>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.
>If your point is just that humans are real so they can affect space and abstract computers are abstract, then real computers also can affect space
How can you affect space? Space is absolutely inert physically. There is no way to affect it.
I think you meant space as in w h i t e s p a c e. But that is basically only more light on your screen, not darkness, as real space is.
>Everything that humans can prove, can be proven by that computable algorithm.
How to have an algorithm prove that 1=1?
How do you know it is true, unless you define it that way first?
So it seems a computer cannot prove that, unless you define it true first.
That however can be proven, as you can define validation to not be able to able to be validated by computer.
As if you feed it the information 1=1 it could be programmed to output “false”, so if the definition of validation is absolute validation with no possibility of a false output, it is clearly wrong, as you can program a computer to falsely claim 1=1 is false.
However I doubt you would do that as you can see the uncomputable consistency and absolute 100% chance truth of 1=1.
This means the whole spectrum of completely false to completely true is available to a computable validation mechanism. A true proof is only true and can only be true as otherwise it would be not a proof, in so far as bivalent logic applies at all (which I will admit it does not always apply).
If you can validate it in a wrong way (meaning a false validation, or deducing the correct conclusion from a false premise, so that you can correctly conclude something that is wrong but correct), that is not really proving.
If you arbitrarily decide or guess whether the proof is accurate or not, it is not a proof.
This statement cannot be computationally verified: This statement cannot be proven.
Ever heard of Gödel?😅
The statement is true, but not provable. As nothing can be proven if you do not have a definition of what is true first. As we can see the Gödel sentence to be true, that entails that we can see true what is not provable, and hence not computationally verifiable too.
So we can realize truth beyond computational verification.
By that definition of validation humans never proved anything, because they sometimes say that 1=1 is false.
Gödel sentence for some formal system can’t be proven in that system, but it can be proven in more powerful system. Humans that see the sentence to be true are just (reasoning in a way equivalent to) using a more powerful formal system. And everything in that system is computably verifiable.