Not everything that is true can be proven

LowQCab

Joined Nov 6, 2012
552
This also applies to People (Life), as you can't actually "prove" anything to any one.

Because it comes down to whether or not they can
imagine the outcome that you are trying to convey,
which is severely limited by their "beliefs",
which are quite often not based on actual experience,
but based on other outside "influences", in combination with, their fear of being "wrong".

........ Well that doesn't prove a thing, because ....... "reasons", or, "I don't like it"...........

Therefore, you have some people who can't be reasoned with.

You have to laugh at this type of stuff or you'll loose you mind.
 

Delta Prime

Joined Nov 15, 2019
1,014
You have to laugh at this type of stuff or you'll loose you mind
Respectfull.You yourself have said. "Question Everything" in a different context of course, it applies here as well, some of us continue to ponder the issue. It is one of those great questions that we don’t normally talk about because we don’t like to mention questions for which we have no good answers. I believe it's innate within us to do just that. To ponder deeply,question everything, it's how we advance as a species. :)
I know there's no science being done here. Point,counterpoint conjecture but they are also a postulate of quantum mechanics, a theory which is one of the pillars of our modern electronic technology.
 
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LowQCab

Joined Nov 6, 2012
552
It's possible to become very good at making a prediction regarding a particular outcome,
you hopefully get better at it the more times you find out that you were wrong.

AKA, Experience.

People who are quick to point fingers of blame because they fear being wrong,
don't accumulate much Experience,
therefore they don't develop Wisdom.

Scary thought.
 

click_here

Joined Sep 22, 2020
190
I love "The game of life" - It was one of the original programs that I wrote in C.

I showed my girlfriend at the time and she said that the graphics looked crap - lol
 

Yaakov

Joined Jan 27, 2019
3,155
Gödel sat in the Vienna Circle for quite a long time knowing he'd proven incompleteness even as Russel worked on Principia Mathematica which Gödel knew was a waste of time. Russel later was very bitter and said that the Principia wasted he best work as a young mathematician. He finally presented incompleteness in 1930.

As an aside, Gödel was quite introverted, and when he went to the Institute for Advanced Study at Princeton he had only one close friend: Einstein, a famous extrovert.
 

bogosort

Joined Sep 24, 2011
674
Haven't watched the video, but the subtitle is "This is Math's Fatal Flaw", which would have made Gödel laugh. Incompleteness only applies to theories, not math. Consequently, he saw incompleteness as joyful proof that there is no limit to mathematical theorems. Incompleteness implies that math is inexhaustible.
 

Thread Starter

nsaspook

Joined Aug 27, 2009
8,382
Haven't watched the video, but the subtitle is "This is Math's Fatal Flaw", which would have made Gödel laugh. Incompleteness only applies to theories, not math. Consequently, he saw incompleteness as joyful proof that there is no limit to mathematical theorems. Incompleteness implies that math is inexhaustible.
Pure mathematics is inexhaustible. So, will there always be problems that can't be solved by existing math rules?
 

bogosort

Joined Sep 24, 2011
674
Pure mathematics is inexhaustible. So, will there always be problems that can't be solved by existing math rules?
Well yes, but we don't need the incompleteness theorems to see that. A simple counting argument suffices; let's just take decision problems, e.g., those that can be modeled as a function that return "yes/no" answers: \[f:\mathbb{Z} \to \{0, 1\}\] The set of all such problems has the cardinality of the continuum, \( 2^{|\mathbb{Z}|} = |\mathbb{R}| \). So there are an uncountable number of decision problems. However, any mathematical proof must necessarily be a finite set of symbols, and so the set of all mathematical proofs is finite. Therefore, we have more problems than we have mathematical proofs.
 

MrSalts

Joined Apr 2, 2020
284
Pure mathematics is inexhaustible. So, will there always be problems that can't be solved by existing math rules?
Yes. Some problems have unknowable answers but the rules of math are known. But people making YouTube videos need titles that attract audiences so, they contradict their own knowledge of the subject to tell that attracted audience something slightly different than the promise in the title. That's MrSalts Theory of 'STEM' YouTube Titles.
 

MrAl

Joined Jun 17, 2014
8,248
Yes and this has been known for some time.
It is interesting how this in itself seems to be true, and that puts some damper on how we interpret reality, and when compared with quantum physics we seem to find a relationship or parallel. Both are saying that reality is very different than our common experience tells us.
A scientist put it in a very concise manner and i will paraphrase:
"The chance that evolution taught us to deal with the true reality of nature is exactly zero".
Dont remember his name but i would bet that is on the web somewhere too.

To me our common experience is due to our simplistic view of nature where we can only see relatively large things and since there are very very tiny things and processes that we cant notice we only notice the conglomeration of the whole which can only be a statistical view. We might refer to this as those small entities being "congealed" by the time we can experience them, so perhaps we see matter only after it has already been congealed from energy, or maybe a dynamic process that energy goes through that makes us see it as a conglomeration of itself.

here is a case in point or close to it:
For years and years and years we viewed the electron as being a single solitary particle, but as of late it is being thought of as being made up of two particles: one for charge and one for spin.
 

Thread Starter

nsaspook

Joined Aug 27, 2009
8,382
Everything that is true *CAN* be proven. Do not confuse our ability to prove something with it's ability to be proven. This is a typical 'man's folly' argument. Man attempts to view everything through his own limitations.
Man attempts to view everything through his own limitations.

Exactly.
 

bogosort

Joined Sep 24, 2011
674
Everything that is true *CAN* be proven. Do not confuse our ability to prove something with it's ability to be proven. This is a typical 'man's folly' argument. Man attempts to view everything through his own limitations.
A proof is ultimately a logical derivation of a true statement within some formal (axiomatic) system. Without the formal system, which defines the language and rules for making such derivations, there is no proof. In other words, a proof is only valid with respect to some given formal system.

Gödel showed that for any such system, if it is powerful enough to express arithmetic over the integers, then it necessarily contains theorems (true statements) that are unprovable. The demonstration of this takes some work, but it is indisputable.

This is not a folly of man; it is a fundamental limitation of any given formal system. But without a formal system, you can't prove anything. So whatever you are talking about, it's not about actual proofs.
 

andrewmm

Joined Feb 25, 2011
1,470
An interesting question,

Personally I 100% agree, based purely on the scientific principle,

We have theories, and laws ( such as ohms law )

To miss quote I think Churchill
the maths we have is crap, but its better than all the alternatives.

Was it not only a few years ago that we "proved" Fermat's Last Theorem

but can we prove quantum theory, or general relativity ?
I doubt it , but I bet there are holes,

but even maths as shown has many holes,

what is 0/0 is one I get asked.

anything divided by zero is infinity,
anything divided by itself is 1
and is 0 a number,


I look forward to some discussion on this
 

bogosort

Joined Sep 24, 2011
674
Was it not only a few years ago that we "proved" Fermat's Last Theorem

but can we prove quantum theory, or general relativity ?
Scientific theories are built from empirical hypotheses, not formal statements, and so can neither be proved nor disproved. At best, we can continue to accept or reject the hypotheses based on the accumulation of evidence.

but even maths as shown has many holes,
What exactly do you mean by "hole"?

what is 0/0 is one I get asked.
In many mathematical contexts, division by zero is simply undefined. It doesn't have to be -- we can define 0/0 axiomatically or as shorthand for a limit. The only restriction is that we don't introduce any inconsistencies.
 

Yaakov

Joined Jan 27, 2019
3,155
Gödel said that no single, consistent formal system can find all true statements in that system. That's why it is incomplete. It was a blow to Hilbert and the Logical Positivists who had a program to logically prove math as the foundation of a theory of everything. They couldn't because formal systems are incomplete.
 
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