Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: This makes all Analytic(Olcott) truth computable Date: Sun, 18 Aug 2024 13:40:30 +0300 Organization: - Lines: 164 Message-ID: References: <20b1dea98eda49e74e822c96b37565bb3eb36013@i2pn2.org> <7f2a1f77084810d4cee18ac3b44251601380b93a@i2pn2.org> <662de0ccc3dc5a5f0be0918d340aa3314d51a348@i2pn2.org> <02642e518edd3aa9152cd47e4e527f21ee53a0e8@i2pn2.org> <60c0214582c7f97e49ef6f8853bff95569774f97@i2pn2.org> <4d8c7b1c69915ebbe108d7f4e29cf6172eac7759@i2pn2.org> <43690773dba43c5d93d11635af0a26532e5be390@i2pn2.org> <6272b80d0aeaca324ac8624dce71945edeb59092@i2pn2.org> <2e642af254f6140ce8711da64f31d4fd8467d58b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 18 Aug 2024 12:40:30 +0200 (CEST) Injection-Info: dont-email.me; posting-host="65f9434b854ff7a88818fe4e27e130bf"; logging-data="2487775"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+DhIYfwqZrNASwl5ssgWiE" User-Agent: Unison/2.2 Cancel-Lock: sha1:DVlVsc068eYZbPd8N/aOLOVpIcg= Bytes: 9013 On 2024-08-17 16:51:22 +0000, olcott said: > On 8/17/2024 11:46 AM, Richard Damon wrote: >> On 8/17/24 12:35 PM, olcott wrote: >>> On 8/17/2024 11:28 AM, Richard Damon wrote: >>>> On 8/17/24 11:47 AM, olcott wrote: >>>>> On 8/17/2024 10:33 AM, Richard Damon wrote: >>>>>> On 8/17/24 11:12 AM, olcott wrote: >>>>>>> On 8/17/2024 9:53 AM, Richard Damon wrote: >>>>>>>> On 8/17/24 10:45 AM, olcott wrote: >>>>>>>>> On 8/17/2024 9:40 AM, Richard Damon wrote: >>>>>>>>>> On 8/17/24 12:05 AM, olcott wrote: >>>>>>>>>>> On 8/16/2024 5:57 PM, Richard Damon wrote: >>>>>>>>>>>> On 8/16/24 6:40 PM, olcott wrote: >>>>>>>>>>>>> On 8/16/2024 5:19 PM, Richard Damon wrote: >>>>>>>>>>>>>> On 8/16/24 6:16 PM, olcott wrote: >>>>>>>>>>>>>>> On 8/16/2024 5:03 PM, Richard Damon wrote: >>>>>>>>>>>>>>>> On 8/16/24 5:35 PM, olcott wrote: >>>>>>>>>>>>>>>>> On 8/16/2024 4:05 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>> On 8/16/24 4:39 PM, olcott wrote: >>>>>>>>>>>>>>>>>>> On 8/16/2024 2:42 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 8/16/24 2:11 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>> On 8/16/2024 11:32 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 8/16/24 7:02 AM, olcott wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> *This abolishes the notion of undecidability* >>>>>>>>>>>>>>>>>>>>>>> As with all math and logic we have expressions of language >>>>>>>>>>>>>>>>>>>>>>> that are true on the basis of their meaning expressed >>>>>>>>>>>>>>>>>>>>>>> in this same language. Unless expression x has a connection >>>>>>>>>>>>>>>>>>>>>>> (through a sequence of true preserving operations) in system >>>>>>>>>>>>>>>>>>>>>>> F to its semantic meanings expressed in language L of F >>>>>>>>>>>>>>>>>>>>>>> x is simply untrue in F. >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> But you clearly don't understand the meaning of "undecidability" >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> Not at all. I am doing the same sort thing that ZFC >>>>>>>>>>>>>>>>>>>>> did to conquer Russell's Paradox. >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> If you want to do that, you need to start at the basics are totally >>>>>>>>>>>>>>>>>>>> reformulate logic. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> ZFC didn't need to do that. All they had to do is >>>>>>>>>>>>>>>>>>> redefine the notion of a set so that it was no longer >>>>>>>>>>>>>>>>>>> incoherent. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> I guess you haven't read the papers of Zermelo and Fraenkel. They >>>>>>>>>>>>>>>>>> created a new definition of what a set was, and then showed what that >>>>>>>>>>>>>>>>>> implies, since by changing the definitions, all the old work of set >>>>>>>>>>>>>>>>>> theory has to be thrown out, and then we see what can be established. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> None of this is changing any more rules. All >>>>>>>>>>>>>>>>> of these are the effects of the change of the >>>>>>>>>>>>>>>>> definition of a set. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> No, they defined not only what WAS a set, but what you could do as >>>>>>>>>>>>>>>> basic operations ON a set. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Axiom of extensibility: the definition of sets being equal, that ZFC is >>>>>>>>>>>>>>>> built on first-order logic. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Axion of regularity/Foundation: This is the rule that a set can not be >>>>>>>>>>>>>>>> a member of itself, and that we can count the members of a set. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> This one is the key that conquered Russell's Paradox. >>>>>>>>>>>>>>> If anything else changed it changed on the basis of this change >>>>>>>>>>>>>>> or was not required to defeat RP. >>>>>>>>>>>>>> >>>>>>>>>>>>>> but they couldn't just "add" it to set theory, they needed to define >>>>>>>>>>>>>> the full set. >>>>>>>>>>>>>> >>>>>>>>>>>>>> I think you problem is you just don't understand how formal logic works. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> I think at a higher level of abstraction. >>>>>>>>>>>> >>>>>>>>>>>> No, you don't, unless you mean by that not bothering to make sure the >>>>>>>>>>>> details work. >>>>>>>>>>>> >>>>>>>>>>>> You can't do fundamental logic in the abstract. >>>>>>>>>>>> >>>>>>>>>>>> That is just called fluff and bluster. >>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> All that they did is just like I said they redefined >>>>>>>>>>>>> what a set is. You provided a whole bunch of details of >>>>>>>>>>>>> how they redefined a set as a rebuttal to my statement >>>>>>>>>>>>> saying that all they did is redefine a set. >>>>>>>>>>>> >>>>>>>>>>>> Showing the sort of thing YOU need to do to redefine logic >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> I said that ZFC redefined the notion of a set to get rid of RP. >>>>>>>>>>> You show the steps of how ZFC redefined a set as your rebuttal. >>>>>>>>>> >>>>>>>>>> No, you said that "ALL THEY DID" was that, and that is just a LIE. >>>>>>>>>> >>>>>>>>>> They developed a full formal system. >>>>>>>>>> >>>>>>>>> >>>>>>>>> They did nothing besides change the definition of >>>>>>>>> a set and the result of this was a new formal system. >>>>>>>>> >>>>>>>> >>>>>>>> I guess you consider all the papers they wrote describing the effects >>>>>>>> of their definitions "nothing" >>>>>>>> >>>>>>> >>>>>>> Not at all and you know this. >>>>>>> One change had many effects yet was still one change. >>>>>>> >>>>>> >>>>>> But would mean nothing without showing the affects of that change. >>>>>> >>>>> >>>>> Yet again with your imprecise use of words. >>>>> When any tiniest portion of the meaning of an expression >>>>> has been defined this teeny tiny piece of the definition >>>>> makes this expression not pure random gibberish. >>>>> >>>>> Meaningless does not mean has less meaning, it is >>>>> an idiom for having zero meaning. >>>>> https://www.britannica.com/dictionary/meaningless >>>>> >>>>> >>>>> >>>> >>>> And your statements have NO Meaning because they are based on LIE. >>>> >>>> We can not use the "ZFC" set theory from *JUST* the definition, but >>>> need all the other rules derived from it. >>> >>> The root cause of all of the changes is the redefinition >>> of what a set is. Likewise with my own redefinition of a >>> formal system by simply defining the details of True(L,x). >>> >>> Once I specify the architecture others can fill in the details. >>> >> >> Yes, the ROOT was that change, but you don't understand that if they >> JUST did that root, and not the other work, Set theory would not have >> been "fixed", as it still wouldn't have been usable. >> > > Defining that no set can be a member of itself would seem > to do the trick. It doesn't if there is another axiom that says or impies that the is a set that contains itself, or if several axioms together imply that. If someting provably exists then it exists even if you can prove that it does not exist. -- Mikko