PeteOlcott wrote: ↑Wed Apr 19, 2023 5:19 pmProlog understands this:
When expressions of formal language have infinite evaluation loops this proves that they are not truth bearers.
You are grasping at straws yet toned down your hostility, that is good.
Prolog is only as powerful as a Turing machine.
There are more powerful models of computation.
And you deserve far more hostility than I have at my disposal. You fucking time-wasting cunt.
These are only imaginary: https://en.wikipedia.org/wiki/Oracle_machine
and cannot possibly be approximated in the real world because the speed of light is not infinite. Oracle machines are based on the false assumption that an infinite number of steps can be performed in no time at all. The actual truth is that an infinite number of steps by definition necessarily never completes.
Everyone knows that your insults merely indicate that you are out of your depth. That is OK. I would be very happy to break my explanations down so that you can understand them. My goal is to make them simple enough than an average eighth grader can validate them.
G asserts its own unprovability in F
Although it is true that G cannot be proved in F the reason that G
cannot be proved in F is that this requires a sequence of inference
steps in F that proves no such sequence of inference steps exists in F.
Si, G asserts its own unprovability in F. Define F please.
Major premise: All humans are mortal. // humans ⊆ mortal
Minor premise: All Greeks are humans. // Greeks ⊆ humans
Conclusion: All Greeks are mortal. // Greeks ⊆ mortal https://en.wikipedia.org/wiki/Syllogism#Basic_structure
The first two lines are the inference steps the last line
is derived as a semantic consequence of the first two lines.
The proof of Gödel's G has the same contradictory structure as the liar paradox:
This sentence is not true. If it is true that makes it untrue. If it is untrue that makes it true.
When you understand this much I will elbaborate.
Well, I'm not all that great at understanding stuff. Apologies because it seems you want to debate the issue with peeps who have a handle on Gödel's infamous theorems. I, alack, am not among them.
My suggestion, for what it's worth, is that you pay more/close attention to G.
"Tom, you're a mathematician!"
"What?! I suck at math!"
"Go look in the mirror!"
"Why?! This is a prank, isn't it?"
"No, go look!"
"By Golly, I am ... a mathematician!"
"See!!"
Last edited by Agent Smith on Wed Apr 19, 2023 7:07 pm, edited 1 time in total.
Si, G asserts its own unprovability in F. Define F please.
Major premise: All humans are mortal. // humans ⊆ mortal
Minor premise: All Greeks are humans. // Greeks ⊆ humans
Conclusion: All Greeks are mortal. // Greeks ⊆ mortal https://en.wikipedia.org/wiki/Syllogism#Basic_structure
The first two lines are the inference steps the last line
is derived as a semantic consequence of the first two lines.
The proof of Gödel's G has the same contradictory structure as the liar paradox:
This sentence is not true. If it is true that makes it untrue. If it is untrue that makes it true.
When you understand this much I will elbaborate.
Well, I'm not all that great in understanding stuff. Apologies because it seems you want to debate the issue with peeps who have a handle on Gödel's infamous theorems. I, alack, am not among them.
My suggestion, for what it's worth, is that you pay more/close attention to G.
"Tom, you're a mathematician!"
"What?! I suck at math!"
"Go look in the mirror!"
"Why?! This is a prank, isn't it?"
"No, go look!"
"By Golly, I am ... a mathematician!"
"See!!"
It might prove more fruitful to discuss these things with people not
having prior exposure to these things because math guys mistake
their learned-by-rote memorization of a bunch of complex steps for
actual understanding of the problem.
Major premise: All humans are mortal. // humans ⊆ mortal
Minor premise: All Greeks are humans. // Greeks ⊆ humans
Conclusion: All Greeks are mortal. // Greeks ⊆ mortal https://en.wikipedia.org/wiki/Syllogism#Basic_structure
The first two lines are the inference steps the last line
is derived as a semantic consequence of the first two lines.
The proof of Gödel's G has the same contradictory structure as the liar paradox:
This sentence is not true. If it is true that makes it untrue. If it is untrue that makes it true.
When you understand this much I will elbaborate.
Well, I'm not all that great in understanding stuff. Apologies because it seems you want to debate the issue with peeps who have a handle on Gödel's infamous theorems. I, alack, am not among them.
My suggestion, for what it's worth, is that you pay more/close attention to G.
"Tom, you're a mathematician!"
"What?! I suck at math!"
"Go look in the mirror!"
"Why?! This is a prank, isn't it?"
"No, go look!"
"By Golly, I am ... a mathematician!"
"See!!"
It might prove more fruitful to discuss these things with people not
having prior exposure to these things because math guys mistake
their learned-by-rote memorization of a bunch of complex steps for
actual understanding of the problem.
Please go through the OP; your own ideas about Gödel's heartwrenching theorems may hold the key to sussing out Gödel's reasoning.
Note Gödel was held in high regard by Einstein, no less.
Well, I'm not all that great in understanding stuff. Apologies because it seems you want to debate the issue with peeps who have a handle on Gödel's infamous theorems. I, alack, am not among them.
My suggestion, for what it's worth, is that you pay more/close attention to G.
"Tom, you're a mathematician!"
"What?! I suck at math!"
"Go look in the mirror!"
"Why?! This is a prank, isn't it?"
"No, go look!"
"By Golly, I am ... a mathematician!"
"See!!"
It might prove more fruitful to discuss these things with people not
having prior exposure to these things because math guys mistake
their learned-by-rote memorization of a bunch of complex steps for
actual understanding of the problem.
Please go through the OP; your own ideas about Gödel's heartwrenching theorems may hold the key to sussing out Gödel's reasoning.
Note Gödel was held in high regard by Einstein, no less.
Gödel starved himself to death because he trusted that only his wife's
cooking could be relied upon on not poisonous and his wife became unavailable.
He did have a close friend that was killed from poisoning so his fear was not
totally unjustified. That he didn't trust his own cooking is the strange part.
Do you understand that the Liar Paradox: "this sentence is not true"
is not a truth bearer? (We must begin with some basis of mutual understanding).
It might prove more fruitful to discuss these things with people not
having prior exposure to these things because math guys mistake
their learned-by-rote memorization of a bunch of complex steps for
actual understanding of the problem.
Please go through the OP; your own ideas about Gödel's heartwrenching theorems may hold the key to sussing out Gödel's reasoning.
Note Gödel was held in high regard by Einstein, no less.
Gödel starved himself to death because he trusted that only his wife's
cooking could be relied upon on not poisonous and his wife became unavailable.
He did have a close friend that was killed from poisoning so his fear was not
totally unjustified. That he didn't trust his own cooking is the strange part.
Do you understand that the Liar Paradox: "this sentence is not true"
is not a truth bearer? (We must begin with some basis of mutual understanding).
All I'm saying is that the odds of Gödel's theorems being wrong is vanishingly small.
Gödel starved himself to death because he trusted that only his wife's
cooking could be relied upon on not poisonous and his wife became unavailable.
He did have a close friend that was killed from poisoning so his fear was not
totally unjustified. That he didn't trust his own cooking is the strange part.
Do you understand that the Liar Paradox: "this sentence is not true"
is not a truth bearer? (We must begin with some basis of mutual understanding).
All I'm saying is that the odds of Gödel's theorems being wrong is vanishingly small.
When what I am saying is fully understood these "odds" become 100%.
I have been working on this since 2004.
To correctly refute any proof only requires correctly refuting its conclusion.
G cannot be proved in F because there is something wrong with G
thus Gödel's conclusion that the reason is that there is something
wrong with F is incorrect.
Gödel starved himself to death because he trusted that only his wife's
cooking could be relied upon on not poisonous and his wife became unavailable.
He did have a close friend that was killed from poisoning so his fear was not
totally unjustified. That he didn't trust his own cooking is the strange part.
Do you understand that the Liar Paradox: "this sentence is not true"
is not a truth bearer? (We must begin with some basis of mutual understanding).
All I'm saying is that the odds of Gödel's theorems being wrong is vanishingly small.
When what I am saying is fully understood these "odds" become 100%.
I have been working on this since 2004.
To correctly refute any proof only requires correctly refuting its conclusion.
G cannot be proved in F because there is something wrong with G
thus Gödel's conclusion that the reason is that there is something
wrong with F is incorrect.
I believe I have an idea of what you're getting at. However, it appears nowhere in your OP.
All I'm saying is that the odds of Gödel's theorems being wrong is vanishingly small.
When what I am saying is fully understood these "odds" become 100%.
I have been working on this since 2004.
To correctly refute any proof only requires correctly refuting its conclusion.
G cannot be proved in F because there is something wrong with G
thus Gödel's conclusion that the reason is that there is something
wrong with F is incorrect.
I believe I have an idea of what you're getting at. However, it appears nowhere in your OP.
Everything is in my first post.
I explained it in simpler less technical terms for you.
When what I am saying is fully understood these "odds" become 100%.
I have been working on this since 2004.
To correctly refute any proof only requires correctly refuting its conclusion.
G cannot be proved in F because there is something wrong with G
thus Gödel's conclusion that the reason is that there is something
wrong with F is incorrect.
I believe I have an idea of what you're getting at. However, it appears nowhere in your OP.
Everything is in my first post.
I explained it in simpler less technical terms for you.
It looks like I'll have do a second pass over the OP.
Food for thought: What does G actually say? I know this looks as though it's time for me ta resign, but can you expand and elaborate on G.
PeteOlcott wrote: ↑Thu Apr 20, 2023 12:06 pm
G := (F ⊬ G)
G asserts its own unprovability in F
The second line is the English Translation of the first line
And I am supposed to believe you that's true?
Don't tell me - show me.
Show me the translation algorithm which given the formula "G := (F ⊬ G)" as an input produces the English sentence "G asserts its own unprovability in F" as an output.
While you are at it show me the reverse-translation algorithm which given the English sentence "G asserts its own unprovability in F" produces the formula "G := (F ⊬ G)"
Unless you can do that there's no way to determine whether "G := (F ⊬ G)" and "G asserts its own unprovability in F" mean the same thing.
You keep getting confused between the linguistic/symbolic representations and what it is they actually represent. Probably because you don't understand Representation theory.
There are diverse approaches to representation theory. The same objects can be studied using methods from algebraic geometry, module theory, analytic number theory, differential geometry, operator theory, algebraic combinatorics and topology
Last edited by Skepdick on Thu Apr 20, 2023 12:44 pm, edited 2 times in total.
