Gödel's work is underestimated, but it takes a good mind to see where his work applies, and how it applies. Many good physicist is not capable to see that Science itself is an Incompleteness. These are the scientific areas:
A: Area that scientists can never know about. Examples are the beginning of time, the beginning of space, and the beginning of energy. We have totally nothing, zero, zilch on their beginning. Do scientists acknowledge this? No, they run away from what is obvious. They even use a scientific falsehood and make all start at the beginning of matter.
B: Area of one-time events.
Example is that beginning of matter. We have a one-time event that cannot be repeated, just like one cannot break a vase twice. One may be able to break the pieces of the vase an additional time, but not the vase itself. Do scientists acknowledge this? Not in the most appropriate way. Yet information is available from one-time events. When I see an omelet, I do not need to see anything else to know 100% that the egg broke. The one-time event can be 'read'. No additional evidence needed, though the ‘reading’ will be limited to acknowledging ‘the obvious.’ How matter came into being can get explained.
C: Area of repeated results.
This is the gold standard of science, of course. Anything that can be repeated by someone else is correctly hailed as the best of what we want to see.
Do scientists acknowledge all this? No, they love to stand in Area C and incorrectly apply the rules of Area C to Areas A and B.
Science is an Incompleteness, yet scientists do not want to acknowledge that.
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When scientists acknowledge their scientific positions, then we can look at Gödel and recognize his work. If scientists acknowledge just their brains instead, then Gödel becomes the figure to get rid of. Gödel is in the way of what scientists like to see as the real answer, but Gödel's work is part and parcel of the real answer.
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The Incompleteness Theorems can stand on their own, but one should start with Gödel's Completeness Theorem.
Yes indeed, we can establish a completed box of just the items (axioms) we are interested in. We can indeed have all people capable of growing a mustache inside one large box.
Yet the genius move is next to discover that the completed box does not exist at the higher level, but rather is self-based. The larger box is where we find more information.
Therefore, the Incompleteness Theorems come into play. Next to the completed box of all people capable of growing a mustache, we also have people not capable of growing a mustache, such as children and most women. So, the large box with all people in it will contain a completed box itself of people capable of growing a mustache, yet that box will not be as large as the larger box.
The axiom cannot be applied to all.
Then, Gödel worked to show if one can get a completed box when inserting an additional smaller box, let's say people capable of maintaining a high-pitched voice throughout life. It turns out that even then the two boxes do not fit the larger box in a completed manner. There are then still people who are not capable of growing mustaches nor did they retain their high-pitched voices.
The larger box is a completeness by itself, while the smaller boxes are Incompletenesses in the larger box. Do you see? The completeness is based on a self-evident axiom, whereas the Incompleteness basically states the same: It is limited to its axioms.
Here is the trick. The universe is NOT the largest box. The universe is just a name tag of all boxes combined. So, there is no largest box, while the largest setting is truly there (the universe is not a unit).
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Long story short. Physicists do not like Gödel because they would then have to admit that the universe is not a unit; that unification is a brain fart of their own making.
The Scientific Realm is larger than the Scientific Reach, exactly the same conclusions when following Gödel’s incompleteness Theorems.
'Einstein, Gödel, and Me"
https://medium.com/@fred-rick/einstein-g%C3%B6del-and-me-5bee14dd0edd
