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There exists a G in F that proves its own unprovability in F
Posted: Tue Apr 25, 2023 5:49 pm
by PeteOlcott
We are therefore confronted with a proposition which asserts its own unprovability. 15
14 Every epistemological antinomy can likewise be used for a similar undecidability proof.
(Gödel 1931:40)
Antinomy
...term often used in logic and epistemology, when describing a paradox or
unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And Related Systems
https://mavdisk.mnsu.edu/pj2943kt/Fall% ... l-1931.pdf
On this basis we define a much more powerful F in a formal system having
its own unprovability operator: ⊬ This eliminates the need for the complexity
of arithmetization and diagonalization.
G := (F ⊬ G) means G is defined to be another name for (F ⊬ G)
https://en.wikipedia.org/wiki/List_of_logic_symbols
∃G ∈ F (G := (F ⊬ G))
There exists a G in F that proves its own unprovability in F
Within this much more powerful F a proof of G in F requires a sequence
of inference steps in F that prove that they themselves do not exist.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 6:51 am
by Agent Smith
Why did ...
Alfonso look up?
Yeah, more or less.
What's more, he kept oooon lookin' up!
Exactamundo!
We must ...
Wir müssen wissen, wir werden wissen!
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 10:11 am
by Skepdick
Olcott, you are a fucking idiot.
Antimonies cease to exist the moment you introduce time/change into your formal system.
P ⇒ ¬P ⇒ P ⇒ ¬P ⇒ P ⇒ ¬P ⇒ P ⇒ ¬P ⇒ P ⇒ ¬P ⇒ P ⇒ ¬P ⇒ P ⇒ ¬P
What you call "contradiction" is just oscillation - a state transition. P as it becomes not-P. As it becomes P again.
Mutability vs Immutability is covered in every basic computer science course...
Here's a free one from MIT:
https://web.mit.edu/6.005/www/fa15/clas ... utability/
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 4:53 pm
by PeteOlcott
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 4:56 pm
by PeteOlcott
PeteOlcott wrote: ↑Wed May 03, 2023 4:53 pm
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
That the liar paradox is not a truth bearer for two different reasons
does not make it a truth bearer.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 6:32 pm
by Harbal
Skepdick wrote: ↑Wed May 03, 2023 10:11 am
Olcott, you are a fucking idiot.
If he don't know by now, I guess he never will.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 6:33 pm
by Skepdick
Harbal wrote: ↑Wed May 03, 2023 6:32 pm
If he don't know by now, I guess he never will.
It's for posterity more than his benifit.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 6:37 pm
by Skepdick
PeteOlcott wrote: ↑Wed May 03, 2023 4:53 pm
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
Olcott, you are a fucking idiot.
Is it true or false that this sentence is not a truth-bearer?
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 8:35 pm
by PeteOlcott
PeteOlcott wrote: ↑Wed May 03, 2023 4:56 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:53 pm
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
That the liar paradox is not a truth bearer for two different reasons
does not make it a truth bearer.
The ignoramus doesn't even understand that questions are not truth bearers.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 9:27 pm
by Skepdick
PeteOlcott wrote: ↑Wed May 03, 2023 8:35 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:56 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:53 pm
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
That the liar paradox is not a truth bearer for two different reasons
does not make it a truth bearer.
The ignoramus doesn't even understand that questions are not truth bearers.
Olcott, you are fucking idiot.
Every inhabited type is a truth-bearer. Every question whose answer is a Boolean is a truth-bearer.
https://en.wikipedia.org/wiki/Type_inhabitation
English: Is the number 4 dvisible by 2?
Mathematics: 4 MOD 2 = 0
Python:
Answer: True.
Re: There exists a G in F that proves its own unprovability in F
Posted: Wed May 03, 2023 10:15 pm
by PeteOlcott
PeteOlcott wrote: ↑Wed May 03, 2023 8:35 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:56 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:53 pm
An ignoramus honestly believes that "this sentence is not true"
becomes a truth bearer with the value of true if you just wait a while.
That the liar paradox is not a truth bearer for two different reasons
does not make it a truth bearer.
The ignoramus doesn't even understand that questions are not truth bearers.
The ignoramus believes that these are merely totally redundant names for
a Declarative Sentence, and there is no difference at all between them.
Declarative Sentence.
Imperative Sentence.
Interrogative Sentence.
Exclamatory Sentence.
Re: There exists a G in F that proves its own unprovability in F
Posted: Thu May 04, 2023 3:14 am
by Skepdick
PeteOlcott wrote: ↑Wed May 03, 2023 10:15 pm
PeteOlcott wrote: ↑Wed May 03, 2023 8:35 pm
PeteOlcott wrote: ↑Wed May 03, 2023 4:56 pm
That the liar paradox is not a truth bearer for two different reasons
does not make it a truth bearer.
The ignoramus doesn't even understand that questions are not truth bearers.
The ignoramus believes that these are merely totally redundant names for
a Declarative Sentence, and there is no difference at all between them.
Declarative Sentence.
Imperative Sentence.
Interrogative Sentence.
Exclamatory Sentence.
Olcott, you are a fucking idiot.
Learn the difference between syntax and semantics.
There is no semantic difference between the declarative sentence "Olcott, you are a fucking idiot!" and the question-answer pair "Olcott, are you a fucking idiot? Yes, you are!"
Re: There exists a G in F that proves its own unprovability in F
Posted: Thu May 04, 2023 3:44 am
by Agent Smith
As far as I can tell, we need to clarify the butter ... er ... I mean Gödel's argument/proof.
We start with ...
Step 1) G is unprovable in F (The Gödel sentence)
Step 2)
Step 3)
.
.
.
The
form
1. Either Paul is a vet or Paul is a flautist
2. Paul is not a flautist
Ergo
3. Paul is vet