What does Godël’s Incompleteness Theorem actually mean and imply? I just saw Ted-Ed’s video on this topic and didn’t fully understand what it means or what the implications of this are.
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Basically, any reasonable mathematical system will have some statements that can never be proven true or false.
The easiest way to understand what this means is, ironically, is by listening to children
“Mom, why is the world round?”
“Because we have gravity, that pulls all the dirt and water into a ball.”
“Why?”
“Because anything with mass emits a little bit of gravity.”
“Why?”
“…. Because it just does…”
**”Why Mother?”**
(Side note: Oversimplified Example is Oversimplified)
The reason most parents get infuriated by this incessant “Why? Why? Why? Why?” is because kids don’t understand this principle yet. If you keep asking “Why”, the answer will eventually become “Because it is”
No matter what system of logic you use, some things just **are**. Every system of logic has certain universal principles that are just facts. You can’t really prove why 1+1=2. That’s just how arithmetic works.
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