Re: The simple essence of Proof Theoretic Semantics

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.

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