Mathematics is one circular reasoning

This blog is written as an explanation why I think mathematics is based on circular arguments. The source of this statement is a blog of Bob about Nassim Harameins' theory when he talks about the Schwarzschild proton. Bob has been so kind to show why the theory of Nassim Haramein is not in line with the actual reality of a proton and which difficulties are met if the theory of a Schwarzschild proton is explored.
Bob answers to my statement that the mathematical equation 1+1=2 is not an empty statement but refers to something real. Although I agree with him that 1+1=2 in reality is not an empty statement, I was talking on a more abstract level. The statement I used as an example is not empty nor does it depend on context. Far from it. What I am trying to show is that the mathematical grammar used is independent from any context. That makes it a very powerful tool to check on reality. Its power is however also its weakness.
First I will show an example of a non evidence created using proper mathematics:

Suppose a=b then 2a + 3b = 3a + 2b <==>
2a - 2b = 3a - 3b <==>
2(a -b) = 3(a -b) <==>
2(a - b)/(a - b) = 3(a - b)/(a - b) <==>
2 = 3.
(Proof 7 from http://www.wiskunst.nl/wiskunde%5Cwiskunde3.htm.)

Using mathematics properly one can create this kind of evidence at will. Every step is sound mathematics, but the conclusion is far from being realistic. The reason that this kind of 'magic' is possible in mathematics is that as long as the criterium is met that what is on the left side is equal on the right side of the assignment, there is nothing wrong with it. That is only becoming possible if the tool used is independent from reality. Independent from reality implies that all statements are made within a closed system. That is equal to saying that all statements are circular arguments. If they would not be circular arguments, they would need something outside the closed system, which would imply that the system was not closed at all.

The reason I made this statement is that some James in the blog of Bob pointed out that scientific theories can only be proven using mathematics. I think that is half the truth. I think the combination of reality with mathematics can prove - at least statistically - that some line of thinking is promising. Reality must play a part in proving the truthfulness of the mathematics applied, otherwise anything can be said to be true. As shown above, as shown in the article of Nassim Haramein. It is only when the combination of reality and mathematics is made that scientifical theories can be proven or refuted.

Exactly the fact that mathematics is a closed system independent from reality makes it so powerful in combination with reality. Reality delivers the facts, the independent language the relationships between the facts. Both left on their own can not perform that job. Facts stay isolated, relationships have no feet in the ground.