Re: Professor Eric Hehner's brilliant work --- isomorphisms

On 4/21/25 11:16 PM, olcott wrote:

On 4/21/2025 7:46 PM, Richard Damon wrote:

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
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(6) Can Carol correctly answer “no” to this (yes/no) question?
https://www.cs.toronto.edu/~hehner/OSS.pdf
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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.

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No it isn't, as Carol is a voltional being while a decider is deterministic.
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How long are you going to pretend that you don't
know what isomorphisms are?

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When are you going to stop[ abusing the term.
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To be an ISO-MORPHISM, they need to be "of the same shape".
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The to things aren't of the same shape, as they aren't even of the same type.
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Thus, your comparison is just an ACTUAL type error, verse you made-up type of type error.
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 Bijective mapping.
 

So, what BIjection are you talking about?
Carol, as she sits there can give two answers, Yes, or No.
Your HHH as it sits in Halt7.c can only give ONE answer, the one it is programmed to give, and that is the wrong one, NO.
If you change H to not abort, it is now a DIFFERENT decider, with a DIFFERENT input PROGRAM (since it includes by reference the decider) and this new decider will just fail to ever answer, so it didn't give the correct answer.
If you change H to still abort, but illogically answer 1, then again we have a different PROGRAM, and a DIFFERENT input, and this program still can give only one answer, the one that its programming dictates, and that is Yes, and for this different input, the correct answer will be No,
Thus showing that the fact that Carol is Volitional, and thus a statement about what she will do is undetermined make it not isomorphic to a question about a decider which is deterministic, and an input that is based on it. This doesn't make the question incorrect, just that the decider will be wrong, as there still is a correct answer to the OBJECTIVE question, which thd problem uses, of what do the program the input represents do.
Sorry, you are just showing your ignorance of what you are talking about, that you don't understand the meaning of the words you are using.