Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge

On 09/07/2026 06:32, olcott wrote:
> On 7/8/2026 3:22 AM, Mikko wrote:
>> On 06/07/2026 18:54, olcott wrote:
>>> On 7/6/2026 4:25 AM, Mikko wrote:
>>>> On 05/07/2026 00:01, olcott wrote:
>>>>> On 7/4/2026 12:11 PM, dbush wrote:
>>>>>> On 7/4/2026 1:07 PM, olcott wrote:
>>>>>>> On 7/4/2026 3:06 AM, Mikko wrote:
>>>>>>>> On 03/07/2026 21:20, olcott wrote:
>>>>>>>>> On 7/3/2026 12:35 PM, André G. Isaak wrote:
>>>>>>>>>> On 2026-07-03 09:38, olcott wrote:
>>>>>>>>>>> On 7/3/2026 4:28 AM, Mikko wrote:
>>>>>>>>>>>> On 02/07/2026 17:49, olcott wrote:
>>>>>>>>>>>>> On 7/2/2026 1:55 AM, Mikko wrote:
>>>>>>>>>>>>>> On 01/07/2026 18:16, olcott wrote:
>>>>>>>>>>>>>>> On 7/1/2026 2:24 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 30/06/2026 16:58, olcott wrote:
>>>>>>>>>>>>>>>>> On 6/30/2026 3:18 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>> On 29/06/2026 16:29, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 6/29/2026 1:14 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>> On 29/06/2026 05:52, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 6/28/2026 3:39 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>> On 27/06/2026 17:50, polcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 20/06/2026 18:32, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> A proof theoretic expression is known to be 
>>>>>>>>>>>>>>>>>>>>>>>>> true when
>>>>>>>>>>>>>>>>>>>>>>>>> it is fully grounded in its atomic base. Only two
>>>>>>>>>>>>>>>>>>>>>>>>> PTS semantics researchers deal with true Dag 
>>>>>>>>>>>>>>>>>>>>>>>>> Prawitz
>>>>>>>>>>>>>>>>>>>>>>>>> is the one that began this. PTS previously only 
>>>>>>>>>>>>>>>>>>>>>>>>> dealt
>>>>>>>>>>>>>>>>>>>>>>>>> with semantic meaning and never got around to 
>>>>>>>>>>>>>>>>>>>>>>>>> true(L,x).
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> That's surprising, disregard for axioms?
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> If there is no sequence of inference steps in Q from
>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
>>>>>>>>>>>>>>>>>>>>>>> ungrounded in the PTS atomic base of Q.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> This does not mean undecidable or incomplete
>>>>>>>>>>>>>>>>>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> It comes close. If ∃x x=S(x) is likewise 
>>>>>>>>>>>>>>>>>>>>>> "ungrounded" but in the
>>>>>>>>>>>>>>>>>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are 
>>>>>>>>>>>>>>>>>>>>>> both undecidable
>>>>>>>>>>>>>>>>>>>>>> and Q is incomplete, bcause that is what the words 
>>>>>>>>>>>>>>>>>>>>>> mean.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Q also can't bake a birthday cake, this does not make
>>>>>>>>>>>>>>>>>>>>> Q in any way "incomplete" relative to what it was
>>>>>>>>>>>>>>>>>>>>> defined to do. Incomplete only counts relative to
>>>>>>>>>>>>>>>>>>>>> its intended purpose. A car without an engine is
>>>>>>>>>>>>>>>>>>>>> incomplete relative to a mode of transportation.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Irrelevant. The definition of completeness 
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> It a misnomer and does not literally mean (as it 
>>>>>>>>>>>>>>>>>>> implies)
>>>>>>>>>>>>>>>>>>> that something is missing that could be added to make
>>>>>>>>>>>>>>>>>>> it complete.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> It does mean that something is missing that could be 
>>>>>>>>>>>>>>>>>> added to
>>>>>>>>>>>>>>>>>> enabe a proof of an unprovable sentence. 
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Base-Extension Semantics (B-eS) allows that.
>>>>>>>>>>>>>>>>> It never was incomplete. It always did what it was 
>>>>>>>>>>>>>>>>> defined to do.
>>>>>>>>>>>>>>>>> When Q is extended to become PA it stops being Q and 
>>>>>>>>>>>>>>>>> becomes PA.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> However, there are theories that reamain incomplete even 
>>>>>>>>>>>>>>>> when
>>>>>>>>>>>>>>>> more postolates are added, as long as there is a way to 
>>>>>>>>>>>>>>>> know
>>>>>>>>>>>>>>>> which sentences are included in the added postulates. 
>>>>>>>>>>>>>>>> Important
>>>>>>>>>>>>>>>> examples include Peano arithmetic and ZFC set theory.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Base-Extension Semantics (B-eS) seems to be essentially a 
>>>>>>>>>>>>>>> cheat.
>>>>>>>>>>>>>>> When we ask what is grounded in an atomic base of Q and we
>>>>>>>>>>>>>>> add axioms to Q to become PA we cheated in that we changed
>>>>>>>>>>>>>>> the original question rather than answered it.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yes, in a sense. But sometimes it is better to have a 
>>>>>>>>>>>>>> partial answer
>>>>>>>>>>>>>> rather than no answer at all. Of course Q with any additional
>>>>>>>>>>>>>> postulate is not Q but if the additional postulates are 
>>>>>>>>>>>>>> true about
>>>>>>>>>>>>>> natural numbers then the strengthened theory is still a 
>>>>>>>>>>>>>> theory of
>>>>>>>>>>>>>> natural numbers. PA is one such strengthened Q but still 
>>>>>>>>>>>>>> incomplete
>>>>>>>>>>>>>> and can be strengthened further.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Is  (∀x, S(x) ≠ x) provable or refutable in Q?
>>>>>>>>>>>>> Yes if you cheat, no if you don't cheat.
>>>>>>>>>>>>
>>>>>>>>>>>> As I already pointed out in another message, which you 
>>>>>>>>>>>> apparently
>>>>>>>>>>>> missed, it is neither. 
>>>>>>>>>>>
>>>>>>>>>>> Thus PTS would say that (∀x, S(x) ≠ x) is semantically
>>>>>>>>>>> undefined in Q.
>>>>>>>>>>
>>>>>>>>>> And that differs from claiming that Q is incomplete exactly 
>>>>>>>>>> how...?
>>>>>>>>>
>>>>>>>>> The base definition of "incomplete" means that it is
>>>>>>>>> not operating according to design spec.
>>>>>>>>
>>>>>>>> No, it is not. The term "incomplete" in its base meaning is
>>>>>>>> appicable to various things that are not exprected to operate.
>>>>>>>>
>>>>>>>
>>>>>>> The English word "incomplete" establishes the base
>>>>>>> meaning (parent node) in the knowledge ontology.
>>>>>>>
>>>>>>> I will not tolerate deceptive terms-of-the-art.
>>>>>>
>>>>>> In other words, you intend to lie by misusing definitions.
>>>>>
>>>>> These definitions are the liars.
>>>>
>>>> Maybe your definitions, but not the usual ones, which tell truthfully
>>>> how the defined words are used and understood by the experts.
>>>>
>>>>> Term-of-the-art
>>>>> A cat is a dalmatian dog
>>>>
>>>> Perhaps some art but neither ailurology nor cynology.
>>>
>>> Within the natural preexisting order of the body
>>> of knowledge saying that incomplete(math) inherits
>>> part of its meaning from incomplete(base) semantic
>>> parent node is simply a lie.
>>
>> There is no natural pre-existing order of the body of the knowledge.
> 
> It is type theory inheritance hierarchy deep ship !!!

THere is no type theory in the real world and consequently the
knowledge of real world does not involve the knowledge of type
theory.

> a feline kitten is not a subtype of boxcar

In natural language there are not subtypes at all. Comparison of
the known properties of feline kttens and boxcars may indicate
that nothing is both a boxcar and a feline kitten.

-- 
Mikko