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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Professor Eric Hehner's brilliant work --- isomorphisms
Date: Mon, 21 Apr 2025 20:46:07 -0400
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On 4/21/25 7:43 PM, olcott wrote:
> On 4/21/2025 5:43 PM, Richard Damon wrote:
>> On 4/21/25 4:27 PM, olcott wrote:
>>> WST Workshop on Termination, Oxford, 2018
>>> Objective and Subjective Specifications
>>> Eric C.R. Hehner
>>> Department of Computer Science, University of Toronto
>>>
>>> (6) Can Carol correctly answer “no” to this (yes/no) question?
>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>
>>> Is the perfect example of isomorphism to the halting problem's 
>>> pathological input. The halting problem input D derives a self- 
>>> contradictory question for H the same way that Carol's question
>>> is self-contradictory for Carol.
>>
>> No it isn't, as Carol is a voltional being while a decider is 
>> deterministic.
>>
> 
> How long are you going to pretend that you don't
> know what isomorphisms are?

When are you going to stop[ abusing the term.

To be an ISO-MORPHISM, they need to be "of the same shape".

The to things aren't of the same shape, as they aren't even of the same 
type.

Thus, your comparison is just an ACTUAL type error, verse you made-up 
type of type error.

> 
>> Thus, the decider has effectively already made its decision on the 
>> input before the input is actually made, and thus the input can use 
>> that answer to thwart it.
>>
>> This just shows a category error in your logic. You don't seem to 
>> understand the deterministic behavior of programs, and the fact that 
>> all their behavior is created as soon as the program is created, even 
>> if they are never actually run or simulated. We just don't know what 
>> that behavior is.
>>
>> This goes back to another of your confusions, about the difference 
>> between Truth (which just is or isn't) and Knowledge, which might not 
>> be yet.
>>
>>>
>>> Credit to Richard Damon for finding the loophole in the original 
>>> question.
>>>
>>> Professor Eric Hehner PhD put the finishing touches on an
>>> earlier idea in serial collaboration with  Daryl McCullough.
>>> I quoted Daryl's work many many times without attribution
>>> before I finally found this original post:
>>>
>>>     You ask someone (we'll call him "Jack") to give a truthful
>>>     yes/no answer to the following question:
>>>
>>>     Will Jack's answer to this question be no?
>>>
>>>     Jack can't possibly give a correct yes/no answer to the question.
>>>
>>>     https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ
>>>
>>>
>>
> 
>