Re: The simple essence of Proof Theoretic Semantics

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

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