There is nothing like the Goedel theorem inside a finite world, in which we operate/live.

This assumes the universe is finite. But aside from that it has two serious problems:

First, finiteness doesn't save you from undecidability.

Second, if in fact the world is finite we get even worse situations. Let for example (n) be your favorite fast growing computable function, say f(n)=A(n,n) where A is the Ackermann function. Consider a question like "does f(10)+2 have an even number of distinct prime factors"? It is likely then that this question is not answerable in our universe even though it is essentially a trivial question from the standpoint of what questions can be answered in Peano Arithmetic.