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Well, the truth itself is the way things are, and like you're saying, there isn't so much we can do to further define that Gödel's result is essentially saying that semantics cannot be reduced to syntax. But there's a second consideration, which is that humans make claims about the way things are

These claims may be considered as sequences of characters, or noises, or perhaps patterns of mental activity On the other hand, (mathematical) proof is a syntactic notion And we call some of these claims true, and other claims.

Truth is what the singer gives to the listener when she’s brave enough to open up and sing from her heart

But still curious about the difference between both of them In our daily life, in general conversation, we generally use these both terms interchangeably Then what is the difference Are they synonym or have specific difference?

There is no absolute truth because we as humans are restrained from ever knowing it is fallacious, what humans can know imposes no restriction on what is And this will only be a way out of the paradox after it specifies which axioms of classical logic are supposed to be dropped, and shows that what is left is enough and otherwise reasonable There are several options described in standard. The first two paragraphs are talking about not necessarily needing to know truth, but the latter two imply that for achieving goals or empowering us to do so, understanding of how the world works (=discovering the truth about the world) is essential.

5 whether truth can exist without language and that truth is an objective reality that exists independently of us are not opposed claims, although they don't imply one another

A platonist would tell you that language, like other mental objects, exists in the ideal realm whether people are around to think about it or not. Truth is a property of propositions, mostly propositions claiming facts Hence truth lives in a completely different domain It rains today is a proposition which claims a fact

The proposition can be true or false On the other hand, facts are not true or false Instead, they are or they are not See also what is the difference between fact.

Finding truths is definitely possible, finding important truths harder

For kierkegaard, the point of the claim truth is subjectivity is that anything that is true is true for a subject In other words and in particular, if the christian story is true, then it changes everything for the subject in a way that cannot be overlooked or erased. Apologies if this question has been asked before, i looked at similar ones and couldn't find one that answered this exact question Is there such a thing as truth completely independent of conditio.

Truth, in the sense you are using it here, is a semantic notion It is not equivalent to proof as you suggest

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