If lie detectors become more accurate, this should do the job?

That assumes that lie detectors are infallible.

Yes to prove it beyond any doubt. I'm not sure it would be physically possible for a lie detector to be perfect.

I can prove that I know math if I can teach someone how to do math (properly).

The fact that you are doubting your existence, shows your existence. The question, in a Wittgensteinian way lacks sense.

In that hypotetical scenario, since you do know that, you must have a reason to know that, right? That reason is either accesible only to you, or to others. If it is accesible only to you, then you have no way of proving to others that you know that.

If it is a reason accesible to others, it must be one that refutes the solipsist who claims that you don't exist outside their imagination. But since it seems that solipsism is logically irrefutable, it would appear that you won't be able to prove that to others, even though you succeed in proving it to yourself (which is implied by the fact that otherwise you would not know with 100% certainty that you exist).

So to begin with: How do you know with 100% certainty that you exist?

What argument (if any) could logically refute the solipsist?

How do I know that I know? I guess my doubt reaches the Munchausen trilemma.

How do I know that I know? — Cidat

Let's say I know with 100% certainty that I exist. — Cidat

It's a hypotetical scenario where you know that with certainty (I thought you took this for granted in your second quoted statement here). That means your belief in that must be true, and also be perfectly justified. The second statement of yours I quoted here implies that you know that you know, and know that you know that you know and so on with complete certainty. (since otherwise you would not know that you exist with 100% certainty).

But the question is: How do you know that? Once you ask that to yourself and answer it to yourself, when someone asks you the same, you'd just have to give the same answer.

But before that you should ask: Is my answer going to be such that others will also know that with certainty, or is it such that it can only can be known with 100% certainty by me?

And if your answer is: “It's just obvious”, then ask yourself: Is it only obvious to me, or is it also obvious to the solipsist?

Can I then prove that I know this? — Cidat

Prove to who/what? Would not you need to know that I exist in order to prove your knowledge of something to me?

Let's say I know with 100% certainty that I exist. Can I then prove that I know this? (It's one thing for something to be true and another to know that it's true.) — Cidat

Interesting technical take on your question.

https://en.wikipedia.org/wiki/Zero-knowledge_proof

If lie detectors become more accurate, this should do the job? — Down The Rabbit Hole

You can be wrong about things but believe them to be true. A lie detector can only determine if you think you are right.

Let's say I know with 100% certainty that I exist. Can I then prove that I know this? (It's one thing for something to be true and another to know that it's true.) — Cidat

You don't have to know you know something in order to know it. After all, if one did, then no one could know anything as to know something would knowing that you know it, which would then require knowng that one knows that one knows it, and so on forever.

So, you know you exist. Why? Because your belief that you exist is true, and there is reason to believe it. You do not know have to know that your belief possesses these properties in order for it to possess them. So knowledge does not require knowledge that one knows.

I think Carnap brought it up and I'm probably butchering his exact idea he has a point. If you think to yourself, what do actually end up concluding? Not that you exist. What follows from "I am thinking" is that "thinking is going on". What thinking is, is quite obscure. We do it all the time, but it's hard to say what it amounts to. You can ask, how can there be thinking without existence? That's likely true, but it doesn't immediately follow from thinking.

This is a problem is science and philosophy, you can't defeat skepticism, there is no final indubitable proof. But let's say that you have very high confidence in the fact that you exist. That's fine, in that everybody who's alive believes the same thing. But say you encounter someone, a friend or a random person, saying "I exist, and I know it for certain." It would be a strange statement to say or even try to argue for. Can you prove this to other people? Well, if they're around you, they'd have to assume or take it for granted that you exist. But as an argument, I don't see how you can proceed. We have to take things for granted, otherwise we couldn't do anything.

You can be wrong about things but believe them to be true. A lie detector can only determine if you think you are right. — Tom Storm

Assuming that we already believe the person subject to the lie detector test exists. The result will prove to us if they know that they exist.

The result will prove to us if they know that they exist. — Down The Rabbit Hole

It will only establish that they think they exist. How do they know it is them doing the thinking?

It will only establish that they think they exist. How do they know it is them doing the thinking? — Tom Storm

If the lie detector shows that they think they exist, and they do in fact exist, they have proven to us that they know they exist.

Sure:

something
[ˈsʌmθɪŋ]
PRONOUN
a thing that is unspecified or unknown.
"we stopped for something to eat" ·
used in various expressions indicating that a description or amount being stated is not exact.
"a wry look, something between amusement and regret" ·

ADVERB
informal
used for emphasis with a following adjective functioning as an adverb.
"my back hurts something terrible" ·

Never thought a lie detector would solve a fundamental metaphysical conundrum

Let's say I know with 100% certainty that I exist. Can I then prove that I know this? — Cidat

Apparently not, though I'm trying to parse a hair here.

First, I perceive a distinction in your words. There is your knowledge about X, on the one hand, and your proof of your knowing on the other hand. No one can know what is in your head, beyond what you say. You may say you know X but no one else can know you know that. As far as the "other" is concerned, you could be lying, or mislead, or, like me, you could be a beginning philosopher struggling with all kinds of existential, ontological, etc. stuff that is over your head. But really, all anyone besides you has is your word for it. That is not proof. And I can't fathom of proof that would convince me you know something.

If you know it 100% and you keep your mouth shut, you are good to go. But if you tell someone you know it, then the burden is upon you to prove it. You can't use anecdote (that which happens a trillion times is likely to happen again, which is debatable and not proof that it will). So what else are you going to come up with as a proof? You might say it is self-evident, but that is not a proof either. You might grab my hand, place it upon you, get all up in my grill and ask "I exist, right!" And yeah, to avoid you kicking my ass I'll say "Sure, you exist." But I don't know you know it. In fact, my conversing with you might constitute my stipulation to your existence. But it is not proof thereof, and it's not proof of your knowledge of it. It's simply a gentlemen's agreement that you exist. A convenience. But not a proof.

There is something called Agrippa’s (or Münchhausen’s) trilemma which states that any justification of truth is endless unless you accept the circular, regressive or axiomatic argument. It basically describes the nature of proof. The axiomatic seems the penultimate solution, the only way to be justified in believing anything. So it appears that proof isn’t possible.

There's a mouthful that's over my head. But I recognize the word trilemma from another thread, so maybe I should go do some reading and less typing. Thanks.