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. — fdrake

That's not what's happening.

All that's happening is that I'm explaining that there is a difference between T_I ("truth in") and T_@ ("truth at"), and that nothing is T_I relative to a world without language (unless platonism is correct).

And then some seem to think that I’m saying that the existence of gold depends on the existence of language, despite me repeatedly denying this.

C'mooon!

All I'm saying is the usual thing in a discussion like this. That your stated position entails things you are claiming to disagree with. Which is what counts as a criticism or refutation attempt. That's been the crux of the thread. I've spelled out what that meant. Your T_@ behaves the same as their T_R, so your T_@ entails their T_R - that implication doesn't really follow, but everyone is behaving as if it does.

And people are behaving as if it does because no one's arguing about what the appropriate truth concept is for possible worlds directly, only appealing to common sense about it.

Your T_@ behaves the same as their T_R, so your T_@ entails their T_R — fdrake

Okay, but what does that have to do with T_I? My claim is that nothing is T_I relative to a world without language but that some things are T_@ relative to a world without language. If all you are claiming is that T_R and T_@ mean the same thing, and so some things are T_R relative to a world without language then this does not contradict anything I'm saying.

Maybe the issue is that you and I have very different interpretations of the difference between truth in a world and truth at a world.

All I mean is to make this distinction:

1. Something true can be said about W (truth at a world)
2. Something true can be said in W (truth in a world)

Which gives us:

3. Something true can be said about a world without language
4. Nothing true can be said in a world without language

(4) is a truism.

And unless platonism is correct, saying something true or false is all there is to truth and falsity – there are no mind-independent abstract truth-bearers.

Maybe the issue is that you and I have very different interpretations of the difference between truth in a world and truth at a world.

All I mean is to make this distinction:

1. Something true can be said about a world without language (truth at a world)
2. Nothing true can be said in a world without language (truth in a world)

And if platonism is incorrect then saying something true or false is all there is to truth and falsity – there are no mind-independent abstract truth-bearers. — Michael

Yeah the distinction makes sense. In the context of the thread, though, it interacts very oddly with lots of things. Truth at a world is something that can obtain of a world without there being truthbearers in it, which would be odd if there were no sense of truth which applied to a world with no truthbearers. In essence, p1 to 20ish of that discussion took to quantifying over truthbearers within a world and saying if no truthbearers, no truths in any sense. Now there are truths in some sense which concern a world and its entities, without necessarily being true in it.

Moreover, your opponents are arguing that to be true is to be true in a world - I think that's what you see it as anyway. And you say that this entails a platonism, like it's a bad thing? But truth at a world has the same trans-world property that made truth in a world incoherent, for you, with regard to truths. So in some sense the following is the case: {that "there is gold" is true at a world}, and that is a fact about a system of possible worlds. And the sense of truth, and the statement {that "there is gold" is true at a world} is something which is transworld, mind-independent, and doesn't care if there are people there or not. If that is stipulated to be a bad thing, making the distinction between truth at and truth in while keeping both in your model of truth concerning possible worlds keeps the bad thing.

Whereas in p1 to 20ish of the thread, the "bad thing" was blocked, because people were explicitly focussing on, and advancing, the (alleged) incoherence of there being truths with no truthbearers. Now it's not incoherent, it's simply platonist. And your interlocutor which keeps true@ and true-in in their account also has one "platonist" account of propositions, true-@. Which isn't really "platonist", it's just transworld, metalogical, whatever. Unless a sense of truth which concerns a world or its elements is platonist when and only when there are no truthbearers in that world but there are truths which concern it or its entities.

Moreover, your opponents are arguing that to be true is to be true in a world - I think that's what you see it as anyway. And you say that this entails a platonism, like it's a bad thing? — fdrake

Well, it's a bad thing if platonism is wrong, which I think it is, and as Banno has claimed to be a mathematical antirealist I take him to be an anti-platonist, and so if he were to claim that to be true is to be true in a world then he would have to abandon his realism in favour of a strong anti-realism, so there appears to be some sort of inconsistency there.

Now it's not incoherent, it's simply platonist. — fdrake

Well, it may be that platonism is incoherent, which some argue it is.

But truth at a world has the same trans-world property that made truth in a world incoherent, for you, with regard to truths. — fdrake

I don't understand this. Take a variation of what I said above:

1. Something true can be said about a world without language
2. Something true can be said in a world without language

(2) is certainly incoherent but (1) doesn't appear to be.

As an example: "the Earth would still exist even humanity were to go extinct". This is an English language sentence about a world in which no English sentence is spoken or written. It seems meaningful and is arguably true (especially if one is a realist).

Although, as I mentioned a few pages ago, whether or not (non a priori) counterfactuals are truth-apt is questionable.

I don't understand this. T — Michael

Here's a worked example.

This is our actual world, A.
There is possible world connected to ours with no humans, as if we were all instantly deleted. Call it A-H.

Just assume that a world with humans has all the truthbearers you'd wish.

There's gold in A. There's gold in A-H. Gold is an entity in both of their domains.
"There is gold" is true at A, "There is gold" is true at A-H.
"There is gold" is true in A. "There is gold" is false in A-H.

Make sense so far?

Alright, so there's this whole logic surrounding all of this. There's a bunch of possible worlds, the actual world... And in that whole system, it turns out to be the case that:

A) "There is gold" is true at A, "There is gold" is true at A-H.
B) "There is gold" is true in A. "There is gold" is false in A-H.

I've bolded "this case". It's a sense of satisfaction, truth, whatevs. That's something which is the case about... a system of possible worlds. Which isn't a possible world, it's a set of them... it has different semantics. So there's a sense of satisfaction, truth, blah which isn't true@... But it's true of the whole system of worlds. If you took the list of all possible worlds in your system of possible worlds, that system of possible worlds would satisfy {"There is gold" is true at A-H}, now is that satisfaction a satisfaction of truth@ or truth-in? It's neither, because it doesn't concern a world. But it concerns all the worlds... So it's transworld in some sense.

In addition, imagine who could possibly make the speech act that "There is gold" is true at A-H. No one could, there's no one with language in A-H. Which means there's a sense of truth which applies of entities in worlds with no humans. A mind independent truth. And it's truth@.

Which thus means that there's two forms of not mind dependent truth if you retain both truth@ and truth-in as part of your account of truth - you've got truth@ from the latter, and some broader metalogical sense of satisfaction regarding systems of possible worlds which you use to set up truth@ and truth-in in the first place.

Then let's assume you're an anti-platonist, that means you jettison truth@ entirely because of the above mind independence. Which means there's only truth-in. When then means it's either false or incoherent to say it's true that there's gold when there's no humans. Or you take another bull's horn and do something fancy with partial functions and a third truth value.

There's gold in A. There's gold in A-H. Gold is an entity in both of their domains.
"There is gold" is true at A, "There is gold" is true at A-H.
"There is gold" is true in A. "There is gold" is false in A-H.

Make sense so far? — fdrake

No, it should be:

"There is gold" is true at A, "There is gold" is true at A-H.
"There is gold" is true in A. "There is gold" doesn't exist in A-H.

In addition, imagine who could possibly make the speech act that "There is gold" is true at A-H. — fdrake

You're doing it right now.

there's no one with language in A-H. — fdrake

That's why there isn't a true sentence in A-H.

Maybe this diagram is easier to understand. The quoted sentences represent true (blue) and false (red) propositions.



Something is true in a world if it appears as a blue sentence in that world's circle. Something is true at a world if its truth conditions appear inside that world's circle.

In the above case there are no truths in World B even though there are two truths at World B.

The platonist places true and false propositions inside the World B circle even though there's nobody in World B to say those things, and I don't think that makes any sense.

"There is gold" is true in A. "There is gold" doesn't exist in A-H. — Michael

Aye! That makes the interpretation function partial. Because it doesn't exist. Or you assign the result of the interpretation to "mu" or something. Or you keep it as false and a total function with bivalence.

You're doing it right now. — Michael

I was doing it right before, under the assumption that the interpretation had to be bivalent and not partial. But it's at least not one of them, so you're in a totally different land truth value wise to what it appeared for the rest of the thread. True, false, "unassigned" - that's you!

You're in a similar position to saying that "2+2=4" isn't true on the domain {1,3}, because there's no symbol for "2+2=4". Which isn't to say that it's false, it's to say that it's not there.

Which isn't to say that it's false, it's to say that it's not there. — fdrake

Yes, precisely. I'm only saying that truth is a property of propositions and that there are no true propositions (truths) in a world without language (i.e inside the World B circle). There are also no false propositions (falsehoods) in a world without language.

Cheers, . Thanks for chiming in.

I don't see that @Michael has addressed what I had to say about the difference between the quantificational and substitutional interpretations. I did invite a re-set of the conversation in the previous page, but that didn't happen. I guess the next step is a broader discussion of the context.

The notion of "in a world" and "at a world" comes about as a result of an attempt to defend propositions against invoking Platonic forms. It's odd, something like insisting that there are propositions while denying that there are abstractions.

Here is the "easy" argument for propositions being mind-independent:

The proposition that there are rocks, which we denote <there are rocks>, does not entail the existence of any beings that have or are capable of having mental states. It entails this neither in a strictly or broadly logical sense. That is, it is possible in the broadest sense for <there are rocks> to be true in the absence of all mental states. But now, if this proposition is possibly true in the absence of mental states, then it possibly exists in the absence of all mental states, and so is mind-independent. This is an easy argument for the mind-independence of at least some propositions. — 7.1 Easy Arguments: Mind-Independence and Abstractness

But Oooo, that implies that there are propositions floating around...! And so the paraphernalia of "in a world" and "at a world" is dreamt up in order to to ward off Plato.

The alternative I offered, a few pages back, is that there are indeed propositions floating around, but that they are harmless. Extensionally, all we have are individuals, a,b,c... These we name, "a", "b","c"... Then we group them: {a,c}, {b}. Then we name the groups: f={a,c}. Then we form propositions, f(a), f(b). Here, some folk, perhaps @Michael, think that we have introduced a new thing into the world — the proposition f(a) — and so need the paraphernalia of "in a world" and "at a world" in order to avoid invoking Platonic forms.

Going over that again, "f(a)" will be true if and only if a is one of the things in the group f. This predicates truth over the faux-individual f(a). But f(a) is nothing more than a name for a group of individuals. No Platonic form has been summoned from hell.

We can happily treat f(a) as an individual, using the quantificational interpretation, but that is just a way of talking about a,b,c... It is a mistake to think that when we talk about propositions we are talking about something in addition to a,b,c..., that there is now something new in the world, the individual f(a), as well as a,b,c...

I'm only saying that truth is a property of propositions and that there are no true propositions (truths) in a world without language (i.e inside the World B circle). There are also no false propositions (falsehoods) in a world without language. — Michael

This invokes the existence of a new entity, the proposition, in the world in question. I hope that what I've set out above shows how this is an error, that {a} will be a member of {a,c} in w regardless of whether or not there is also language in w.

This invokes the existence of a new entity, the proposition, in the word in question. — Banno

It doesn't. We simply say true or false things or we don't, and that's all there is to truth and falsity. Your suggestion that there are truths in World B even though nothing true is being said in World B makes no sense – unless you're arguing for platonism, which I also think makes no sense.

But there are true things being said in World A about World B.

Your suggestion that there are truths in World B even though nothing true is being said in World B makes no sense — Michael

An yet {a} is still a member of {a,c}, even if there is no one in the world to say it.

Hence what we say is not all there is to truth and falsity. There is, in addition, what is the case - {a,c}

"truths in World B" is a misunderstanding. I think I've set out how. I don't see as I can help you any further.

Hence what we say is not all there is to truth and falsity. There is, in addition, what is the case. — Banno

I didn't say that saying things is all there is to truth and falsity. I said that saying true and false things is all there is to truth and falsity.

The diagram above is very clear. The existence of gold determines whether what we say is true or false, but it is nonetheless what we say that is true or false, not some other thing such that there are truths even if nothing true is said and falsehoods even if nothing false is said.

Then what you have been arguing for has changed; or was poorly expressed; or was trivial, all along.

A waste of time.

or was trivial, all along. — Banno

Yes, as it was always meant to be. It was a simple remark about how people were being imprecise with their use of the terms "true" and "truth". I thought this post from 11 days ago was clear enough, and yet still people were misunderstanding me and accusing me of saying something I'm not, despite me repeatedly and explicitly saying that I am being misunderstood and am not saying what I am being accused of saying.

accusing me of saying something I'm not. — Michael

As it stands, I have no clear idea of what the point you were attempting to make was. My apologies for attempting to take you seriously.

I will try not to do it again.

Cheers, ↪fdrake. Thanks for chiming in. — Banno

I be trying. Thank you for your thanks.

The alternative I offered, a few pages back, is that there are indeed propositions floating around, but that they are harmless. Extensionally, all we have are individuals, a,b,c... These we name, "a", "b","c"... Then we group them: {a,c}, {b}. Then we name the groups: f={a,c}. Then we form propositions, f(a), f(b). Here, some folk, perhaps Michael, think that we have introduced a new thing into the world — the proposition f(a) — and so need the paraphernalia of "in a world" and "at a world" in order to avoid invoking Platonic forms. — Banno

I think that dodges the issue as stated in thread but not the spirit of the challenge it poses. I don't exactly believe what I'm writing below, I'm just trying to make the discussion productive by providing a bridge.

You've got "we" group them there, which ultimately comes down to why "we" get to form propositions like f( a ) to begin with, right? What the algebra is doing is modelling sentences like "there are rocks" by associating that with a sentence in the logic like "there is at least one x such that x is in R", and R is just a list of rocks. Even if we say God invented the constant symbols we still have to make the predicates.

What that does, if you don't grant the existence of "truthbearers" in a world to begin with, is stop you from forming sentences like "there are rocks" using that algebra in that world. In that world the predicate "is a rock" isn't an empty predicate - it's also not truth-apt as it's missing an argument. The quantified expression "there are rocks" is, however, blocked from being formed. Why? Because what's at stake is whether it makes sense to be able to form it in that world.

What about "outside" that world? @Michael and I got into that a bit. Because there's definitely resources to define sentences independently of worlds, and if you took a world without humans but which had rocks, "there are rocks" somehow makes sense for it (truth@ but not truth-in), even though truthbearers don't... exist... in the same way for that world as they seem to when humans are about. We're still working on that I think.

An yet {a} is still a member of {a,c}, even if there is no one in the world to say it. — Banno

That would be true@. Or T_@ as I called it in a prior post. As in "there is an x such that x is a" is true when quantified over that domain. Which @Michael seems to accept as a cromulent thing. For you that seems to be the only way to talk about true and false, which I called T_R in my attempt at clarification. T_@ looks to be your "true". But truth-in works more like {"there is x" is T_I with regard to W} iff {x in W & a truthbearer for "there is x" is in W}, which is T_@ for x and also T_@ but applied to sentences.

Hence the confusion in thread IMO. You end up having the ability to form sentences being some weird transworldly thing, because it still makes sense if you stipulated a whole bunch of possible worlds with no truthbearers in them. Which is odd when the logic is supposed to describe how sentences work. It'd be like saying recipes exist without food.

Which chimes with:

The platonist places true and false propositions inside the World B circle even though there's nobody in World B to say those things, and I don't think that makes any sense. — Michael

I don't care too much about which account is true, they both seem like cromulent ways of doing business. It's just two ways of answering "If a tree falls in the forest and no one hears it does it make a sound...", Michael says no or "mu" or "cannot compute", @Banno says yes, in ye olde page 2-10 @Leontiskos sort of says "yes, because God hears it" and @Wayfarer sort of says "no, because what it means to be a sound is to be heard".

As it stands, I have no clear idea of what the point you were attempting to make was. My apologies for attempting to take you seriously.

I will try not to do it again. — Banno

This line of discussion started from this comment of mine:

What some are saying is that "a truth" means "a true proposition" and "a falsehood" means "a false proposition", that a proposition requires a language, and that a language requires a mind.

This is not to say that a mind is sufficient; only that it is necessary. The (often mind-independent) thing that the proposition describes is also necessary (to determine whether or not the proposition is a truth or a falsehood).

So the claim is that when all life dies out there will be gold in Boorara but no truths or falsehoods because there will be no propositions. — Michael

In even simpler terms, there is gold in Boorara even if nothing is being said but there are no truths if nothing true is being said and no falsehoods if nothing false is being said.

You finally now seem to agree with me.

This line of discussion started from this comment of mine: — Michael

...which was in turn a reply to a comment of mine. Should I not have taken you as responding to my

For "A world without any minds", isn't it true at the very least that there are no minds?

So we have at least one truth. — Banno

??

This is quite mad.

Given that nothing true is being said in a world without minds, nothing is true in a world without minds.

But something true is being said in the actual world in which there are minds at/about a world without minds.

Ok, so you tied yourself in a knot by thinking about in and at. You OK now?

In particular, since it now appears to have been the source of your considerations, do we agree that for "A world without any minds", it is true at the very least that there are no minds?

Edit: If it helps you keep on track, we can add that no one in that world can think, say, believe or otherwise have an attitude towards that proposition...

I'm not tying myself in knots. I'm making this very simple observation:



There are no truths in World B because nothing true is being said in World B.

But there is a truth in World A because something true (about World B) is being said in World A.

Is it true that there are no minds in world B?

Is it true that there are no minds in world B? — Banno

This can mean one of two things:

1. Are there no minds in World B?
2. Is "there are no minds in World B" true?

The answer to both is "yes".

And as the diagram shows, "there are no minds in World B" is a truth in World A about World B, not a truth in World B.

The answer to both is "yes". — Michael

That could have saved us a lot of time.

And as the diagram shows, "there are no minds in World B" is a truth in World A about World B, not a truth in World B. — Michael

But this sentence wasn't true before you uttered it, right? That's truth anti-realism. A truth realist would say it was true before you said it.

But this sentence wasn't true before you uttered it, right? — frank

There wasn't a sentence before it was uttered.

That's truth anti-realism. A truth realist would say it was true before you said it. — frank

The anti-realist (at least of Dummett's kind) says that if a sentence is true then it's possible to know that it's true (subject to the appropriate restrictions as per Fitch's paradox), whereas the realist allows for the possibility that some true sentences are unknowably true.