XPost: comp.theory, sci.logic, sci.math
From: 643-408-1753@kylheku.com
On 2025-11-22, olcott wrote:
> On 11/22/2025 12:08 AM, Kaz Kylheku wrote:
>> On 2025-11-22, olcott wrote:
>>> With the halting problem counter example input
>>> where input D does the opposite of whatever
>>> decider H reports this specific H/D is exactly
>>> isomorphic to the Liar Paradox.
>>
>> No it isn't. The Liar Paradox has an indeterminate
>> truth value; the H/D pair does not contain any
>> proposition with an indeterminate truth value.
>>
>
> With the halting problem counter example input
> where input D does the opposite of whatever decider
> H reports this specific H/D pair is exactly
> isomorphic to the Liar Paradox.
>
> When the behavior of D depends on the return
> value of H and D does the opposite of whatever
> H returns the H/D pair itself is a yes/no question
> that lacks a correct yes/no answer.
Umm, no; there has to be a self-negation in order to have a Liar
Paradox. For instance "This sentence has four words" contains a
contradiction: the sentence's "behavior" of having a word count of five
contradicts an assertion that is found in the same sentence. Yet there
is no paradox: the sentence readily identifies as having a false value.
> Every yes/no question that lacks a correct yes/no answer
> is isomorphic to this question:
The correct answer is 1 in the H/D pair in which H returns 0.
It is not lacking. Just like the correct answer is "five words"
in "This sentence has four words".
> Is this sentence true or false: "This sentence is not true" ?
> What correct Boolean value should H return to D?
The correct value is 1.
--
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
|
