Are there unknowable truths?

@Broseph I'm not 100% sure, but I think it may be that polls created before a certain date don't show results before you choose an option, and polls created after that do. I remember it always being that you can't see the results until you've voted, and it only changed recently.

Truths must be computably-true, so there is a minimal Busy Beaver with a well-defined value that can't be known.

@Mira Good point, I wasn't even thinking of that when I made this. My go-to example of an unknowable truth comes from Fitch's argument:

I just flipped a coin and picked it up without looking at the result. No one will ever know which side it landed on. Therefore, one of the following is true: "The coin landed heads, but no one will ever know this," or "The coin landed tails, but no one will ever know this." Whichever of these two statements is true is unknowable, since knowing it would make it false, and it is impossible by definition to know a false statement.

@JosephNoonan What if they infer the initial conditions of our universe and simulate it forward up to the point that the coin flip concluded and know the outcome because our universe is superdeterministic? Then both are false.

@Mira Both are false assuming somebody actually does that (extremely unlikely). The point isn't that one of the statements is necessarily true; it's that, given that one of the sentences is true (which is almost surely the case), then it's unknowable.

@JosephNoonan this is a very weak argument. Your hypothesis is a presupposition of your question. You are saying if A and B are true, then B is true it is not wrong just not super surprising.

For this to be a good argument you need to proof that one of your two statements must be true.

@AlexbGoode

if A and B are true, then B is true

That's not what the argument is saying at all. The argument proves from the statement that a truth is in fact unknown that another truth is unknowable. In particular, "A is unknown," implies that "A & A is unknown," is unknowable. It's a well-known theorem that some people consider paradoxical because it means you can prove that an unknowable truth exists just from the fact that an unknown truth exists.

I used the particular example of the coin because I can say with near-certainty that no one knows how it landed, and no one ever will, and therefore, I can point to, "The coin landed heads, but no one will ever know this," as unknowable. This is not the same thing as claiming that, "The coin landed heads," is unknowable, which I am not claiming.

Also, the argument doesn't necessarily require that no one ever knows how the coin landed. It depends on whether you require all truths to be timeless or not. If you don't, then the argument will go through just fine with only the assumption that the result of the coin flip is currently unknown.

@JosephNoonan I am not getting this. You say:

The coin landed heads, but no one will ever know this

Which I translate to A = the coin lands heads and B = no one knows the coin landed heads. To have a world where B must be true there have to be facts that are unknowable. Otherwise there might be no facts that no one knows and your proof is about an empty set of facts.

@AlexbGoode You are confusing "unknown" with "unknowable". The argument doesn't claim that B must be true, just that B is in fact true.

The thing that must be true is that (A&B) is not known. This is true because it's logically impossible to know it (If you knew A&B, then you would know A, which would make B false, and by definition, you can't know a false statement). So if there is a single example of a true statement of the form "A, and A is not known", then there is an unknowable truth. I claim that the coin gives us an example, since my coin either landed heads or tails, but no one will ever know which. It doesn't matter if it's possible for someone to know whether the coin landed heads or tails, because that's not the unknowable truth whose existence the argument proves.

@JosephNoonan

So if there is a single example of a true statement of the form "A, and A is not known", then there is an unknowable truth.

To make sure that such an example exists you need to have an unknowable A. I'd argue that to proof that there exists (at least) one A that is unknown (for all time) you need to proof that A is unknowable. Hence my claim that your premise already assumes there is unknowable facts.

@AlexbGoode There's no reason that A would need to be unknowable for it to be unknown, or even forever unknown. I think it's just a completely unreasonable epistemic standard to say that we can only know that an unknown statement exists if the statement is unknowable.

@JosephNoonan The busy beaver is far more convincing to me. That just seems like a semantic game more than a real truth.

What if the universe is a simulation and the overseers are constantly monitoring every step of it? Then everything that happens is known at all times, and your implication is vacuous.

"81% of Americans say they believe in God", and presumably an omniscient god knows all truths at all times, possibly before you even constructed the experiment. So you already have to modify it to "unknowable to everybody except God" to convince them, and then you need a Theology degree to account for the evidence chain of how Heavenly truths might leak to Earth.

@Mira

That just seems like a semantic game more than a real truth.

I'm not sure what you mean by this. If "A & A is not known" is true, then it's a real truth.

What if the universe is a simulation and the overseers are constantly monitoring every step of it? Then everything that happens is known at all times, and your implication is vacuous.

Even if simulators know everything about the simulation, that doesn't imply that they know everything period. In any case, I don't think objections of the form, "But what if [implausible skeptical scenario] is true? Then your premises are false," are good objections to any argument. I'm arguing that the premises are in fact true, not that they would be true even in some skeptical scenario.

"81% of Americans say they believe in God", and presumably an omniscient god knows all truths at all times, possibly before you even constructed the experiment.

Yes, if God exists, and the traditional beliefs about him are true, then there are no unknown truths, and therefore no statements of the form "A & A is unknown" are true. Whether this is a good objection depends on how plausible you think God's existence is. Even in this case, though, the word "knowable" can be modified to "knowable by humans," and the argument goes through exactly as before to prove that there are some truths that it is impossible for a human to know. The required modification shouldn't make this example any less convincing than the busy beaver example, though, since if God exists, he also knows all values of the busy beaver function.

then you need a Theology degree to account for the evidence chain of how Heavenly truths might leak to Earth.

You need no such thing. The argument goes through exactly the same way as it did before if you restrict the scope of "known" and "knowable" to only include truths that are known/knowable by humans. It's impossible for a human to know, "A, and A is not known by any humans," since knowing that statement would imply that A is in fact known by a human, making the statement false.

@JosephNoonan I'll try to be more precise with argument. You are claiming

if A and B = 'A is unknown' than C = 'A and B' is unknowable

Let's assume, for the sake of argument, B is true, but A is knowable to avoid circular reasoning. Then, we agree, that C unknown. But that does not mean it is unknowable. It is just unknown. Since A is knowable so is C, it only depends on A. It just turns out that, by construction, C is false in this case. To ensure that there is unknowable true value you need to assume A is unknowable. Assuming A is simply unknown is not enough. Your argument makes the jump from 'unknown' to 'unknowable' as a language trick not as a rigorous conclusion.

Edit: I got it now. Thanks for engaging :)

@AlexbGoode Wait, I'm confused as to whether you got the argument or not. C doesn't depend only on A, it depends on A and B. The reason C is unknowable is that knowing A makes B false, so you can never know both at the same time, and hence never know C.

There is a bit of a trick in the argument, which is that, while it's impossible to know that C is true, it is possible to know whether C is true (If you knew A, you would know that C is false). It's possible to know that C is false but impossible to know that C is true, even when it is.