Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory,sci.logic Subject: Re: D correctly simulated by H cannot possibly halt --- templates and infinite sets Date: Wed, 29 May 2024 20:55:44 -0500 Organization: A noiseless patient Spider Lines: 83 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 30 May 2024 03:55:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="0a722b73a14c6c7bef786c05822a9348"; logging-data="1589884"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+6HMyXCIo0ns8VT62DAoY9" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:5gZBoxufX9oC0dauKnwGoAV2CXc= Content-Language: en-US In-Reply-To: Bytes: 4064 On 5/29/2024 8:25 PM, Richard Damon wrote: > On 5/29/24 9:12 PM, olcott wrote: >> On 5/29/2024 8:02 PM, Richard Damon wrote: >>> On 5/29/24 8:53 PM, olcott wrote: >>>> On 5/29/2024 7:47 PM, Richard Damon wrote: >>>>> On 5/29/24 8:21 PM, olcott wrote: >>>>>> On 5/29/2024 7:09 PM, Richard Damon wrote: >>>>>>> On 5/29/24 8:01 PM, olcott wrote: >>>>>>>> On 5/29/2024 6:47 PM, Richard Damon wrote: >>>>>>>>>> *Formalizing the Linz Proof structure* >>>>>>>>>> ∃H  ∈ Turing_Machines >>>>>>>>>> ∀x  ∈ Turing_Machines_Descriptions >>>>>>>>>> ∀y  ∈ Finite_Strings >>>>>>>>>> such that H(x,y) = Halts(x,y) >>>>>>>>>> >>>>>>>>> >>>>>>>>> And since NO H, can get right the H^ built to contradict IT, >>>>>>>>> that claim is proven false. >>>>>>>>> >>>>>>>> >>>>>>>> YOU KEEP TRYING TO GET AWAY WITH CHANGING THE SUBJECT >>>>>>>> THE ABOVE FORMALIZATION IS CORRECT >>>>>>>> >>>>>>> >>>>>>> How? >>>>>>> >>>>>> >>>>>> The above is the question that Linz asks and the he gets >>>>>> an answer of no, no such H exists. >>>>>> >>>>>> >>>>> >>>>> So, you now agree with Linz. Good. >>>>> >>>> >>>> I said that Linz says that. The point is that the Linz >>>> template examines an infinite set of Turing Machine / input >>>> pairs the same way my H/D template references an infinite set >>>> of C function / input pairs. >>>> >>> >>> The difference is, In Linz's formulation, each machine is >>> INDIVIDUALLY EVALUTED with its inputs, >> >> >> *No that is never the case* > > > Of course it is. > > >> >> When Ĥ is applied to ⟨Ĥ⟩ >> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞ >> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn >> >> The entire category of every decider/input pair is examined ALL AT ONCE. >> No one is dumb enough to look at each element of an infinite set >> one at a time because they know this takes literally forever. >> > > Why do you say that? > > How do you run ALL the machines at once? > When the category is examined all at once then there is no need to look at each individual element. > Maybe you can think of all of them running INDIVIDUALLY in parrallel, > but each machine does what that machine does with the input that THAT > machine was given. > > You just don't understand what you are talking about. > Existential quantification always looks at all the elements of an infinite set. -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer