Can a statement be true or false if it is not possible to determine which it is, even in principle? — T Clark

Can such a statement be constructed?

"This statement is true or it is not possible to determine that this statement is true".

If the statement is false, then it is not possible to determine that it is true. It can't be determined to be true if it is false.

If the statement is true, nothing is said about it's being determinate - the left of the disjunction can have either value.

So the truth value of the statement cannot be determined.

I started working on a response to your post but quickly started running around in circles. I'm still thinking about it and I'll get back to you later.

1) Can a statement be true or false if it is not possible to determine which it is, even in principle? — T Clark

I want to clarify this. Do you mean we have an idea that we can conceivably prove to be true or false, but we don't currently have the means to do it? Or do you mean an idea that we have no conceivable means of even trying to prove it true or false?

So for example, someone might say, "Tomorrow I may die." In this case, you have to wait until tomorrow to come for you to figure out if you do indeed die tomorrow.

However, if I say, "Tomorrow I will die in my sleep.", will you ever be able to confirm that? I'm assuming of course that in your sleep you would not be conscious of your death. So if you died, you would never know. But lets say you don't die tomorrow, but go into a deep coma. You then die the following day. In this case, it was impossible for you to confirm whether your statement was true or false.

I want to clarify this. Do you mean we have an idea that we can conceivably prove to be true or false, but we don't currently have the means to do it? Or do you mean an idea that we have no conceivable means of even trying to prove it true or false? — Philosophim

The example I used in the OP may clarify things.

I think the multiverse interpretation of quantum mechanics is meaningless because I believe it is not possible to demonstrate if it is true or false, but, I can't prove it is not possible. Given that, what is the status of the multiverse interpretation.

I think the multiverse interpretation of quantum mechanics is meaningless because I believe it is not possible to demonstrate if it is true or false, but, I can't prove it is not possible. Given that, what is the status of the multiverse interpretation. — T Clark

Ok, I think I see what you're going for. In this case, I would say you would know what it would take to prove multiverse theory true or false, (humanity discovering an answer), you just believe it is impossible that humanity will ever have the capability to do so.

This is really a combined question with a premise.

a. It is impossible for humanity to ever discover if multiverse theory is true or false.
b. Consequently, the multiverse interpretation of quantum mechanics is meaningless.

As some could quibble with "meaningless", lets change it to "unprovable".

If A is true, then b is true by consequence. But it could happen that tomorrow mankind discovers multiverse theory is true or false. Therefore this proposal is more of a prediction such as, "Tomorrow the sun will rise again." As such, the only thing we can do in this case is wait. Maybe humanity will discover the truth about multiverse theory, and maybe they won't.

If A is true, then b is true by consequence. But it could happen that tomorrow mankind discovers multiverse theory is true or false. Therefore this proposal is more of a prediction such as, "Tomorrow the sun will rise again." As such, the only thing we can do in this case is wait. Maybe humanity will discover the truth about multiverse theory, and maybe they won't. — Philosophim

Yes, I think you've laid the argument out correctly. You've raised another question in my mind. Here it is:

Since there is no evidence whether it is possible to determine the truth or falseness of the multiverse interpretation of QM, should that interpretation be given serious consideration as a scientific theory?

Since there is no evidence whether it is possible to determine the truth or falseness of the multiverse interpretation of QM, should that interpretation be given serious consideration as a scientific theory? — T Clark

In short, no. But that theory might inspire funding into trying to see if its possible to prove multiverse theory. You would absolutely need to prove multiverse theory first. But humans are often times fueled by dreams that lead us to truths we would never find otherwise.

I'm still thinking about it — T Clark

Me too.

"This statement is true and it is not possible to determine that this statement is true" seems to be determinately false.

"This statement is true or it is not possible to determine that this statement is false"... well, if it is true, then of course one can't determine it to be false, so that looks determinately true.

Then we could play with conditionals...

"If it is not possible to determine that this statement is true then it is true"...

Question 1) Can a statement be true or false if it is not possible to determine which it is, even in principle?
Statement 1) Since there is no evidence whether it is possible to determine the truth or falseness of the multiverse interpretation of QM, should that interpretation be given serious consideration as a scientific theory? — T Clark

There may be no evidence today determining the truth or falseness of the multiverse interpretation of QM, but there may be evidence next year. As @Philosophim wrote: "Maybe humanity will discover the truth about multiverse theory, and maybe they won't"

Question 1) refers to a proposition that it is not possible even in principle to determine whether true or false.

As it may be possible to determine whether the proposition "there is a multiverse" is true or false, it is therefore possible in principle to determine that the proposition "there is a multiverse" is true or false.

Therefore, question 1) has no bearing on statement 1).

(Although I am not sure everyone would agree that there is no evidence for a multiverse)

I can't decide whether the question as to whether propositions that are undecidable for us can nonetheless be true or false is itself undecidable or not — Janus

This doesn't seem to lead anywhere, because it involves a vicious epistemic circle. Truth or falsity are established in the framework of some epistemic standards. Janus's statement questions one epistemic standard, which is fine, but the resolution will require some other epistemic standards, distinct from the one that is being questioned.

@T Clark

Let's, arguendo, agree that you're right and metaphysical claims, for reasons we need to be informed of, can't be true/false.

The following are neither true nor false:

1. Cook
2 Kplx zgfd
3. This sentence is false (liar sentence)
4. &×*
.
.
.

Then, as per you, the following too are neither true nor false:

1. Free will exists
2. God doesn't exist
.
.
.

Are you saying "Kplx zgfd" = "God doesn't exist"? Am I missing something?

@Janus I can't decide whether the question as to whether propositions that are undecidable for us can nonetheless be true or false is itself undecidable or not"

Starting with @T Clark's question "Can a statement be true or false if it is not possible to determine which it is, even in principle?"
Considering "there is a god beyond our comprehension" as an example of a proposition which we can never know even in principle whether true or false.
So, the answer to @T Clark's question is yes, a proposition such as "there is a god beyond our comprehension" not only can be true or false but must be either true or false.

In answer to @SophistiCat's question as to where does this lead, it leads to the knowledge that there are some things that are beyond our comprehension.

There may be no evidence today determining the truth or falseness of the multiverse interpretation of QM, but there may be evidence next year. As Philosophim wrote: "Maybe humanity will discover the truth about multiverse theory, and maybe they won't" — RussellA

That's the question I'm wrestling with. I think, although I'm not sure, that there's a standard that has to be met. It's like they say, you can't prove a negative. There has to be a point where I stop and say "We've found no evidence. We can't see any way of testing this hypothesis. That's the best we can do." I don't know if we are at that place yet with the QM multiverse interpretation or, say, string theory. It is my understanding that many scientists think we are.

This doesn't seem to lead anywhere, because it involves a vicious epistemic circle. Truth or falsity are established in the framework of some epistemic standards. Janus's statement questions one epistemic standard, which is fine, but the resolution will require some other epistemic standards, distinct from the one that is being questioned. — SophistiCat

An example would be helpful if you can think of one.

The following are neither true nor false:

1. Cook
2 Kplx zgfd
3. This sentence is false (liar sentence)
4. &×* — TheMadFool

1, 2, and 4 are not propositions. This argument doesn't apply to them. 3, the liar's paradox has always bothered me. @Banno made a similar comment earlier in the thread. I'm still working on a response.

Then, as per you, the following too are neither true nor false:

1. Free will exists
2. God doesn't exist
. — TheMadFool

I think "Free will exists" is a metaphysical question and is neither true nor false. Let's not get into a discussion of the merits of that position right now. I've acknowledged several times in various threads that I am ambivalent about how existence of a specific God or gods fits into metaphysics. It would seem that the existence of the Christian God is a matter of fact, and, thus, not a metaphysical question. Again, I don't want to get into the specifics of this particular issue in this thread.

Am I missing something? — TheMadFool

I don't think your argument, to the extent your response even provides one, has any merit.

So, the answer to T Clark's question is yes, a proposition such as "there is a god beyond our comprehension" not only can be true or false but must be either true or false. — RussellA

I don't understand how you reach that conclusion.

In answer to SophistiCat's question as to where does this lead, it leads to the knowledge that there are some things that are beyond our comprehension. — RussellA

I don't agree with that either.

An example would be helpful if you can think of one. — T Clark

Speaking of epistemic standards, or perhaps just clarifying the question: how do you judge whether a proposition is true or false, decidable or undecidable? Does truth or falsity just mean your opinion on the matter, or do you mean objective truth? By decidable do you mean whether you are able to make up your mind or, again, decidability in some objective sense?

Do you consider any method of evaluation or something more specific, e.g. empirical, scientific test? (When you talk about interpretations of quantum mechanics, for example, it sounds like you mean the latter, to the exclusion of any other standard.)

Any of these questions admit multiple answers, depending on what you want to do. The trick in not getting bogged down in pseudo-paradoxes is being upfront and consistent.

how do you judge whether a proposition is true or false — SophistiCat

Justification

decidable or undecidable — SophistiCat

That is the question on the table. Here's what I wrote in a previous response to @RussellA.

That's the question I'm wrestling with. I think, although I'm not sure, that there's a standard that has to be met. It's like they say, you can't prove a negative. There has to be a point where I stop and say "We've found no evidence. We can't see any way of testing this hypothesis. That's the best we can do." I don't know if we are at that place yet with the QM multiverse interpretation or, say, string theory. It is my understanding that many scientists think we are. — T Clark

(When you talk about interpretations of quantum mechanics, for example, it sounds like you mean the latter, to the exclusion of any other standard.) — SophistiCat

It is my understanding that all interpretations of QM are equivalent in that they have not been verified and may not be verifiable.

There has to be a point where I stop and say "We've found no evidence. We can't see any way of testing this hypothesis. That's the best we can do." I don't know if we are at that place yet with the QM multiverse interpretation or, say, string theory. It is my understanding that many scientists think we are. — T Clark

I call these philosophies Gandolfian theories. There are plenty of people who postulate what Gandolf from The Lord of the Rings would do in a certain situation. How was he feeling? How was he thinking? But at the end of the day, everyone forgot that Gandalf wasn't real. if he was real, we could take all of these conversations seriously, and it would probably solve a lot of problems and mysteries in life. But he's not.

For me, to find that part where I say, "There's no way of testing this hypothesis," I invent a hypothesis that cannot be tested, and try to think why I cannot test it. Take an invisible unicorn for example. Perhaps there are invisible undectable unicorns that exist. It seems in our head like it could be true. But that's nothing we can actively test in reality, because its undetectable.

If you cannot apply an idea to reality, then it is a Gandolfian idea. It can be a lot of fun to think about, but ultimately, its fiction.

I'm still working on a response. — T Clark

Don't forget to include me in your reply after you've thought things through.

1, 2, and 4 are not propositions. — T Clark

1. Non-propositions are neither true nor false.
2. Metaphysical claims are neither true nor false.

How do you distinguish non-propositions from metaphysical claims?

How do you distinguish non-propositions from metaphysical claims? — TheMadFool

Yep.

Aesthetics?

how do you judge whether a proposition is true or false — SophistiCat

Justification — T Clark

Well, that doesn't say much. Justification for whom? Just you, or "us" (as in your response to RussellA), or some kind of objective justification (if that's not an oxymoron)? And what kind of justification?

If it is a matter of what you personally hold to be true or false, decided, undecided or undecidable, then there doesn't seem to be much to puzzle over. Whatever isn't decidedly true or false is perforce neither true nor false. So setting setting that edge case aside, what is it exactly that you are asking?

It is my understanding that all interpretations of QM are equivalent in that they have not been verified and may not be verifiable. — T Clark

Interpretations of QM are equivalent with respect to a particular epistemic standard: that of being empirically distinguishable. But some people prefer one interpretation to another, even while acknowledging that they are empirically indistinguishable. So clearly there can be other epistemic standards at work.

1) Can a statement be true or false if it is not possible to determine which it is, even in principle? Then, if we can decide that question — T Clark

Depends on how truth is understood. Some will insist that there can be no use to asserting a proposition whose status is unknowable, so it's just a bad question.

A realist might be bound to say there is a use for this sort of thing.

) What happens if we can't determine if the truth of a statement is decidable in principle or not? — T Clark

Methodological realism.

Yep.

Aesthetics? — Banno

When it comes to metaphysics, a pulchra mendacium (beautiful lie) is acceptable and maybe even desirable/preferrable à la gennaion pseudos (noble lie)?

Imagine if people knew for certain God was a fairy tale?

Bedlam!

a beautiful lie is acceptable — TheMadFool

But a lie is false.

@T Clark's question is about statements the truth of which are indeterminate. A lie does not have an indeterminate truth value. It is false.

Then Janus came up with this, which set me thinking: — T Clark

To be true or false as a particular claim requires meeting the test of being a statement to which both the principle of noncontradiction and the law of the excluded middle apply.

If the the PNC fails to apply, the statement is logically vague. It is neither true nor false.

If the LEM fails to apply, the statement is logically general. I would say this covers the recursive or self-referential case where the statement is seemingly both true and false at the same time.

The subject where this issue most often comes to mind for me is interpretations of quantum mechanics and, in particular, the multiverse interpretation. In my mind, unless there is an experiment or theoretical development that can determine which interpretation is correct, then anything beyond the Shut Up and Calculate Interpretation is meaningless. — T Clark

In practice, decidability is a pragmatic exercise. I would say that while we can model the world as if it has counterfactual definiteness all the way down - and so is seems that bivalent logic ought to apply - in fact Nature I only admits to being relatively divided. This makes it vague or indeterminate at base.

This is a view quantum theory looks to confirm. The Planck constant defines a fundamental grain of uncertainty.

So there are three ways to go on quantum decoherence. You can get hung up on the bivalent question of whether there is a definite collapse to classicality or instead no collapse and hence MWI. The third answer would be to say that decoherence is a reduction towards classicality, but never a complete one. Some degree of indeterminacy or vagueness remains. The PNC never completely applies.

So both MWI and classicality get ruled out as being logically imposed fictions on our metaphysics. If we expand our metaphysics to include the concepts of vagueness and generality, some of the major historical blocks on metaphysical thought start to fall away.

Imagine if people knew for certain God was a fairy tale? — TheMadFool

But we do know that Thor is a fairytale.

But a lie is false.

@T Clark's question is about statements the truth of which are indeterminate. A lie does not have an indeterminate truth value. It is false. — Banno

Indeed! However what's the best course of action when you don't know if a proposition is true or false? Assuming it's false seems more reasonable than assuming it's true.

Too, @T Clark hasn't really said anything about how metaphysical claims aren't true or false. They are clearly propositions as per the objections he raised to my post.

Another issue is whether he means to say metaphysical claims can be true/false but can't be verified/falsified like peusdoscience or does he think that metaphysical claims are propositions to which truth values are N/A?

In addition, what about other truth values like both true and false (neither true nor false is a contradiction) and what of multivalent logic? T Clark's stand on metaphysical claims is very Buddhist. See Nagarjuna's tetralemma and Siddhartha Gautama's cryptic response to the metaphysical question "does the Buddha live after death?" @Wayfarer will probably explain it better.

There's a large literature on the truth value of metaphysical statements.

The notion that metaphysical statements are neither true nor false won't bare a load. Metaphysical statements are taken as true, but unjustified.

Like that the bishop stays on it's own coloured squares. There's no reason for it, but it is true.

Metaphysical statements are taken as true, but unjustified. — Banno

You mean true/false, right?

Of course if this is some kind of Gödelian move, I'm willing to get on board.