...and the trouble with that is that there doesn't seem to be any obvious problem with Z. — Banno

So you can't see that the fact that Z does the opposite of whatever
H says makes saying the correct thing a logical impossibility for H?

Well, no. The correct thing to do is conclude that H is impossible; that there are things which cannot be computed.

Well, no. The correct thing to do is conclude that H is impossible; that there are things which cannot be computed.
8 hours ago — Banno

That is all that it takes to determine that the halting problem as defined is invalid.
Another logically impossible problem is making a CAD system that can draw square
circles. In other words it must draw a thing that <is> a Circle and simultaneously
<is not> a Circle.

All undecidable decision problems are simply invalid because their problem definition
requires the logically impossible.

@sime?

Well, no. The correct thing to do is conclude that H is impossible; that there are things which cannot be computed. — Banno

When a human is asked a question that is defined to have no correct answer
such as: What time it is (yes or no)? we know to reject the question and not
blame the human.

When a computer program is presented with data that has been defined to
have no correct answer (Boolean return value) we blame the program and
not the data.

This is inconsistent. Professor Hehner and I both agree that any program
specification that lacks a correct (Boolean return value) for some inputs
proves that this specification is unsatisfiable thus incorrect.

Repetition and appeal to (supposed) authority.

↪PL Olcott Repetition and appeal to (supposed) authority. — Banno

I keep trying to make my words more clear. That a PhD computer science professor perfectly agrees with my exact words provides a subtantial weight of evidence that I am not simply a crackpot.

Most people start with the idea that I must be a crackpot thus pay no attenton to what I actually say and put ALL of their energy into pointing out mistakes that turn out to not exist.

I wouldn't be here apart from trying to help articulate the point.

That's why I've asked you to show as explicitly as you can where Carol's question occurs.

In the other thread I suggested that the analogue would be "Will Program Z loop forever if fed itself as input?" — Banno

↪PL Olcott I wouldn't be here apart from trying to help articulate the point.

That's why I've asked you to show as explicitly as you can where Carol's question occurs.

In the other thread I suggested that the analogue would be "Will Program Z loop forever if fed itself as input?"
— Banno — Banno

That depends on what your H does and you didn't say.

I have spent two full time years making the x86utm operating system so that I could make a real H and Z so I have complete proof what they do and why and how they do it. My H is called H and my current Z is called D.

Any expert C programmer can follow this proof by examining all of its source-code.
The key essence of this source-code is on page 1 of this paper.

Termination Analyzer H is Not Fooled by Pathological Input D
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D

Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem, — Prof Kirk Pruhs

:smile:

↪PL Olcott
Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem,
— Prof Kirk Pruhs — Banno

My H simulates its D until it can see that D keeps calling H in recursive
simulation. Then it aborts this simulation and returns 0 for non-halting.
Page 1 of my paper shows all of the details of this to any expert C programmer.

What you have done is to display the contradiction that we all agree on. It's what you conclude from that which is problematic.

↪PL Olcott What you have done is to display the contradiction that we all agree on. It's what you conclude from that which is problematic. — Banno

These words may be a little too technical for you.

It seems that everyone agrees with this:
(a) When the halting problem is defined with a program
specification that requires an H to report on the behavior
of the direct execution of D(D) that does the opposite of
whatever Boolean value that H returns then this is an
unsatisfiable program specification.

(b) An unsatisfiable program specification is merely
the inability to do the logically impossible thus places
no actual limit on anyone or anything.

These words may be a little too technical for you. — PL Olcott

:wink: You don't have to be here. No need to respond if my comments are not useful.

Or is it that what you have to say cannot be made sufficiently clear?

You started this with Carol's question, went on to claim that Gödel's theorem was wrong, backtracked to Turing and now obfuscate.

That it is possible to write a program which undermines H shows that H cannot be applied to all programs. Quod Erat Demonstrandum.

You started this with Carol's question, went on to claim that Gödel's theorem was wrong, backtracked to Turing and now obfuscate. — Banno

I just totally proved my whole point if and only if you fully understand all of its words.
I have to write them so that computer programmers and computer scientists can
most easily understand them.

This key point mostly uses ordinary words.
The inability to do the logically impossible places no actual limit on anyone or anything.

Anyone that agrees with the above point agrees with the complete essence of our proof.

I just totally proved my whole point if and only if you fully understand all of its words. — PL Olcott

:rofl:

If you would prove Turing wrong, you will need more than mere assertion.

If you would prove Turing wrong, you will need more than mere assertion. — Banno

You did not pay attention to the words that were targeted for you:

This key point mostly uses ordinary words.
The inability to do the logically impossible places no actual limit on anyone or anything.

Anyone that agrees with the above point agrees with the complete essence of our proof.

We've already agreed that a reductio argument uses a logical impossibility to show that an assumption is in error; and that Turing's argument is a reductio.

Hadn't we?

That is, a logical impossibility places a limit on the viability of our assumptions... to adopt your odd wording.
If one's assumptions lead to contradiction, then at least one is in error. Assuming we can produce H leads to contradiction. Hence we cannot produce H.

If one's assumptions lead to contradiction, then at least one is in error. Assuming we can produce H leads to contradiction. Hence we cannot produce H. — Banno

We also cannot correctly determine the square root of a stack of pancakes.
Logical impossibilities never create actual limits.
Logical impossibilities never create actual limits.
Logical impossibilities never create actual limits.
Logical impossibilities never create actual limits.

We also cannot correctly determine the square root of a stack of pancakes. — PL Olcott

Yep. Quite agree. If your conclusion is a logical impossibility, there is something amiss with your assumptions.

Or with your process.

Yep. Quite agree. If your conclusion is a logical impossibility, there is something amiss with your assumptions. — Banno

When the halting problem is defined such that solving it is logically impossible
then we reject this problem definition as unsound for the same reason that
we reject this question as unsound: What time is it (yes or no)?

Every question that is defined to have no correct answer is an incorrect
question.

Yeah, OK. No progress to be made here. Publish your article and then invite me to the ceremony when you win the Turing Award so you can say "I told you so".

↪PL Olcott Yeah, OK. No progress to be made here. Publish your article and then invite me to the ceremony when you win the Turing Award so you can say "I told you so". — Banno

Like always there is no sense publishing anything until some people understand
that the words are correct. There are now two people in the world that understand
this and everyone else seems to be so sure that we are wrong that they can't
even pay complete 100% attention to a single sentence.

It's an inveterate issue in Psychoceramics.

↪PL Olcott Yeah, OK. No progress to be made here. Publish your article and then invite me to the ceremony when you win the Turing Award so you can say "I told you so". — Banno

I have a completely different proof that shows every single detail of
how H does correctly determine the halt status of the impossible input.

I'm sure you do.

↪PL Olcott It's an inveterate issue in Psychoceramics. — Banno

That a PhD computer science professor of decades has his own
proof of this and agrees that my proof is correct provides sufficiently
compelling evidence that this is not the case. He has been published
several times in the two most prestigious computer science journals.

@PL Olcott "logically impossible" is not recognized in philosophy. It's either "illogical" or "impossible". The two are used in different contexts.

Impossibility in philosophy is used in the physical event -- i.e. it's impossible to be in two places at the same exact time. Another one, it's impossible for humans to fly in the air.
Illogical is what you mean when you say a circle cannot be a square. Of course you would object to my description as you might think, but squares and circles are physical objects. Actually, they are conceptual objects, hence, logical in the sense of "it makes sense by definition that a circle has 360 degree rotation while the sum of the degree of the square is also 360".

PL Olcott "logically impossible" is not recognized in philosophy. It's either "illogical" or "impossible". The two are used in different contexts. — L'éléphant

Logically impossible is the strongest kind of impossible.
A thing that is required to have simultaneous mutually exclusive properties
like a square circle that must be round and must not be round is logically
impossible. Making a perfect angel food cake using only house bricks for
ingredients might be possible by rearranging the atoms of the bricks.

"logically impossible" is not recognized in philosophy. — L'éléphant

Yeah, it is. (p & ~p). Contradiction.

This entry is about worlds that are not possible, with “possible” understood in an unrestricted sense. Start with the intuitive idea of the totality of possible worlds, which capture all and only the genuine possibilities. The worlds we are interested in are not in there. These worlds are often called logically impossible worlds, as logical laws such as the Law of Non-Contradiction or the Law of Excluded Middle are assumed to be the most general and topic-neutral: they are supposed to hold at all possible worlds. From now on, we are talking of impossible worlds simpliciter, meaning worlds that are not possible with respect to an unrestricted notion of possibility, however this is further characterized. — Impossible Worlds (Stanford Encyclopaedia, my bolding)

i.e. it's impossible to be in two places at the same exact time. — L'éléphant

Tell that to an electron in a double-slit experiment.