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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 20:56:17 +0100
Organization: A noiseless patient Spider
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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.