XPost: comp.theory, comp.lang.c++, comp.lang.c
From: polcott333@gmail.com
On 10/3/2025 6:25 PM, Kaz Kylheku wrote:
> On 2025-10-03, olcott wrote:
>> On 10/3/2025 4:50 PM, Kaz Kylheku wrote:
>>> On 2025-10-03, olcott wrote:
>>>> This concept must be named or it cannot
>>>> be referenced. I must reference it.
>>>> It must be a simple and accurate name.
>>>>
>>>> WTF would you call it?
>>>>
>>>> The set of H/P pairs such that:
>>>> For decider H and input P
>>>> If H says halts then P loops
>>>> If H says loops then P halts
>>>> making H(P) always incorrect.
>>>
>>> This is not /your/ concept; it is something you should have
>>> understood properly 20 years ago.
>>>
>>
>> It isn't that I didn't understand this 22 years ago.
>> I understood this the whole time. It is that 22 years
>
> As little as five years go or so you still believed that there
> is supposed to be a /single/ case that is undecidable.
>
My words may have seemed to have indicated that.
>> ago I spotted its bogus liar paradox structure.
>
> Because you didn't understand it at the time, but given what you should
> know now, you should see that it's not the same at all.
>
> The diagonal case, though it contains a self-reference, is not a truth
> statement and it is not asserting its own falsehood.
>
> The details of the self-reference matter.
>
Yes that is why I coined the term pathological
self-reference(Olcott 2004). All my old posts
are still out there. I can still directly reply to them.
> For instance, these sentence are just as self-referential as the
> Liar Paradox, yet we can cheerfully assign them truth values:
>
> This sentence has five words. (True)
> This sentence has four words. (False)
>
> Like the Liar sentence, these sentences are making a logical assertion.
> Unlike the Liar sentence, they are not simply making a logical assertion
> about their truth value; they are making an assertion about a property
> different from their truth value.
>
> By talking about something other than their own truth value, the
> logical assertion is anchored to something external.
>
> The following sentence is self-referential, yet talks about nothing but
> its truth value:
>
> This sentence is true.
>
> this is still just internal: the logical assertion talking about its
> own truth. We can assign the value True or False to this sentence
> without contradiction---but that is a problem almost if not just as bad
> as not being able to assign a truth value!
>
None-the-less it is still semantically faulty.
> So anyway, in the diagonal trick used for reasoning about halting,
> the self-reference is much more like:
>
> This sentence has four words.
>
> than it is like:
>
> This sentence is false.
>
Incorrect.
For the set of H/P pairs of
decider H and input P:
If H says halts then P loops
If H says loops then P halts
making H(P) always incorrect.
Is much more liar paradox like.
The pathological self-reference(Olcott 2004)
is indirect instead of direct.
> The H decider isn't asserting something about the truth value of its
> subject; it is anchored to a different property, halting,
> which is like word count, or any other property.
>
> The "opposite behavior" is something as if we could make
> a sentence that changes its word count to something other than
> what it has been counted by some procedure.
>
> Suppose H is a word count procedure. Let the sentence D be:
>
> In this sentence, 'Church-Turing' is two words, except if H says
> that this sentence has an even number of words, in which case it
> is one word.
>
> Thus if we allow sentences to stipulate how many words comprise a
> hyphenated compound which occurs in them, and if we allow such
> stipulations to refer to word counting functions, then the word count
> function becomes incomputable. :)
>
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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