Re: The simple essence of Proof Theoretic Semantics

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.

''Twas brillig, and the slithey toves did did gyre and gimble in the 
wabe.' is meaningless. 'five plus six equals seven' is wrong but 
meaningful. Neither are provable.

If an expression P is provable in PTS, then its negation ¬P is 
unprovable, but to say that it is meaningless is simply wrong. We often 
discuss statements which are false and need to do so. If they were truly 
meaningless we would have no reason to do so.

André

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