Just found this on youtube and thought I’d use or abuse it to explain my thoughts on the matter.
Now, I’d like to begin by saying that the circle cannot encompass the universe, the circle encompasses only the idea of the universe. In other words, this description only applies to our perception of the universe and not to the universe an Sich. The basic implication of this is that the incompleteness theorem does not apply to the universe, but to our mind; it applies to all our models, all human concepts and systems, including math, logic, words et cetera, but it does not apply to the universe itself. For while we can never know the whole truth, the universe itself does not care about this. And the reason we can’t know the whole and there will always be unknowns outside our circle of understanding, is because the brain is smaller than the universe. We have fewer neurons and connection between neurons than is needed to describe the position and velocity of every particle in the universe. Therefore we metaphorize, categorize and simplify the universe into groups and concepts and singular words with extensive definitions.
There are a few problems in the youtube presentation. 1) There’s no reason to assume that the outside is that exact opposite of the inside. When it comes to all other human knowledge, including the five postulates, the assumptions are relative to the conclusions and not their opposites. 2) Information and consciousness are both part of the universe and so does not belong to the outside (read God). It’s true that information is not just light, but information is still material, just in the shape of more complex phenomena, like a TV broadcast or a theatre play. It’s still material, but not limited to nothing but photons. Of course, information as we define it requires that someone perceives the light with their neurons, but the neurons and the retina and the chemical reaction (photoisomerization) between the photons and the retina are all material. 3) If God is outside, then according the the theorem, that is not the end, instead we can include God with the universe and draw a circle around that and make an assumption outside of it. Just because we think God is a special concept doesn’t mean it is; it follows the same rules as other concept in the theorem. Instead, the whole point, which appears to us this way, is that it goes on forever, we make a new circle and a new outside over and over again, because that’s how the brain works. No matter how much we know, there will still be an endless supply of new and ever unique experiences that can by definition never be identical to the neural pattern of understanding in the brain.
If we look at the description assuming that the U represents our understanding of the universe and not the universe itself, then the idea comes full circle. According to the incompleteness theorem, when we step outside the circle we make assumption. Now I won’t assume that we can infer God from the circle, instead I will assume that the incompleteness theorem is true. If it is, then it proves that it is. That’s what we call a circular definition and all logic is true only if the premises equal the conclusion, i.e. if it’s a circular definition. And the premises are assumed. So, if we assume the incompleteness theorem, we also prove that logic proves that logic is true. Which is a circular definition, which means it is true.
If you apply this to all knowledge (our perception of the universe) you find that the incompleteness theorem is true for all our knowledge. Therefore I feel justified in assuming what we can infer what is outside our understanding. And what can infer? We can infer that although our minds are smaller than the universe, it is wisest to assume that the patterns we see in the small sample we understand, is true for the whole of the universe. And what we see is that consciousness is material, that there is no soul, that the universe and life arranged itself bottoms up through motion and evolution and so on. Of course, we must be hesitant to assume we know everything. Our sample might be misrepresentative of the majority of the universe and we must be humble about our limitations. What we must NOT do is assume that the universe is the complete opposite of how we understand it. If for all we can figure the sun is a burning ball of proton plasma, then it is not wise to assume it is a metaphysical deity. So although we must be humble about the extent of our understanding, it is crucial to bear in mind that it is wise to assume that the sample reflects the whole and unwise to assume that it implies the exact opposite. I.e. it is wise to assume the universe is material and unwise to assume it is metaphysical. Of course, this depends on the definition of material too. It’s become quite popular to use energy and information and quantum randomness to hint at a metaphysical reality, but these are still material concepts within the incompleteness circle and should not be treated any other way.