Could you explain Godel's Incompleteness Theorem to a layman?

[AngryCarl2]

Yes

No

Allow me to elucidate

Updates

+1 y

I wasn't really expecting to get any answers but I got a bunch of good ones. Good job!

[TheSpaceGnome]

It is the idea that a math formula that explains how everything works cannot be found, because the mathematician will always be starting with assumptions when doing deductive reasoning/calculations.

It is a fancy way to say that when you use guesses to deduce an answer, it can be the wrong answer, and trying to put a bunch of "maybe wrong answers" together to figure out how they connect to eachother and what governs them, doesn't work.

[TheSpaceGnome]

Basically its a math model that says all math models are missing data.

[AngryCarl2]

"It is the idea that a math formula that explains how everything works cannot be found, "
This is correct. It's not assumptions that are the problem, since those can be proved either true or false. The problem is that the axioms are insufficient.

[TheSpaceGnome]

An axiom is a fancy word for a truth, when the truths are insufficient, you are left with assumptions as part of your equations, which is why a math formula that explains how everything works cannot be found. So assumptions are the problem.

[TheSpaceGnome]

I refrained from using the term axiom before because it's not layman vocabulary, and instead disected the words and their meanings to their simplest points.

[TheSpaceGnome]

Another way to look at it, is if you saw a bunch of scrambled alphabet letters, and tried to figure out what words they initially spelled and what sentences they made. You would have access to all the evidence, but not all the information needed to figure out each word and what order to put them in, and no math formula is going to tell you the answer. So when you go to other piles of letters, and have the same problem, and then you try to write a book based on the paragraphs each pile originally had, its never going to be accurate.

[AngryCarl2]

Yes, that's a good point.

[TheSpaceGnome]

Glad I could help, I knew about this concept ages ago just from life experience in realizing when I could or couldn't figure something out, I didn't know about Godel though, or the term axiom. I used to just call them data points or facts.

[jshm2]

Basically that its mathematically impossible to know everything, let alone prove everything.

It basically laughs in the face of atheists, scientism and logic whores. All who claim to "know," when they are merely throwing conjectures.

[RolandCuthbert]

Well, you can do proofs within a given context. Like a scientist can predict that the sun will rise tomorrow at a certain time. And he can talk about the rules within physics that allow him to be accurate with such predictions. The issue is, going all the way back to the foundations of mathematics, he still has to make assumptions.

We assume certain things to be true, but we don't have a "proof". We just have assumptions.

[AngryCarl2]

@jshm2 In essence you're correct. But the theorem only applies to mathematics, not the other stuff you mentioned.

[slatyb]

Athiests don't claim to know. We simply refuse to accept unsubstantiated mythology.

[slatyb]

It's a statement about a set of mathematical axioms. It has no effect on the validity of scientific models or the application of logic to real world problems.

[RolandCuthbert]

I can't remember this! Does it have to do with the foundation of mathematics. We often wonder if mathematics is just a concept we invented or was it simply there before humans came along.

I think this is about trying to show that there isn't a way to make the claim that mathematics is divorced from human assumption and biases when describing the universe.

That mathematics includes assumptions at its foundation that we simply assume to be true. We have no way to prove these assumptions. But no one questions it. In other words, mathematics is incomplete, because at its foundation there are core assumptions. There isn't anything we can do to find evidence or gather facts about these assumptions.

[AngryCarl2]

You are warm. It's not that the assumptions are wrong, it's just that they are insufficient to prove (or disprove) all mathematical statements.

[RolandCuthbert]

OH, I am not saying the assumptions are wrong. I apologize. I kind of made a mess of my post because I was literally writing my thoughts instead of thinking it through.

It is that these are assumptions with no proofs. We have no way to prove if these assumptions are true. That is the incompleteness. Or at least that's what I think it is supposed to be.

It has been a long time since I looked at this.

[AngryCarl2]

Exactly right. Thanks for commenting.

[slatyb]

I can tell them what it says but I couldn't explain the proof.

[AngryCarl2]

If you can understand it you're way ahead of must people.

[AngryCarl2]

*most people

[slatyb]

Most people would be lost with Cantor's proof that the real numbers are uncountable.

[FunkyMonkee]

Not completely.

[AngryCarl2]

Same here. Even people who understand what it is struggle to explain it.