PeteOlcott wrote: ↑Wed Apr 19, 2023 4:22 pm No one can point to any mistake only because I am correct.
When a simulating halt decider correctly simulates N steps of its input it derives the exact same N steps that a pure UTM would derive because it is itself a UTM with extra features.
My reviewers cannot show that any of the extra features added to the UTM change the behavior of the simulated input for the first N steps of simulation:
(a) Watching the behavior doesn't change it.
(b) Matching non-halting behavior patterns doesn't change it
(c) Even aborting the simulation after N steps doesn't change the first N steps.
Because of all this we can know that the first N steps of input D simulated by simulating halt decider H are the actual behavior that D presents to H for these same N steps.
computation that halts… “the Turing machine will halt whenever it enters a final state” (Linz-1990:234)
When we see (after N steps) that D correctly simulated by H cannot possibly reach its simulated final state in any finite number of steps of correct simulation then we have conclusive proof that D presents non-halting behavior to H.
Copyright 2020 PL Olcott
Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (317-320)
No one can point to any mistake only because I am correct that you are incorrect about being correct.
And so on, and so forth... with transfinfinite induction.
PeteOlcott wrote: ↑Wed Apr 19, 2023 4:22 pm No one can point to any mistake only because I am correct.
When a simulating halt decider correctly simulates N steps of its input it derives the exact same N steps that a pure UTM would derive because it is itself a UTM with extra features.
My reviewers cannot show that any of the extra features added to the UTM change the behavior of the simulated input for the first N steps of simulation:
(a) Watching the behavior doesn't change it.
(b) Matching non-halting behavior patterns doesn't change it
(c) Even aborting the simulation after N steps doesn't change the first N steps.
Because of all this we can know that the first N steps of input D simulated by simulating halt decider H are the actual behavior that D presents to H for these same N steps.
computation that halts… “the Turing machine will halt whenever it enters a final state” (Linz-1990:234)
When we see (after N steps) that D correctly simulated by H cannot possibly reach its simulated final state in any finite number of steps of correct simulation then we have conclusive proof that D presents non-halting behavior to H.
Copyright 2020 PL Olcott
Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (317-320)
No one can point to any mistake only because I am correct that you are incorrect about being correct.
And so on, and so forth... with transfinfinite induction.
Even stupid people can tell that is nonsense.
If I made a mistake the mistake can be pointed out.
If I made no mistake then no mistake can be pointed out.
The key basis of my current proof provided above changed the mind of one of my reviewers that had previously disagreed with everything that I said for several years.
PeteOlcott wrote: ↑Wed Apr 19, 2023 4:40 pm
Even stupid people can tell that is nonsense.
If I made a mistake the mistake can be pointed out.
If I made no mistake then no mistake can be pointed out.
Precisely!
You can't point to ANY mistake in my saying that you are wrong!
PeteOlcott wrote: ↑Wed Apr 19, 2023 4:40 pm
Even stupid people can tell that is nonsense.
If I made a mistake the mistake can be pointed out.
If I made no mistake then no mistake can be pointed out.
Precisely!
You can't point to ANY mistake in my saying that you are wrong!
The mistake is that your statement is pure rhetoric entirely bereft of any supporting reasoning. On the other hand I already provided a whole page of supporting reasoning for my view.
I can understand that you may not believe that any supporting reasoning is required. Conspiracy theorists count a consensus of opinion of their groupthink reference group as the same thing as verified facts.
Hopefully the settlement of the Dominion suit will change some of their minds.
PeteOlcott wrote: ↑Wed Apr 19, 2023 4:40 pm
Even stupid people can tell that is nonsense.
If I made a mistake the mistake can be pointed out.
If I made no mistake then no mistake can be pointed out.
Precisely!
You can't point to ANY mistake in my saying that you are wrong!
The mistake is that your statement is pure rhetoric entirely bereft of any supporting reasoning. On the other hand I already provided a whole page of supporting reasoning for my view.
I can understand that you may not believe that any supporting reasoning is required. Conspiracy theorists count a consensus of opinion of their groupthink reference group as the same thing as verified facts.
Hopefully the settlement of the Dominion suit will change some of their minds.
Can your system derrive contradictions? No it can't.
So it's NOT Turing complete. So you are wrong about the "universality" of your system.
Agent Smith wrote: ↑Wed Apr 19, 2023 4:58 pm
Where's the reactor?
It's here ... er ... it was here, where is it?
You misplaced a reactor?
Oh no! What time is it?
Time ta build a new reactor!
This is not the time for jokes! Quick, find it, find it!!
Gentlemen, gentlemen! Relax. The reactor is where it is. We are where we are or ... were in this case. The reactor will be found, of that I'm certain.
It could be anywhere!!
It could be anywhere?! No, no, it can't be anywhere. As we all know, anywhere is nowhere and nowhere is .... yes?
Sigh, somewhere?
Exactly! The reactor is somewhere! Look somewhere ... for the ... what is it we're lookin' for ... ah! ... a ... I mean the reactor!
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.
You can't point to ANY mistake in my saying that you are wrong!
The mistake is that your statement is pure rhetoric entirely bereft of any supporting reasoning. On the other hand I already provided a whole page of supporting reasoning for my view.
I can understand that you may not believe that any supporting reasoning is required. Conspiracy theorists count a consensus of opinion of their groupthink reference group as the same thing as verified facts.
Hopefully the settlement of the Dominion suit will change some of their minds.
Can your system derrive contradictions? No it can't.
So it's NOT Turing complete. So you are wrong about the "universality" of your system.
Q.E.D
In other words you are saying that you are sure that the Liar Paradox is true or false because a Turing complete model of computation would have to be able to show this.
PeteOlcott wrote: ↑Wed Apr 19, 2023 5:03 pm
In other words you are saying that you are sure that the Liar Paradox is true or false because a Turing complete model of computation would have to be able to show this.
Sure.
It's true after x mod 2 computations.
It's false after (x +1) mod 2 computations.
The liar's paradox is a bit like "Is the number of sand grains in the universe odd or even?"
PeteOlcott wrote: ↑Wed Apr 19, 2023 5:03 pm
In other words you are saying that you are sure that the Liar Paradox is true or false because a Turing complete model of computation would have to be able to show this.
Sure.
It's true after x mod 2 computations.
It's false after (x +1) mod 2 computations.
The liar's paradox is a bit like "Is the number of sand grains in the universe odd or even?"
Well, it's one or the other...
This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about?
It is not true about being not true about being not true...
Ah so you have an infinite cycle in your evaluation loop thus are not a truth bearer.
Because the Prolog Liar Paradox has an “uninstantiated subterm of itself” we can know that unification will fail because it specifies “some kind of infinite structure.” The quotes come from: (Clocksin and Mellish 2003:255)
Last edited by PeteOlcott on Wed Apr 19, 2023 5:18 pm, edited 1 time in total.
PeteOlcott wrote: ↑Wed Apr 19, 2023 5:03 pm
In other words you are saying that you are sure that the Liar Paradox is true or false because a Turing complete model of computation would have to be able to show this.
Sure.
It's true after x mod 2 computations.
It's false after (x +1) mod 2 computations.
The liar's paradox is a bit like "Is the number of sand grains in the universe odd or even?"
Well, it's one or the other...
This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about?
It is not true about being not true about being not true...
Ah so you have an infinite cycle in your evaluation loop.
Because the Prolog Liar Paradox has an “uninstantiated subterm of itself” we can know that unification will fail because it specifies “some kind of infinite structure.”
The quotes come from: (Clocksin and Mellish 2003:255)
It's true after x mod 2 computations.
It's false after (x +1) mod 2 computations.
The liar's paradox is a bit like "Is the number of sand grains in the universe odd or even?"
Well, it's one or the other...
This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about?
It is not true about being not true about being not true...
Ah so you have an infinite cycle in your evaluation loop.
Because the Prolog Liar Paradox has an “uninstantiated subterm of itself” we can know that unification will fail because it specifies “some kind of infinite structure.”
The quotes come from: (Clocksin and Mellish 2003:255)
You can't handle infinities? There's your error.
Use a model of computation which can.
Prolog 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.
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.
Agent Smith wrote: ↑Wed Apr 19, 2023 4:58 pm
Where's the reactor?
It's here ... er ... it was here, where is it?
You misplaced a reactor?
Oh no! What time is it?
Time ta build a new reactor!
This is not the time for jokes! Quick, find it, find it!!
Gentlemen, gentlemen! Relax. The reactor is where it is. We are where we are or ... were in this case. The reactor will be found, of that I'm certain.
It could be anywhere!!
It could be anywhere?! No, no, it can't be anywhere. As we all know, anywhere is nowhere and nowhere is .... yes?
Sigh, somewhere?
Exactly! The reactor is somewhere! Look somewhere ... for the ... what is it we're lookin' for ... ah! ... a ... I mean the reactor!
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.
Agent Smith wrote: ↑Wed Apr 19, 2023 4:58 pm
Where's the reactor?
It's here ... er ... it was here, where is it?
You misplaced a reactor?
Oh no! What time is it?
Time ta build a new reactor!
This is not the time for jokes! Quick, find it, find it!!
Gentlemen, gentlemen! Relax. The reactor is where it is. We are where we are or ... were in this case. The reactor will be found, of that I'm certain.
It could be anywhere!!
It could be anywhere?! No, no, it can't be anywhere. As we all know, anywhere is nowhere and nowhere is .... yes?
Sigh, somewhere?
Exactly! The reactor is somewhere! Look somewhere ... for the ... what is it we're lookin' for ... ah! ... a ... I mean the reactor!
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.
Last edited by PeteOlcott on Wed Apr 19, 2023 6:34 pm, edited 1 time in total.
