Pathological self reference is a syntactic property.Skepdick wrote: ↑Mon May 29, 2023 8:24 amOlcott, you are a fucking idiot.PeteOlcott wrote: ↑Sun May 28, 2023 5:28 pm Prolog correctly detects the pathological self-reference error thus
rejects the Liar Paradox (and every other expression with the same error)
as erroneous. This by itself totally nullifies Tarski's undefinability Theorem
that utterly depends on the Liar Paradox expression.
But the diagonal lemma yields a counterexample to this equivalence,
by giving a "liar" formula S such that S ⟺ ¬True(g(S)) holds in N.
This is a contradiction. QED.
https://en.wikipedia.org/wiki/Tarski%27 ... neral_form
In all this fucking time you still haven't figured out that one of the things valid formal systems DO is preserve semantic properties under transformations. Whatever those properties may be.
So if your formal system encodes the semantic property of "pathological" self-reference, and this semantic property is distinct from NON-pathological self-reference then it's on you to present the decision procedure which sorts the pathological from the non-pathological self-references. It's also on you to show that this property is preserved under all transformations! e.g a non-pathological self-rerefence isn't turned into a pathological one; and that a pathological self-reference isn't turned into a non-pathological one. This would violate the validity of your system.
So where is the source code for the decider which, when given ANY self-referential expression returns a Boolean such that Boolean:True represents the fact that the expression is pathological; and Boolean:False representing the fact that the expression is NOT pathological?
Will you ever internalise the implication of Rice's theorem? All non-trivial semantic properties of formal systems are undecidable!!!
https://en.wikipedia.org/wiki/Rice's_theorem
Why is The Gettier problem still considered an open issue?
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Re: Why is The Gettier problem still considered an open issue?
Re: Why is The Gettier problem still considered an open issue?
And who does the stipulation?PeteOlcott wrote: ↑Mon May 29, 2023 1:18 pmThe computer does it itself.Age wrote: ↑Mon May 29, 2023 8:16 amBut WHO IS the ONE who gets to STIPULATE what IS TRUE FROM what IS NOT TRUE?PeteOlcott wrote: ↑Sun May 28, 2023 4:45 pm In Prolog and the architecture of the formal system that I am proposing expressions are only true if they can be deduced from expressions of language that have been stipulated to be true.
For example, can ANY one 'put their hand up' for that job?
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Re: Why is The Gettier problem still considered an open issue?
ChatGPT was able to figure out that {baby kittens} are not any type of {ten story office building}Skepdick wrote: ↑Mon May 29, 2023 1:22 pmAnd who does the stipulation?
Re: Why is The Gettier problem still considered an open issue?
All self-references are syntactic - that goes without saying.
But if you are going to sort the pathological from the non-pathological self-references you need a decider.
Show me the source code.
Last edited by Skepdick on Mon May 29, 2023 2:11 pm, edited 3 times in total.
Re: Why is The Gettier problem still considered an open issue?
Sure.PeteOlcott wrote: ↑Mon May 29, 2023 1:26 pmChatGPT was able to figure out that {baby kittens} are not any type of {ten story office building}
Based on the stipulations done by whom?
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Re: Why is The Gettier problem still considered an open issue?
https://github.com/SWI-Prolog/swipl
Re: Why is The Gettier problem still considered an open issue?
That's not a decider. That's a Prolog interpreter.PeteOlcott wrote: ↑Mon May 29, 2023 5:08 pmhttps://github.com/SWI-Prolog/swipl
Do you actually understand the difference?
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Re: Why is The Gettier problem still considered an open issue?
?- LP = not(true(LP)).Skepdick wrote: ↑Mon May 29, 2023 5:22 pmThat's not a decider. That's a Prolog interpreter.
Do you actually understand the difference?
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Any expression with pathological self-reference is rejected, thus it is a decider in this case.
Re: Why is The Gettier problem still considered an open issue?
No idea what those functions are but that's not a decider.PeteOlcott wrote: ↑Mon May 29, 2023 5:41 pm?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Any expression with pathological self-reference is rejected, thus it is a decider in this case.
A decider takes a single string as an input and returns a boolean.
This doesn't.
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Re: Why is The Gettier problem still considered an open issue?
I just found out that the other lines are not needed.Skepdick wrote: ↑Mon May 29, 2023 5:44 pmNo idea what those functions are but that's not a decider.PeteOlcott wrote: ↑Mon May 29, 2023 5:41 pm?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Any expression with pathological self-reference is rejected, thus it is a decider in this case.
A decider takes a single string as an input and returns a boolean.
This doesn't.
This line invokes the decider:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Re: Why is The Gettier problem still considered an open issue?
Can you even read the bloody documentation?PeteOlcott wrote: ↑Mon May 29, 2023 6:05 pmI just found out that the other lines are not needed.Skepdick wrote: ↑Mon May 29, 2023 5:44 pmNo idea what those functions are but that's not a decider.PeteOlcott wrote: ↑Mon May 29, 2023 5:41 pm
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Any expression with pathological self-reference is rejected, thus it is a decider in this case.
A decider takes a single string as an input and returns a boolean.
This doesn't.
This line invokes the decider:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This returns "false" even for non-pathological self-references.
https://www.swi-prolog.org/pldoc/man?pr ... rs_check/2
Surely this is supposed to return "true" ?!?That is, a variable only unifies to a term if this term does not contain the variable itself. To illustrate this, consider the two queries below.Code: Select all
1 ?- A = f(A). A = f(A). 2 ?- unify_with_occurs_check(A, f(A)). false.
Code: Select all
?- unify_with_occurs_check(A, A+1).
false.
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Re: Why is The Gettier problem still considered an open issue?
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated subterm of itself. In this example, foo(Y) is matched against Y, which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated subterm of itself. In this example, foo(Y) is matched against Y, which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of infinite structure.
END:(Clocksin & Mellish 2003:254)
Last edited by PeteOlcott on Tue May 30, 2023 4:06 am, edited 1 time in total.
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Re: Why is The Gettier problem still considered an open issue?
It is not impossible for a Chatbot to have sufficiently complete and correct model of the world to very effectively argue against claims of election fraud in the 2020 presidential election.Age wrote: ↑Mon May 29, 2023 8:11 amBut Who is going to program WHICH WAY the chat it is going to LOOK AT and VIEW 'things'?PeteOlcott wrote: ↑Sun May 28, 2023 2:14 pmSo we can make a Chatbot that unceasingly argues against each and everyone of these people on social media every which way thus quelling counter-factual disinformation before it ever gets started.
you keep appearing to completely MISS or MISUNDERSTAND the ACTUAL ISSUE hereFalse.PeteOlcott wrote: ↑Sun May 28, 2023 2:14 pm No one will ever make any attempt to do this while they believe that the Tarski undefinability theorem is true.WHEN, and IF, you EVER PROVIDE ANY so-called 'real life' examples here, then I WILL SHOW and PROVE HOW and WHY what you want to design and achieve here will NEVER WORK.PeteOlcott wrote: ↑Sun May 28, 2023 2:14 pm I have already shown how prolog screens out the Liar Paradox, and since the Tarski undefinability theorem has only the Liar Paradox as its basis his whole theorem utterly ceases to prove its point.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.Although 'godel's theorem', the 'liars paradox', and 'tarski's undefinability' are all False, Wrong, Inaccurate, Incorrect, and/or incomplete in and of themselves, it is NOT 'these things' that is STOPPING you from achieving what you want here.PeteOlcott wrote: ↑Sun May 28, 2023 2:14 pm https://en.wikipedia.org/wiki/Tarski%27 ... neral_form
In my system (having the same architecture as the Prolog inference model) the truth of expressions of language is derived from Facts and/or deduced from Facts based on Rules. The Liar Paradox (in this system) is simply untrue. Such a system cannot be incomplete in the Gödel sense because Unprovable(L,x) simply means Untrue(L,x).
What IS ACTUALLY STOPPING you is the Fact that 'it' IS an IMPOSSIBLE goal.
you are just SAYING and USING 'these things' to 'TRY TO' BLAME for NIT YET achieving what you want here.
The simple fact that there is no evidence of election fraud sufficient to change the results of the 2020 election is an excellent basis to begin with.
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Re: Why is The Gettier problem still considered an open issue?
A cycle is another word for pathological self-reference.Skepdick wrote: ↑Mon May 29, 2023 7:00 pmCan you even read the bloody documentation?PeteOlcott wrote: ↑Mon May 29, 2023 6:05 pmI just found out that the other lines are not needed.
This line invokes the decider:
?- unify_with_occurs_check(LP, not(true(LP))).
false.
This returns "false" even for non-pathological self-references.
https://www.swi-prolog.org/pldoc/man?pr ... rs_check/2
Surely this is supposed to return "true" ?!?That is, a variable only unifies to a term if this term does not contain the variable itself. To illustrate this, consider the two queries below.Code: Select all
1 ?- A = f(A). A = f(A). 2 ?- unify_with_occurs_check(A, f(A)). false.
Code: Select all
?- unify_with_occurs_check(A, A+1). false.
See my Clocksin & Mellish quote.
Re: Why is The Gettier problem still considered an open issue?
A cycle is another word for self-reference. Recursion (a.k.a induction) is built upon it.PeteOlcott wrote: ↑Thu Jun 01, 2023 9:03 pm A cycle is another word for pathological self-reference.
See my Clocksin & Mellish quote.
It's on you to explain which self-references are "pathological" and which aren't.
There's no problem with infinite structures either. Programming languages with lazy evaluation (e.g Haskell) handle infinite data structures all the time.
https://en.wikipedia.org/wiki/Evaluatio ... ll_by_need
Here's the (infinite) set of natural numbers being assigned to a variable in Haskell.
Code: Select all
λ> let n = [0..]
n :: (Num a, Enum a) => [a]