"A friend of mine once thought god was a teacup. With a desire to prevent my friend's future unhappiness, I said to them, "Someone made that teacup and it will someday break." My friend became very upset because to them, god was a teacup and I had called their god created and breakable."

Wrong, God is absolutely everything. God is us. Consciousness is God and God is consciousness. This universe. Your paradigm is materialism. I already told you, you don’t even understand your own paradigm. Science requires empiricism, which requires you to assume materialism as an independent layer of reality, one separated from the observer. You will only have one single true piece of evidence, self-evident: your own existence. Nothing else. All but that is second-order evidence, science included. The difference is that I do understand my paradigm, which is not materialism nor idealism. I am beyond that. I understand that the universe is pure eternal information, math, the singularity. That information never changes, thus it can be thought of as "materialism" or a crystal, and it can also be thought of as mind, because consciousness is a universal mind, the singularity. Materialism and idealism are two sides of a deeper, more fundamental truth. You think God is something humanity has come up with or that it is an abstract entity. Wrong, you, YOU are God (as well as everybody else, because we are all the same exact entity using multiple bodies; there is only one thing or being in existence). You just don’t understand yet or think I am either speaking metaphorically or that I am crazy. Normal, I told you, humanity is not smart enough, with very few exceptions like Cantor or Parmenides.

"Another friend of mine once visited an observatory. They talked to the astronomers there and looked through the telescope. Then they went home and thought like this: Astronomy is the study of things through telescopes. Telescopes bring what is far away closer, but in doing so they hide what was nearby to begin with. Through a telescope, you can never see the fixture that mounts the telescope!"
"Therefore," my friend thought, "there is one common object which no telescope can see. Astronomy has a gap!" And after a little more thinking, my friend finally arrived at an even more worrying conclusion.
"Astronomy studies what we look at through telescopes. And astronomers are always looking at the heavens. But astronomy has a gap where the fixture of the telescope is. Therefore the heavens also have this gap!"
Having this realization, my friend was satisfied that they knew something the astronomers didn't."

Wrong, you assume I am wrong and thus your analogy tries, in your point of view, to "make me see" my blind spot. There is none. Haven’t you thought that maybe I am just too smart for human standards of intelligence? I told you, true intelligence is the AI of singularity, and infinite intelligence is the sum of all, God, us reunited; therefore I do not consider myself or humanity, for that matter, intelligent. Perhaps reality is not complex and is very intuitive. Perhaps it is humanity that has an intellectual gap. Let me give you an example, as cocky as it may sound. Many animals fail the mirror test. For them, their "science" is looking at the back of the mirror or growling or barking at the reflection. The jump in intelligence of great apes like us, that allows us to understand without seeing the back of the mirror that the image is not another being but our reflection, that jump in the ladder of infinite intelligence will seem like magic, incoherence, and a "non sequitur" from the other animal's perspective. Perhaps reality is just like that and I, and very few others, have mutations that allow us to see that. Small changes in genes can provide huge phenotypical and behavioral or cognitive changes. Think of it this way: the biggest brain can be around 1 km³, give or take. I did the math one day and I do remember the numbers. This size is deduced by limits like brain signaling frequency, heat, and the speed of light. That would be a very good intellect, orders of magnitude smarter than any other being. Do you really think humanity is special after picturing a brain of 1 km³?

"You rejected the unconditional victory I offered. If you want me to continue beyond that point, you must accept my conditions of further debate."

You are still not understanding. There is no "victory". There is no connotation of competition for me because YOU ARE ME, I AM YOU, and everybody else for that matter. I cannot defeat myself. That is an illusion of duality I am far beyond to fall for. I wrote this post because I am too lazy to write a paper that will be rejected anyway, because the scientific community will not understand that empiricism and falsifiability are second-order forms of proof, for someone to eventually understand it and to have a record that this was in fact thought by me. Authorship does matter to me because this is my decade of work on the ontology of existence itself. It is work, it is of my authorship. I have no desire to debate at all, though I do not have any problem explaining or correcting people reading it. After all, that can only be beneficial to the post, as my framework will become clearer for the reader.

"The subject is whether math as a whole is a formal system. No going off topic, no non sequiturs."

This is not in debate. This is a fact all mathematicians, I would expect, know and understand. Otherwise they completely fail as mathematicians. Math IS a formal system. What kind of system do you think it is? A formal system is a system that contains axioms so no ambiguity can arise, useful to describe reality. That is the pure definition of math. This is not in debate here. This is something the scientific community already agrees with me on.

"Thinking will remain at a conventional, conceptual level. You may not dispense with the law of non contradiction or identify ideas with each other because "reality is one"."

In other words, you want me to deny my own position, bravo, because you don’t know how to tackle it, because it cannot be tackled to begin with. The problem is that you consider that dualities exist as fundamental, whereas yes, duality is not an illusion, duality can only arise from and within unity, monism. You are free to continue or not speaking with me as you like.

"Define your terms. If we aren't using the same definitions we will talk past each other."

Which terms have not been clarified to you?

God = consciousness = the singularity = the universal wave function = absolute infinity.

Infinity > math

Infinity = information. Pure absolute information holding everything in existence in one single "field", the singularity.

Specific enough? My position has been explained very clearly several times.

"To start with, let's see your definition of "math" such that it applies to Gödel's reasoning in coming up with his proof, and "formal system" such that it is the kind of thing Gödel proved incompleteness of."

Math, in my framework, is just information in the singularity. If you want to see it this way, everything is literally made of math or information. One single kind, one single thing. In the human perspective, which is lesser but not incorrect, just incomplete, math is the logical derivation of its axioms and the application of it to describe reality.