Another rebuttal of Halting Problem?

[wij]

I just found an article about the Halting Problem.
https://arxiv.org/pdf/1906.05340.pdf

In the conclusion section:
The idea of a universal halting test seems reasonable, but cannot be
for-
malised as a consistent specification. It has no model and does not
exist as
a conceptual object. Assuming its conceptual existence leads to a
paradox.
The halting problem is universally used in university courses on
Computer
Science to illustrate the limits of computation. Hehner claims the
halting
problem is misconceived......

It looks like what olcott now is claiming. Am I missing something?

[olcott]

He is one of three authors that agree on this.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[immibis]

On 1/21/24 20:24, olcott wrote:
> On 1/21/2024 1:22 PM, wij wrote:
>> I just found an article about the Halting Problem.
>> https://arxiv.org/pdf/1906.05340.pdf
>>
>> In the conclusion section:
>> The idea of a universal halting test seems reasonable, but cannot be
>> for-
>> malised as a consistent specification. It has no model and does not
>> exist as
>> a conceptual object. Assuming its conceptual existence leads to a
>> paradox.
>> The halting problem is universally used in university courses on
>> Computer
>> Science to illustrate the limits of computation. Hehner claims the
>> halting
>> problem is misconceived......
>>
>> It looks like what olcott now is claiming. Am I missing something?
>>
>>
>
> He is one of three authors that agree on this.
>

It is known that if you restrict the halting problem to programs with a
certain memory limit, it can be solved by a halting decider which uses
more memory than the limit. When a program has limited memory, it has to
halt or loop within a certain number of steps (2 to the power of the
number of bits of memory available, including the program counter/state
number). The Linz counterexample program doesn't lead to a
contradiction, because it uses more memory than the limit, so the
halting decider is unable to analyze it.

Stoddart has the same idea as Olcott: there's a hidden variable which
tells the program whether it's already in a simulation, and the program
does something different if it's in a simulation than if it isn't.
However, this is just dishonesty and lies, because we have not written
all of the input as the input. If we honestly write all of the input to
a function as the input to the function, instead of dishonestly hiding
it, then the mistake is obvious:

H(p, InS1) = ....
S = if H(S, true) then Loop end.
Question: what is H(S, false)?

the above is not Linz's counterexample.

[olcott]

*Professor Stoddart doesn't say anything like this*
You didn't read what he said you only guessed what he said.

[Richard Damon]

I think the problem he is seeing is that the property of "Halting" can
not be uniformly determined in Finite Time.

That is all that I can get from his statement of:

The idea of a universal halting test seems reasonable, but cannot be

formalised as a consistent specification.

There certainly CAN be defined formal test that define Halting, the
issue is that non-halting is defined by the non-existence of a number N
for the number of steps needed to reach a final state.

Some people just don't like the fact that it can be absolutely provable
what the answer is (and thus unknowable), even if we know from the
definition, that it must be one or the other.

This leads us to a great divide in logics. The classical branch accepts
that some truth is only established by infinite chains of connections,
and thus can not be proven with a finite proof, and thus is unknowable.

Others don't accept that, and require Truth to be only established by
Finite chains. The problem then is, such logic system need to greatly
limit the domain they attempt to cover, as otherwise you get into
endless chains of asking if a question can be asked, at which point you
need to ask if you can even ask about asking the questions. Only when
the domain is restricted in a way that the answer MUST be determinable
with finite work, can we break the cycle.

For instance, if we limit ourselves to Finite State Machines (which
could be Turing Machines with a fixed finite tape, or a classical
program in a computer with limited memory) then we can be sure that the
answer is determinable with a finite amount of work.

[olcott]

Tarski did not understand that the Liar Paradox is not a truth bearer
thus cannot possibly be true or false. His ignorance got him so confused
that he thought that he proved that True(L,x) cannot be defined because
True(Tarski_theory, LP) does not work.

Three computer science professors agree with this same reasoning when
it is applied to the halting problem computer-example input. I wrote
a paper unifying their views on this. I can't publish it on most
pre-print servers because academic journal will not accept any paper
that is published on the pre-print servers that I have access to.

[Richard Damon]

I'll ask one more time, exactly WHERE in the proof did he do this? He
shows that if True(L, x) exists that the Liar Paradox is a true
statement, but not what you say.

>
> Three computer science professors agree with this same reasoning when
> it is applied to the halting problem computer-example input. I wrote
> a paper unifying their views on this. I can't publish it on most
> pre-print servers because academic journal will not accept any paper
> that is published on the pre-print servers that I have access to.
>

So, why haven't you put it out to an actual peer-reviewed paper?

Is it that you know they will reject it?

Of course, since you already have a web site, you can publish anything
you want on it, but that might still run afoul of not previouslu
published requirements.

Of course, considering the level of writing you have shown so far, the
idea of rejection is probably the BETTER result, as if they did publish
it you would just be put on record as the fraud you are in the comments
section of the next issue of the journal.

[immibis]

Professor Stoddart quite literally says it. His hidden variable is
called InS1. Did you read what he wrote? I think you are lying.

[olcott]

"He shows that if True(L, x) exists that the Liar Paradox is a true."

That is a perfect paraphrase of my position of what he said.

Why this is nutty on his part requires you to understand a term
that is not in logic or math, it is only in philosophy of logic:
{truth bearer}.

When Tarski tried to show that the Liar Paradox is true or
false we have the exact same situation as this question:
What time is it (yes or no)?

Self-contradictory statements like the like the Liar Paradox
and questions do not have a truth value because they are
not {truth bearers}.

[olcott]

It was rejected on the basis that the summary and unification
of the views of three computer science professors does not
include anything new.

[immibis]

You agree it's not in logic or math. Well he talked about logic and
math, not philosophy. So you agree that in logic and math, the liar
paradox is true?

[immibis]

Isn't solving the halting problem (by saying that a halting program
doesn't halt) something new?

[wij]

Sorry, I can only respond with what I perceived. I cannot grasp all the
idea
you tried to say.
Q: Why can something involving infinity be reasoned and provide valid
result?
My answer is: A proposition containing something involving infinity
that cannot
be evaluated still may yield valid result. Because there are Tautology/
Contradiction in logic expression.
E.g. Some sub-propositions like (A OR ~A), (A AND A~) can be evaluated,
if we
are lucky, those A's involving infinity can be evaluated. Of course,
there still lots inconsistency in the understanding of 'infinity'.

> This leads us to a great divide in logics. The classical branch
> accepts
> that some truth is only established by infinite chains of
> connections,
> and thus can not be proven with a finite proof, and thus is
> unknowable.
>
> Others don't accept that, and require Truth to be only established by
> Finite chains. The problem then is, such logic system need to greatly
> limit the domain they attempt to cover, as otherwise you get into
> endless chains of asking if a question can be asked, at which point
> you
> need to ask if you can even ask about asking the questions. Only when
> the domain is restricted in a way that the answer MUST be
> determinable
> with finite work, can we break the cycle.

IMO, a valid proof (also a 'procedure') must terminate. But from what
all those papers infinity I saw, all are messy.

> For instance, if we limit ourselves to Finite State Machines (which
> could be Turing Machines with a fixed finite tape, or a classical
> program in a computer with limited memory) then we can be sure that
> the
> answer is determinable with a finite amount of work.

Thanks for your explanation in plain English.
As said, propositions involving infinity can conditionally be solved.

[olcott]

Good catch. That was part of his intermediate analysis
and his conclusion does not reference anything like that.

[olcott]

I agree that it a ridiculously foolish thing to say.

The ignorance of logic and math does not derive any
sort of truth. It seems that most of your own whole
basis is that your ignorance some how derives truth.

[immibis]

So math does not prove that 1+1=2?

[olcott]

I was very careful to not add any new material to what these
three professors said, thus preventing a crank rejection.

They seemed to agree that the halting problem itself is incorrect.
That is certainly the case when one expects H to report on the
direct execution of D(D) and thus ignore the actual behavior
that it actually sees.

[immibis]

If you are talking about section 5, he says that S (which is what he
calls D) does not exist.

Do you think that D does not exist?

There is a well-defined procedure to construct Turing machine D (or S).
What happens if we follow the procedure? Does our hand always get a
cramp, so that we can't write down D because it doesn't exist?

It is like saying that a blahrg is 4 squares next to each other, and a
blahrg does not exist. So what happens if I draw 4 squares next to each
other? Isn't that a blahrg?

[olcott]

Always with the strawman deception.
Do you want me to start calling you a liar?

If you don't want me to start calling you a liar
then quit using the strawman deception.

It was pointed out that logic and math are clueless
about the Liar Paradox.

By providing an example of what logic and math are
not clueless about as your rebuttal you switched to
the strawman deception. Please quit that !!!

[immibis]

On 1/21/24 22:11, olcott wrote:
>
> I was very careful to not add any new material to what these
> three professors said, thus preventing a crank rejection.

I see. You are right, that would not be material for a peer-reviewed
paper. They are expected to contain new knowledge that is not already
obvious to everyone in the field.

>
> They seemed to agree that the halting problem itself is incorrect.
> That is certainly the case when one expects H to report on the
> direct execution of D(D) and thus ignore the actual behavior
> that it actually sees.
>

If H used an ARM simulator instead of an x86 one, but the program was
still written for x86, and the first x86 instruction of D was (by
coincidence) the same as a return instruction in ARM, would the correct
return value be 1?

[olcott]

On 1/21/2024 3:13 PM, immibis wrote:
> On 1/21/24 22:04, olcott wrote:
>> On 1/21/2024 2:48 PM, immibis wrote:
>>> On 1/21/24 20:54, olcott wrote:
>>>> *Professor Stoddart doesn't say anything like this*
>>>> You didn't read what he said you only guessed what he said.
>>>>
>>>
>>> Professor Stoddart quite literally says it. His hidden variable is
>>> called InS1. Did you read what he wrote? I think you are lying.
>>>
>>
>> Good catch. That was part of his intermediate analysis
>> and his conclusion does not reference anything like that.
>>
>
> If you are talking about section 5, he says that S (which is what he
> calls D) does not exist.

*Read Stoddart's conclusion*
*Read Stoddart's conclusion*
*Read Stoddart's conclusion*
*Read Stoddart's conclusion*

I and wij are talking about the fact that three computer science
professors agree that the halting problem itself is wrong.

wij only referred to Stoddart's view, yet also quoted Professor
Hehner's agreement. This is two of the three.

[olcott]

On 1/21/2024 3:18 PM, immibis wrote:
> On 1/21/24 22:11, olcott wrote:
>>
>> I was very careful to not add any new material to what these
>> three professors said, thus preventing a crank rejection.
>
> I see. You are right, that would not be material for a peer-reviewed
> paper. They are expected to contain new knowledge that is not already
> obvious to everyone in the field.

The fact that three computer science professor's

agree that the halting problem itself is incorrect

was new to these same computer science professors.

It is certainly not obvious to everyone in the field

that the halting problem itself is incorrect.

[immibis]

Didn't Tarski translate the Liar Paradox into logic and mathematics?

[immibis]

On 1/21/24 22:20, olcott wrote:
> On 1/21/2024 3:13 PM, immibis wrote:
>> On 1/21/24 22:04, olcott wrote:
>>> On 1/21/2024 2:48 PM, immibis wrote:
>>>> On 1/21/24 20:54, olcott wrote:
>>>>> *Professor Stoddart doesn't say anything like this*
>>>>> You didn't read what he said you only guessed what he said.
>>>>>
>>>>
>>>> Professor Stoddart quite literally says it. His hidden variable is
>>>> called InS1. Did you read what he wrote? I think you are lying.
>>>>
>>>
>>> Good catch. That was part of his intermediate analysis
>>> and his conclusion does not reference anything like that.
>>>
>>
>> If you are talking about section 5, he says that S (which is what he
>> calls D) does not exist.
>
> *Read Stoddart's conclusion*
> *Read Stoddart's conclusion*
> *Read Stoddart's conclusion*
> *Read Stoddart's conclusion*
>
> I and wij are talking about the fact that three computer science
> professors agree that the halting problem itself is wrong.
>
> wij only referred to Stoddart's view, yet also quoted Professor
> Hehner's agreement. This is two of the three.
>

You dishonestly ignored the question part of the post you replied to.

[olcott]

The key thing that Tarski missed is that expressions of language
that are not truth bearers cannot possibly have any truth value.
*This was his fatal mistake*

[Richard Damon]

Nope, you said that he assumed the Liars Paradox has a logic value.

The assumption was just that True(L,x) existed.

From that assumption, through valid and sound logic, comes out the
statement the the Liar's Paradox is True.

Since this is a false statement, the initial assumption must be false.

You don't seem to understand any of the basic terms of logic.

It is a simple application of the valid logical inference:

If x -> y, and NOT y, then NOT x.

Commonly called "Proof by Contradiction" (but maybe more accurate would
be refutation by Contradiction.

> Why this is nutty on his part requires you to understand a term
> that is not in logic or math, it is only in philosophy of logic:
> {truth bearer}.

And where did he assume a value for a non-truth bearer.

HE PROVED a value for a non-truthbear from an assumption.

This proves the assumption can not be true.

>
> When Tarski tried to show that the Liar Paradox is true or
> false we have the exact same situation as this question:
> What time is it (yes or no)?

But he didn't ASK the question, he showed that an assumption PROVES a
falsehood.

>
> Self-contradictory statements like the like the Liar Paradox
> and questions do not have a truth value because they are
> not {truth bearers}.
>
>

Right, so anything that proves that they do must not be true, like the
existance of True(L,x)

[olcott]

I soon as I hit the first fatal flaw quit reading.

*Read Stoddart's conclusion*
*Read Stoddart's conclusion*
*Read Stoddart's conclusion*

Don't freaking attempt to change the subject away from this.

[Richard Damon]

So, then why are you afraid to do something to keep you from being able
to publish it, if you know it can't get a Journal Publishing already?

[olcott]

No that it only half of the assumption.
The other half is that True(tarski_theory, "this sentence is not true")
must be true or false. That half was Tarksi's fatal flaw.

[Richard Damon]

I think your problem is you don't understand what they are saying.

it seems their view is that a property that can only be determined with
infinite work should not be allowed to be defined as a property.

THe problem with that in Computability Theory is that the one of the
major points is to determine WHAT properties meet that criteria. i.e.
the question of what properties are "Computable" aka "Decidable" (of
decision compuations).

Remove that from the basis of the Theory, and it becomes a somewhat
minor piece of theory.

[immibis]

True(tarski_theory, "this sentence is not true") is actually a
mathematical statement consisting of elementary operations such as
addition, multiplication, and quantifiers. Can you show how to use these
basic parts to build a statement that is not true or false?

[Richard Damon]

There is actually a lot of logic that can be done on "Infinity", and
often a meta-system might be able to reduce the infinity to something
finite.

One key can be the discovering of something that induction can be
applied to, this will reduce a countable infinity to a finite operation.

[immibis]

So you admit to dishonesty. Nice. I don't think you've read any part of
Stoddart's writing except for the conclusion.

I think you'll also find that Stoddart failed to formalize anything.

[immibis]

So a statement such as "∀x (x = 5)" can be neither true nor false?

[olcott]

When I put the same thing into Prolog
it is rejected as semantically unsound.

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

[Richard Damon]

But you don't understand what he is actually saying, likely because YOU
didn't read the whole thing, but jumped to the end to read the
conclusion without understanding the context. This seems to be your
standard operating procedure.

[Richard Damon]

No, he FULLY understood that, so any assumption that proves that it has
one, must be false.

You just don't understand how logic works.

But, of coure, you have admittd you do your logic backwards, so that
seems normal.

[Richard Damon]

Where do you see that as an INPUT assumption, and not a result of a proof?

LINE please.

[olcott]

It is Stoddart's conclusion thus agreeing with Hehner's
conclusion that the halting problem itself is incorrect.

[olcott]

Yet another strawman deception

[olcott]

line (3)

[olcott]

"Tarski’s undefinability theorem is really just the
ancient paradox of the liar, dressed up in formal wear."

https://web.mit.edu/24.242/www/Tarskitruth.pdf

[olcott]

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

[Richard Damon]

So, you don't, since you didn't actually answer the comment.

I guess you are just admitting that you don't know what you are talking
about and agree that your statement was just a lie.

Where did he take as a ASSUMPTION that the liar's paradox had a truth value.

[olcott]

∀x ∈ ℕ (x = 5) is false

[immibis]

That isn't how Tarski works. No wonder you don't understand the halting
problem either.

[olcott]

That you can't comprehend Prolog does not mean that I am wrong.

[immibis]

And what can we learn from this?

Tarski says that if True(L,p) exists then the liar paradox has a truth
value.

The liar paradox doesn't have a truth value, therefore True(L,p) doesn't
exist.

[immibis]

On 1/21/24 23:36, olcott wrote:

Thanks for admitting you understand neither.

[immibis]

Every time you say "strawman deception" it will be read as "I, Olcott,
admit to being wrong"

[olcott]

THAT IS HOW THE LIAR PARADOX WORKS

Tarski didn't understand that the correct
evaluation of the Liar Paradox requires
an infinite cycle in the directed graph
of its evaluation sequence.

Do you know these terms:
cycle
directed graph
evaluation sequence

[olcott]

That you can't see how that reasoning is unsound proves
that you don't understand these things.

That True(L, x) cannot prove that x is true or false
when x cannot possibly be true or false proves nothing
about True(L, x).

[Richard Damon]

You mean the (3) on page 275?

The one preeeded by: "from (1) and (2) we obtain immediately"

Thus (3) isn't an assumption but a proven statement.

Also (3) says x is not Provable if and only if x is not True

(Which applies only for a particuar x that was derived in (1).


Of course, you don't accept that statement, but you need to try to find
the error in that logic (which I doubt exists)

YOu are just showing how little you understand about how logic works.
You can't seem to read these papers and understand them.

[olcott]

*I simplified the language here are his exact words*

The proof of the halting problem assumes a universal halt
test exists and then provides S as an example of a program
that the test cannot handle. But S is not a program at all.
It is not even a conceptual object, and this is due to
inconsistencies in the specification of the halting function.
(Stoddart: 2017)

[Richard Damon]

So, are you relying on some paper without attribution?

That sounds like appeal to Authority when you can't name the Authority.

Sounds like the opinion of some unnamed person.

[Richard Damon]

On 1/21/24 6:00 PM, olcott wrote:
> On 1/21/2024 4:53 PM, immibis wrote:
>> On 1/21/24 23:41, olcott wrote:
>>> On 1/21/2024 4:32 PM, Richard Damon wrote:
>>>>
>>>> Where do you see that as an INPUT assumption, and not a result of a
>>>> proof?
>>>>
>>>> LINE please.
>>>
>>> "Tarski’s undefinability theorem is really just the
>>> ancient paradox of the liar, dressed up in formal wear."
>>>
>>> https://web.mit.edu/24.242/www/Tarskitruth.pdf
>>>
>>
>> And what can we learn from this?
>>
>> Tarski says that if True(L,p) exists then the liar paradox has a truth
>> value.
>>
>> The liar paradox doesn't have a truth value, therefore True(L,p)
>> doesn't exist.
>
> That you can't see how that reasoning is unsound proves
> that you don't understand these things.
>
> That True(L, x) cannot prove that x is true or false
> when x cannot possibly be true or false proves nothing
> about True(L, x).
>

But where did he ASK True(L, x) to resolve a statement that didn't have
a truth value?

He shows from the unprobability property that Truth can not be computed.

Asking True(L, x) on a statement x that is TRUE but not provable shows
the error.

[olcott]

I provide an example that cannot possibly be true or false
and you provide a counter-example as a rebuttal that is
definitely false: ∀x ∈ ℕ (x = 5) is false

THAT IS THE STRAWMAN DECEPTION

[Richard Damon]

That you answer a question with Prolog that didn't apply to Prolog shows
you don;t know what you are doing.

In fact, it shows that you don't understand how logic works, as much
logic is beyond what Prolog can handle, so if you only understand what
Prolog does, and alwasy go to it, you don't understand how logic works.

[Richard Damon]

And where did he do that?

Not line (3)

[olcott]

(3) x ∉ Provable if and only if x ∈ True.

Is like assuming that cows are dogs because it rejects
the way that an actual True(L, x) predicate works:
∀x ∈ L (True(L,x) ≡ (L ⊢ x))

[olcott]

Where did Tarski say that i=he didn't understand things?

He never understood that his understanding was incorrect
so there is no place where he says that.

My Prolog proves that the Liar Paradox is neither
true nor false. Tarski never understood that.

[immibis]

Is there a way to make it neither true nor false?

[immibis]

So when we get a pencil and a sheet of paper and follow the procedure to
construct S, what did we construct?

[immibis]

It isn't how Tarski works.

>
> Tarski didn't understand that the correct
> evaluation of the Liar Paradox requires
> an infinite cycle in the directed graph
> of its evaluation sequence.

You don't understand the difference between diagonalization and infinite
recursion.

Do you think the real numbers are countable?

[immibis]

So you don't understand the proof and you just argue because you don't
like the conclusion.

Which is ironic, because you also make conclusions that nobody else
likes. You think that a halting program is non-halting.

[olcott]

No that is why it is the strawman deception

[olcott]

Something like the square root of a dead rabbit,
an incoherent concept.

[Richard Damon]

I can't see how he can claim that S isn't a program, except that he
doesn't understand that H, to be a decider, MUST return its answer to
its caller (and not printing an error message and aborting if it can't
get an answer).

In other words, he seem to have fundamental issues with the basic
definitions of Computation Theory.

I also find little background for him giving any evidence that he is
considered an expert in the field, verses just an ordinary Hack
publishing to lesser tiered Journels. (Was this even peer reviewed, or
is this site just like your pre-pub site?

Appeal to Authority is a fallacy, and a weak argument, appeal to a
random-joe isn't even a weak argument.

[olcott]

Diagonalization is a process by which we know that
x is unprovable in L that makes sure to ignore the
reason why x is unprovable in L.

unify_with_occurs_check(LP, not(true(LP))).
correctly determines that LP is unprovable
BECAUSE the directed graph of its evaluation
sequence contains an infinite cycle.

[Richard Damon]

Your whole arguement is a Strawman Deception, as you change the question
that the Halting decider needs to answer.

IF it isn't about the behavior of the actual program described by the
input, it is just a strawman.

Of course, since you modified D so it is no longer a program, you
painted yourself into a corner. You CAN'T look at the behavior of the
program D, as D doesn't define its behavior anymore, but needs an
unspecified H.

[olcott]

Not at all. After 10,000 hours of careful thought over many years
I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x))
is the correct way to encode a consistent and correct Truth(L,x)
predicate. It even works correctly with natural language
that has been formalized with something like Montague Grammar.

What Tarski does is like refuting that 2 + 3 = 5
by starting with the assumption that numbers do not exist.

When we replace this

(3) x ∉ Provable if and only if x ∈ True.

with this

(3) x ∈ Provable if and only if x ∈ True.

Then Tarski gets the True(L, x) predicate
that he falsely assumed was impossible.

[Richard Damon]

So, you can't poimt to any error in what he wrote, because you just
don't understand him. In fact, from what I remember, when he shows that
the existance of a definiton of True(L, x) we prove the liar is true, he
points out that this is impossible, and thus the definition of truth can
not exist.

If it didn't say it, then he wasn't wrong to say it.

Thus, your whole argument is just a LIE and a Strawman.

Since you LIE about everything, nothing you say matters.

[immibis]

Then why can I calculate the square root of living rabbits and dead
hamsters using the same algorithm?

[immibis]

So there's no way to make a formula that's neither true nor false, but
somehow this formula Tarski made is neither true nor false, according to
you?

[immibis]

On 1/22/24 01:21, olcott wrote:
> Not at all. After 10,000 hours of careful thought over many years

> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the correct way to encode a consistent and correct Truth(L,x)

> predicate. It even works correctly with natural language
> that has been formalized with something like Montague Grammar.

Tarski proved that if you put ⊢ in your logic system, then your logic
system is inconsistent and wrong.

[olcott]

He is a computer science professor with a PhD and you are not.
He is simply saying the same thing that I have been saying since 2004.

Alan Turing's Halting Problem is incorrectly formed (PART-TWO) sci.logic
On 6/20/2004 11:31 AM, Peter Olcott wrote:
> PREMISES:
> (1) The Halting Problem was specified in such a way that a solution
> was defined to be impossible.
>
> (2) The set of questions that are defined to not have any possible
> correct answer(s) forms a proper subset of all possible questions.
> …
> CONCLUSION:
> Therefore the Halting Problem is an ill-formed question.

[immibis]

So are the real numbers countable? Isn't Cantor's number pathologically
self-referential, making his argument invalid?

> unify_with_occurs_check(LP, not(true(LP))).
> correctly determines that LP is unprovable
> BECAUSE the directed graph of its evaluation
> sequence contains an infinite cycle.
>

Provability doesn't give a flying fuck about evaluation cycles, whatever
those are.

x = x + 1 - 1

is provable, true, and contains an infinite evaluation cycle.

[Richard Damon]

But that is a statement PROVEN from the previous, so you can't argue
with it without showing which premise or logical step was invalid.

That you can't make sense of the statement doesn't make it wrong, and
your analogy just fails.

Note True(L, x) is NOT saying x is PROVABLE in L, it is saying that X is
TRUE in L, there is a difference, as he has shown that the system has
unprovable statements, in fact, that is part of the meaning of (3).

That you refuse to accept that fact, just shows that you are WRONG, and
STUPID.

You are just showing that you FAIL at understanding logic,

[olcott]

There is no way to make a formula that is definitely false
into a formula that is neither true nor false.

This merely changes the subject away from the subject
of formulas that are neither true nor false.

Every correct formulation of "This sentence is not true"

is neither true nor false.

[immibis]

On 1/22/24 01:27, olcott wrote:
>
> He is a computer science professor with a PhD and you are not.
> He is simply saying the same thing that I have been saying since 2004.
>
> Alan Turing's Halting Problem is incorrectly formed (PART-TWO)  sci.logic
> On 6/20/2004 11:31 AM, Peter Olcott wrote:
> > PREMISES:
> > (1) The Halting Problem was specified in such a way that a solution
> > was defined to be impossible.
> >
> > (2) The set of questions that are defined to not have any possible
> > correct answer(s) forms a proper subset of all possible questions.
> > …
> > CONCLUSION:
> > Therefore the Halting Problem is an ill-formed question.
> >
>

So if I ask you how to fly to the sun, it's an ill-formed question
because you can't do it?

[olcott]

When we replace his line

[Richard Damon]

Nope. First, you don't understand what Traski meant by a "Definition" of
a predicate. He meant, effectively, able to write a program that always
gives the answer in finite time. It is a computability definition. So,
until you can come up with an algorithm to determine if a statement is
provable in finite time, you don't have a "definition"

Second, True is not the same thing as provable. He has established that
systems can have (and in fact, some system MUST have) unprovable
statements that ARE true. That is what (3) implies.

>
> What Tarski does is like refuting that 2 + 3 = 5
> by starting with the assumption that numbers do not exist.

More of your LIES.

Where did he say ANYTHING like that.

Show where he said something like that or prove yourself a LAIR, AGAIN.

>
> When we replace this
> (3) x ∉ Provable if and only if x ∈ True.
> with this
> (3) x ∈ Provable if and only if x ∈ True.
> Then Tarski gets the True(L, x) predicate
> that he falsely assumed was impossible.
>

But he proves that your (3) is not true, and in fact, for the x he
derived this form that is distinctly false.

Remember (3) isn't an assumption or a premise to evaluate, it is a
statement proven from previous statements.

Your argument is just proving that you don't know what you are doing.

[olcott]

It sure does in Prolog.
If every other system is too stupid to pay attention to this
then that is the fault of these stupid systems.

I created my own branch of logic called Minimal Type Theory
to prove these things before I discovered that Prolog already
did this.

[immibis]

Can you make a formula that is definitely true into one that is neither
true nor false?

>
> This merely changes the subject away from the subject
> of formulas that are neither true nor false.
>
> Every correct formulation of "This sentence is not true"
> is neither true nor false.
>

What if I said, x∈ℕ, x=1-x
This is the liar paradox expressed in natural numbers.
Is it neither true nor false?

[Richard Damon]

So, you don't know how to writte a program. Not even one you have
written before.

[immibis]

On 1/22/24 01:34, olcott wrote:
> On 1/21/2024 6:26 PM, immibis wrote:
>> On 1/22/24 01:21, olcott wrote:
>>> Not at all. After 10,000 hours of careful thought over many years
>>> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the correct
>>> way to encode a consistent and correct Truth(L,x)
>>> predicate. It even works correctly with natural language
>>> that has been formalized with something like Montague Grammar.
>>
>> Tarski proved that if you put ⊢ in your logic system, then your logic
>> system is inconsistent and wrong.
>>
>
> When we replace his line
> (3) x ∉ Provable if and only if x ∈ True.
> with this
> (3) x ∈ Provable if and only if x ∈ True.
>
> Then Tarski gets the True(L, x) predicate that he falsely
> assumed was impossible.
>

But then line (3) is a lie.

[olcott]

Get in a space shuttle and fly to the Sun.

An ill-formed question is any question that was defined
such that it cannot possibly have a correct answer.

What time is it (yes or no)?
is an ill-formed question.

Is this sentence: "This sentence is not true."
true or false?

Is the ill-formed question that baffled Tarski.

[olcott]

Show me all the steps of computing the square-root of a dead rabbit.

[olcott]

No line (3) has been corrected to eliminate Tarki's
mistake. Lines (1) and (2) are erased.

[olcott]

We erase lines (1) and (2) and replace line (3) with this

(3) x ∈ Provable if and only if x ∈ True.

Then Tarski gets the truth predicate that he falsely assumed was
impossible.

[olcott]

Or we replace line (1)
(1) x ∉ Provable if and only if p
with this
(1) x ∈ Provable if and only if p

[Richard Damon]

You mean he earned a Pile it Higher and Deeper? So what.

I know many PhD that are idiots, all it means is they stayed in school
long enough to earn their Univeristy enough money, and wrote a paper
that they fiured didn't embarrass them.

To be clear, many PhDs are smart and intelgent people, and it takes some
talent to get into and through such a program, but just having a PhD
doesn't mean you are great (or even good).

I was qualified and offered the opportunity to get a PhD (well, actually
an ScD, but that is basically the same thing) but turned it down as I
saw that completing the program wasn't going to actually teach me that
much more (except how to write academic papers) and I would learn more
by going into industry and actually do the work.

A degree opens doors, but you need to prove what you know with what you
do. He doesn't seem to have generated much actual recognition from
others, so I don't see any evidence that his opinion means much.

[immibis]

On 1/22/24 01:37, olcott wrote:
> On 1/21/2024 6:27 PM, immibis wrote:
>> On 1/22/24 01:13, olcott wrote:
>>> On 1/21/2024 6:04 PM, immibis wrote:
>>>> On 1/21/24 23:56, olcott wrote:
>>>>> Tarski didn't understand that the correct
>>>>> evaluation of the Liar Paradox requires
>>>>> an infinite cycle in the directed graph
>>>>> of its evaluation sequence.
>>>>
>>>> You don't understand the difference between diagonalization and
>>>> infinite recursion.
>>>>
>>>> Do you think the real numbers are countable?
>>>
>>> Diagonalization is a process by which we know that
>>> x is unprovable in L that makes sure to ignore the
>>> reason why x is unprovable in L.
>>>
>>
>> So are the real numbers countable? Isn't Cantor's number
>> pathologically self-referential, making his argument invalid?
>>
>>> unify_with_occurs_check(LP, not(true(LP))).
>>> correctly determines that LP is unprovable
>>> BECAUSE the directed graph of its evaluation
>>> sequence contains an infinite cycle.
>>>
>>
>> Provability doesn't give a flying fuck about evaluation cycles,
>> whatever those are.
>>
>
> It sure does in Prolog.

Then Prolog is wrong.

[immibis]

On 1/22/24 01:44, olcott wrote:
> On 1/21/2024 6:38 PM, immibis wrote:
>> On 1/22/24 01:34, olcott wrote:
>>> On 1/21/2024 6:26 PM, immibis wrote:
>>>> On 1/22/24 01:21, olcott wrote:
>>>>> Not at all. After 10,000 hours of careful thought over many years
>>>>> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the
>>>>> correct way to encode a consistent and correct Truth(L,x)
>>>>> predicate. It even works correctly with natural language
>>>>> that has been formalized with something like Montague Grammar.
>>>>
>>>> Tarski proved that if you put ⊢ in your logic system, then your
>>>> logic system is inconsistent and wrong.
>>>>
>>>
>>> When we replace his line
>>> (3) x ∉ Provable if and only if x ∈ True.
>>> with this
>>> (3) x ∈ Provable if and only if x ∈ True.
>>>
>>> Then Tarski gets the True(L, x) predicate that he falsely
>>> assumed was impossible.
>>>
>>
>> But then line (3) is a lie.
>
> No line (3) has been corrected to eliminate Tarki's
> mistake. Lines (1) and (2) are erased.
>

When we replace the line
(3) Humans don't have wings
with this
(3) Humans do have wings
then we learn that Olcott can fly to the sun.

[immibis]

Show me the steps of computing the square root of a living rabbit, which
you believe is possible.

[Richard Damon]

On 1/21/24 7:34 PM, olcott wrote:
> On 1/21/2024 6:26 PM, immibis wrote:
>> On 1/22/24 01:21, olcott wrote:
>>> Not at all. After 10,000 hours of careful thought over many years
>>> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the correct
>>> way to encode a consistent and correct Truth(L,x)
>>> predicate. It even works correctly with natural language
>>> that has been formalized with something like Montague Grammar.
>>
>> Tarski proved that if you put ⊢ in your logic system, then your logic
>> system is inconsistent and wrong.
>>
>
> When we replace his line
> (3) x ∉ Provable if and only if x ∈ True.
> with this
> (3) x ∈ Provable if and only if x ∈ True.
>
> Then Tarski gets the True(L, x) predicate that he falsely
> assumed was impossible.
>

No, we get a contradiction, since from (1) and (2) we get

x ∉ Provable if and only if x ∈ True.

so if we also have

x ∈ Provable if and only if x ∈ True.

Then x must be both Provable and Unprovable.


You are just proving your stupidity.

[immibis]

On 1/22/24 01:41, olcott wrote:
> On 1/21/2024 6:33 PM, immibis wrote:
>> On 1/22/24 01:27, olcott wrote:
>>>
>>> He is a computer science professor with a PhD and you are not.
>>> He is simply saying the same thing that I have been saying since 2004.
>>>
>>> Alan Turing's Halting Problem is incorrectly formed (PART-TWO)
>>> sci.logic
>>> On 6/20/2004 11:31 AM, Peter Olcott wrote:
>>>  > PREMISES:
>>>  > (1) The Halting Problem was specified in such a way that a solution
>>>  > was defined to be impossible.
>>>  >
>>>  > (2) The set of questions that are defined to not have any possible
>>>  > correct answer(s) forms a proper subset of all possible questions.
>>>  > …
>>>  > CONCLUSION:
>>>  > Therefore the Halting Problem is an ill-formed question.
>>>  >
>>>
>>
>> So if I ask you how to fly to the sun, it's an ill-formed question
>> because you can't do it?
>>
>
> Get in a space shuttle and fly to the Sun.
>
> An ill-formed question is any question that was defined
> such that it cannot possibly have a correct answer.

You don't have a space shuttle, so that was an incorrect answer. The
question was ill-formed.

[olcott]

That Prolog pays attention to details that other systems
ignore make it wrong is like saying that ignorance is
knowledge and knowledge is incorrect.

[Richard Damon]

On 1/21/24 7:44 PM, olcott wrote:
> On 1/21/2024 6:38 PM, immibis wrote:
>> On 1/22/24 01:34, olcott wrote:
>>> On 1/21/2024 6:26 PM, immibis wrote:
>>>> On 1/22/24 01:21, olcott wrote:
>>>>> Not at all. After 10,000 hours of careful thought over many years
>>>>> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the
>>>>> correct way to encode a consistent and correct Truth(L,x)
>>>>> predicate. It even works correctly with natural language
>>>>> that has been formalized with something like Montague Grammar.
>>>>
>>>> Tarski proved that if you put ⊢ in your logic system, then your
>>>> logic system is inconsistent and wrong.
>>>>
>>>
>>> When we replace his line
>>> (3) x ∉ Provable if and only if x ∈ True.
>>> with this
>>> (3) x ∈ Provable if and only if x ∈ True.
>>>
>>> Then Tarski gets the True(L, x) predicate that he falsely
>>> assumed was impossible.
>>>
>>
>> But then line (3) is a lie.
>
> No line (3) has been corrected to eliminate Tarki's
> mistake. Lines (1) and (2) are erased.
>

No, they are still there.

And you get a contradiction that now x is both Provable and unprovable

You don't get to "erase" true statements.

You are just proving you don't understand how logic works.

[olcott]

On 1/21/2024 6:52 PM, Richard Damon wrote:
> On 1/21/24 7:34 PM, olcott wrote:
>> On 1/21/2024 6:26 PM, immibis wrote:
>>> On 1/22/24 01:21, olcott wrote:
>>>> Not at all. After 10,000 hours of careful thought over many years
>>>> I have determined this: ∀x ∈ L (True(L,x) ≡ (L ⊢ x) > is the correct
>>>> way to encode a consistent and correct Truth(L,x)
>>>> predicate. It even works correctly with natural language
>>>> that has been formalized with something like Montague Grammar.
>>>
>>> Tarski proved that if you put ⊢ in your logic system, then your logic
>>> system is inconsistent and wrong.
>>>
>>
>> When we replace his line
>> (3) x ∉ Provable if and only if x ∈ True.
>> with this
>> (3) x ∈ Provable if and only if x ∈ True.
>>
>> Then Tarski gets the True(L, x) predicate that he falsely
>> assumed was impossible.
>>
>
> No, we get a contradiction, since from (1) and (2) we get

We get rid of (1) and (2) and begin with

(3) x ∈ Provable if and only if x ∈ True.