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Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: olcott <polcott333@gmail.com> Newsgroups: comp.theory Subject: Re: What it would take... People to address my points with reasoning instead of rhetoric -- RP Date: Tue, 13 May 2025 22:06:14 -0500 Organization: A noiseless patient Spider Lines: 94 Message-ID: <10011b6$29e7u$4@dont-email.me> References: <vvm948$34h6g$2@dont-email.me> <87v7q5n3sc.fsf@bsb.me.uk> <vvtf7n$17c1i$5@dont-email.me> <87plgdmldp.fsf@bsb.me.uk> <vvudut$1ife1$1@dont-email.me> <vvuii0$1j0qo$1@dont-email.me> <vvuk0d$1j6s0$5@dont-email.me> <vvvbtd$1ov7e$10@dont-email.me> <vvvpia$1tcfq$1@dont-email.me> <vvvqd1$1tgam$1@dont-email.me> <vvvrhl$1so2t$2@dont-email.me> <vvvtki$1tgam$3@dont-email.me> <vvvud5$1so2t$3@dont-email.me> <1000ce4$21dtc$3@dont-email.me> <1000q52$24gr3$2@dont-email.me> <1000qss$24jh0$2@dont-email.me> <1000rfv$24gr3$6@dont-email.me> <1000s0e$24sr2$1@dont-email.me> <1000s6d$24gr3$8@dont-email.me> <1000t1a$24sr2$4@dont-email.me> <1000t8e$24gr3$11@dont-email.me> <1000vs5$29e7u$1@dont-email.me> <100101g$24gr3$14@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 14 May 2025 05:06:15 +0200 (CEST) Injection-Info: dont-email.me; posting-host="1b4c815c0318038d25de37dcdc1ad225"; logging-data="2406654"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/bImKf99f4pTfRwpWQCc2p" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:qhi/HhmFwzmZmrFQofVtujUiaa8= X-Antivirus: Norton (VPS 250513-6, 5/13/2025), Outbound message In-Reply-To: <100101g$24gr3$14@dont-email.me> Content-Language: en-US X-Antivirus-Status: Clean On 5/13/2025 9:44 PM, dbush wrote: > On 5/13/2025 10:41 PM, olcott wrote: >> On 5/13/2025 8:56 PM, dbush wrote: >>> On 5/13/2025 9:52 PM, olcott wrote: >>>> On 5/13/2025 8:38 PM, dbush wrote: >>>>> On 5/13/2025 9:35 PM, olcott wrote: >>>>>> On 5/13/2025 8:26 PM, dbush wrote: >>>>>>> On 5/13/2025 9:16 PM, olcott wrote: >>>>>>>> On 5/13/2025 8:03 PM, dbush wrote: >>>>>>>>> Nope. Russell's Paradox was derived from the base axioms of >>>>>>>>> naive set theory, proving the whole system was inconsistent. >>>>>>>>> >>>>>>>>> In contrast, there is nothing in existing computation theory >>>>>>>>> that requires that a halt decider exists. >>>>>>> >>>>>>> I see you made no attempt to refute the above statement. Unless >>>>>>> you can show from the axioms of computation theory that the >>>>>>> following requirements can be met, your argument has no basis: >>>>>>> >>>>>>> >>>>>>> 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 >>>>>>> >>>>>>> >>>>>>>>> >>>>>>>>>> A halt decider doesn't exist >>>>>>>>>> for the same reason that the set of all sets >>>>>>>>>> that do not contain themselves does not exist. >>>>>>>>>> *As defined both were simply wrong-headed ideas* >>>>>>>>> >>>>>>>>> There's nothing wrong-headed about wanting to know if any >>>>>>>>> arbitrary algorithm X with input Y will halt when executed >>>>>>>>> directly. >>>>>>>> >>>>>>>> Yes there is. I have proven this countless times. >>>>>>> >>>>>>> That requirements are impossible to satisfy doesn't make them >>>>>>> wrong. It just makes them impossible to satisfy, which is a >>>>>>> perfectly reasonable conclusion. >>>>>>> >>>>>>> >>>>>> >>>>>> It did with Russell's Paradox. >>>>>> ZFC rejected the whole foundation upon which >>>>>> RP was built. >>>>>> >>>>>> ZFC did not solve some other Russell's Paradox >>>>>> it rejected the whole idea of RP as nonsense. >>>>>> >>>>> >>>>> Unless you can show from the axioms of computation theory that the >>>>> following requirements can be met, your argument has no basis: >>>>> >>>> >>>> Alternatively I can do what ZFC did and over-rule >>>> the whole foundation upon which the HP proofs are build. >>> >>> You mean the assumption that the following requirements (which are >>> *not* part of the axioms of computation theory) can be satisfied? >>> The assumption that Linz and other proved was false and that you >>> *explicitly* agreed with? >>> >> >> The conventional halting problem proofs have your >> requirements as its foundation. >> > > They have the *assumption* that the requirements can be met, and via > proof by contradiction show the assumption to be false. > > And the fact that the requirements can't be met is fine, just like the > the fact that these requirements can't be met is fine: > > A mythic number is a number N such that N > 5 and N < 2. We can also say that no computation can compute the square root of a dead rabbit. In none of these cases is computation actually limited. We could equally say that no whale can give birth to a pigeon. This places no actual limit on the behavior of whales. Whales were never meant to give birth to pigeons. -- Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer