[Math Challenge]: Prove to me that I am wrong.

alexpontik

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Hi all,

Why say that the following phrase is nonsense?
“The consistency of axioms cannot be proved within their own system.”

Because:
A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself.
If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsistently with regard to those axioms…but…
if the system keeps behaving inconsistently with regard to some axioms and cannot prove to itself that it does so with regard to those axioms, then it doesn’t seem to me it can consistently keep regarding them as axioms for the system, and then something else replaces them, and that something else is what the system calls axioms for itself.


The way humans make sense of the world around them, is either one that is funny for them, or it is one that is not funny for them.
If the way humans make sense of the world around them is not funny for them…for a long time, those people don’t have a good time…for a long time, and they may forget that…
The way one makes sense of the world around one, is funny for one, or it wouldn’t be funny for one...
 
What you are asking, essentially, is that if we have defined addition as 1 + 1 = 2, 1 + 2 = 3, etc. then can we prove that our addition law is correct using only the addition law? The argument must clearly be circular so the answer is no.

Are you "challenging" us to prove you are wrong or are you "daring" us to prove you wrong? The first is acceptable for this site, the other is just trolling.

-Dan
 
I am challenging you, and this is like a treasure hunt for you.
check comments under youtube song titled "Sarah Silverman in London", if you want more info search my facebook page.

or just prove me wrong....
 
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let me try an extensive argument with examples...

We start with some examples, regarding the argument I am making here.

Examples (the formal argument is provided under the challenge section)
for a child to walk, a child balances its body on its feet, and for the child to learn to walk, the child has to be able to prove that to itself, within its system, meaning once the child learns how to balance as described earlier, the child thinks, "I think I get how to walk",
or otherwise said,
"you have to balance your body on your feet to walk" is an axiom in order to be able to walk, and even children can prove this to themselves within their system.

"Most birds can fly" is an axiom in the reality I observe, that birds seem to be able to prove to themselves.
"If you are a bird, and you really sense that you can fly from your nature, then you can learn how to really fly", is an axiom that I observe birds are able to prove to themselves within their own system.

But, if we look at humans again, since one may say that animals are off limits for what we are discussing...
being able to make sense of the world around you by just observing and talking about it, is an axiom humans follow in order to have fun in reality
as when humans are talking nonsense, they haven't thought yet, how reality...really makes sense,
and other humans can prove that to them, so that...

then they can prove what makes sense to themselves, within their own system, after thinking about what was said alone, without bothering other humans with nonsense, before they prove it to themselves...by thinking about it.

Challenge <-- Prove to me that I am wrong (examples are provided above, if you don't understand below)
Why say that the following phrase is nonsense?
“The consistency of axioms cannot be proved within their own system.”
Because:
A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself.
If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsistently with regard to those axioms…but…
if the system keeps behaving inconsistently with regard to some axioms and cannot prove to itself that it does so with regard to those axioms, then it doesn’t seem to me it can consistently keep regarding them as axioms for the system, and then something else replaces them, and that something else is what the system calls axioms for itself.

Or if you want it explained in any other way...let's experiment with physics:
AXIOM: In any experiment conducted in reality, nothing can happen as a result, some-thing can happen as a result, or...something else can happen as a result.
This is an axiom that seems consistent and complete to me, and I dare say...logical.
Isn't it? If it doesn't seem to you, here's why I think that:

Physics as a science, progresses as follows:
1.There is a current theory, at any given time.
2.A candidate theory, which is more exact regarding what really is happening, appears from research as a proposed new theory.
3. Experiments have to be conducted to verify the new theory.
4. When experiments are conducted, they can have the following results.
5. Nothing happens, the experiments fail to show any results, which has happened in the past.
6. Something happens, the experiments had the expected results, which has hap-pened in the past, and science keeps following its path.
7. Something else happens...which was the case with some previous experiments...or else we wouldn't be looking for a new theory, as then all experiments would point only to something, and nothing else...but up to now, this isn't the case, and the future still happens next, and not before next happens.
8. What seems to be happening, is that before people actually make things in their lives that do something...they make things that don't do something exactly...and they find that early at best, or late at worst...but the complete story they all know from the beginning, pretty consistently, it seems to me...as it could be the case with the argument I am making here and below.

Or if you are still unconvinced, and you want it explained using casual language:
After someone says that "the consistency of axioms cannot be proved within their own system", can someone prove to oneself that in order for one to relax, one simply starts relaxing and waits, or is this inconsistent with someone's logic, and then someone cannot relax? Why?
If you want to naturally relax, you simply start doing that(relaxing) and you wait... and you can notice yourself after doing that again and again, that this is an axiom to relax, that you can consistently prove to yourself.
If you want to understand the logic of relaxing, the logic of relaxing is to have a simple common word which describes the starting point of naturally relaxing...if you want to use more words to describe that starting point of naturally relaxing, then this is less relaxing...than simply relaxing.
If you don't want to understand the nature of relaxing, don't worry too much about it, just relax and do something else.


Links regarding the challenge. Check on section "incompleteness theorem" number 2 (links are provided so that you understand what we are discussing


Kind regards, and thank you for your patience,
no one.
 
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So again, what is it we are trying to discuss? I'm a Physicist so maybe I'm missing a crucial but somewhat evasive point. If we establish a set of axioms then we are defining a logical system of some kind. But how can you talk about proving any of these axioms? If you can prove the axiom by using any of the other axioms then we can drop that axiom from the system. This is what I am understanding what we are taking about from what you are saying and I don't see why any elaborate mechanism needs to be discussed.

-Dan
 
So again, what is it we are trying to discuss? I'm a Physicist so maybe I'm missing a crucial but somewhat evasive point. If we establish a set of axioms then we are defining a logical system of some kind. But how can you talk about proving any of these axioms? If you can prove the axiom by using any of the other axioms then we can drop that axiom from the system. This is what I am understanding what we are taking about from what you are saying and I don't see why any elaborate mechanism needs to be discussed.

-Dan
Hi Dan,
let me try to explain myself as close to what you wrote as I can.
If we establish a set of axioms then we are defining a logical system of some kind.
I have to add here that the axioms established have to be observed consistently in reality, otherwise any logical system defined using those axioms, is unrealistic, it seems to me, and it also seems to me that up to here you won't disagree. Why?
Because if you disagree with me up to here, you have established a set of axioms in your life, which even if you don't observe consistently in reality, you still consider them realistic, or you didn't read what I wrote exactly above, and you are not interested into having a productive conversation.
How is it possible to be able for me, not knowing who you are, to be able to write the above?

Because it seems to me that what I wrote above is common sense, for those who really want to make sense of the world around them, as physicists do.
Here, you may disagree with me saying what I wrote above is common sense , and this is why we are discussing...
but with the statement that physicists really want to make sense of the world around them, it doesn't seem to me that you will disagree.
Why, I will explain to you below.

But how can you talk about proving any of these axioms?
Here I disagree, and let me explain why.
A proof, is language written down that humans can make sense of (symbols, words, drawings etc...) which others, by reading what is written down, they end up learning something that they didn't know how it makes sense for them to consider it true.

For example:
let's take the Pythagorean theorem, in a right angle triangle, the sum of squares of the sides of the right angle, are equal to the square of the hypotenuse. (a^2+b^2=c^2, is how we usually write that with symbols, ^ denotes power)
Any of the proofs of the Pythagorean theorem, explains to anyone who is reading the proof, how the above statement is true.
Every proof that is different than the others which made sense for humans to keep, and show it to others, proves the same statement, but using a different way...
...and those ways, humans can read, and if they are patient while reading and think, they can make sense of them.
Still, not every human who will be presented any of these ways, will be patient to read and think, even though there are more than one ways to prove the Pythagorean theorem.

If you can prove the axiom by using any of the other axioms then we can drop that axiom from the system.
If by proving axioms, using other axioms, you can drop the initial axioms from the system, then as you keep doing that (dropping axioms from the system),
you either end up with a group of axioms, which are self evident, meaning even children can prove these to themselves,
or you end up with nothing, in which case the way you are following is not logical (the way that you are doing, doesn't make sense).

When you end up with a group of axioms, which are self evident, meaning even children can prove these to themselves, then no further summarization is needed, as the universe couldn't make logic easier to follow, than the logic that you have to follow from the beginning of your life.

This is what I am understanding what we are taking about from what you are saying and I don't see why any elaborate mechanism needs to be discussed.
The ways humans make sense of the world can be common, or it can diverge.
Why the ways humans make sense of the world can diverge is simple to explain.
In that case, humans haven't spend time and effort to think how to make sense of the world in a common way yet, or there are humans trying to waste other human's time and effort with their stories.





So where do all these lead us to?
You claimed to be a physicist, prove it to me. I'm adding comment on a previous text using this format to be easily distinguishable.



Physics as a science, progresses as follows:

1.There is a current theory, at any given time.
What is a theory: summarize your observations and if they happen in reality again and again, that is a theory that seems to be happening, for real, is the definition being used in this text.

2.A candidate theory, which is more exact regarding what really is happening, appears from research as a proposed new theory.
I hope you don't want to debate that, up to now this is what has been happening , you know that already as a physicist, no?

3. Experiments have to be conducted to verify the new theory.
If you are a physicist, you know that also and that is also not up to debate with a real physicist, unless you are a prophet...

4. When experiments are conducted, they can have the following results.
Here, you need to do you thought experiments, in order to verify that your intuition as a physicist, is aligned with the physical reality.

5. Nothing happens, the experiments fail to show any results, which has happened in the past.
That has happened many time up to now, no?
Not every experiment yield results.


6. Something happens, the experiments had the expected results, which has happened in the past, and science keeps following its path.
That has happened many time up to now, no?
There are experiment yielding the expected results, this is why there are theories in physics, that are verifiable in reality, by experiments...


7. Something else happens...which was the case with some previous experiments...or else we wouldn't be looking for a new theory, as then all experiments would point only to something, and nothing else...but up to now, this isn't the case, and the future still happens next, and not before next happens.
That has happened many time up to now, no?
If it didn't, why do physicists always keep coming with all those new theories to explain something in past experiments, that they didn't expect with their previous theories?
So, past experiments, up to now, point to also something else happening apart from what the physicists, up to now, expected.
And physicists, know that as well.


8. What seems to be happening, is that before people actually make things in their lives that do something...they make things that don't do something exactly...and they find that early at best, or late at worst...but the complete story they all know from the beginning, pretty consistently, it seems to me...as it could be the case with the argument I am making here and below.
There is a difference between what makes sense, and what not, and this difference is only for those who spend time and effort to think about, and usually physicists do try to think about it...let's see.

You don't believe me that something else than anything you can imagine, seems to be happening around you?



Here's more ways for you to read and think about...
Way 1:
· Something else than what humans can imagine has been happening around humans up to now since the beginning of humans…
· or else before humans, what does it seem to you was happening in reality?..
· Something that happened before humans, but that Humans imaginEd after their histoRy startEd GETting REAL, and not something else than what they can imagine?!.

Way 2:
Pick a coin, choose a side and flip it as freely as you want to live. (if you don't know what freely means, you are not free to reply to me...)
After you can decide the side the coin ends up facing you right, all the time, I have a question for you...
Regardless of the time and space you live, why didn't you come earlier to tell me about it?

Way 3:
When one imagines something (when one imagines that one is a physicist in your case)
When one imagines something, something else is happening around one, because if you really think otherwise....
When one imagines something, something else isn't happening around one, but if you think this is really ok for you...
If in the end, when one imagines something, something else isn't happening around one, then...
...it doesn't seem to me where inside one imagines something, does it seem to you?

Way 4:
And in the end, if what seemed to be happening around you was something that you knew, and it was a problem for you anyone to say that something else than anything anyone can imagine seems to be happening, why didn't you go earlier to tell that person not to say that?
Why? Because if anyone wanted to say that something else than anything anyone can imagine seems to be happening, and you knew it all, why didn't you go tell that anyone before anyone said something else?


So there are many ways written above, I am waiting to see if you are reading, or if you are wasting my time (as I have been wasting with other geniuses in other forums)...

...so keep in mind from the beginning...I really am telling you that something else than anything anyone can imagine, seems to be happening around you....and...
...I really am saying to you that it is only a matter of time and effort for you to realize that, because if you don't, you are just wasting other people's time and effort (how that is you will find if you read, and reply in a way that show to me that at least you can reason simply, as real physicists can...)
 
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