Self Referential Undecidability Construed as Incorrect Questions

PL Olcott

Self Referential Undecidability Construed as Incorrect Questions
Linguistics understands that the context of who is asked a question does change the meaning of some questions. This same reasoning applies to decision problems.

When the context of who is asked a question determines whether or not a question has a correct answer then this context can never be correctly ignored.

When a yes/no question posed to a person has no correct yes/no answer from this person then this question is construed as incorrect within the full context of who is asked.

This same reasoning applies when the input to a decider has no correct accept/reject return value from this decider.

It does not matter that the question has a correct answer from someone else or the input to the decider can be decided by another decider.

In both cases we have an incorrect question because it has no correct answer within the full context of the question.

Original words by PhD computer science professor:
Can Carol correctly answer “no” to this question?
Let's ask Carol. If she says “yes”, she's saying that “no” is the correct answer for her, so “yes” is incorrect. If she says “no”, she's saying that she cannot correctly answer “no”, which is her answer. So both answers are incorrect. Carol cannot answer the question correctly.

Because:
(1) Both "yes" and "no" are the wrong answer from Carol.

(2) Linguistics understands that the context of who is asked changes the
meaning of this question, thus this context cannot be correctly ignored.

(3) An incorrect yes/no question is defined as any yes/no question
lacking a correct yes/no answer.

Then the question is an incorrect question when posed to Carol

This same reasoning equally applies to a termination analyzer H that
reports on an input D that does the opposite of whatever halt status
that H returns.

When the full context is of who is asked is considered then
Does D halt on its input? is an incorrect question for H.

unenlightened

↪PL Olcott

Yes, "no". — Jack

(or vice versa)

It is a solution to paradox to rule it out as soon as it rears its head, on an ad hoc basis, ie.
Rule: "if it leads to paradox it is ruled out."

But this does not seem to really get to grips with the thing.

"Will Jack's answer to this question be no?" is ruled out, but
"Will Jack's answer to this question be yes?" is ruled in.

Why? Or rather, why does one lead to paradox and the other does not? is that question ruled out?

G. Spencer-Brown has the bones of a more fruitful resolution of these things that you might find interesting. https://thephilosophyforum.com/discussion/14599/reading-the-laws-of-form-by-george-spencer-brown/p1

javi2541997

You ask someone (we'll call him "Jack") to give a truthful
> yes/no answer to the following question... — PL Olcott

Then the question is an incorrect question when posed to Jack — PL Olcott

As far as I have understood your reasoning, I think the latter fails to follow the original pattern of your premises. Firstly, you were asking for truthful yes/no answers to a specific question: 'Will Jack's answer to this question be no?' Not giving any relevance to whether the question is correct or incorrect, because you focused on the result, not the beginning. But, on the second group of premises, you focus on the questions instead. Rather than switching the 'context' - as you claim in your arguments - I think you are switching the meaning.

But maybe I am wrong, and I don't have a clue about what is going on. :smile:

PL Olcott

---

PL Olcott

↪unenlightened

I changed the words to the better words of the PhD computer science professor.

PL Olcott

↪javi2541997

I changed the words to the better words of the PhD computer science professor.

javi2541997

I changed the words to the better words of the PhD computer science professor. — PL Olcott

Can Carol correctly answer “no” to this question?
Let's ask Carol. If she says “yes”, she's saying that “no” is the correct answer for her, so “yes” is incorrect. If she says “no”, she's saying that she cannot correctly answer “no”, which is her answer. So both answers are incorrect. Carol cannot answer the question correctly.

Because:
(1) Both "yes" and "no" are the wrong answer from Carol. — PL Olcott

I see what you mean now. It is a paradox.

Yet, I think we can get a different result if we switch the assertions. The Anti-Liar paradox teaches us that the form of a proposition can determine its own truth or falsehood only if it is either a tautology or a contradiction. Neither the Carol's answer nor the possible answer is either a tautology or a contradiction.

Because:

A) If Carol's answer is true, then what she says is true. Therefore, it is the correct answer.

B) If Carol's answer is false, then what she says is false. Therefore, it is the wrong answer.

There is a possible alternative for Carol to answer correctly. Whether it is true or not that Carol can actually answer 'no' to the question itself.

PL Olcott

↪javi2541997

We must not change Carol's question because it is the exact same form as
the most important theorem in computer science the halting theorem.
A PhD computer science professor wrote Carol's question with this in mind.

Once we understand that any yes/no question that lacks a correct answer
(within the linguistically required context of who is asked) is an incorrect
question then

We understand that Carol's question and the halting theorem decider/input
pair are also merely incorrect questions.

The halting theorem proves that a halt decider cannot possibly return a
correct true/false value when its input does the opposite of whatever Boolean
value that it returns. https://simple.wikipedia.org/wiki/Halting_problem

Since this turns out to merely be an incorrect question it does not place
any actual limit on computation. The fact that a baker cannot bake an
angel food cake using only house bricks for ingredients place no limit
on the baker's baking skill.

javi2541997

↪PL Olcott

I haven't changed the question. I claimed that Carol is actually capable of answering 'no'. I mean, there is not a contradiction between the question and the possibly answer from Carol. There must be something about this paradox that makes the assertion of Carol as true... or false. :smile:

I do not see it as an 'incorrect' question/answer but whether the assertions are either true or false. Can Carol correctly answer 'no' to this question? There is a true possibility that Carol could do so.

PL Olcott

Can Carol correctly answer 'no' to this question? There is a true possibility that Carol could do so. — javi2541997

This is very tricky like the Liar Paradox: "This sentence is not true" <is> not true yet does not make it true because if it was true then it would not be not true.

We have the exact same issue with Carol's question.
Carol cannot correctly answer her question yet when she says "no" then she has correctly answered her question making "no" the wrong answer.

When Carol says "yes" this means that she can correctly answer her question with "no" yet we just proved that is incorrect.

javi2541997

Carol cannot correctly answer her question yet when she says "no" then she has correctly answered her question making "no" the wrong answer.

When Carol says "yes" this means that she can correctly answer her question with "no" yet we just proved that is incorrect. — PL Olcott

I agree. This is getting tricky, yes. I understand that it is proven that Carol cannot answer with 'yes' to claim that she can answer 'no' to the question. According to this context, it is getting more paradoxical, and I think this was the main point of your thread. What I do not understand is why you consider the question as 'wrong' when we are debating whether Carol is capable of answering the question correctly.

I mean: 'yes/no' doesn't affect the possibility of Carol answering as the question requires. At least, we can agree that the assertion of Carol answering as required is true.

PL Olcott

What I do not understand is why you consider the question as 'wrong' when we are debating whether Carol is capable of answering the question correctly. — javi2541997

Some (if not all) undecidable decision problems are only "undecidable" because there is something wrong with the problem. When zero elements of the entire solution set provide the correct answer then this indicates that there is something wrong with the problem.

If I ask you how many feet long is the color of your car? no one can provide a correct answer because the question itself is incorrect. The same thing happens when a self-contradictory question is asked.

PL Olcott

What I do not understand is why you consider the question as 'wrong' when we are debating whether Carol is capable of answering the question correctly. — javi2541997

One thing that I found in my 20 year long quest is that self-contradictory expressions are not true. As a corollary to this self-contradictory questions are incorrect.

When we add one more step that the context of who is asked a question is a mandatory aspect of the full meaning of this question then Carol's question is incorrect for Carol.

javi2541997

If I ask you how many feet long is the color of your car? no one can provide a correct answer because the question itself is incorrect. The same thing happens when a self-contradictory question is asked. — PL Olcott

I understand it better now, thanks!

One thing that I found in my 20 year long quest is that self-contradictory expressions are not true. As a corollary to this self-contradictory questions are incorrect. — PL Olcott

Basically, you claim that Carol's answer will always be incorrect because the question itself is incorrect too. So, we are lead to a self-contradictory result endlessly. Although I agree with you, and now I understand your thread a bit better, I still do not see the correlation between 'yes/no' - or 'correct/incorrect' - and true and false.

I think that the question being incorrect doesn't mean that Carol's answer is false. Actually, it is true that she is able to answer but not with the patterns given because the question is 'wrong'.

PL Olcott

I still do not see the correlation between 'yes/no' - or 'correct/incorrect' - and true and false. — javi2541997

Carol's question is incorrect for Carol, thus it is the fault of the question and not the falt of Carol for the lack of correct answer from Carol.

There no is element in the entire solution set of {yes, no} that Carol can use as her answer thus making the question incorrect on the basis of the definition of incorrect question.

An incorrect yes/no (technically polar) question is any yes/no question lacking a correct answer from the set of {yes, no} or {true, false}.

A self-contradictory (thus incorrect) question is the analog to a self-contradictory statement such as:
"This sentence is not true".

javi2541997

↪PL Olcott

Ah, the incorrect side is the recipient (Carol) because her answer would be incorrect using the two sets 'yes/no'. Well, I am starting to think that Carol is not human, and I am misunderstanding her and 'she' is a computer program or something related. If she were a human, the possibilities of answering would be longer than just two options.

An incorrect yes/no (technically polar) question is any yes/no question lacking a correct answer from the set of {yes, no} or {true, false} — PL Olcott

Here is where I disagree with you.

Correct/incorrect are not related to the truth or false in your question to Carol. Again, if they are either true or false, there must be something about them that makes them true or false. Your objection to the truth or falsehood cannot be determined in the context. In a sense, this means that Carol ('P' or predicate) consists of nothing but p with a predication of truth (thus, she can actually answer, but the question is incorrect). We can say that the truth or falsehood of Carol's answer is 'undetermined'.

PL Olcott

Correct/incorrect are not related to the truth or false in your question to Carol. — javi2541997

Is this sentence true or false? "This sentence is not true" is an incorrect question because the Liar Paradox is neither true nor false and the solution set is limited to {true, false}.

The same thing applies to Carol's question when posed to Carol:
Can Carol correctly answer “no” to this question?

Since both yes and no are an incorrect answer from Carol this conclusively proves that Carol's question meets the stipulated definition of an incorrect question when posed to Carol.

An incorrect question is defined as the case whenever a yes/no question posed to a person has no correct yes/no answer from this person then this question is incorrect when posed to this person.

Alkis Piskas

Linguistics understands that the context of who is asked a question does change the meaning of some questions ... When the context of who is asked a question determines ... — PL Olcott

I assume of course that "who" refers to a person. But does a person have a context?
I'm afraid that by this word you mean something else, e.g. background, or you apply it incorrectly, e.g. you mean the context in which one talks. Or even something else. I can't know.
And then you repeat it: "When the context of who is asked a question determines ..."

When the context of who is asked a question determines whether or not a question has a correct answer then this context can never be correctly ignored. — PL Olcott

1) A question cannot have a correct answer. What can be correct is the answer given to that question. So maybe you mean that the question can receive a correct answer?
Or that the question can have more than one correct answers?
2) What does "correctly ignored" mean? Do you mean "correctly answered"?

See, these things are not details. One has to be as exact and clear in ones thesis, hypothesis, proposition, etc. in philosophy as in science

My intention is not to criticize you, but to pinpoint important elements in a philosophical discussion. And I'm addressed to the general public, because I see the phenomenon of lack of clarity and misuse of terms only too often.

By extension, all this applies and is an answer to your topic itself: If the context in which a question is asked is missing or not clear, of course this question might receive not incorrect, but inappropriate answers, i.e. answers "out of context" or "off-topic", as we use to say. A classic example is an ambiguous question that can be answered with both "Yes" and "No", about which you talked in your description.

One must also add, that in philosophy, unlike in science, we cannot talk about "correct" answers. Logical schemes, fallacious arguments, etc. are an exception, since they are special elements used in argumentation, hypotheses, propositions, etc., which are borrowed from the science of Logic.

PL Olcott

1) A question cannot have a correct answer. — Alkis Piskas

"Is the living mammal of an elephant any type of fifteen story office building?"
has the correct answer of "no".

Is the following sentence true or false: "This sentence is not true."
has no correct answer from the set of {true, false}.

My intention is not to criticize you, but to pinpoint important elements in a philosophical discussion. And I'm addressed to the general public, because I see the phenomenon of lack of clarity and misuse of terms only too often. — Alkis Piskas

My purpose of being here is to get feedback so that I can make my words clear enough so that they can be understood as correct.

When a decision problem decider/input pair lacks a correct Boolean return value from this decider then this decision problem instance is semantically unsound.

javi2541997

Since both yes and no are an incorrect answer from Carol this conclusively proves that Carol's question meets the stipulated definition of an incorrect question when posed to Carol. — PL Olcott

Well, if we want to go further and make these premises even trickier, we can assert that Carol is not forced to answer in any case. So, there is a possibility for Carol to answer with an omission. Yet again, I claim that the 'incorrect' question doesn't depend whether is posed on Carol or not.

So, we haven't proved anything conclusively yet. :smile:

javi2541997

By extension, all this applies and is an answer to your topic itself: If the context in which a question is asked is mission or not clear, of course this question might receive not incorrect, but inappropriate answers, i.e. answers "out of context" or "off-topic", as we use to say. A classic example is an ambiguous question that can be answered with both "Yes" and "No", about which you talked in your description. — Alkis Piskas

:up:

PL Olcott

Yet again, I claim that the 'incorrect' question doesn't depend whether is posed on Carol or not. — javi2541997

The PhD computer science professor that has been published in several highly esteemed computer science journals disagrees.
(a) Yes is not a correct answer from Carol.
(b) No is not a correct answer from Carol.
(c) No answer is not a correct answer from Carol.
We have exhaustively examined every possibility and thus proven every action taken by Carol does not result in a correct answer.

PL Olcott

By extension, all this applies and is an answer to your topic itself: If the context in which a question is asked is mission or not clear, of course this question might receive not incorrect, but inappropriate answers, i.e. answers "out of context" or "off-topic", as we use to say. A classic example is an ambiguous question that can be answered with both "Yes" and "No", about which you talked in your description. — Alkis Piskas

When the solution set is restricted to {yes, no} and no element of this solution set is a correct answer from Carol then the question posed to Carol is incorrect.

javi2541997

(c) No answer is not a correct answer from Carol.
We have exhaustively examined every possibility and thus proven every action taken by Carol does not result in a correct answer. — PL Olcott

Interesting...

Let me think about this deeply. Maybe I can come back with more substantive comments, and see other possibilities. I appreciate how you considered each feasible scenario of Carol's behaviour. I still believe that there can be a possible correct answer.

Alkis Piskas

"Is the living mammal of an elephant any type of fifteen story office building?"
has the correct answer of "no". — PL Olcott

No, it is wrong to say that a question has a correct answer. It is wrong even to say that a question has any answer at all. A question is asked by a person and is addressed to anor person or persons in order to receive, to be given an answer. And then, the answer does not go to the question, it does not become a property of the question; it goes to whom asked the question.
Indeed, sometimes we say "your question includes the answer" or the "question replies to itself", etc. But these are only fiigures of speech.
Moreover, we are talking about a "correct" answer, something which even is more difficult to be attributed to a question.
So we can say that the correct answer to the question "Is the living mammal of an elephant any type of fifteen story office building?" is "No".

I hope this is clear by now.

Is the following sentence true or false: "This sentence is not true."
has no correct answer from the set of {true, false}. — PL Olcott

This is a known self-contraditory statement. It cannot be answered (with "true" or "false"). That's all.
This, as any other question, does not and cannot have an answer. I explained that in detail above.

My purpose of being here is to get feedback so that I can make my words clear enough so that they can be understood as correct. — PL Olcott

I appreciate this. I hope I have contributed in some way,

(BTW, what about my second question, "What does 'correctly ignored' mean? Do you mean 'correctly answered'?" Have you sorted this out?)

When a decision problem decider/input pair lacks a correct Boolean return value from this decider then this decision problem instance is semantically unsound. — PL Olcott

I wouldn't state it like that myself, but I agree. :smile:

Alkis Piskas

↪javi2541997

Hi friend! Long time no see!
Check this: When I visited TPF a few minutes ago, I had in mind to check about your recent activity (comments)! How can you call this (in Japanese)? :smile:

Alkis Piskas

↪PL Olcott

BTW, the was an spelling error in my sentence "the context in which a question is asked is ~~mission~~ missing or not clear".

When the solution set is restricted to {yes, no} and no element of this solution set is a correct answer from Carol then the question posed to Carol is incorrect. — PL Olcott

Well, depending on the question-statement, I would rather say ambiguous or circular or self-contradictory or --if it refers to an argument-- a fallacious argument.
I think that the attributes "correct" and "incorrect" are too general and/or ambiguous themselves.

PL Olcott

"Is the living mammal of an elephant any type of fifteen story office building?"
has the correct answer of "no".
— PL Olcott
No, it is wrong to say that a question has a correct answer. — Alkis Piskas

That seems to be a ridiculous statement on your part. It is like you are saying
that it is impossible to determine whether or not an elephant is a fifteen story
office building. How would you phrase the exact same idea that I am referring to?

When a decision problem decider/input pair lacks a correct Boolean return value from this decider then this decision problem instance is semantically unsound.
— PL Olcott
I wouldn't state it like that myself, but I agree. :smile: — Alkis Piskas

Most people call this an undecidable instance, yet it is not at all any
matter of the decider not being able to figure out which of true/false
is the correct return value. It is a matter of both true and false are
incorrect return values.

PL Olcott

Well, depending on the question-statement, I would rather say ambiguous or circular or self-contradictory or --if it refers to an argument-- a fallacious argument. — Alkis Piskas

It is clear that self-contradictory expressions are untrue and unfalse because they are self-contradictory. Analogous reasoning applies to self-contradictory questions.

It the same way that the Liar Paradox: "This sentence is not true" is an incorrect statement self-contradictory questions are incorrect questions.

Is this sentence true or false: "This sentence is not true" is an incorrect question because zero elements of the entire solution set of {true, false} are a correct answer.

Then we apply this same reasoning to self-contradictory decision problem instances.
When neither return value of {true, false} is correct for a decider/input pair then this
decider/input pair is essentially an incorrect question.

Alkis Piskas

But maybe I am wrong, and I don't have a clue about what is going on. :smile: — javi2541997

You are not wrong. And I think you do have a clue, and a correct one. @PL Olcott is simply confused. Besides being rude.

I would check more of your recent messages but it's got late. Maybe tomorrow ...

PL Olcott

Let me think about this deeply. Maybe I can come back with more substantive comments, and see other possibilities. I appreciate how you considered each feasible scenario of Carol's behaviour. I still believe that there can be a possible correct answer. — javi2541997

That is great.
(a) Carol answers "no" and she is wrong.
(b) Carol answers "yes" and she is wrong.
(c) Carol does anything else and she has not provided an answer within the solution set of {yes,no}.

Self Referential Undecidability Construed as Incorrect Questions

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