While there are Universal Principles that govern life, how we interpret these principles will differ.
When I was a young child I absolutely without a doubt believed in Santa Clause and my whole world revolved around everything my parents taught me and lived by. As I grew up and matured (still in process) naturally my understanding of life in general evolved and deepened.
As we grow, hopefully we get focused on the essence of everything.
You just prompted me to look up Goedel's theorem. Here's what AI came up with:
Notably: "Expanding horizons: To find new truths, we must constantly invent new axioms from outside the current system." Reality, in other words, has a way to become larger than we thought requiring us to find new truths if we care to reflect on it.
The entire AI quote:
Truth is absolute, but provability is limited.
Kurt Gödel proved that in mathematics, these two concepts are not the same.
## The Core Difference
* Truth: A statement is true if it matches reality.
* Provability: A statement is provable if you can reach it using a step-by-step chain of logic starting from a set of rules (axioms).
## The Big Discovery
Before Gödel, mathematicians thought truth and provability were identical. They believed that if a math statement was true, you could always find a proof for it eventually.
Gödel proved this belief wrong:
* True but unprovable: He created a math statement that effectively says, "This statement cannot be proven."
* The paradox: If that statement is false, then it can be proven, which means your math system proves a lie.
* The conclusion: To keep math honest and free of contradictions, that statement must be true. Therefore, a true statement exists that logic cannot prove.
## The Philosophical Impact
* Limits of mind: Human logic and computers cannot solve every mathematical truth.
* Expanding horizons: To find new truths, we must constantly invent new axioms from outside the current system.
If you want to explore further, let me know if we should look at:
* How this applies to AI and human consciousness
* The specific math riddle Gödel used to construct his statement
* How Alan Turing used this to find limits in computer software
We are all like those wise men touching different parts of the elephant to determine what an elephant is. Maybe some people don't even know there is an elephant? But I think you nailed it with the word humility. I won't attempt to type/spell the other one!
While there are Universal Principles that govern life, how we interpret these principles will differ.
When I was a young child I absolutely without a doubt believed in Santa Clause and my whole world revolved around everything my parents taught me and lived by. As I grew up and matured (still in process) naturally my understanding of life in general evolved and deepened.
As we grow, hopefully we get focused on the essence of everything.
Perhaps the real work begins not with better explanations or answers, but with noticing when we've stopped letting evidence count against us.
This is well stated.
You just prompted me to look up Goedel's theorem. Here's what AI came up with:
Notably: "Expanding horizons: To find new truths, we must constantly invent new axioms from outside the current system." Reality, in other words, has a way to become larger than we thought requiring us to find new truths if we care to reflect on it.
The entire AI quote:
Truth is absolute, but provability is limited.
Kurt Gödel proved that in mathematics, these two concepts are not the same.
## The Core Difference
* Truth: A statement is true if it matches reality.
* Provability: A statement is provable if you can reach it using a step-by-step chain of logic starting from a set of rules (axioms).
## The Big Discovery
Before Gödel, mathematicians thought truth and provability were identical. They believed that if a math statement was true, you could always find a proof for it eventually.
Gödel proved this belief wrong:
* True but unprovable: He created a math statement that effectively says, "This statement cannot be proven."
* The paradox: If that statement is false, then it can be proven, which means your math system proves a lie.
* The conclusion: To keep math honest and free of contradictions, that statement must be true. Therefore, a true statement exists that logic cannot prove.
## The Philosophical Impact
* Limits of mind: Human logic and computers cannot solve every mathematical truth.
* Expanding horizons: To find new truths, we must constantly invent new axioms from outside the current system.
If you want to explore further, let me know if we should look at:
* How this applies to AI and human consciousness
* The specific math riddle Gödel used to construct his statement
* How Alan Turing used this to find limits in computer software
We are all like those wise men touching different parts of the elephant to determine what an elephant is. Maybe some people don't even know there is an elephant? But I think you nailed it with the word humility. I won't attempt to type/spell the other one!