Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 3:57 PM, dbush wrote:
> On 7/1/2026 4:50 PM, olcott wrote:
>> On 7/1/2026 3:37 PM, dbush wrote:
>>> On 7/1/2026 4:29 PM, olcott wrote:
>>>> On 7/1/2026 3:13 PM, André G. Isaak wrote:
>>>>> On 2026-07-01 13:53, olcott wrote:
>>>>>> On 7/1/2026 2:31 PM, André G. Isaak wrote:
>>>>>>> On 2026-07-01 12:51, olcott wrote:
>>>>>>>> On 7/1/2026 1:45 PM, André G. Isaak wrote:
>>>>>>>>> On 2026-07-01 12:15, dbush wrote:
>>>>>>>>>> On 7/1/2026 2:01 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>>> The same thing as: "cats are animals" expressed in
>>>>>>>>>>> English has no English meaning in Chinese.
>>>>>>>>>>
>>>>>>>>>> I didn't ask for an example.  I asked for a definition of what 
>>>>>>>>>> it mean for the truth value of a statement to not exist in a 
>>>>>>>>>> formal system.
>>>>>>>>>
>>>>>>>>> I'm actually not convinced that Olcott understands what a 
>>>>>>>>> definition is. I've frequently asked him for definitions and he 
>>>>>>>>> invariably responds with an example or an analogy (assuming he 
>>>>>>>>> responds at all). He doesn't get that examples don't take the 
>>>>>>>>> place of definitions. Examples can be useful for clarifying 
>>>>>>>>> definitions, but they aren't particularly useful on their own.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> You want a definition look-it-up.
>>>>>>>
>>>>>>> Until someone publishes an Olcott to Standard English dictionary, 
>>>>>>> this isn't really an option.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> True(L, X) ≡ ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
>>>>>> has been updated to this
>>>>>>
>>>>>> True(L, X):= ∃Γ ⊆ AtomicFacts(L) (Γ ⊢ X)
>>>>>
>>>>> That claims what it means to have the truth value 'true' (or at 
>>>>> least it would if you defined AtomicFacts in a coherent way). It 
>>>>> doesn't in any way clarify what you think it means for something to 
>>>>> not have a truth value.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> When I define a term hundreds of times and you did
>>>> not bother to pay attention that is your mistake
>>>> and your fault.
>>>>
>>>
>>> You gave no such definition of what it means for the truth value of a 
>>> statement to not exist in a formal system.
>>>
>>> A valid answer would look something like this:
>>>
>>> "The truth value of a statement does not exist in a formal system 
>>> when ..."
>>>
>>> Now complete the sentence.
>>
>> It is neither provable nor refutable in F.
> 
> Good.  So when you say "The truth value of (∀ x, S(x) ≠ x) does not 
> exist in Q", you mean "(∀ x, S(x) ≠ x) is unprovable in Q", which is 
> commonly known.
> 
> So once again, you're saying the same thing as everyone else but using 
> different words.
> 

Not really. It is normally thought of as undecidable
meaning that Q is incomplete meaning that Q is deficient.

The Halting Problem counter-example input is more like
the Liar Paradox. For HHH(DD) DD is bad input not at all
the same thing as saying that computation is fundamentally
limited.

> And just to remind everyone, the following terms mean the same as 
> "unprovable" as per the definitions given by olcott:
> 
> - truth value doesn't exist
> - out-of-scope
> - not semantically grounded
> - not grounded in the atomic base
> - not a confirmed statement
> 
> 
> 
> 
>> I have said this so many thousands of times over
>> the years that it did not occur to me that I did
>> not fully spell this out this time.
>>
>>
> 


-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).