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Groups > comp.theory > #137055
| From | olcott <polcott333@gmail.com> |
|---|---|
| Newsgroups | comp.theory, sci.logic, sci.math, sci.lang |
| Subject | Re: A new category of thought |
| Date | 2025-12-02 08:00 -0600 |
| Organization | A noiseless patient Spider |
| Message-ID | <10gmre5$2blfd$1@dont-email.me> (permalink) |
| References | (5 earlier) <20251129132843.374@kylheku.com> <10gfqb6$3p2df$1@dont-email.me> <10gjsku$18h21$1@dont-email.me> <10gkiev$1h8eo$1@dont-email.me> <10gm9do$24og8$1@dont-email.me> |
Cross-posted to 4 groups.
On 12/2/2025 2:53 AM, Mikko wrote: > olcott kirjoitti 1.12.2025 klo 19.15: >> On 12/1/2025 5:02 AM, Mikko wrote: >>> olcott kirjoitti 29.11.2025 klo 23.59: >>> >>> G := (F ⊬ G) // G says of itself that it is unprovable in F >>> >>> With a reasonable type system that is a type error: >>> - the symbol ⊬ requires a sentence on the right side >>> - the value of the ⊬ operation is a truth value >>> - the symbol := requires the same type on both sides >>> - thus G must be both a sentence and a truth value >>> >>> But G cannot be both. A sentence has a truth value but it isn't one. >>> >> >> % This sentence cannot be proven in F >> ?- G = not(provable(F, G)). >> G = not(provable(F, G)). >> ?- unify_with_occurs_check(G, not(provable(F, G))). >> false. >> >> It is an expression of language having no truth value >> because it is not a logic sentence. >> >> https://en.wikipedia.org/wiki/Sentence_(mathematical_logic) > > Yes, that is the exxential difference between the two G's. > The expession F ⊬ G has a truth value because it is either > true or false I propose that is a false assumption. G := (F ⊬ G) expands to (F ⊬ (F ⊬ (F ⊬ (F ⊬ (F ⊬ (F ⊬ ...)))))) and Prolog agrees G = not(provable(F, G)). expands to: not(provable(F, not(provable(F, not(provable(F, ...)))))) We completely bypass all of this by creating a formal language that fully integrates semantics directly in the syntax. In this case not provable in F simply means not true in F. Truthmaker Maximalism is an entire field of philosophy that deals with this. We can implement the notion of a Tarski theory / meta-theory in a single formal language implementing Gödel's 1944 "theory of simple types". "This sentence is not true" has a semantic type of ~truth_bearer. That is what makes this sentence true: This sentence is not true: "This sentence is not true" > that G is no provable in F, and the same truth > value is given to G in the expression G := (F ⊬ G). The > Prolog term not(provable(F, G)) does not have a truth value. Yes you are getting it now. > After G = not(provable(F, G)) the value of G is that data > structure, so it has no truth value, unlike the G in > G := (F ⊬ G). > Maybe we should stick with the Prolog then. I only created Minimal Type Theory because I didn't know that Prolog could to the same thing. Because I created Minimal Type Theory I know that pathological self-reference(Olcott 2004) creates cycles in the directed graph of evaluation sequence thus showing that evaluation gets stuck in an infinite loop never reaching a truth value. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 10:32 -0600
Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 17:53 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 12:07 -0600
Re: A new category of thought dbush <dbush.mobile@gmail.com> - 2025-11-29 13:19 -0500
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 16:55 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:04 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 11:49 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 09:26 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:36 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-03 09:09 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:50 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-04 08:46 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:52 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:21 -0600
Re: A new category of thought André G. Isaak <agisaak@gm.invalid> - 2025-12-05 19:57 -0700
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 21:18 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:01 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:40 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:47 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:16 -0600
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:04 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 09:55 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:43 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-06 22:16 -0500
Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-06 21:50 -0600
Re: A new category of thought Python <python@cccp.invalid> - 2025-12-07 05:32 +0000
Re: A new category of thought Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-12-07 15:49 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 11:38 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 07:32 -0500
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 07:37 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 17:55 -0500
Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-07 17:15 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-07 21:50 -0500
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:26 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 07:40 -0500
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 12:47 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 19:18 -0500
Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-08 19:00 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:24 -0500
Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 20:34 -0600
Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 21:57 -0500
Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:16 -0600
Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 22:22 -0500
Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 21:50 -0600
Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-08 23:20 -0500
Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-08 22:30 -0600
Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
Re: Key new insight into halting undecidability polcott <polcott333@gmail.com> - 2025-12-09 10:05 -0600
Re: Key new insight into halting undecidability Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 02:14 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 21:21 -0600
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 07:07 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:41 -0600
Re: A new category of thought Python <python@cccp.invalid> - 2025-12-08 19:39 +0000
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:57 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 11:30 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:53 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:33 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:42 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 09:03 -0600
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-08 06:12 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 07:59 -0600
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-08 10:18 -0600
Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 20:23 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 14:51 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 16:27 -0500
Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 15:53 -0800
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:17 -0500
Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 16:35 -0800
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 20:10 -0500
Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:49 -0800
Re: A new category of thought "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 19:50 -0800
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:59 +0000
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-12-01 23:11 -0500
Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 21:39 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 15:59 -0600
Re: A new category of thought Kaz Kylheku <046-301-5902@kylheku.com> - 2025-11-29 22:44 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-11-29 17:19 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 19:21 -0500
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:13 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 19:50 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-01 13:02 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 11:15 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-02 10:53 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-02 08:00 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:41 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-03 09:59 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-05 10:48 +0200
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-05 09:30 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-05 10:41 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-06 10:37 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-06 06:24 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:39 +0200
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-07 08:59 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-09 15:15 +0200
Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-09 10:22 -0600
Re: A new category of thought polcott <polcott333@gmail.com> - 2025-12-09 12:04 -0600
Re: A new category of thought Mikko <mikko.levanto@iki.fi> - 2025-12-14 13:02 +0200
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-02 01:39 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 20:01 -0600
Re: A new category of thought Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-01 17:37 +0000
Re: A new category of thought olcott <polcott333@gmail.com> - 2025-12-01 13:44 -0600
Re: A new category of thought Richard Damon <Richard@Damon-Family.org> - 2025-11-29 15:08 -0500
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