Gödel’s Incompleteness Theorem

Revised March 6, 2021; #2 added March 24, 2021

Introduction

1. Mathematician Kurt Gödel, in his Incompleteness Theorem, proved that it is impossible to find complete “truth” or “complete explanations” of a system from WITHIN a system.

  • No theory that any scientist discovers is, thus, cannot be proven to be the “ultimate truth.” This is another way of saying that one cannot comprehend the complete picture of the system IF one is within the system. Then only parts of the system can be studied.
A Simple Description of Gödel’s Incompleteness Theorem

2. The following video provides a simple explanation without going into details.

  • At 8 minutes, he says, “What is outside ‘this world’ is not ‘matter’, not energy, not space, and outside of time.”  It may be possible to get a “complete and self-consistent picture only from the “outside” That is Nibbāna.
  • The Buddha, once attaining Nibbāna, was able to “look from the outside and “see things as they are.”
  • No one else, looking from within can EVER figure out the ultimate truth about this world.
  • The second video below is interesting. He assigns “outside of the universe” to God. Other than that, his conclusion is perfect.
Wrong Conclusion

  • The key question regarding a “God” or “Creator” is: Is He (God) inside the system or outside? If He is inside, then He is also subjected to Gödel’s theorem. If He is outside, how can He affect things from the outside? “Inside” and “outside” are mutually exclusive!
Nibbāna Is Outside This World

3. The Buddha transcended “this world” by developing his mind; see “The Grand Unified Theory of Dhamma” for a description of the 31 realms of existence.

  • This is again something that a human being cannot prove. One accepts, as I have, of the truth of that by examining the evidence: that the Buddha was able to explain so much about “this world” 2500 years ago. By “this world,” it means not only the Earth or even this universe but also total existence.
  • Of course, the Buddha lived in this world until the death of the physical body. However, his mind had transcended this world. Attaining Nibbāna is reached at the Buddhahood or the Arahanthood. That Nibbāna would be complete at Parinibbāna at the death of the physical body.

4. The only way to disprove what I stated above is to find inconsistencies within the Buddha Dhamma (this is the same method used by the scientists in assessing scientific theories). I have not found any. See, “Buddha Dhamma: Non-Perceivability and Self-Consistency.”

  • If you find anything inconsistent about the Buddha Dhamma, that is because there have been numerous “alterations” over the past 2500 years. But if you find any inconsistencies at this site, please let me know. If there are any, that is due to my possible carelessness or ignorance, and I would fix them.
  • In fact, this is the only way to get rid of any inconsistent “bits and pieces.” Just like if you have a piece of a puzzle at the wrong place that will only hinder the progress of solving the puzzle, having wrong information somewhere will only slow down our progress in “figuring out the pure version of the Buddha Dhamma.”
  • However, I do believe that the “big pieces of the puzzle” are incorrect places here.
I Hope Scientists Would Become Interested in Buddha Dhamma

5. Kurt Gödel would have really enjoyed Buddha Dhamma. It would have been tremendous if he was alive to go through the material here and point out any inconsistencies. Many of the scientists that I admire, including Einstein, Feynman, Gödel, Heisenberg, de Broglie, Sagan, and many more, would have easily grasped the message of the Buddha. Unfortunately, they never came across the pure Dhamma; David Bohm came close.

  • I hope the current generation of scientists and philosophers will get an opportunity to examine the pure Dhamma.

6. I do not want wrong impressions to come out of this post. I love science and physics in particular. Before discovering the pure Dhamma, physics was my passion, and I still try to keep up with new findings.

  • Yet, I have realized that discovering how inert matter behaves is a minute fraction of the whole existence’s knowledge. We cannot even discover everything about “matter” until we start finding out more about the “mind.”  The Buddha said, “mano pubbaṅgamā dhammā…” or “the mind precedes everything in this world….”.

7. Let me give some examples. Albert Einstein introduced his Special Theory of Relativity in 1905 and his General Theory of Relativity in 1915. The first showed that Newton’s Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light. The second showed that Newton’s Law of Gravitation was also only approximately correct, breaking down when gravitation became very strong.

  • We could not see anything wrong with Newton’s laws of motion until we developed technologies that transcended our “level of consciousness”; see, “Expanding ‘Consciousness’ by Using Technology.” They worked well within our “probing sensitivities.” Even today, scientists do not use relativity equations to map out rocket trajectories to the Moon; Newton’s equations are good enough to that.
  • In the same way, everything that science discovers expands our horizons but never will provide the “ultimate answers.” We can find “everything about this world” just by purifying our minds; see, “Expanding ‘Consciousness’ by Purifying the Mind.”
  • The above statements may not mean much right now. However, I ask you to be patient and go through the material at the website, and gradually you may realize what I am trying to say.
Testable Predictions

8. A “good theory” is all about “testable predictions.” As I stated on the home page, I try to present material on Buddha Dhamma as a “theory on how nature works.” As I pointed out in many essays, many of the “predictions” or “statements” about this world’s nature have proven to be correct by science over the years, especially during the past few hundred years.

  • I can make another prediction just for the records. Darwin’s theory of evolution will be proven to be only partly correct and only for limited spans of time. The theory of evolution is correct only over the recent past of this planet, where we can trace past events using radiocarbon dating techniques. The oldest dates that can be reliably measured by radiocarbon dating go back to around 50,000 years ago. Even if we put the limit at a million years, that is only a tiny fraction of over four billion years lifespan of the planet.
  • What is correctly stated in the theory of evolution is that species arise when conditions become suitable for them to arise  AND  for them to survive.
Some Aspects of Buddha Dhamma Not Amenable to Mundane Interpretations

9. However, it is dangerous to talk about concepts that are not amenable to our minds. That will lead only to “loss of faith.” It would be impossible to explain to someone who time-traveled to the present time from several hundred years ago how a light bulb can light up just by flipping a switch. There is no way for that person to “grasp” the concept of an electric current; he/she would believe it to be a “magic trick.”

  • The Buddha never revealed any details of nature that were not discernible to at least his top disciples at that time. Let me give an example from the Tipiṭaka. One time Ven. Moggallana, who was only second to the Buddha in abhiññā (supernormal) powers, saw many beings in the peta realm near the Gijjakuta mountain. Beings in the peta realm have invisible bodies that only those with abhiññā powers can see.
  • So, none of the Arahants who had abhiññā powers could see those petas, and they told Ven. Moggallana, “how come we cannot see them?”. Ven. Moggallana told them to ask the Buddha. The Buddha told those Arahants that he had actually seen them previously. When the bhikkhus asked why the Buddha did not mention it to them, he told them that, “If I tell you something that you cannot verify by yourselves, that will only lead to doubts. That is why I did not mention it. But now that Moggallana has seen them, there is at least one person there to confirm it”.
  • See, “Buddhahood Associated Controversies” and “Buddha Dhamma – A Scientific Approach.”

10. Even today, there are people with abhiññā powers that can see some of these beings in other realms. My teacher Thero says he can see them, and I have no reason to doubt them. Developing abhiññā powers requires being able to get to the fourth jhāna AND then working to develop those powers. So, it is not an easy task. If I ever get to that stage, I will mention that here.

  • Developing abhiññā powers or even jhānā is not necessary to attain Nibbāna. One can even attain the Arahanthood without developing any jhāna ahead of time.
  • It is important to experience the “cooling down” of Nibbāna even without getting to the Sotāpanna stage. That itself provides an incentive to continue with the practice; see, “How to Taste Nibbāna.”

References

For those who would like to read more on this subject, the following references could be useful. However, I do not encourage anyone to “go off track.” I included this section to point out that all existing scientific theories are incomplete because they all were generated within the system. The Buddha was able to transcend “this world” and thus was able to provide a complete world view.

“Gödel’s Proof,” by Ernst Nagel and James R. Newman (2001).

“Gödel – A Life of Logic”, by John L. Casti and Werner DePauli (2000).

“Incompleteness: The Proof and Paradox of Kurt Gödel,” Rebecca Goldstein (2005).

“There’s Something About Gödel,” Francesco Berto (2009).

“Gödel, Escher, Bach – An Eternal Golden Braid”, by Douglas R. Hofstadter (1979).

Next, “Consciousness – A Dhamma Perspective“, ………

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