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: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement) Date: Thu, 23 May 2024 11:09:55 +0300 Organization: - Lines: 253 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 23 May 2024 10:09:56 +0200 (CEST) Injection-Info: dont-email.me; posting-host="9a65a24d86b46493377912dff2237f52"; logging-data="1760341"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Z1bk6GtEgi596p52Umv/r" User-Agent: Unison/2.2 Cancel-Lock: sha1:25b4IarA060p1gC04tD7xnZEnsc= Bytes: 13704 On 2024-05-23 01:03:44 +0000, Richard Damon said: > On 5/22/24 7:55 PM, olcott wrote: >> On 5/22/2024 6:01 PM, Richard Damon wrote: >>> On 5/22/24 3:52 PM, olcott wrote: >>>> On 5/22/2024 11:58 AM, Mikko wrote: >>>>> On 2024-05-22 15:55:39 +0000, olcott said: >>>>> >>>>>> On 5/22/2024 2:57 AM, Mikko wrote: >>>>>>> On 2024-05-21 14:36:29 +0000, olcott said: >>>>>>> >>>>>>>> On 5/21/2024 3:05 AM, Mikko wrote: >>>>>>>>> On 2024-05-20 17:48:40 +0000, olcott said: >>>>>>>>> >>>>>>>>>> On 5/20/2024 2:55 AM, Mikko wrote: >>>>>>>>>>> On 2024-05-19 14:15:51 +0000, olcott said: >>>>>>>>>>> >>>>>>>>>>>> On 5/19/2024 9:03 AM, Mikko wrote: >>>>>>>>>>>>> On 2024-05-19 13:41:56 +0000, olcott said: >>>>>>>>>>>>> >>>>>>>>>>>>>> On 5/19/2024 6:55 AM, Richard Damon wrote: >>>>>>>>>>>>>>> On 5/18/24 11:47 PM, olcott wrote: >>>>>>>>>>>>>>>> On 5/18/2024 6:04 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>> On 5/18/24 6:47 PM, olcott wrote: >>>>>>>>>>>>>>>>>> On 5/18/2024 5:22 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 5/18/24 4:00 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>> On 5/18/2024 2:57 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 5/18/24 3:46 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 12:38 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/18/24 1:26 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 11:56 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 5/18/24 12:48 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 9:32 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/18/24 10:15 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 7:43 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> No, your system contradicts itself. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>> You have never shown this. >>>>>>>>>>>>>>>>>>>>>>>>>>>> The most you have shown is a lack of understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> Truth Teller Paradox. >>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>> No, I have, but you don't understand the proof, it seems because you >>>>>>>>>>>>>>>>>>>>>>>>>>> don't know what a "Truth Predicate" has been defined to be. >>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every >>>>>>>>>>>>>>>>>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth >>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations that derive x from >>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>> And thus, When True(L, p) established a sequence of truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations eminationg from ~True(L, p) by returning false, it >>>>>>>>>>>>>>>>>>>>>>>>> contradicts itself. The problem is that True, in making an answer of >>>>>>>>>>>>>>>>>>>>>>>>> false, has asserted that such a sequence exists. >>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>> On 5/13/2024 9:31 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>  > On 5/13/24 10:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>  >> On 5/13/2024 7:29 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>  >>> >>>>>>>>>>>>>>>>>>>>>>>>  >>> Remember, p defined as ~True(L, p) ... >>>>>>>>>>>>>>>>>>>>>>>>  >> >>>>>>>>>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive p? >>>>>>>>>>>>>>>>>>>>>>>>  > No, so True(L, p) is false >>>>>>>>>>>>>>>>>>>>>>>>  >> >>>>>>>>>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive ~p? >>>>>>>>>>>>>>>>>>>>>>>>  > >>>>>>>>>>>>>>>>>>>>>>>>  > No, so False(L, p) is false, >>>>>>>>>>>>>>>>>>>>>>>>  > >>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>> *To help you concentrate I repeated this* >>>>>>>>>>>>>>>>>>>>>>>> The Liar Paradox and your formalized Liar Paradox both >>>>>>>>>>>>>>>>>>>>>>>> contradict themselves that is why they must be screened >>>>>>>>>>>>>>>>>>>>>>>> out as type mismatch error non-truth-bearers *BEFORE THAT OCCURS* >>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>> And the Truth Predicate isn't allowed to "filter" out expressions. >>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> YOU ALREADY KNOW THAT IT DOESN'T >>>>>>>>>>>>>>>>>>>>>> WE HAVE BEEN OVER THIS AGAIN AND AGAIN >>>>>>>>>>>>>>>>>>>>>> THE FORMAL SYSTEM USES THE TRUE AND FALSE PREDICATE >>>>>>>>>>>>>>>>>>>>>> TO FILTER OUT TYPE MISMATCH ERROR >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> The first thing that the formal system does with any >>>>>>>>>>>>>>>>>>>>>> arbitrary finite string input is see if it is a Truth-bearer: >>>>>>>>>>>>>>>>>>>>>> Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> No, we can ask True(L, x) for any expression x and get an answer. >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> The system is designed so you can ask this, yet non-truth-bearers >>>>>>>>>>>>>>>>>>>> are rejected before True(L, x) is allowed to be called. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> Not allowed. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every >>>>>>>>>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth >>>>>>>>>>>>>>>>>> preserving operations that derive x from >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> A set of finite string semantic meanings that form an accurate >>>>>>>>>>>>>>>>>> verbal model of the general knowledge of the actual world that >>>>>>>>>>>>>>>>>> form a finite set of finite strings that are stipulated to have >>>>>>>>>>>>>>>>>> the semantic value of Boolean true. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> So, for a statement x to be false, it says that there must be a >>>>>>>>>>>>>>>>> sequence of truth perserving operations that derive ~x from, right? >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Yes we must build from mutual agreement, good. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> So do you still say that for p defined in L as ~True(L, p) that your >>>>>>>>>>>>>>>>> definition will say that True(L, p) will return false? >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> It is the perfectly isomorphic to this: >>>>>>>>>>>>>>>> True(English, "This sentence is not true") >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Nope, Because "This sentece is not true" can be a non-truth-bearer, but >>>>>>>>>>>>>>> by its definition, True(L, x) can not. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> True(L,x) is always a truth bearer. >>>>>>>>>>>>>> when x is defined as True(L,x) then x is not a truth bearer. >>>>>>>>>>>>> >>>>>>>>>>>>> When x is defined as True(L,x) then x is what True(L,x) is, >>>>>>>>>>>>> in this case a truth bearer. >>>>>>>>>>> >>>>>>>>>>>> This is known as the Truth Teller Paradox >>>>>>>>>>> >>>>>>>>>>> Doesn't matter. But ir you say that "x is not a truth bearer" then, >>>>>>>>>>> by a truth preserving transformation, you imply that True(L,x) is >>>>>>>>>> >>>>>>>>>> True(English, "a cat is an animal) is true >>>>>>>>>> LP := ~True(L, LP) expands to ~True(~True(~True(~True(...)))) >>>>>>>>> >>>>>>>>> No, it doesn't. It is a syntax error to have the same symbol on >>>>>>>>> both sides ":=" so the expansion is not justified. >>>>>>>> >>>>>>>> ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩. >>>>>>>> *The sentence ψ is of course not self-referential in a strict sense*, >>>>>>>> but mathematically it behaves like one. >>>>>>>> https://plato.stanford.edu/entries/self-reference/#ConSemPar >>>>>>> >>>>>>> Your quote omitted important details. One is that the claim is not >>>>>>> true about every theory but is about first order arithmetic and its >>>>>>> extension. Another one is that ϕ(x) is that the claim is about >>>>>>> every formula ϕ(x). >>>>>>> >>>>>> >>>>>> *The whole article is about self-reference* >>>>>> The ONLY detail that I am referring to is that it is conventional to >>>>>> formalize self-reference incorrectly. >>>>>> >>>>>> *Richard and both fixed that* >>>>>> >>>>>> On 5/13/2024 9:31 PM, Richard Damon wrote: >>>>>>  > On 5/13/24 10:03 PM, olcott wrote: >>>>>>  >> On 5/13/2024 7:29 PM, Richard Damon wrote: >>>>>>  >>> >>>>>>  >>> Remember, p defined as ~True(L, p) ... >>>>>> >>>>>> x := y means x is defined to be another name for y >>>>> >>>>> Another name for the meaning of y. Therefore any pair of sentences that >>>>> are otherwise equal but one contains x where rhe other contains y is a pair >>>>> of equally true sentences. For example, if p defined as ~True(L, ⟨p⟩) >>>> ========== REMAINDER OF ARTICLE TRUNCATED ==========