Re: The simple essence of Proof Theoretic Semantics

On 7/3/2026 8:10 PM, dbush wrote:
> On 7/3/2026 6:37 PM, olcott wrote:
>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>> On 2026-07-03 12:36, olcott wrote:
>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>
>>>>> If an algorithm takes an input and produces an output, that is by 
>>>>> definition a mapping. 
>>>> That only proves that the definition is incoherent.
>>>> The coherent way that it actually works is that
>>>> inputs are transformed into outputs by applying
>>>> finite string transformation rules to inputs to
>>>> derive outputs.
>>>
>>> Apparently you don't understand the difference between a mapping and 
>>> an algorithm. They are two different things.
>>>
>>> André
>>>
>>
>> A function that ignores its input and only returns 0
>> is not any sort of halt function.
>>
> 
> It is a partial halt decider that correctly reports the halt status of 
> any algorithm that halts when executed directly and incorrectly reports 
> the halt status of algorithms that halt when executed directly.

Correction: it correctly reports the halt status of any algorithm that 
*does not* halt when executed directly.

> 
> If you disagree, point out exactly which part of the below requirements 
> is violated in doing so.  If you dishonestly trim this, it will be taken 
> as your official, on-the-record admission that the below requirements 
> are satisfied for the subset of algorithms that halt when executed 
> directly.
> 
> 
> Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
> described as <X> with input Y:
> 
> A solution to the halting problem is an algorithm H that computes the 
> following mapping:
> 
> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
>