[Ethan Clive Osgoode]

Those who choose your position end up running into Goedel’s Theorem

Why? What does Goedel's theorem have to do with this?

[Pelham]

Goedel’s theorem shows that Hilbert’s program is impossible and that mathematics itself is built upon faith assumptions, the axioms that we find that we have to use. There are no closed, self-defining systems. “logical systems of arithmetic can never contain a valid proof of their own consistency.”