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From: immibis <news@immibis.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Halt deciders accurately predict future behavior based on past
 behavior
Date: Sat, 16 Mar 2024 22:09:05 +0100
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On 16/03/24 20:58, olcott wrote:
> On 3/16/2024 2:56 PM, immibis wrote:
>> On 16/03/24 19:19, olcott wrote:
>>> On 3/16/2024 12:30 PM, immibis wrote:
>>>> On 16/03/24 16:28, olcott wrote:
>>>>> The original halt status criteria has the impossible requirement
>>>>> that H(D,D) must report on behavior that it does not actually see.
>>>>> Requiring H to be clairvoyant is an unreasonable requirement.
>>>>
>>>> The purpose of a halting decider is to be clairvoyant. A halting 
>>>> decider must decide that a program will never halt even if we run it 
>>>> forever, without actually running it forever.
>>>>
>>> Not at all. Something like mathematical induction accurately
>>> extrapolates what the future behavior would be:
>>
>> In other words: mathematical induction is clairvoyant.
> 
> Not at all. Mathematical induction extrapolates on the basis of
> what it sees. Requiring H(D,D) to report on behavior that it cannot
> even see is incorrect.

In other words: Mathematical induction reports on behaviour that it 
cannot even see.