On 10/22/2024 2:39 AM, Mikko wrote:
> On 2024-10-22 02:04:14 +0000, olcott said:
>
>> On 10/16/2024 11:37 AM, Mikko wrote:
>>> On 2024-10-16 14:27:09 +0000, olcott said:
>>>
>>>> The whole notion of undecidability is anchored in ignoring the fact
>>>> that
>>>> some expressions of language are simply not truth bearers.
>>>
>>> A formal theory is undecidable if there is no Turing machine that
>>> determines whether a formula of that theory is a theorem of that
>>> theory or not. Whether an expression is a truth bearer is not
>>> relevant. Either there is a valid proof of that formula or there
>>> is not. No third possibility.
>>>
>>
>> After being continually interrupted by emergencies
>> interrupting other emergencies...
>>
>> If the answer to the question: Is X a formula of theory Y
>> cannot be determined to be yes or no then the question
>> itself is somehow incorrect.
>
> There are several possibilities.
>
> A theory may be intentionally incomplete. For example, group theory
> leaves several important question unanswered. There are infinitely
> may different groups and group axioms must be true in every group.
>
> Another possibility is that a theory is poorly constructed: the
> author just failed to include an important postulate.
>
> Then there is the possibility that the purpose of the theory is
> incompatible with decidability, for example arithmetic.
>
>> An incorrect question is an expression of language that
>> is not a truth bearer translated into question form.
>>
>> When "X a formula of theory Y" is neither true nor false
>> then "X a formula of theory Y" is not a truth bearer.
>
> Whether AB = BA is not answered by group theory but is alwasy
> true or false about specific A and B and universally true in
> some groups but not all.
>
See my most recent reply to Richard it sums up
my position most succinctly.
--
Copyright 2024 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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