Dear Mihai Panoschi Panoschi,
Thank you for your response!
Since you disagree with Professor Cristinel Stocia, you should direct your disagreements to them.
Grammar errors and such are something I can look over. I am also failing to see how the statement goes against Godel's Incompleteness Theorems and its computational analogue, Turing Machine.
To quote you, "It's logically inconsistent since Gödel's results express exactly the opposite, namely, the even in mathematics there can never be a complete and self-sufficient system of knowledge grounded on a finite set of axioms, therefore mathematics is inexhaustible in itself."
Actually, Godel merely says if a formal system can express or encode arithmetic then it cannot prove its self consistency with a finite set of axioms. So if a finite set of axioms strong enough to encode or interpret arithmetic is incomplete in the sense we will have statements which we cannot decide it is true of false with the statements we have. Which is what Professor Cristinel Stocia's clearly states; if there exists a mathematical structure isomorphic to our physical reality, we cannot prove its self consistency. The implicit assumption is that such a structure much include formal systems strong enough to encode or interpret facts about arithmetic. They state, " Our knowledge will always be limited by Godel incompleteness (Godel, 1931) and Turing's noncomputability result (Turing, 1937)". It is very clear to those familiar with Godel and Turing's results. The limitations are we cannot verify the consistency of the mathematical structure.
As for the hypothesis being unfalsifiable, that itself is not true. Read Principle 2, "The collection of all true propositions about our physical world admits a mathematical model"
Thus, if have a mathematical model ( which we can derive from the said mathematical structure), that produces all the true propositions as verified through observation, measurement, and experiments we have a way of connecting the mathematical structure to the physical world. Whether or not they are the mathematical structure itself is a useful abstraction or actually exists is a separate question.
Professor Stocia cites Tegmark, and I think if you refer his work you would fine a more detailed explanation of a mathematical structure, how it is corresponds to our physical world ( by doing a set of mathematical operations deriving physical symmetries) and such.
Again, I am no expert here, but the extend Professor Stocia detailed her work, and from what I know I see and understand I cannot detect any "anamoly", and grammar errors while unfortunate is something I have no interest in penalizing someone for.
Kind Regards,
Raiyan Reza