It is funny how you say two things at the same time and then pick your position, Rygoldenm.
“Godel explicitly avoided making ontological statements, hence his theorems cannot (by definition) be used to say anything about the universe at large — only formal systems.”
Because what is then the universe at large?
It turns out that there is no formal system called the universe.
Worse, it is not a system at all, and this is so easy to show.
First, reiterating how the Big Bang was a one-time event, so your brain must work in that field and not in a field where repeatable outcomes are found. Then, it is simple as 1, 2, 3.
Start with planet Earth as a unit.
Then, recognize how the Solar System is only a unit if we call it out as a unit of units.
Moving on to the Milky Way, we have to call this out as a unit of units of units.
Then, the largest jump: The universe.
We cannot call it out as a unit. It is not a unit. There are no smaller universal units that make up the large unit then called universe. That is not the structure of the universe. Rather, it is a name tag indicating an all-inclusive outcome, emphasis all-inclusive (which is why I had to mention again that the Big Bang was a one-time event).
So, I stand on the shoulders of Gödel, and I can see the universe as not being a unit.
Then, in combination with Gödel’s Incompleteness Theorems, we have the two legs to move forward. Again, the issue with the article is about the idea that a singularity can exist.
This combination of Gödel and the correct structure of what the universe is show that a singularity is a brain fart. Good scientists would not engage themselves in talking incorrect structures.
I hope you agree that there is no scientific evidence (nothing at all) that singularities can exist. Singularities are pronounced on paper only, in models of calculation, which points out the source of the singularities: the human being him- or herself creating that model on paper.
A singularity is the same as stating that God is Almighty. It means that God would be a Cyclops and that is of course not possible (if God can already be declared possible).
Physicists are working with a model created on paper, and they did not realize they drew a Cyclops.
Thank you for your additional reply, which I appreciate a lot. Yet a structure that cannot be must not be used by scientists.
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My mathematical evidence is that all systems vying for completion will encounter how zero is part and parcel of that system. As such, there is always a higher level in which incompleteness is the outcome. That is the same Gödel pronounced, but then coming in from the other direction.
I call it a proof, yet it is about the foundation of the mathematical numbers. Once a person declares 1, 2, 3, 4, 5, I have the evidence that 0 is then automatically included. All systems, all structures have zero included if they desire to reach the largest of levels.
If interested in my recent article:
“Einstein, Gödel, and Me”
https://medium.com/@fred-rick/einstein-g%C3%B6del-and-me-5bee14dd0edd
