what you're simply saying, even if you think you've simply said nothing of the sort.

Then perhaps you can tell me which, if either, of these you disagree with?

1. "a truth" means "a true sentence"
2. Sentences are not mind-independent abstract objects à la platonism

I'm simply not saying either.

Then you're not addressing what I'm saying, because those are all I'm saying.

C'mooon man, you know as well as I do that repeatedly shifting the frame of the discussion away from how people are disagreeing with you stops people from having a productive discussion. Can we not have another 32 pages of it. I've provided you a very, very thorough breakdown here. It's your choice whether you want to engage with it or not.