Re: The simple essence of Proof Theoretic Semantics

On 2026-06-30 15:56, olcott wrote:
> On 6/30/2026 4:18 PM, André G. Isaak wrote:
>> On 2026-06-29 21:06, olcott wrote:
>>> On 6/29/2026 9:49 PM, André G. Isaak wrote:
>>>> On 2026-06-29 20:42, olcott wrote:
>>
>>>>> Those are specific concrete examples of how
>>>>> Proof Theoretic Semantics rejects expressions
>>>>> as Proof Theoretic Semantically incoherent.
>>>>
>>>> No, they are not. No author writing in the framework of proof- 
>>>> theoretic semantics has ever offered those examples or comparable 
>>>> examples or made any claims about 'rejecting expressions as proof 
>>>> theoretic semantically incoherent'. And there's nothing incoherent 
>>>> about the statement 'no number is equal to its successor' which is 
>>>> the example under discussion.
>>>>
>>>> André
>>>>
>>>
>>> None-the-less what I have said remains completely true.
>>> What I have spent 28 years reverse-engineering from first
>>> principles is exactly that. That no one applied PTS
>>> exactly that way before does not mean that it is not
>>> exactly correct PTS.
>>
>> Unfortunately, your say so carries very little weight.
>>
>> Would you agree that there is a difference between a statement being 
>> false and a statement being meaningless?
>>
> 
> Of course and that is such a dumb question that I
> ignored it.

But your interpretation of PTS claims that there is no difference. You 
claim that unprovable statements are meaningless; but any false 
statement will be unprovable in a consistent logic.

PA can prove that 2 + 3 = 5
PA can't prove that 2 + 3 ≠ 5

But the latter isn't meaningless, it's simply false.

You're simply wrong when you assert that PTS claims that unprovable 
claims are meaningless; that's simply not a coherent view.

André

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