Re: The simple essence of Proof Theoretic Semantics

On 2026-07-01 14:52, olcott wrote:
> On 7/1/2026 3:50 PM, André G. Isaak wrote:

>>> Any expression X that is unprovable in any formal
>>> system F is untrue in that formal system F
>>>
>>> Any expression X that is irrefutable in any formal
>>> system F is unfalse in that formal system F.
>>
>> So now you have a four-valued logic? (true, false, untrue, unfalse).
>>
> 
> Like the expression: "What time is it?"
> we have true, false, not truth apt.

So a three-valued system. Then the same remarks apply. You need to 
actually define your three-valued system and show how the basic logical 
operators actually work in that system.

And your natural language example is entirely unrevealing. Natural 
language distinguishes between interrogative and declarative sentences. 
Q has only declarative sentences and declarative sentences, by 
definition, are sentences which evaluate to a truth value.

And in standard logic there is this thing called the law of the excluded 
middle which states that every declarative sentence is either true or 
false. You can't just introduce some concept like "not truth apt" 
without completely redefining logic from the ground up. You haven't made 
even the feeblest attempt at doing this. You simply introduce concepts 
as if they will magically fit into an existing system rather than 
exploring what the consequences of introducing such concepts would 
actually have

>> If so, you'll need to define what all of these values actually mean, 
>> and you'll need to completely redefine all of the basic logical 
>> operators so that they account for these four values.
>>
>> 5 = 5 is irrefutable in Q. According to what you say above that makes 
>> it 'unfalse'. How is that different from being 'true'?

No answer?

André

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