Re: The simple essence of Proof Theoretic Semantics

On 7/1/2026 4:10 PM, André G. Isaak wrote:
> 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.
> 

It is not a three-valued system as these are commonly
understood. When we go with the expressiveness of
natural language then construing all sentences as
true or false is directly seen to be as stupid as it
has always been.

> 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.
> 
Because logic only has propositions that it incorrectly assumed
must be true or false it stupidly ignores the third possibility
of semantically ill-formed.

> 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. 

Not truth apt and not a truth bearer already has established
well-defined meanings that logic stupidly ignores.

The law of the excluded middle forces logicians to stupidly
classify semantic nonsense as true or false.

> 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
> 

Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system

Has been inherently the way that true on the basis
of meaning expressed in language HAS ALWAYS WORKED.

Expressions of language are ONLY true, or false on
the basis of their connections to other Expressions
of language.

-- 
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).