Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2020-12-07 09:43:30

AlexPontik
Member
Registered: 2020-05-22
Posts: 9
Website

### Gödel's incompleteness theorems...get ready for fun...

1.Prove that the following phrase is wrong.
“If a logical system is consistent, it cannot be complete.”

Proof:
Choose as a logical system the system consisting of:
•    a coin,
•    a lifeform on earth whose purpose is to flip the coin and try to guess which side the coin ends up facing the lifeform, let’s say a human, since they have this ability
•    and finally the rest from the previous two, the coin and the lifeform,  out of all there is, meaning reality, where the lifeform can test what seems to be happening , and what doesn’t.

The above system seems to be a logical system, since it can be defined above, and can be tested in reality for consistency and completeness, in general and specifically (this follows next in the text in case you are in a hurry to find it here…)

The reasoning for the choice of the logical system:
In reality, out of all the human written knowledge, specifically for the laws of physics written down by humans and remain as laws of physics up to now, they seem to be happening consistently to humans since the beginning of humanity, up to now, and there is available human knowledge written  down which verifies this, up to now, by having recorded experiments’ results done in the past in reality, testing these laws of physics, so that the ones that remain and make up the laws of physics, are still consistent with reality.

Out of the human written knowledge, specifically the laws of  physics written down by humans, in the end, are what seems to humans to be happening around them in reality, up to now.
Laws of physics seem to be written down when reality can make common sense to humans with language, as a species, and they write down how that is, generally and for specific occasions.
When laws of physics remain in human knowledge, what is written down makes common sense to humans who otherwise had no prior experience of one another up close in reality, what is written down has been tested in reality, and experiments up to now verify the results expected.

If all the laws physics where one day found to be inconsistent with reality, then humans cannot be part of any logical system as a lifeform, as their logic is not what seems to be happening in reality, and the logic in reality replaces them at sometime. If this is assumed as true the initial sentence is wrong, as humans are not part of a logical systems, and cannot write down such sentences.
However, up until now what seems to be happening is that some of the laws of physics humans write down remain consistent, meaning they don’t change, remain written down, and are not forgotten, and some are proven inconsistent with reality, and are either changed, or forgotten, and the what was previously written down, is not any more a law of physics.

With this in mind, one law in physics does not change, can be written down, and should not be forgotten.

The basic law of physics, or what seems to be happening in reality for humans:
The basic law of physics is that “physics tells you what seems to be happening in reality for humans, and what happens next in reality, humans don’t know before next passes and now comes in reality”, or simplified “what happens next, happens next in reality”.

The proof for the basic law of physics “physics tells you what seems to be happening in reality for humans, and what happens next in reality, humans don’t know before next passes and now comes in reality” is both consistent and complete as a logical system is provided below:
•    1.Conduct the following experiment in reality:
Pick a coin choose a side and flip it as freely as you want to live.
•    2.Conduct the following thought experiment in your imagination:
After you can decide the side the coin end up facing you right all the time, and regardless of the space and time where you live, I have a question for you.
•    3.Here’s the problem and here is the solution to the problem:
Why didn’t you come here now to tell me about it?

Observation:
o    No one came to tell me, regardless of whether I wasn’t expecting anyone to come, or I tried to leave my mind free to the endless possibilities of reality with the hope of expecting anyone/anything…
Further Observation:
o    … time passed…and no one came again…
Furthest Observation:
o    …time passed…and again and again no one came…so in order not to waste any more of the readers time and effort here’s my
Final Observation:
o    it seems to me that some humans don’t know what seems to be happening in reality
o    or they would be here now to tell me about it, since they would know already what happens next in reality, before I write anything here now, so here is what seems to be happening in reality…
o    Something else than anything humans can imagine happens in reality, it happens consistently, and it happens from the beginning of human recorded knowledge, up to now, and for all recorded knowledge which is the same as “physics tells you what seems to be happening in reality for humans, and what happens next in reality, humans don’t know before next passes and now comes in reality” and the proof that this statement is happening in reality and not in someone’s imagination is the disproof of

2.Prove that the following sentence is wrong.
“The consistency of axioms cannot be proved within their own system.”

Proof:
Beginning:
1.When the consistency of axioms cannot be proved within their own system, the system cannot do what it does in reality, because

2.Otherwise when the consistency of axioms cannot be proved within their own system, the system can do what it does in reality, but

3.If in the end when the consistency of axioms cannot be proved within their own system, the system can do what it does in reality, it doesn’t seem to me that the “system” cannot consistently and completely prove in reality that what happens next, happens next in reality and that this is an axiom for the system.
Middle:
1.When the system cannot prove that what happens next, happens next in reality, then reality happens next and the system doesn’t know what seems to be happening in reality, because

2.Otherwise when the system cannot prove that what happens next, happens next in reality, then reality doesn’t happen next, or the system knows what seems to be happening in reality, but

3.If in the end when the system cannot prove that what happens next, happens next in reality, then reality doesn’t happen next, or the system knows what seem to be happening in reality, it doesn’t seem to me that the system is not reality itself.

The end : humans as a logical system is:
1.When one human cannot prove that what happens next, happens next in reality, then reality happens next, and this human doesn’t know what seems to be happening in reality, because

2.Otherwise when one human cannot prove that what happens next, happens next in reality, then reality doesn’t happen next, or this human knows what seems to be happening in reality, but

3.If in the end when one human cannot prove that what happens next, happens next in reality, then reality doesn’t happen next, or this human knows what seem to be happening in reality, it doesn’t seem to me that there isn’t freedom out of all there is in reality for the rest humans to prove this to that one human.

Or otherwise phrased for the human lifeform, as a logical system:
•    Conduct the following experiment in reality:
Pick a coin choose a side and flip it as freely as you want to live.
•    Conduct the following thought experiment in your imagination:
After you can decide the side the coin end up facing you right all the time, and regardless of the space and time where you live, I have a question for you.
•    Here’s the problem and here is the solution to the problem:
Why didn’t you come here now to tell me about it?

Well, it seems to me you didn’t because I just proved none of the rest of you couldn’t, regardless of the space and time where you live, or have I missed something out of all there is, or have I done something untrue, dishonest, or unjust, to what there might be?
That I do not know, because I do know that what happens next, happens next in reality, and reality doesn’t seem to lie to me, but humans do seem to do so sometimes.

1.My Friend, you want the rest from the rest?
2.Ask the rest for the rest, and you will get the rest.
3.Why are you bothering, the rest of us?

Offline