Re: The simple essence of Proof Theoretic Semantics

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)



-- 
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).