On 1/6/2023 3:35 PM, Richard Damon wrote:
> On 1/6/23 4:18 PM, olcott wrote:
>> On 1/6/2023 1:58 PM, Jeffrey Rubard wrote:
>>> On Friday, January 6, 2023 at 11:27:00 AM UTC-8, olcott wrote:
>>>> On 1/6/2023 1:18 PM, Richard Damon wrote:
>>>>> On 1/6/23 1:46 PM, olcott wrote:
>>>>>> On 1/6/2023 12:35 PM, Richard Damon wrote:
>>>>>>> On 1/6/23 1:06 PM, olcott wrote:
>>>>>>>> On 1/6/2023 11:35 AM, Richard Damon wrote:
>>>>>
>>>>>>>>>
>>>>>>>>> Right, and since the Godel Sentence G says that there does not
>>>>>>>>> exist a number g that meets a specific primitive recursive
>>>>>>>>> relationship, and we can show that:
>>>>>>>>>
>>>>>>>>> 0 does not meet that relationship
>>>>>>>>> 1 does not meet that relationship
>>>>>>>>> 2 does not meet that relationship
>>>>>>>>> ...
>>>>>>>>> n does not meet that relationship (from the meta-theory)
>>>>>>>>> ...
>>>>>>>>>
>>>>>>>>> and in the meta-theory we can show that in the theory we could
>>>>>>>>> continue this sequence forever (from the structure of that
>>>>>>>>> specific
>>>>>>>>> primative recursive relatonship), we thus have an INFINITE set of
>>>>>>>>> truth persevering operations that show that G is True.
>>>>>>>>>
>>>>>>>>> Since a Proof is a finite set of truth perserving operations,
>>>>>>>>> we do
>>>>>>>>> not have a proof of G in the Theory, thus, we can say that the
>>>>>>>>> statement G is True in F, but not Provable in F.
>>>>>>>>
>>>>>>>> If G is not provable in F then there is a sequence of truth
>>>>>>>> preserving
>>>>>>>> operations in F that proves that G is not provable in F,
>>>>>>>> otherwise G
>>>>>>>> is not true in F.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> No, not being provable and not being True are different things.
>>>>>>>
>>>>>> If there is no finite or infinite sequence of truth preserving
>>>>>> operations in F that proves that G is not provable in F then there
>>>>>> is no
>>>>>> semantic connection in F from G to its truth maker in F, thus G is
>>>>>> not
>>>>>> true in F.
>>>>>>
>>>>>
>>>>> The statement "G is Not Provable in F" and the statement "G is True in
>>>>> F" are different statments, so are not based on the same set of
>>>>> operations.
>>>>>
>>>> None-the-less if there is no semantic connection in F from G in F to
>>>> its
>>>> truth maker in F then G is not true in F.
>>>> --
>>>> Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
>>>> hits a target no one else can see." Arthur Schopenhauer
>>>
>>> "Also: Truthmaker theory is part of philosophy of language, not
>>> formal logic per se, and you do not even appear to understand it 'as
>>> is'."
>>
>>
>> I am creating/discovering the elemental nature of analytical truth
>> itself. This is an overarching idea that applies all all ideas, thus not
>> limited to any specific subject domain.
>>
>> When I say {truth maker} I mean the semantic connection from an
>> analytical expression of language to the key natural language axioms
>> that make this expression true.
>>
>
> Which means you have the theory BACKWARDS, as the connections flow FROM
> the axioms of the system TO the statement to be decided.
>
When proving that {cats} <are> {living things}
and we only know that
{cats} <are> {animals}
{animals} <are> {living things}
we must start with {cats} <are> {living things}
and work backwards, every automated theorem prover works this way.

https://en.wikipedia.org/wiki/Backward_chaining

--
Copyright 2022 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/6/23 4:44 PM, olcott wrote:
> On 1/6/2023 3:35 PM, Richard Damon wrote:
>> On 1/6/23 4:18 PM, olcott wrote:
>>> On 1/6/2023 1:58 PM, Jeffrey Rubard wrote:
>>>> On Friday, January 6, 2023 at 11:27:00 AM UTC-8, olcott wrote:
>>>>> On 1/6/2023 1:18 PM, Richard Damon wrote:
>>>>>> On 1/6/23 1:46 PM, olcott wrote:
>>>>>>> On 1/6/2023 12:35 PM, Richard Damon wrote:
>>>>>>>> On 1/6/23 1:06 PM, olcott wrote:
>>>>>>>>> On 1/6/2023 11:35 AM, Richard Damon wrote:
>>>>>>
>>>>>>>>>>
>>>>>>>>>> Right, and since the Godel Sentence G says that there does not
>>>>>>>>>> exist a number g that meets a specific primitive recursive
>>>>>>>>>> relationship, and we can show that:
>>>>>>>>>>
>>>>>>>>>> 0 does not meet that relationship
>>>>>>>>>> 1 does not meet that relationship
>>>>>>>>>> 2 does not meet that relationship
>>>>>>>>>> ...
>>>>>>>>>> n does not meet that relationship (from the meta-theory)
>>>>>>>>>> ...
>>>>>>>>>>
>>>>>>>>>> and in the meta-theory we can show that in the theory we could
>>>>>>>>>> continue this sequence forever (from the structure of that
>>>>>>>>>> specific
>>>>>>>>>> primative recursive relatonship), we thus have an INFINITE set of
>>>>>>>>>> truth persevering operations that show that G is True.
>>>>>>>>>>
>>>>>>>>>> Since a Proof is a finite set of truth perserving operations,
>>>>>>>>>> we do
>>>>>>>>>> not have a proof of G in the Theory, thus, we can say that the
>>>>>>>>>> statement G is True in F, but not Provable in F.
>>>>>>>>>
>>>>>>>>> If G is not provable in F then there is a sequence of truth
>>>>>>>>> preserving
>>>>>>>>> operations in F that proves that G is not provable in F,
>>>>>>>>> otherwise G
>>>>>>>>> is not true in F.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> No, not being provable and not being True are different things.
>>>>>>>>
>>>>>>> If there is no finite or infinite sequence of truth preserving
>>>>>>> operations in F that proves that G is not provable in F then
>>>>>>> there is no
>>>>>>> semantic connection in F from G to its truth maker in F, thus G
>>>>>>> is not
>>>>>>> true in F.
>>>>>>>
>>>>>>
>>>>>> The statement "G is Not Provable in F" and the statement "G is
>>>>>> True in
>>>>>> F" are different statments, so are not based on the same set of
>>>>>> operations.
>>>>>>
>>>>> None-the-less if there is no semantic connection in F from G in F
>>>>> to its
>>>>> truth maker in F then G is not true in F.
>>>>> --
>>>>> Copyright 2022 Olcott "Talent hits a target no one else can hit;
>>>>> Genius
>>>>> hits a target no one else can see." Arthur Schopenhauer
>>>>
>>>> "Also: Truthmaker theory is part of philosophy of language, not
>>>> formal logic per se, and you do not even appear to understand it 'as
>>>> is'."
>>>
>>>
>>> I am creating/discovering the elemental nature of analytical truth
>>> itself. This is an overarching idea that applies all all ideas, thus not
>>> limited to any specific subject domain.
>>>
>>> When I say {truth maker} I mean the semantic connection from an
>>> analytical expression of language to the key natural language axioms
>>> that make this expression true.
>>>
>>
>> Which means you have the theory BACKWARDS, as the connections flow
>> FROM the axioms of the system TO the statement to be decided.
>>
> When proving that {cats} <are> {living things}
> and we only know that
> {cats} <are> {animals}
> {animals} <are> {living things}
> we must start with {cats} <are> {living things}
> and work backwards, every automated theorem prover works this way.
>
> https://en.wikipedia.org/wiki/Backward_chaining
>

Nope, not one MUST, but one can.

Note, "Back Chaining" works primarily is simpler systems.

As I remember, it is really mostly usable in First Order logic system
(which seems to be the only ones you understand).