Tag Kurt Gödel

The rational skeptic world view

Geir Isene 56 Comments

Humans have always tried to make sense of the world we live in. We have always tried to come up with simple explanations that covers what we see. From the four elements and a flat earth inside a dome to a spherical earth and a heliocentric world view, our view of the world has evolved. But the quest has always been to come up with a complete and consistent model that will explain all of existence. Just like Newton’s classical physics. He viewed the world as clockwork obeying a complete and consistent set of physical laws. And when those laws didn’t quite fit the bill, Einstein extended this quest with his theories of relativity. His goal was to come up with a grand unifying theory that could be encompassed in an equation no longer than two inches.

Einstein’s famous discussion with Niels Bohr where the former exclaimed “God does not play dice” was his rejection of the spookiness of quantum mechanics. This branch of physics seemed to destroy the quest to unearth a model for an ultimately orderly and rational, complete and consistent world.

And despite the hints like Heisenberg’s Uncertainty Principle, the Double Slit Experiment and Bell’s theorem, some physicists still believe in a deterministic world where everything is neatly explained and codified.

Graphics by Geir Isene

Had they only looked to mathematical philosophy and seen the same quest fail there. At the start of the 20th century, there was this adventure in mathematics where the major thinkers of that field tried to codify all of mathematics into neat axioms and rules to rule’em all. But alas, Kurt Gödel shot it all down with his Incompleteness Theorems. And decidedly so. There cannot be any complex axiomatic system that is both complete and consistent. And to those who would like to believe that the universe we can observe is all that can be, mathematics is a subset of our universe. And as the universe is then a superset of mathematics, then the universe itself cannot be both consistent and complete. And that has some profound implications that I will cover in a OnePageBook sometime in the future.

Now, what prompted me to again delve into this? I was inteviewed by Aaron Smith-Levin the other day, and one of the comments on the resulting Youtube video read:

“Geir, so much of your world view hinges on the “law” a system cannot be both complete and stable, including the large conclusion that humans are spiritual beings, have you ever questioned the conclusion on systems, and if the conclusion about systems were the opposite, would you conclude you are not a spiritual being? If you were not a spiritual being, would you feel you should adapt the rational skeptic world view?”

To which I answered:

“The proof that complex axiomatic systems cannot be both consistent and complete is among the most solid mathematical achievements in human history. It’s irrefutable. So is the double slit experiment, the Heisenberg Uncertainty Principle and Bell’s theorem. There is nothing rational about refuting any of these. They all point in the direction of consciousness being non-physical. Read my OnePageBook in free will for details: https://isene.me/2017/07/17/free-will-do-you-really-have-a-choice/”

Just like the old, classical Newtonian world view was naive, I believe the modern “rational skeptic world view” to be equally naive.

As for the rest of the interview, here it is:

A remarkable book

Geir Isene 147 Comments

I place on the top book shelf, albeit a notch below “Jonathan Livingston Seagull“, among books that has had deep impact on my views – the remarkable “Logicomix“.

An epic search for truth, through the eyes of Bertrand Russel rendered in an epic form. The blending of the foundational quest in mathematics and the aesthetics of great comic artwork. It is easy to understand why this book has been given awards across the boards – it presents deep concepts in an ingenious and simple way.

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We are taken through the basic concepts of foundational logic – from Aristotle to the modern masters such as Bertrand Russel, Alfred North Whitehead, Ludwig Wittgenstein and Kurt Gödel.

The genius of Wittgenstein was news to me. He represents some fascinating insight into the foundations of so called reality and its limitations.

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… because:

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And the quest culminates with the profound realization og Gödel in his incompleteness theorems. I have covered this before, but a clearer summary of what I consider to be Man’s greatest intellectual achievement to date would be along these lines:

  1. If the system is consistent, it cannot be complete.
  2. The consistency of the axioms cannot be proven within the system.

Gödel’s first incompleteness theorem showed that a system of logic could not be both consistent and complete. According to the theorem, within every sufficiently powerful logical system, there exists a statement G that essentially reads, “The statement G cannot be proved.” Such a statement is a sort of Catch-22: if G is provable, then it is false, and the system is therefore inconsistent; and if G is not provable, then it is true, and the system is therefore incomplete.

Gödel’s second incompleteness theorem shows that no formal system extending basic arithmetic can be used to prove its own consistency. Thus, the statement “there are no contradictions in the system H” cannot be proven in system H unless there are contradictions in the system (in which case it can be proven both true and false).

This is precisely why the “the meaning of the world does not reside in the world“. Which in essence gives a foundation for free will.