Gödel's Incompleteness Theorems

>>9087056
>What are the practical and philosophical ramifications of this, in your opinions?
That, moreso than dealing a blow to Hilbert's program and nominalism, it dealt a blow to mathematical realists as well. It would be absurd to imagine than something that is in the nature would be incomplete, or incompatible with one another. It also proves to be a challenge to classical logic, by proving that not all statements are either true or false

>>9087056
It directly follows from Gödels incompleteness that for any two rational numbers a and b so that a < b there exists a rational number c so that a < c < b. Before Gödel theorems such as this one were unheard of and even unprovable before kurts necessary advancements to the theory of axiomatic proof.