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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko <mikko.levanto@iki.fi> Newsgroups: sci.logic Subject: Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement) Date: Fri, 24 May 2024 12:25:33 +0300 Organization: - Lines: 211 Message-ID: <v2pmed$28vp6$1@dont-email.me> References: <v1mljr$1q5ee$4@dont-email.me> <v2937a$2jfci$1@dont-email.me> <v294e1$1a3tk$22@i2pn2.org> <v297m8$2k4a6$1@dont-email.me> <v2a7p7$1ct7p$2@i2pn2.org> <v2ad5l$2qlho$1@dont-email.me> <v2ae6h$1ct7p$5@i2pn2.org> <v2am4p$2sdl6$1@dont-email.me> <v2amkc$1ct7p$13@i2pn2.org> <v2aobj$2sdma$5@dont-email.me> <v2ap1t$1ct7o$9@i2pn2.org> <v2b0jd$2u8oi$1@dont-email.me> <v2b17b$1ct7p$16@i2pn2.org> <v2b1dr$2u8oi$3@dont-email.me> <v2b9mo$1ecj9$2@i2pn2.org> <v2bb6d$308qd$2@dont-email.me> <v2bc5o$1ecj9$3@i2pn2.org> <v2bsog$36vvc$1@dont-email.me> <v2cpb1$1g2n8$1@i2pn2.org> <v2cvj6$3ddo5$1@dont-email.me> <v2d0qp$3dlkm$1@dont-email.me> <v2d1io$3dplm$1@dont-email.me> <v2evl5$3snmj$1@dont-email.me> <v2g2dp$3ugq$1@dont-email.me> <v2hkkl$ggq9$1@dont-email.me> <v2ibhe$ksut$1@dont-email.me> <v2k8go$1363g$1@dont-email.me> <v2l4hr$188bi$3@dont-email.me> <v2l87m$19619$1@dont-email.me> <v2lies$1b4kp$1@dont-email.me> <v2msns$1lhu4$1@dont-email.me> <v2ng1a$1or9h$6@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 24 May 2024 11:25:34 +0200 (CEST) Injection-Info: dont-email.me; posting-host="2d3fff391b2fd23565a4469345235b57"; logging-data="2391846"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18ddTRD0O/eOxpHcXbAYy5m" User-Agent: Unison/2.2 Cancel-Lock: sha1:SYA0Z3p07vfzVKSWYXnYCFrjobs= Bytes: 12258 On 2024-05-23 13:23:54 +0000, olcott said: > On 5/23/2024 2:54 AM, Mikko wrote: >> On 2024-05-22 19:52:59 +0000, olcott said: >> >>> 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 ==========