Atheism and anger: does majority rule? True, I like the paradox, "This statement is a lie". If I am a liar, it's true. If I am truthful, it is a lie. The paradox exists because of Order. If we make the assumption that everything by default is false, and only when we have understanding, we create truth. Therefore, truth is always born from the false. Put another way, Chaos comes first. From Chaos, Order is created. As the objective is to create truth, it will always contain the former because truth is supported and upheld by the false. That is its opposite. There is no further integration required because by their very nature they are already integrated.
The same applies to maths and numbers. For a long time, zero was not acknowledged but it was always implied. Zero is infinite (chaos), from this One is formed. A division of the infinite making it now divided. It can be seen as a boundary from infinity, putting infinitiy on the outside of the one (or as we would write it 01).
Knowledge could be likened to a jigsaw puzzle. When all the corners fit, you accept it as "new" knowledge and the piece is placed within the picture. Beliefs are the pile of puzzle pieces you group together because they are "similar" to the picture or they relate to each other. Some people like to put all the straight edges together is a pile, or match them by colour. It doesn't matter how it's done, what matters is that it takes place. People have different ways of making the piles, as people have different beliefs. When you have enough puzzle pieces together, you can start putting them in place (converting them to knowledge).
So, belief is a precursor to knowledge but not necessarily. Some peoples beliefs are simply wrong. If pointed out, the wise ones will change their beliefs. All of this is performed using the power of discernment.
If you have a belief, it's because you don't have the knowledge, or you have only part of it. You cannot believe something you know, and you cannot know something you believe. They are exclusive. .
Are there any truths that exist that you don't know? Of course not. Because your knowledge to you is truth, unless by the power of discernment, you realise the belief was wrong, in which case it is dropped and subtitude. Science does precisely the same thing and has been doing so for years. Today X is scientific fact, but tomorrow when it's proved wrong, Y will be scientific fact and X will be dropped and forgotten.