"It seems like you should be able to determine whether any statement is true or false." What Gödel showed is that truths exists at their specific levels and not at the overall level. A wonderful outcome.
This means that a context must be given before a truth is declared.
The example I always use is blue, which means something different in a paint store than on the couch with the shrink. Blue is a truth indeed, but it is the context that declares what that truth is.
As Gödel showed, there is just a single truth in the universe, and it is a negative: There is no overall truth. There is no positive truth at the overall level.
A good article, Mark, and I like how you describe the influence this book and Gödel had on your life.
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I came up with other ways to say what Gödel says. It is all pretty basic once we take that required step down from the overall level.
Mathematics is already a limited systematic approach when we realize, that next to the decimal system we also have the binary system. Both can be used to declare the exact same realities.
Examining both systems, we can see that the binary system does not contain the 1 that is expressed in the decimal system -- they are different.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
111010011, 1101, 10001, 1011101
While the 1 in the decimal system can be seen as singular (simplistic), it is non-sensical to state that the 1s in the binary system are singular. This means that unity in the decimal system is very easy to express with 1, but that it gets to be complex to express unity in the binary system. Folks have to agree that, for instance, 110111010011 is the same as what we capture with the word unity and from that moment on it was captured indeed. The shortcuts we can take with the decimal system are indeed shortcuts and they may fail to capture reality as it truly exists at the universal level.
Gödel provided us therefore the negative answer we should be interested in about our universe: it is not unified. He also provided the following example that matter in the universe desires to be convergent, but that at the universal level there is no convergence. Planet and star are completed in their convergence, having become single masses. Solar system and galaxy show convergence, while not able to become a single mass. Anything larger than a galaxy, and convergence is not seen. We either see divergence or a complete lack of a collective behavior.
Yes, bottom up is the only available approach to understand our universe. The word universe is a collective term; it does not point to an actual entity. Space as the vast nothing is, for instance, not connected to any of the other parts of the universe we find in that vast nothing. The parts try to establish their own self-based realities; they do not relate to a universal level.
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You express the book real well, Mark. Allow me a few more points.
Consciousness is the result of the linear and the non-linear. When reviewing matter, we can see that neutrons and protons are linear, while electrons are non-linear though loosely tied to the positive protons.
QM is a charged subatomic reality, while the addition of electrons ensures that the universe at a GR level is neutral in charge. We have two differently charged realities we live in.
Two realities automatically express consciousness (on the condition that consciousness can get expressed).
Finally, Gödel also did not see what he had delivered. He himself had focused on his own field of expertise, and while he was able to see the other fields relatively well, he also had a few blunders expressing himself about the structures of the universe (suggesting how the universe as a whole could be spinning the example that shows he had not neutralized all ideas in his own mind yet, a little bit of an enigma, but not a surprise in a world in which information overload has been the norm for a real long time).
Thank you for writing about Gödel. I love it.
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Mark, if interested, I wrote about the possibility that energy always being a closed system can nevertheless mean there are two closed systems, still closed from an overall perspective. I hope you will read it and provide me your comments.
'Two Closed Systems, Not One'
https://fred-rick.medium.com/two-closed-systems-not-one-3d66da5b8dff
