Re: The simple essence of Proof Theoretic Semantics

On 2026-06-29 20:17, olcott wrote:
> On 6/29/2026 8:54 PM, André G. Isaak wrote:
>> On 2026-06-29 19:19, olcott wrote:
>>> On 6/29/2026 8:01 PM, André G. Isaak wrote:
>>>> On 2026-06-29 18:37, olcott wrote:
>>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote:
>>>>>> On 2026-06-29 17:36, olcott wrote:
>>>>
>>>>>>> It does seem that they do agree that no proof
>>>>>>> of G can possibly exist in PA does means that
>>>>>>> G has no semantic meaning in PA.
>>>>>>
>>>>>> I've not seen anyone operating in PTS who says anything remotely 
>>>>>> like that. They do not agree with this; rather, you are projecting 
>>>>>> your own peculiar views onto their theory.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Because they beat around the bush about that using
>>>>> terminology that varies across every author.
>>>>
>>>> It's not that they are beating around the bush; it's that they 
>>>> aren't actually saying what you want them to say. Face it, you 
>>>> really don't understand the PTS literature as it is above your head.
>>>>
>>>> André
>>>>
>>>
>>> PTS is the way that meaning actually works.
>>> We can make a simpler analogy in that English
>>> words are meaningless until they are defined.
>>>
>>> The PTS connection of an expression in Q to
>>> its axioms Q is analogous to the connection
>>> of an English word to its definition.
>>>
>>> A proof merely looks to see if a definition
>>> exists and if it does not then the English
>>> Word / Expression of Q remains meaningless.
>>
>> That's not what PTS says; that's simply you.
>>
>> There is a difference between meaningless and wrong.
>>
> % This sentence is not true.
> ?- LP = not(true(LP)).
> LP = not(true(LP)).
> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.
> 
> Olcott's Minimal Type Theory
> G ↔ ¬Prov_PA(⌜G⌝)
> Directed Graph of evaluation sequence
> 00 ↔               01 02
> 01 G
> 02 ¬               03
> 03 Prov_PA         04
> 04 Gödel_Number_of 01  // cycle indicates no well-founded justification 
> tree exists.

That's completely nonresponsive. You're simply copying and pasting text 
from previous posts without any explanation of how you think it relates 
to the point I made (which you disingenuously snipped).

The Liar's Paradox isn't what I am discussing. I am discussing the fact 
that 'no number is equal to its successor' can't be proven in Q. That 
statement has absolutely no similarities to the Liar's Paradox.

André

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