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Path: ...!feeds.phibee-telecom.net!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: immibis <news@immibis.com> Newsgroups: comp.theory,sci.logic Subject: Re: A computable function that reports on the behavior of its actual self is not allowed Date: Tue, 14 May 2024 02:41:26 +0200 Organization: A noiseless patient Spider Lines: 41 Message-ID: <v1ubvm$3p0hu$1@dont-email.me> References: <v1r566$2uo21$1@dont-email.me> <v1smrp$3clsp$1@dont-email.me> <v1t563$3g3o3$2@dont-email.me> <v1u201$3mvsa$2@dont-email.me> <v1u5so$3nqc3$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 14 May 2024 02:41:27 +0200 (CEST) Injection-Info: dont-email.me; posting-host="ad3621092433e9edc823f28b4a08f9d8"; logging-data="3965502"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/FxsfT947OgPf54QBTRzDS" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:0wnJ4Be0CmvgEjxEjiTlcxbOkVU= In-Reply-To: <v1u5so$3nqc3$2@dont-email.me> Content-Language: en-US Bytes: 3106 On 14/05/24 00:57, olcott wrote: > On 5/13/2024 4:50 PM, immibis wrote: >> On 13/05/24 15:39, olcott wrote: >>> On 5/13/2024 4:34 AM, Fred. Zwarts wrote: >>>> Op 12.mei.2024 om 21:27 schreef olcott: >>>>> Computable functions are the basic objects of study in computability >>>>> theory. Computable functions are the formalized analogue of the >>>>> intuitive notion of algorithms, in the sense that a function is >>>>> computable if there exists an algorithm that can do the job of the >>>>> function, i.e. given an input of the function domain it can return the >>>>> corresponding output. >>>>> https://en.wikipedia.org/wiki/Computable_function >>>>> >>>>> A computable function that reports on the behavior of its actual >>>>> self (or reports on the behavior of its caller) is not allowed. >>>> >>>> So, olcott uses his authority to create a new problem. Why would >>>> anybody be interested in such limitation? >>>> >>> >>> The definition of computable function is an axiomatic basis >>> not any mere authority. >>> >> There's no axiom that says computable functions aren't allowed to have >> themselves as input. > > If you are 100% precise with the meaning of your words you > already know that no executed embedded_H can possibly report > on its own behavior because no TM can take another TM as input. If you are 90% precise with the meaning of your words you know that the halting problem is about the machine description of a Turing Machine and that is OBVIOUSLY what I meant. If you are 110% precise with the meaning of your words you know that you said computable functions aren't the same as Turing machines and that a function which takes a function as input can exist in some theories (more commonly in computer science rather than mathematics) and is called a higher-order function. https://en.wikipedia.org/wiki/Higher-order_function