As discussed, GIT doesn't imply the existence of things outside of a system - simply that the system can ask questions about itself that it can't answer.''
I mean we can already stop here because he is already wrong, do you not agree?
Ok let's break this down step by step. For now lets assume that we can apply Gödel’s Incompleteness Theorem (GIT) to the universe. We can circle back and challenge that assumption later if you wish.
What GIT shows is that any coherent and logical system can ask questions about itself that it cannot answer.
If the universe is incomplete it means that logic and science cannot tell us what lies outside of the system aka outside of the universe. We can only extrapolate general proprieties. For example we know it's not more universe meaning it is not time, space, energy, or matter.
You said yourself what GIT shows, it doesn't show that there must be something outside the universe, you just said it? We don't know if there is something outside the universe to begin with.
We can deduce as Perry Marshall does that whatever is outside of the universe is boundless, immaterial, indivisible and an uncaused cause. These basic properties match very well with the religious concept of God but this is not the only possibility. Nihilist believe that there is nothing outside the universe. Infinite nothingness could perhaps be argued to also fulfill these criteria.
Why? How are we deducing this?
GIT does not prove God it simply shows that the concept of God is logical. It also suggests that it may never be possible to prove God with logic. Logic may only be able to show us that God is possible, logical, and consistent.
Why is this important?
1) GIT is useful as it provides an counter to those who argue that God is illogical. It shows that God as described by monotheism is consistent with what we can logically conclude may exist outside of the universe. GIT does not prove God.
2) GIT also highlights the limitations of science and logic. It suggests that God is a logical first axiom. It also suggests that nihilism is a logical first axiom.
3) GIT suggests that science may never be able to resolve this question. No matter how sophisticated intelligent or advanced we become this fundamental tension between theism and nihilism may never go away as the answer to this question lies outside of the system. Faith therefore will probably always remain necessary and refusal to take a position in the hopes of some scientific breakthrough is unlikely to be fruitful.
4) Finally GIT it highlights the symmetry between religious and nihilist thinking at the level of first principles. Both the nihilist and the theist must ultimately relay on faith.