Try thinking this way: subjective truth "needs" objective truth, like you need water. This is the necessity I am talking about: every truth must be true. Subjective truth must be objectively true, otherwise it is false. You can believe something to be true only as long as there is the possibility of "truth," of which you must know the conditions of existence, otherwise you cannot believe anything to be "true." And what are these conditions? Precisely that "every (subjective) truth must be (objectively) true."

"subjective truth "needs" objective truth". If that means anything at all, it means that if you think that something is true, then that something is true. But that is obviously false. I very often think that something is true, but then, it turns out not to be true. I have then made a mistake. It is true that I am writing this post, but it does not have to be true that I am writing this post. I could have been doing something different, like milking a cow. It is also false that every truth must be true, since there are many truths that don't need to be true. I am replying to you, that is true. But I don't need to be replying to you, and I might not. What, perhaps you mean is that it must be that if a statement is true, then the statement is true. And, I suppose that everyone agrees with that. It is like saying that if something is a banana, then it is a banana. Who would disagree? .

"You can believe something to be true only as long as there is the possibility of "truth," of which you must know the conditions of existence, otherwise you cannot believe anything to be "true." "

Sorry, but I don't know what that means. Are you sure it is in English?

No, it means that for you to think that something is true you need some objective support on the world outside of your mind.

Neither, since "this sentence" does not refer to anything.

Funny, I thought "this sentence" referred to "this sentence is false." Even more funny: I still think that. And the funniest: all logicians that have treated that issue and keep calling it "self-reference" think that too.

what are you

You refer to a famous paradox. Unfortunately, it is an error in thinking: there is a fallacy of equivocation on the term "FALSE". For example, If the sentence read "this sentence is akward" what would be the problem? The term Truth can be used in at least three contexts:
1) Truth functionality - the kind of thing a tableux would diagram or a truth tree diagram would express.
2) Truth in content - the kind of truth that we know by experience or truth we practically know; the words correspond to something human beings know about in reality.
3) Truth as means of a method - the kind of thing deduction does; a method of derriving things from other known things.

The problem is if I say one of the context above, you will then switch and say "no I meant something else" or something like that. You play the game of a slippery fish that can't be pinned down due to its slickness. I go one way then you purposely go another way to make sure we don't pick the same context. So why not change the word in question? Let's change the one term "FALSE" and see if the problem remains? This sentence is in english. This expresses no problems. This sentence is simple. This sentence is a little vauge but not a paradox. Come on, dude the problem is the switch in context.
That if the sentence is true in functionality (that is a truth table shows it false)then the literal words in the sentence express truth in content. In other words, the sentence should read "it is true that what this sentence expresses is false." No paradox there. People want the reply: "if the sentence is false, then the sentence is true." That causes confusion because how can something be true at the same time being false? Those people do not notice the switch of context! Rewording the sentence crushes the emotional effect people are seeking!

This is an old topic, so i don't know if it will matter, but anyways,

the statement: "This sentence is false"

is not a paradox at all. Like totally. It's not that the statement is neither true or false (which I interpret as it is not possible for it to be true OR false, i haven't yet find any statement that is absolutely valueless, please let me know if you do). I read here that most people already know that:
s1: "this sentence is false"
is like saying
s2:"it is false"
we don't know what "this sentence" in s1 and "it" in s2 refer to. It could be anything, or it could be nothing. Let's decide if it's true or false:

Let's make the STATEMENT false. Assume "this sentence" refer to "I maybe a girl", then:
This sentence is false is false. Thus:
This sentence is true is true.
No contradiction whatsoever.

Now, let's make it true. Assume "the sentence" refer to " I am a girl and not a girl", then:
This sentence is false is true. So:
This sentence is true is false.
Works perfectly.

This kind of statement is kind of special because i think it is one of the few statements for which absolutely every existing (logical) thing will agree that it could be either one. not neither. It's like the exact middle of absolute truth and absolute falsehood.

There could be a mistake in my logic, but now I just want to get this out, because I think we can learn from this "paradox".
A lot of debates end up with lots of swearing with no resolution because the debaters don't even know if they are talking about the same thing. If we do, I'm sure more debates will end beautifully. Amen.